Elastic neutrino-electron scattering within the effective field - - PowerPoint PPT Presentation

elastic neutrino electron scattering within the effective
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Elastic neutrino-electron scattering within the effective field - - PowerPoint PPT Presentation

New Perspectives 2019 10 June, 2019 Fermilab, USA Elastic neutrino-electron scattering within the effective field theory Oleksandr Tomalak 1 Elastic neutrino-electron scattering - historic channel in discovery of weak neutral currents


slide-1
SLIDE 1

Oleksandr Tomalak

Elastic neutrino-electron scattering

  • 1

10 June, 2019

within the effective field theory

New Perspectives 2019 Fermilab, USA

slide-2
SLIDE 2

2

Elastic neutrino-electron scattering

  • historic channel in discovery of weak neutral currents
  • solar neutrino studies
  • reactor antineutrino studies
  • measurement of total cross section and Weinberg angle

CHARM (1988), CHARM-II (1994), BNL-E734 (1990), LAMPF (1993), LSND (2001) Savannah river (1976), Krasnoyarsk (1990), Rovno (1993), MUNU (2005), TEXONO (2010), GEMMA (2012) Gargamelle (1973) Kamiokande, SNO, Super-Kamiokande I-IV, Borexino, Hyper-Kamiokande

slide-3
SLIDE 3

3

Elastic neutrino-electron scattering

  • EFT-based calculation with % accuracy was absent
  • relatively clean tool to constrain neutrino flux in DUNE
  • standard candle to constrain neutrino flux:

MINERvA (2016), MINERvA and NOvA analyses ongoing

  • small cross section scales as electron mass m:

10-4-10-3 of cross section on nucleons and nuclei uncertainty from 9% to 6%

  • historic channel in discovery of weak neutral currents
  • solar neutrino studies
  • reactor antineutrino studies
  • measurement of total cross section and Weinberg angle

CHARM (1988), CHARM-II (1994), BNL-E734 (1990), LAMPF (1993), LSND (2001) Savannah river (1976), Krasnoyarsk (1990), Rovno (1993), MUNU (2005), TEXONO (2010), GEMMA (2012) Gargamelle (1973) Kamiokande, SNO, Super-Kamiokande I-IV, Borexino, Hyper-Kamiokande

slide-4
SLIDE 4

4

Neutrino scattering in EFT. Matching

  • tree-level matching to low-energy EFT:

cL = 2 √ 2GF

  • sin2 θW − 0.5 + δν,νe
  • <latexit sha1_base64="ynM2bfblRwt6aLjl2sdUmK2Ejk=">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</latexit>

cR = 2 √ 2GF sin2 θW

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ν e e ν

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ν e e ν

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ν e ν e

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W

<latexit sha1_base64="iwDr9lDME/gocupjs2b0usOSKsA=">AB6HicdVDLSsNAFJ3UV42vqks3g6XgKiStNe1CLpx2YJ9QBvKZDpx04ezEyEvoFblwo4lY/xr0b8W+ctCpW8MCFwzn3cu69bsSokKb5oWldW17Lr+sbm1vZObnevJcKY9LEIQt5x0WCMBqQpqSkU7ECfJdRtru+CL12zeECxoGV3ISEcdHw4B6FCOpEa7n8ubRrFqV60yNA2zfFyx7ZQUqydWCVqGOUP+7FU/jV7e9Xo/9YbhDj2SAxQ0J0LTOSToK4pJiRqd6LBYkQHqMh6SoaIJ8IJ5ktOoUFpQygF3JVgYQz9fdEgnwhJr6rOn0kR0Iv/DFT9cdciJexUloEMWSBHie5MUMyhCmZ8MB5QRLNlEYU7VshCPEdYqueoJ3xfCv8nraJhlYxiw8zXzsEcWXADsERsIANauAS1ETYEDALbgHD9q1dqc9ak/z1oz2NbMPFqA9fwKFUJCM</latexit>

Z

<latexit sha1_base64="GpG16vhOVy3ltGaV7TYonW+MyRY=">AB6HicdVDLSsNAFJ3UV42vqks3g0VwFZLWmnYhFt24bME+sA1lMp20YycPZiZCf0CNy4Ucasf496N+DdOWhUreODC4Zx7OfdeN2JUSNP80DILi0vLK9lVfW19Y3Mrt73TFGHMWngkIW87SJBGA1IQ1LJSDviBPkuIy13dJ76rRvCBQ2DSzmOiOjQUA9ipFUv2ql8ubRqFiV6wSNA2zdFS27ZQUKsdWEVqGOUX+9FU/iV7e9Vov9bthzj2SAxQ0J0LDOSToK4pJiRid6NBYkQHqEB6SgaIJ8IJ5kuOoEHSulDL+SqAgmn6u+JBPlCjH1XdfpIDoV+8MdM1R9zLkp6ZSehQRLEuBZkhczKEOYng37lBMs2VgRhDlVy0I8RBxhqZ6jnvB9KfyfNAuGVTQKdTNfPQMzZMEe2AeHwAI2qILUAMNgAEBt+AePGjX2p32qD3NWjPa18wumIP2/AmJ3JCP</latexit>

neutral current charged current Leff = −¯ νγµPLν · ¯ eγµ(cLPL + cRPR)e

<latexit sha1_base64="Gr9NZoaDepWPbE6WtGjstjtXT9w=">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</latexit>

Weinberg (1967), 't Hooft (1971)

PL = 1 − γ5 2 PR = 1 + γ5 2

<latexit sha1_base64="jIVJtqzhKgEG4nBepEiUg5r0U8=">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</latexit>
  • projectors on chiral states:

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

e

<latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>

e

<latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>

e

<latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>

e

<latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

e

<latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

e

<latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>
slide-5
SLIDE 5

5

Neutrino scattering in EFT. Matching

  • tree-level matching to low-energy EFT:

cL = 2 √ 2GF

  • sin2 θW − 0.5 + δν,νe
  • <latexit sha1_base64="ynM2bfblRwt6aLjl2sdUmK2Ejk=">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</latexit>

cR = 2 √ 2GF sin2 θW

<latexit sha1_base64="u/FMGMO3n+w9HKfNQ+219GtlrM=">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</latexit>

ν e e ν

<latexit sha1_base64="GkESPxKba7qd8chOZu8CwF70w=">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</latexit>

ν e e ν

<latexit sha1_base64="hlEoz5iZCA+c2SAOsHsGDEQXdaI=">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</latexit>

ν e ν e

<latexit sha1_base64="7nlTwNFcBzOB/iPeq9AWQ+uWkic=">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</latexit>

W

<latexit sha1_base64="iwDr9lDME/gocupjs2b0usOSKsA=">AB6HicdVDLSsNAFJ3UV42vqks3g6XgKiStNe1CLpx2YJ9QBvKZDpx04ezEyEvoFblwo4lY/xr0b8W+ctCpW8MCFwzn3cu69bsSokKb5oWldW17Lr+sbm1vZObnevJcKY9LEIQt5x0WCMBqQpqSkU7ECfJdRtru+CL12zeECxoGV3ISEcdHw4B6FCOpEa7n8ubRrFqV60yNA2zfFyx7ZQUqydWCVqGOUP+7FU/jV7e9Xo/9YbhDj2SAxQ0J0LTOSToK4pJiRqd6LBYkQHqMh6SoaIJ8IJ5ktOoUFpQygF3JVgYQz9fdEgnwhJr6rOn0kR0Iv/DFT9cdciJexUloEMWSBHie5MUMyhCmZ8MB5QRLNlEYU7VshCPEdYqueoJ3xfCv8nraJhlYxiw8zXzsEcWXADsERsIANauAS1ETYEDALbgHD9q1dqc9ak/z1oz2NbMPFqA9fwKFUJCM</latexit>

Z

<latexit sha1_base64="GpG16vhOVy3ltGaV7TYonW+MyRY=">AB6HicdVDLSsNAFJ3UV42vqks3g0VwFZLWmnYhFt24bME+sA1lMp20YycPZiZCf0CNy4Ucasf496N+DdOWhUreODC4Zx7OfdeN2JUSNP80DILi0vLK9lVfW19Y3Mrt73TFGHMWngkIW87SJBGA1IQ1LJSDviBPkuIy13dJ76rRvCBQ2DSzmOiOjQUA9ipFUv2ql8ubRqFiV6wSNA2zdFS27ZQUKsdWEVqGOUX+9FU/iV7e9Vov9bthzj2SAxQ0J0LDOSToK4pJiRid6NBYkQHqEB6SgaIJ8IJ5kuOoEHSulDL+SqAgmn6u+JBPlCjH1XdfpIDoV+8MdM1R9zLkp6ZSehQRLEuBZkhczKEOYng37lBMs2VgRhDlVy0I8RBxhqZ6jnvB9KfyfNAuGVTQKdTNfPQMzZMEe2AeHwAI2qILUAMNgAEBt+AePGjX2p32qD3NWjPa18wumIP2/AmJ3JCP</latexit>

neutral current charged current

−igλµ p2

Z − M 2 Z

<latexit sha1_base64="TveJys0Zx2nH2u0iNuxUBuHkXus=">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</latexit>

−igλµ p2

W − M 2 W

<latexit sha1_base64="GWOxCL28qOsFWhwJe9LiYtsts=">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</latexit>

Leff = −¯ νγµPLν · ¯ eγµ(cLPL + cRPR)e

<latexit sha1_base64="Gr9NZoaDepWPbE6WtGjstjtXT9w=">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</latexit>

PL = 1 − γ5 2 PR = 1 + γ5 2

<latexit sha1_base64="jIVJtqzhKgEG4nBepEiUg5r0U8=">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</latexit>
  • projectors on chiral states:

Weinberg (1967), 't Hooft (1971)

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

e

<latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>

e

<latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>

e

<latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>

e

<latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

e

<latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

e

<latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>
slide-6
SLIDE 6

6

Neutrino scattering in EFT. Matching

  • tree-level matching to low-energy EFT:

cL = 2 √ 2GF

  • sin2 θW − 0.5 + δν,νe
  • <latexit sha1_base64="ynM2bfblRwt6aLjl2sdUmK2Ejk=">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</latexit>

cR = 2 √ 2GF sin2 θW

<latexit sha1_base64="u/FMGMO3n+w9HKfNQ+219GtlrM=">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</latexit>

ν e e ν

<latexit sha1_base64="GkESPxKba7qd8chOZu8CwF70w=">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</latexit>

ν e e ν

<latexit sha1_base64="hlEoz5iZCA+c2SAOsHsGDEQXdaI=">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</latexit>

ν e ν e

<latexit sha1_base64="7nlTwNFcBzOB/iPeq9AWQ+uWkic=">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</latexit>

W

<latexit sha1_base64="iwDr9lDME/gocupjs2b0usOSKsA=">AB6HicdVDLSsNAFJ3UV42vqks3g6XgKiStNe1CLpx2YJ9QBvKZDpx04ezEyEvoFblwo4lY/xr0b8W+ctCpW8MCFwzn3cu69bsSokKb5oWldW17Lr+sbm1vZObnevJcKY9LEIQt5x0WCMBqQpqSkU7ECfJdRtru+CL12zeECxoGV3ISEcdHw4B6FCOpEa7n8ubRrFqV60yNA2zfFyx7ZQUqydWCVqGOUP+7FU/jV7e9Xo/9YbhDj2SAxQ0J0LTOSToK4pJiRqd6LBYkQHqMh6SoaIJ8IJ5ktOoUFpQygF3JVgYQz9fdEgnwhJr6rOn0kR0Iv/DFT9cdciJexUloEMWSBHie5MUMyhCmZ8MB5QRLNlEYU7VshCPEdYqueoJ3xfCv8nraJhlYxiw8zXzsEcWXADsERsIANauAS1ETYEDALbgHD9q1dqc9ak/z1oz2NbMPFqA9fwKFUJCM</latexit>

Z

<latexit sha1_base64="GpG16vhOVy3ltGaV7TYonW+MyRY=">AB6HicdVDLSsNAFJ3UV42vqks3g0VwFZLWmnYhFt24bME+sA1lMp20YycPZiZCf0CNy4Ucasf496N+DdOWhUreODC4Zx7OfdeN2JUSNP80DILi0vLK9lVfW19Y3Mrt73TFGHMWngkIW87SJBGA1IQ1LJSDviBPkuIy13dJ76rRvCBQ2DSzmOiOjQUA9ipFUv2ql8ubRqFiV6wSNA2zdFS27ZQUKsdWEVqGOUX+9FU/iV7e9Vov9bthzj2SAxQ0J0LDOSToK4pJiRid6NBYkQHqEB6SgaIJ8IJ5kuOoEHSulDL+SqAgmn6u+JBPlCjH1XdfpIDoV+8MdM1R9zLkp6ZSehQRLEuBZkhczKEOYng37lBMs2VgRhDlVy0I8RBxhqZ6jnvB9KfyfNAuGVTQKdTNfPQMzZMEe2AeHwAI2qILUAMNgAEBt+AePGjX2p32qD3NWjPa18wumIP2/AmJ3JCP</latexit>

neutral current charged current

ig √ 2γλPLδννe

<latexit sha1_base64="ua8R4pERIRHrG1rsTv5D+SGBWlQ=">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</latexit>

ig √ 2γµPLδννe

<latexit sha1_base64="WYCKu/qVT0KDEmZJj8oW74XeNo=">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</latexit>

ig 2 cos θW γλPL

<latexit sha1_base64="I0q5uAlUiYgZX+oqH3qkNQEJtWs=">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</latexit>

ig cos θW γµ ⇥ sin2 θW − 0.5

  • PL + sin2 θW PR

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−igλµ p2

Z − M 2 Z

<latexit sha1_base64="TveJys0Zx2nH2u0iNuxUBuHkXus=">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</latexit>

−igλµ p2

W − M 2 W

<latexit sha1_base64="GWOxCL28qOsFWhwJe9LiYtsts=">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</latexit>

Leff = −¯ νγµPLν · ¯ eγµ(cLPL + cRPR)e

<latexit sha1_base64="Gr9NZoaDepWPbE6WtGjstjtXT9w=">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</latexit>

PL = 1 − γ5 2 PR = 1 + γ5 2

<latexit sha1_base64="jIVJtqzhKgEG4nBepEiUg5r0U8=">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</latexit>
  • projectors on chiral states:

Weinberg (1967), 't Hooft (1971)

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

e

<latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>

e

<latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>

e

<latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>

e

<latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

e

<latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

e

<latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>
slide-7
SLIDE 7

−igλµ p2

Z − M 2 Z

<latexit sha1_base64="TveJys0Zx2nH2u0iNuxUBuHkXus=">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</latexit>

−igλµ p2

W − M 2 W

<latexit sha1_base64="GWOxCL28qOsFWhwJe9LiYtsts=">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</latexit>

7

Neutrino scattering in EFT. Matching

  • integrate out W and Z at tree level
  • tree-level matching to low-energy EFT:

PL = 1 − γ5 2 PR = 1 + γ5 2

<latexit sha1_base64="jIVJtqzhKgEG4nBepEiUg5r0U8=">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</latexit>
  • projectors on chiral states:

cL = 2 √ 2GF

  • sin2 θW − 0.5 + δν,νe
  • <latexit sha1_base64="ynM2bfblRwt6aLjl2sdUmK2Ejk=">ACUnicdVJNb9NAEN2ErxAKDXDksqKq1AqwbJeQ5oBUFQk4cCgSaSrVwVpvxsmq67XZHSMFy7+BK7+Av1MJceGHcOEAjBNaUSRGunpzRvNzNtNCq0c+v63VvS5StXr3Wud2+s3by13rt959DlpZUwkrnO7VEiHGhlYIQKNRwVFkSWaBgnJ8+a+vg9WKdy8wYXBUwyMTMqVIgUXFPyTjKBM5tVr2q+VMe8si9s1iFNT/jX9TnkufEakhxi1TKvCUxzgFPOaPuO/1+QMeTUETUWmfEgZA3VYNZvjdtzb8L1wOBgGfdL6/ce7g0EDwuGTYIcHnr+Mjb3tjx+KzudPB3HvSzTNZmBQamFc8eBX+CkEhaV1FB3o9JBIeSJmMExQSMycJNqaUnN4mZ8jS3lAb5kv27oxKZc4sIWVzm+tu/lNs2PihVGY7k4qZYoSwcjVpLTUHPeGMynyoJEvSAgpFW0LJdzYVEegYy4exS/n9wGHrBjhe+Jjf2So67B67z7ZYwAZsj71kB2zEJDtl39lP9qv1tfWjTb9kJW23/vTcZReivfYbJnS2dg=</latexit>

cR = 2 √ 2GF sin2 θW

<latexit sha1_base64="u/FMGMO3n+w9HKfNQ+219GtlrM=">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</latexit>

ν e e ν

<latexit sha1_base64="GkESPxKba7qd8chOZu8CwF70w=">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</latexit>

M 2

W = M 2 Z cos2 θW

<latexit sha1_base64="moQko4Yk1kmYujkXcnw9FsLVh0=">ACBXicdVC7SgNBFJ31bXxFLUYFMFq2V0fawpBtLERFIwRTVxmJzdmcPbBzF0hBCsLP8IvsLBRsbW2tBT9GcTFRU8MzhnHu5954wlUKj47xaPb19/QODQ8OFkdGx8Yni5NSBTjLFocwTmajDkGmQIoYyCpRwmCpgUSihEp5t5X7lHJQWSbyPrRqETuNRUNwhkYKirM7J15Qoes0/49olSf6xKNVbAKyoBIU5x3bK/kld4U6trOyvOb7OfFKq+4SdW2ng/mNucX3N/5ejcovlTrCc8iJFLpvWx6RYazOFgku4KFQzDSnjZ+wUjg2NWQS61u6cUEXjFKnjUSZFyPtqD872izSuhWFpjJi2NSFhT9mrn6bv0ZhY63WFnGaIcS8O6mRSYoJzUOhdaGAo2wZwrgSZlnKm0wxjqBMBl+H0v/JgWe7S7a3Z8LYJF0MkRkyRxaJS3yQbJLikTi7JDbkj9aVdWs9WI/d0h7rs2ea/IL19AENcprf</latexit>

ν e e ν

<latexit sha1_base64="hlEoz5iZCA+c2SAOsHsGDEQXdaI=">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</latexit>

ν e ν e

<latexit sha1_base64="7nlTwNFcBzOB/iPeq9AWQ+uWkic=">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</latexit>

W

<latexit sha1_base64="iwDr9lDME/gocupjs2b0usOSKsA=">AB6HicdVDLSsNAFJ3UV42vqks3g6XgKiStNe1CLpx2YJ9QBvKZDpx04ezEyEvoFblwo4lY/xr0b8W+ctCpW8MCFwzn3cu69bsSokKb5oWldW17Lr+sbm1vZObnevJcKY9LEIQt5x0WCMBqQpqSkU7ECfJdRtru+CL12zeECxoGV3ISEcdHw4B6FCOpEa7n8ubRrFqV60yNA2zfFyx7ZQUqydWCVqGOUP+7FU/jV7e9Xo/9YbhDj2SAxQ0J0LTOSToK4pJiRqd6LBYkQHqMh6SoaIJ8IJ5ktOoUFpQygF3JVgYQz9fdEgnwhJr6rOn0kR0Iv/DFT9cdciJexUloEMWSBHie5MUMyhCmZ8MB5QRLNlEYU7VshCPEdYqueoJ3xfCv8nraJhlYxiw8zXzsEcWXADsERsIANauAS1ETYEDALbgHD9q1dqc9ak/z1oz2NbMPFqA9fwKFUJCM</latexit>

Z

<latexit sha1_base64="GpG16vhOVy3ltGaV7TYonW+MyRY=">AB6HicdVDLSsNAFJ3UV42vqks3g0VwFZLWmnYhFt24bME+sA1lMp20YycPZiZCf0CNy4Ucasf496N+DdOWhUreODC4Zx7OfdeN2JUSNP80DILi0vLK9lVfW19Y3Mrt73TFGHMWngkIW87SJBGA1IQ1LJSDviBPkuIy13dJ76rRvCBQ2DSzmOiOjQUA9ipFUv2ql8ubRqFiV6wSNA2zdFS27ZQUKsdWEVqGOUX+9FU/iV7e9Vov9bthzj2SAxQ0J0LDOSToK4pJiRid6NBYkQHqEB6SgaIJ8IJ5kuOoEHSulDL+SqAgmn6u+JBPlCjH1XdfpIDoV+8MdM1R9zLkp6ZSehQRLEuBZkhczKEOYng37lBMs2VgRhDlVy0I8RBxhqZ6jnvB9KfyfNAuGVTQKdTNfPQMzZMEe2AeHwAI2qILUAMNgAEBt+AePGjX2p32qD3NWjPa18wumIP2/AmJ3JCP</latexit>

neutral current charged current

ig √ 2γλPLδννe

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ig √ 2γµPLδννe

<latexit sha1_base64="WYCKu/qVT0KDEmZJj8oW74XeNo=">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</latexit>

ig 2 cos θW γλPL

<latexit sha1_base64="I0q5uAlUiYgZX+oqH3qkNQEJtWs=">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</latexit>

ig cos θW γµ ⇥ sin2 θW − 0.5

  • PL + sin2 θW PR

<latexit sha1_base64="CnpjprmX9ENbC4jgmDriDz9AKc=">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</latexit>

e = g sin θW

<latexit sha1_base64="Mr/9k8+kFMHlRiyh4+c1g7+TjOM=">AB/HicdVDLSgNBEJyNrxhfUY9eBoPgadnNw5iDEPTiUcEYIQlhdtJBmdnl5leISz6K148KOLVD/Hm3zgbI6hoQUNR1U13VxBLYdDz3p3c3PzC4lJ+ubCyura+UdzcujRojm0eCQjfRUwA1IoaKFACVexBhYGEtrB9Unmt29AGxGpC5zE0AvZSImh4Ayt1C9uAz2iI9o1QtEujgFZv90vljy3Kg3/Br1XK9WPazXM1JuHPgV6rveFCUyw1m/+NYdRDwJQSGXzJiO78XYS5lGwSXcFrqJgZjxazaCjqWKhWB6fT4W7pnlQEdRtqWQjpVv0+kLDRmEga2M2Q4Nr+9TPzL6yQ4POylQsUJguKfi4aJpBjRLAk6EBo4yokljGthb6V8zDTjaPMq2BC+PqX/k8uy61fc8nm1DyexZEnO2SX7BOf1EmTnJIz0iKcTMg9eSRPzp3z4Dw7L5+tOWc2s01+wHn9AI7ElBk=</latexit>

GF = √ 2g2 8M 2

W

<latexit sha1_base64="S/FIAL5U8oTc01ucOMuRhAKp83c=">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</latexit>

Leff = −¯ νγµPLν · ¯ eγµ(cLPL + cRPR)e

<latexit sha1_base64="Gr9NZoaDepWPbE6WtGjstjtXT9w=">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</latexit>

Weinberg (1967), 't Hooft (1971)

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

e

<latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>

e

<latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>

e

<latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>

e

<latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>

e

<latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

e

<latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>
slide-8
SLIDE 8

8

Neutrino scattering in EFT. Matching

  • muon lifetime measurement improves precision
  • matching at order ααs: left- and right-handed couplings

MS

<latexit sha1_base64="mkpRabcheDQVQtMx4RdWfJv5DxM=">AB/3icbVBLS8NAGNzUV62vqODFS7AInkpSBT0WvXgRKtoHNKFstpt26T7C7kYoMQf/ihcPinj1b3jz37hpc9DWgYVhZr7dbyeMKVHadb+t0tLyupaeb2ysbm1vWPv7rWVSCTCLSokN0QKkwJxy1NMXdWGLIQo74fgq9zsPWCoi+L2exDhgcMhJRBDURurbBz6DeiRZ6gsTy29Jb+6yrG9X3Zo7hbNIvIJUQYFm3/7yBwIlDHONKFSq57mxDlIoNUEUZxU/UTiGaAyHuGcohwyrIJ3unznHRhk4kZDmcO1M1d8TKWRKTVhokvm2at7Lxf+8XqKjiyAlPE405mj2UJRQRwsnL8MZEImRphNDIJLE7OqgEZQaVNZxZTgzX95kbTrNe+0Vr89qzYuizrK4BAcgRPgXPQANegCVoAgUfwDF7Bm/VkvVjv1scsWrKmX3wB9bnDwgnlsA=</latexit>
  • consider only leading in GF terms: loop corrections in α, αs

MSM (µ) = MEFT (µ)

<latexit sha1_base64="zT2rCy1bjfR7G9e0nY7ba/av3xY=">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</latexit>

MULAN (2012)

  • exploit GF for one combination of electroweak parameters

GF = 1.1663787(6) × 10−5 GeV−2

<latexit sha1_base64="h073e0rV6uIRUpdGQl9UYroM74I=">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</latexit>
  • SM symmetries and universality leave 8 couplings to determine:

3 for leptons and 5 for quarks besides top

µ = MZ

<latexit sha1_base64="ig3COi3j7LfegcRCFljqDU2iCo=">AB8HicdVDLSgMxFM3UV62vqks3wSK4Gmam1bYLoejGjVDBPrQdSiZN29AkMyQZoQz9CjcuFHr57jzb8y0FVT0wIXDOfdy7z1BxKjSjvNhZaWV1bXsu5jc2t7Z387l5ThbHEpIFDFsp2gBRhVJCGpqRdiQJ4gEjrWB8kfqteyIVDcWNnkTE52go6IBipI102+UxPINXvbtevuDYXrXiFKvQsZ2TUqVcTolXPXWL0LWdGQpgXov/97thzjmRGjMkFId14m0nyCpKWZkmuvGikQIj9GQdAwViBPlJ7ODp/DIKH04CKUpoeFM/T6RIK7UhAemkyM9Ur+9VPzL68R6UPETKqJYE4HniwYxgzqE6fewTyXBmk0MQVhScyvEIyQR1iajnAnh61P4P2l6tlu0vetSoXa+iCMLDsAhOAYuKIMauAR10AYcPAnsCzJa1H68V6nbdmrMXMPvgB6+0TCb2P7A=</latexit>

cL = 2 √ 2GF

  • sin2 θW − 0.5 + δν,νe
  • <latexit sha1_base64="ynM2bfblRwt6aLjl2sdUmK2Ejk=">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</latexit>

cR = 2 √ 2GF sin2 θW

<latexit sha1_base64="u/FMGMO3n+w9HKfNQ+219GtlrM=">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</latexit>
  • tree-level matching to low-energy EFT:

GF = √ 2g2 8M 2

W

<latexit sha1_base64="S/FIAL5U8oTc01ucOMuRhAKp83c=">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</latexit>

Leff = −¯ νγµPLν · ¯ eγµ(cLPL + cRPR)e

<latexit sha1_base64="Gr9NZoaDepWPbE6WtGjstjtXT9w=">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</latexit>
  • matching of amplitudes, renormalized in scheme:

Weinberg (1967), 't Hooft (1971)

slide-9
SLIDE 9

9

Running to low scales

  • integrate out top at Z scale
  • only one EFT coupling
  • αs becomes too strong
  • hadronic physics down to 140 MeV
  • theory with leptons:
  • ne unknown coupling
  • integrate out GeV particles

changes with scale

  • PDG running for α, αs

MZ

<latexit sha1_base64="Z982f1amNq6H5eUnLkLx+QwIM0k=">AB6nicdVDLSsNAFJ3UV62vquDGzWApuApJa027K3XjRmjRPrANZTKdtEMnD2YmQgn9BDcuFHr1r/wC9y58VuctCpW8MCFwzn3cu89TsiokIbxrqWldW19LrmY3Nre2d7O5eSwQRx6SJAxbwjoMEYdQnTUklI52QE+Q5jLSd8Vnit28IFzTwr+QkJLaHhj51KUZSZcX/et+NmfohYpVMUvQ0I3SdmyElKonJpFaOrGDLnqQeODvtRe6/3sW28Q4MgjvsQMCdE1jVDaMeKSYkamV4kSIjwGA1JV1EfeUTY8ezUKcwrZQDdgKvyJZypvydi5Akx8RzV6SE5Epn8HzNRf8yFVdIt2zH1w0gSH83uRGDMoDJ43BAOcGSTRBmFN1LMQjxBGWKh4Vwven8H/SKuhmUS80VBo1MEcaHIjcAxMYIEqOAd10AQYDMEtuAcPGtPutEftad6a0r5m9sECtOdPWH+Rrw=</latexit>

mb

<latexit sha1_base64="agrK2VR1EhHFgJtKJUwzKJ7C/lw=">AB6nicdVDLSsNAFJ3UV62vquDGzWApuApJak27K3XjskX7gDaUyXTSDp08mJkIJfQT3LhQxK1b/8IvcOfGb3HSqljBAxcO59zLvfe4EaNCGsa7lZXVvfyG7mtrZ3dvfy+wdtEcYckxYOWci7LhKE0YC0JWMdCNOkO8y0nEnF6nfuSFc0DC4ltOIOD4aBdSjGEklXfkDd5AvGLpVtatmGRq6UT6r2HZKrOq5WYKmbsxRqB01P+hL/bUxyL/1hyGOfRJIzJAQPdOIpJMgLilmZJbrx4JECE/QiPQUDZBPhJPMT53BolKG0Au5qkDCufp7IkG+EFPfVZ0+kmORK/4xU/XHXFolvYqT0CKJQnwYpMXMyhDmD4Oh5QTLNlUEYQ5VcdCPEYcYaniUSF8fwr/J21LN0u61VRp1MECWXAMTsApMIENauASNEALYDACt+AePGhMu9MetadFa0b7mjkES9CePwGVX5HX</latexit>

<latexit sha1_base64="v4U/eD7i/qLVzUQOx/ARY9cjvOs=">AB7XicdVDLSsNAFJ3UV62vquDGzWApuApJak27K3XjsgX7gDaUyXTSjp08mJkIJfQf3LhQxK0r/8IvcOfGb3HSqljBAxcO59zLvfe4EaNCGsa7lZXVvfyG7mtrZ3dvfy+wdtEcYckxYOWci7LhKE0YC0JWMdCNOkO8y0nEnF6nfuSFc0DC4ktOIOD4aBdSjGEkltf1BX6J4kC8YulW1q2YZGrpRPqvYdkqs6rlZgqZuzFGoHTU/6Ev9tTHIv/WHIY59EkjMkBA904ikyAuKWZkluvHgkQIT9CI9BQNkE+Ek8yvncGiUobQC7mqQMK5+nsiQb4QU9VnT6SY5Er/jFT9cdcWiW9ipPQIolCfBikxczKEOY/g6HlBMs2VQRhDlVx0I8RhxhqRJSIXx/Cv8nbUs3S7rVGnUwQJZcAxOwCkwgQ1q4BI0QAtgcA1uwT140ELtTnvUnhatGe1r5hAsQXv+BPQMkzk=</latexit>

mc

<latexit sha1_base64="xguVl6SeAwFNaqUcbQMSi6cKV5E=">AB6nicdVDLSsNAFJ3UV62vquDGzWApuApJak27K3XjskX7gDaUyXTSDp08mJkIJfQT3LhQxK1b/8IvcOfGb3HSqljBAxcO59zLvfe4EaNCGsa7lZXVvfyG7mtrZ3dvfy+wdtEcYckxYOWci7LhKE0YC0JWMdCNOkO8y0nEnF6nfuSFc0DC4ltOIOD4aBdSjGEklXfkDPMgXDN2q2lWzDA3dKJ9VbDslVvXcLEFTN+Yo1I6aH/Sl/toY5N/6wxDHPgkZkiInmlE0kQlxQzMsv1Y0EihCdoRHqKBsgnwknmp85gUSlD6IVcVSDhXP09kSBfiKnvqk4fybHIFf+YqfpjLq2SXsVJaBDFkgR4scmLGZQhTB+HQ8oJlmyqCMKcqmMhHiOsFTxqBC+P4X/k7almyXdaqo06mCBLDgGJ+AUmMAGNXAJGqAFMBiBW3APHjSm3WmP2tOiNaN9zRyCJWjPn5bjkdg=</latexit>

<latexit sha1_base64="wrky59xaKSyqQlBuf9qS2sZUBs=">AB7HicdVDLSsNAFJ3UV62vquDGzWApuApJqrbuSt24bMG0hTaUyXTSDp1MwsxEKHf4MaFIm7d+Rd+gTs3fovTh2IFD1w4nHMv97jx4xKZVkfRmZldW19I7uZ29re2d3L7x80ZQITFwcsUi0fSQJo5y4ipG2rEgKPQZafmjq6nfuiVC0ojfqHFMvBANOA0oRkpLbtjrxrSXL1imNQO0TKdyXrbPNLGcywu7BO2FVageNT7pa+2t3su/d/sRTkLCFWZIyo5txcpLkVAUMzLJdRNJYoRHaEA6mnIUEumls2MnsKiVPgwioYsrOFN/T6QolHIc+rozRGoc8U/5lT9MZdWqaDipZTHiSIczcFCYMqgtPXYZ8KghUba4KwoPpYiIdIKx0QDqE70/h/6TpmHbJdBo6jRqYIwuOwQk4BTYogyq4BnXgAgwouAMP4NHgxr3xZDzPWzPGYuYQLMF4+QLrLpKZ</latexit>

ν ? e e ν

<latexit sha1_base64="62PY9jMj5nB0TpZKRdxb4+FpdY=">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</latexit>
  • perator mixing

f

<latexit sha1_base64="W0Cd3NqFKV/2uVsCn5yScPns9ik=">ACFXicZVC7SgNBFJ31GeMraqnIoghWyW4stAzaWCZgHhCD3J3c1SHzWGZmhRBSWtkq/koaO7G19hv8CJ08EGMODBzOuZd75kQJZ8YGwac3N7+wuLScWcmurq1vbOa2tmtGpZpilSqudCMCg5xJrFpmOTYSjSAijvWoczH06/eoDVPynYTbAm4lSxmFKyTKvFN7jDIByP4sySckMPS3qDy9bA/KN/kvq/biqYCpaUcjGmGQWJbPdCWUY797HVqMAHagVtsOipBoGn1RkH7/pFT2n6stHvS+iP170YPhDFdEblJAfbOZI/+mUP15w6ZeOzVo/JLUo6fhSnHLfKn/4b/NFLu4A1cyF9ekdaKDWlTMVoVA1Tiojh0Dsq2tEsChU4ixKwXIvms/N/PLKkV8+FJvlhx1Z2TMTJklxyQYxKSU1Iil6RMqoQSJI/kiTx7L96r9+a9j0fnvMnODpmC9/EDwYSjbg=</latexit>

f

<latexit sha1_base64="W0Cd3NqFKV/2uVsCn5yScPns9ik=">ACFXicZVC7SgNBFJ31GeMraqnIoghWyW4stAzaWCZgHhCD3J3c1SHzWGZmhRBSWtkq/koaO7G19hv8CJ08EGMODBzOuZd75kQJZ8YGwac3N7+wuLScWcmurq1vbOa2tmtGpZpilSqudCMCg5xJrFpmOTYSjSAijvWoczH06/eoDVPynYTbAm4lSxmFKyTKvFN7jDIByP4sySckMPS3qDy9bA/KN/kvq/biqYCpaUcjGmGQWJbPdCWUY797HVqMAHagVtsOipBoGn1RkH7/pFT2n6stHvS+iP170YPhDFdEblJAfbOZI/+mUP15w6ZeOzVo/JLUo6fhSnHLfKn/4b/NFLu4A1cyF9ekdaKDWlTMVoVA1Tiojh0Dsq2tEsChU4ixKwXIvms/N/PLKkV8+FJvlhx1Z2TMTJklxyQYxKSU1Iil6RMqoQSJI/kiTx7L96r9+a9j0fnvMnODpmC9/EDwYSjbg=</latexit>

Qf

<latexit sha1_base64="b3nFdM3I7FVdDZDSEGmnoIMHXY=">ACF3icZVC7SgNBFJ31GeMramz+ACrZDcWo2lgm6UYgh3J3cjUPmsczMCiHkE2wVf8TWQhBbSz9EW50kIsYcGDicy/3zIlTzowNgndvanpmdm4+t5BfXFpeWS2srdeMyjTFiCqu9GUMBjmTGFlmOV6mGkHEHC/izsnAv7hBbZiS57abYkNAW7KEUbBOqs2k2ZhOygGQ/iTJPwh20c7H4/PN4uflWbh6qlaCZQWsrBmHoYpLbRA20Z5djPX2UGU6AdaGPdUQkCTaM3jNr3d53S8hOl3ZPWH6p/N3ogjOmK2E0KsNcmv/vPHKi/5tgpmxw2ekymUVJR5eSjPtW+YOP+y2mkVredQSoZi6sT69BA7WunrEIpcg4qaQ4dgzIlrZKAIdOKcGuFCD7rHwfz+TpFYuhvFctVd0xGyJFNskX2SEgOyBE5JRUSEUra5JbckXvwXvyXrzX0eiU97OzQcbgvX0DJw6k0A=</latexit>

γ

<latexit sha1_base64="xCrXyBYaW3OLP43sakS6BcVoAgY=">ACGnicZVC7SgNBFJ31GeMraqnIoghWyW4stAzaWCZgomBCuDu5G8fMY5mZFUJIaW+r+CGp7cTWxm/wI3SiBhzYOBwzr3cMydKODM2CD68mdm5+YXFzFJ2eWV1bT23sVkzKtUq1Rxpa8iMiZxKpluNVohFExPEy6pwN/cs71IYpeWG7CTYEtCWLGQXrpFq9DUJAM7cf5IMR/GkS/pD90s6g8nm/Oyg3c1/1lqKpQGkpB2OuwyCxjR5oyjHfraeGkyAdqCN145KEGgavVHavn/glJYfK+2etP5I/bvRA2FMV0RuUoC9MdmDf+ZQ/TUnTtn4pNFjMktSjq+FKfct8of/t1vMY3U8q4jQDVzYX16AxqodQ1NRChUjZMKimPHgGxpqwRw6BRi7EoBsu8aC/3M01qxXx4lC9WXHWnZIwM2SZ75JCE5JiUyDkpkyqh5JY8kEfy5D17L96r9zYenfF+drbIBLz3b9ckpZk=</latexit>

f

<latexit sha1_base64="W0Cd3NqFKV/2uVsCn5yScPns9ik=">ACFXicZVC7SgNBFJ31GeMraqnIoghWyW4stAzaWCZgHhCD3J3c1SHzWGZmhRBSWtkq/koaO7G19hv8CJ08EGMODBzOuZd75kQJZ8YGwac3N7+wuLScWcmurq1vbOa2tmtGpZpilSqudCMCg5xJrFpmOTYSjSAijvWoczH06/eoDVPynYTbAm4lSxmFKyTKvFN7jDIByP4sySckMPS3qDy9bA/KN/kvq/biqYCpaUcjGmGQWJbPdCWUY797HVqMAHagVtsOipBoGn1RkH7/pFT2n6stHvS+iP170YPhDFdEblJAfbOZI/+mUP15w6ZeOzVo/JLUo6fhSnHLfKn/4b/NFLu4A1cyF9ekdaKDWlTMVoVA1Tiojh0Dsq2tEsChU4ixKwXIvms/N/PLKkV8+FJvlhx1Z2TMTJklxyQYxKSU1Iil6RMqoQSJI/kiTx7L96r9+a9j0fnvMnODpmC9/EDwYSjbg=</latexit>

f

<latexit sha1_base64="W0Cd3NqFKV/2uVsCn5yScPns9ik=">ACFXicZVC7SgNBFJ31GeMraqnIoghWyW4stAzaWCZgHhCD3J3c1SHzWGZmhRBSWtkq/koaO7G19hv8CJ08EGMODBzOuZd75kQJZ8YGwac3N7+wuLScWcmurq1vbOa2tmtGpZpilSqudCMCg5xJrFpmOTYSjSAijvWoczH06/eoDVPynYTbAm4lSxmFKyTKvFN7jDIByP4sySckMPS3qDy9bA/KN/kvq/biqYCpaUcjGmGQWJbPdCWUY797HVqMAHagVtsOipBoGn1RkH7/pFT2n6stHvS+iP170YPhDFdEblJAfbOZI/+mUP15w6ZeOzVo/JLUo6fhSnHLfKn/4b/NFLu4A1cyF9ekdaKDWlTMVoVA1Tiojh0Dsq2tEsChU4ixKwXIvms/N/PLKkV8+FJvlhx1Z2TMTJklxyQYxKSU1Iil6RMqoQSJI/kiTx7L96r9+a9j0fnvMnODpmC9/EDwYSjbg=</latexit>

Qf

<latexit sha1_base64="b3nFdM3I7FVdDZDSEGmnoIMHXY=">ACF3icZVC7SgNBFJ31GeMramz+ACrZDcWo2lgm6UYgh3J3cjUPmsczMCiHkE2wVf8TWQhBbSz9EW50kIsYcGDicy/3zIlTzowNgndvanpmdm4+t5BfXFpeWS2srdeMyjTFiCqu9GUMBjmTGFlmOV6mGkHEHC/izsnAv7hBbZiS57abYkNAW7KEUbBOqs2k2ZhOygGQ/iTJPwh20c7H4/PN4uflWbh6qlaCZQWsrBmHoYpLbRA20Z5djPX2UGU6AdaGPdUQkCTaM3jNr3d53S8hOl3ZPWH6p/N3ogjOmK2E0KsNcmv/vPHKi/5tgpmxw2ekymUVJR5eSjPtW+YOP+y2mkVredQSoZi6sT69BA7WunrEIpcg4qaQ4dgzIlrZKAIdOKcGuFCD7rHwfz+TpFYuhvFctVd0xGyJFNskX2SEgOyBE5JRUSEUra5JbckXvwXvyXrzX0eiU97OzQcbgvX0DJw6k0A=</latexit>

γ

<latexit sha1_base64="xCrXyBYaW3OLP43sakS6BcVoAgY=">ACGnicZVC7SgNBFJ31GeMraqnIoghWyW4stAzaWCZgomBCuDu5G8fMY5mZFUJIaW+r+CGp7cTWxm/wI3SiBhzYOBwzr3cMydKODM2CD68mdm5+YXFzFJ2eWV1bT23sVkzKtUq1Rxpa8iMiZxKpluNVohFExPEy6pwN/cs71IYpeWG7CTYEtCWLGQXrpFq9DUJAM7cf5IMR/GkS/pD90s6g8nm/Oyg3c1/1lqKpQGkpB2OuwyCxjR5oyjHfraeGkyAdqCN145KEGgavVHavn/glJYfK+2etP5I/bvRA2FMV0RuUoC9MdmDf+ZQ/TUnTtn4pNFjMktSjq+FKfct8of/t1vMY3U8q4jQDVzYX16AxqodQ1NRChUjZMKimPHgGxpqwRw6BRi7EoBsu8aC/3M01qxXx4lC9WXHWnZIwM2SZ75JCE5JiUyDkpkyqh5JY8kEfy5D17L96r9zYenfF+drbIBLz3b9ckpZk=</latexit>γ <latexit sha1_base64="xCrXyBYaW3OLP43sakS6BcVoAgY=">ACGnicZVC7SgNBFJ31GeMraqnIoghWyW4stAzaWCZgomBCuDu5G8fMY5mZFUJIaW+r+CGp7cTWxm/wI3SiBhzYOBwzr3cMydKODM2CD68mdm5+YXFzFJ2eWV1bT23sVkzKtUq1Rxpa8iMiZxKpluNVohFExPEy6pwN/cs71IYpeWG7CTYEtCWLGQXrpFq9DUJAM7cf5IMR/GkS/pD90s6g8nm/Oyg3c1/1lqKpQGkpB2OuwyCxjR5oyjHfraeGkyAdqCN145KEGgavVHavn/glJYfK+2etP5I/bvRA2FMV0RuUoC9MdmDf+ZQ/TUnTtn4pNFjMktSjq+FKfct8of/t1vMY3U8q4jQDVzYX16AxqodQ1NRChUjZMKimPHgGxpqwRw6BRi7EoBsu8aC/3M01qxXx4lC9WXHWnZIwM2SZ75JCE5JiUyDkpkyqh5JY8kEfy5D17L96r9zYenfF+drbIBLz3b9ckpZk=</latexit>γ <latexit sha1_base64="IoELSitFJaTQ4WT4pr8f01q0csw=">AB7XicbVDLSgNBEJyNrxhfUY9eBoPgKexGQY9BLx4jmAckS+idzCZj5rHMzAphyT948aCIV/Hm3/jJNmDJhY0FXdHdFCWfG+v63V1hb39jcKm6Xdnb39g/Kh0cto1JNaJMornQnAkM5k7RpmeW0k2gKIuK0HY1vZ37iWrDlHywk4SGAoaSxYyAdVKrNwQhoF+u+FV/DrxKgpxUI5Gv/zVGyiSCiot4WBMN/ATG2agLSOcTku91NAEyBiGtOuoBEFNmM2vneIzpwxwrLQrafFc/T2RgTBmIiLXKcCOzLI3E/zuqmNr8OMyS1VJLFojl2Co8ex0PmKbE8okjQDRzt2IyAg3EuoBKLoRg+eV0qpVg4tq7f6yUr/J4yiE3SKzlGArlAd3aEGaiKCHtEzekVvnvJevHfvY9Fa8PKZY/QH3ucPiDmPGQ=</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

e, f

<latexit sha1_base64="iWaQfvkxvh9Rfqbav1n4je9lSjQ=">AB63icbVBNS8NAEJ3Ur1q/qh69LBbBg5SkCnosevFYwX5AG8pmO2mX7iZhdyOU0r/gxYMiXv1D3vw3btoctPXBwO9GWbmBYng2rjut1NYW9/Y3Cpul3Z29/YPyodHLR2nimGTxSJWnYBqFDzCpuFGYCdRSGUgsB2M7zK/YRK8zh6NJMEfUmHEQ85oyaT8IKE/XLFrbpzkFXi5aQCORr98ldvELNUYmSYoFp3PTcx/pQqw5nAWamXakwoG9Mhdi2NqETtT+e3zsiZVQYkjJWtyJC5+ntiSqXWExnYTknNSC97mfif101NeONPeZSkBiO2WBSmgpiYZI+TAVfIjJhYQpni9lbCRlRZmw8JRuCt/zyKmnVqt5ltfZwVanf5nEU4QRO4Rw8uIY63EMDmsBgBM/wCm+OdF6cd+dj0Vpw8plj+APn8wdI+o29</latexit>

e, f

<latexit sha1_base64="iWaQfvkxvh9Rfqbav1n4je9lSjQ=">AB63icbVBNS8NAEJ3Ur1q/qh69LBbBg5SkCnosevFYwX5AG8pmO2mX7iZhdyOU0r/gxYMiXv1D3vw3btoctPXBwO9GWbmBYng2rjut1NYW9/Y3Cpul3Z29/YPyodHLR2nimGTxSJWnYBqFDzCpuFGYCdRSGUgsB2M7zK/YRK8zh6NJMEfUmHEQ85oyaT8IKE/XLFrbpzkFXi5aQCORr98ldvELNUYmSYoFp3PTcx/pQqw5nAWamXakwoG9Mhdi2NqETtT+e3zsiZVQYkjJWtyJC5+ntiSqXWExnYTknNSC97mfif101NeONPeZSkBiO2WBSmgpiYZI+TAVfIjJhYQpni9lbCRlRZmw8JRuCt/zyKmnVqt5ltfZwVanf5nEU4QRO4Rw8uIY63EMDmsBgBM/wCm+OdF6cd+dj0Vpw8plj+APn8wdI+o29</latexit>

f

<latexit sha1_base64="aj1VrWgqSrqkgqJ/bLgtsTmRK/w=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlZtgvV9yqOwdZJV5OKpCj0S9/9QYxSyOUhgmqdzE+NnVBnOBE5LvVRjQtmYDrFrqaQRaj+bHzolZ1YZkDBWtqQhc/X3REYjrSdRYDsjakZ62ZuJ/3nd1ITXfsZlkhqUbLEoTAUxMZl9TQZcITNiYglitbCRtRZmx2ZRsCN7y6ukXat6F9Va87JSv8njKMIJnMI5eHAFdbiDBrSAcIzvMKb8+i8O/Ox6K14OQzx/AHzucPzD+M7g=</latexit>

f

<latexit sha1_base64="aj1VrWgqSrqkgqJ/bLgtsTmRK/w=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlZtgvV9yqOwdZJV5OKpCj0S9/9QYxSyOUhgmqdzE+NnVBnOBE5LvVRjQtmYDrFrqaQRaj+bHzolZ1YZkDBWtqQhc/X3REYjrSdRYDsjakZ62ZuJ/3nd1ITXfsZlkhqUbLEoTAUxMZl9TQZcITNiYglitbCRtRZmx2ZRsCN7y6ukXat6F9Va87JSv8njKMIJnMI5eHAFdbiDBrSAcIzvMKb8+i8O/Ox6K14OQzx/AHzucPzD+M7g=</latexit>
slide-10
SLIDE 10

10

  • integrate out top at Z scale
  • only one EFT coupling

ν ? e e ν

<latexit sha1_base64="62PY9jMj5nB0TpZKRdxb4+FpdY=">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</latexit>
  • αs becomes too strong
  • hadronic physics down to 140 MeV
  • theory with leptons:
  • ne unknown coupling
  • integrate out GeV particles

changes with scale

  • PDG running for α, αs
  • perator mixing

MZ

<latexit sha1_base64="Z982f1amNq6H5eUnLkLx+QwIM0k=">AB6nicdVDLSsNAFJ3UV62vquDGzWApuApJa027K3XjRmjRPrANZTKdtEMnD2YmQgn9BDcuFHr1r/wC9y58VuctCpW8MCFwzn3cu89TsiokIbxrqWldW19LrmY3Nre2d7O5eSwQRx6SJAxbwjoMEYdQnTUklI52QE+Q5jLSd8Vnit28IFzTwr+QkJLaHhj51KUZSZcX/et+NmfohYpVMUvQ0I3SdmyElKonJpFaOrGDLnqQeODvtRe6/3sW28Q4MgjvsQMCdE1jVDaMeKSYkamV4kSIjwGA1JV1EfeUTY8ezUKcwrZQDdgKvyJZypvydi5Akx8RzV6SE5Epn8HzNRf8yFVdIt2zH1w0gSH83uRGDMoDJ43BAOcGSTRBmFN1LMQjxBGWKh4Vwven8H/SKuhmUS80VBo1MEcaHIjcAxMYIEqOAd10AQYDMEtuAcPGtPutEftad6a0r5m9sECtOdPWH+Rrw=</latexit>

mb

<latexit sha1_base64="agrK2VR1EhHFgJtKJUwzKJ7C/lw=">AB6nicdVDLSsNAFJ3UV62vquDGzWApuApJak27K3XjskX7gDaUyXTSDp08mJkIJfQT3LhQxK1b/8IvcOfGb3HSqljBAxcO59zLvfe4EaNCGsa7lZXVvfyG7mtrZ3dvfy+wdtEcYckxYOWci7LhKE0YC0JWMdCNOkO8y0nEnF6nfuSFc0DC4ltOIOD4aBdSjGEklXfkDd5AvGLpVtatmGRq6UT6r2HZKrOq5WYKmbsxRqB01P+hL/bUxyL/1hyGOfRJIzJAQPdOIpJMgLilmZJbrx4JECE/QiPQUDZBPhJPMT53BolKG0Au5qkDCufp7IkG+EFPfVZ0+kmORK/4xU/XHXFolvYqT0CKJQnwYpMXMyhDmD4Oh5QTLNlUEYQ5VcdCPEYcYaniUSF8fwr/J21LN0u61VRp1MECWXAMTsApMIENauASNEALYDACt+AePGhMu9MetadFa0b7mjkES9CePwGVX5HX</latexit>

<latexit sha1_base64="v4U/eD7i/qLVzUQOx/ARY9cjvOs=">AB7XicdVDLSsNAFJ3UV62vquDGzWApuApJak27K3XjsgX7gDaUyXTSjp08mJkIJfQf3LhQxK0r/8IvcOfGb3HSqljBAxcO59zLvfe4EaNCGsa7lZXVvfyG7mtrZ3dvfy+wdtEcYckxYOWci7LhKE0YC0JWMdCNOkO8y0nEnF6nfuSFc0DC4ktOIOD4aBdSjGEkltf1BX6J4kC8YulW1q2YZGrpRPqvYdkqs6rlZgqZuzFGoHTU/6Ev9tTHIv/WHIY59EkjMkBA904ikyAuKWZkluvHgkQIT9CI9BQNkE+Ek8yvncGiUobQC7mqQMK5+nsiQb4QU9VnT6SY5Er/jFT9cdcWiW9ipPQIolCfBikxczKEOY/g6HlBMs2VQRhDlVx0I8RhxhqRJSIXx/Cv8nbUs3S7rVGnUwQJZcAxOwCkwgQ1q4BI0QAtgcA1uwT140ELtTnvUnhatGe1r5hAsQXv+BPQMkzk=</latexit>

mc

<latexit sha1_base64="xguVl6SeAwFNaqUcbQMSi6cKV5E=">AB6nicdVDLSsNAFJ3UV62vquDGzWApuApJak27K3XjskX7gDaUyXTSDp08mJkIJfQT3LhQxK1b/8IvcOfGb3HSqljBAxcO59zLvfe4EaNCGsa7lZXVvfyG7mtrZ3dvfy+wdtEcYckxYOWci7LhKE0YC0JWMdCNOkO8y0nEnF6nfuSFc0DC4ltOIOD4aBdSjGEklXfkDPMgXDN2q2lWzDA3dKJ9VbDslVvXcLEFTN+Yo1I6aH/Sl/toY5N/6wxDHPgkZkiInmlE0kQlxQzMsv1Y0EihCdoRHqKBsgnwknmp85gUSlD6IVcVSDhXP09kSBfiKnvqk4fybHIFf+YqfpjLq2SXsVJaBDFkgR4scmLGZQhTB+HQ8oJlmyqCMKcqmMhHiOsFTxqBC+P4X/k7almyXdaqo06mCBLDgGJ+AUmMAGNXAJGqAFMBiBW3APHjSm3WmP2tOiNaN9zRyCJWjPn5bjkdg=</latexit>

<latexit sha1_base64="wrky59xaKSyqQlBuf9qS2sZUBs=">AB7HicdVDLSsNAFJ3UV62vquDGzWApuApJqrbuSt24bMG0hTaUyXTSDp1MwsxEKHf4MaFIm7d+Rd+gTs3fovTh2IFD1w4nHMv97jx4xKZVkfRmZldW19I7uZ29re2d3L7x80ZQITFwcsUi0fSQJo5y4ipG2rEgKPQZafmjq6nfuiVC0ojfqHFMvBANOA0oRkpLbtjrxrSXL1imNQO0TKdyXrbPNLGcywu7BO2FVageNT7pa+2t3su/d/sRTkLCFWZIyo5txcpLkVAUMzLJdRNJYoRHaEA6mnIUEumls2MnsKiVPgwioYsrOFN/T6QolHIc+rozRGoc8U/5lT9MZdWqaDipZTHiSIczcFCYMqgtPXYZ8KghUba4KwoPpYiIdIKx0QDqE70/h/6TpmHbJdBo6jRqYIwuOwQk4BTYogyq4BnXgAgwouAMP4NHgxr3xZDzPWzPGYuYQLMF4+QLrLpKZ</latexit>

Running to low scales

f

<latexit sha1_base64="W0Cd3NqFKV/2uVsCn5yScPns9ik=">ACFXicZVC7SgNBFJ31GeMraqnIoghWyW4stAzaWCZgHhCD3J3c1SHzWGZmhRBSWtkq/koaO7G19hv8CJ08EGMODBzOuZd75kQJZ8YGwac3N7+wuLScWcmurq1vbOa2tmtGpZpilSqudCMCg5xJrFpmOTYSjSAijvWoczH06/eoDVPynYTbAm4lSxmFKyTKvFN7jDIByP4sySckMPS3qDy9bA/KN/kvq/biqYCpaUcjGmGQWJbPdCWUY797HVqMAHagVtsOipBoGn1RkH7/pFT2n6stHvS+iP170YPhDFdEblJAfbOZI/+mUP15w6ZeOzVo/JLUo6fhSnHLfKn/4b/NFLu4A1cyF9ekdaKDWlTMVoVA1Tiojh0Dsq2tEsChU4ixKwXIvms/N/PLKkV8+FJvlhx1Z2TMTJklxyQYxKSU1Iil6RMqoQSJI/kiTx7L96r9+a9j0fnvMnODpmC9/EDwYSjbg=</latexit>

f

<latexit sha1_base64="W0Cd3NqFKV/2uVsCn5yScPns9ik=">ACFXicZVC7SgNBFJ31GeMraqnIoghWyW4stAzaWCZgHhCD3J3c1SHzWGZmhRBSWtkq/koaO7G19hv8CJ08EGMODBzOuZd75kQJZ8YGwac3N7+wuLScWcmurq1vbOa2tmtGpZpilSqudCMCg5xJrFpmOTYSjSAijvWoczH06/eoDVPynYTbAm4lSxmFKyTKvFN7jDIByP4sySckMPS3qDy9bA/KN/kvq/biqYCpaUcjGmGQWJbPdCWUY797HVqMAHagVtsOipBoGn1RkH7/pFT2n6stHvS+iP170YPhDFdEblJAfbOZI/+mUP15w6ZeOzVo/JLUo6fhSnHLfKn/4b/NFLu4A1cyF9ekdaKDWlTMVoVA1Tiojh0Dsq2tEsChU4ixKwXIvms/N/PLKkV8+FJvlhx1Z2TMTJklxyQYxKSU1Iil6RMqoQSJI/kiTx7L96r9+a9j0fnvMnODpmC9/EDwYSjbg=</latexit>

Qf

<latexit sha1_base64="b3nFdM3I7FVdDZDSEGmnoIMHXY=">ACF3icZVC7SgNBFJ31GeMramz+ACrZDcWo2lgm6UYgh3J3cjUPmsczMCiHkE2wVf8TWQhBbSz9EW50kIsYcGDicy/3zIlTzowNgndvanpmdm4+t5BfXFpeWS2srdeMyjTFiCqu9GUMBjmTGFlmOV6mGkHEHC/izsnAv7hBbZiS57abYkNAW7KEUbBOqs2k2ZhOygGQ/iTJPwh20c7H4/PN4uflWbh6qlaCZQWsrBmHoYpLbRA20Z5djPX2UGU6AdaGPdUQkCTaM3jNr3d53S8hOl3ZPWH6p/N3ogjOmK2E0KsNcmv/vPHKi/5tgpmxw2ekymUVJR5eSjPtW+YOP+y2mkVredQSoZi6sT69BA7WunrEIpcg4qaQ4dgzIlrZKAIdOKcGuFCD7rHwfz+TpFYuhvFctVd0xGyJFNskX2SEgOyBE5JRUSEUra5JbckXvwXvyXrzX0eiU97OzQcbgvX0DJw6k0A=</latexit>

γ

<latexit sha1_base64="xCrXyBYaW3OLP43sakS6BcVoAgY=">ACGnicZVC7SgNBFJ31GeMraqnIoghWyW4stAzaWCZgomBCuDu5G8fMY5mZFUJIaW+r+CGp7cTWxm/wI3SiBhzYOBwzr3cMydKODM2CD68mdm5+YXFzFJ2eWV1bT23sVkzKtUq1Rxpa8iMiZxKpluNVohFExPEy6pwN/cs71IYpeWG7CTYEtCWLGQXrpFq9DUJAM7cf5IMR/GkS/pD90s6g8nm/Oyg3c1/1lqKpQGkpB2OuwyCxjR5oyjHfraeGkyAdqCN145KEGgavVHavn/glJYfK+2etP5I/bvRA2FMV0RuUoC9MdmDf+ZQ/TUnTtn4pNFjMktSjq+FKfct8of/t1vMY3U8q4jQDVzYX16AxqodQ1NRChUjZMKimPHgGxpqwRw6BRi7EoBsu8aC/3M01qxXx4lC9WXHWnZIwM2SZ75JCE5JiUyDkpkyqh5JY8kEfy5D17L96r9zYenfF+drbIBLz3b9ckpZk=</latexit>

f

<latexit sha1_base64="W0Cd3NqFKV/2uVsCn5yScPns9ik=">ACFXicZVC7SgNBFJ31GeMraqnIoghWyW4stAzaWCZgHhCD3J3c1SHzWGZmhRBSWtkq/koaO7G19hv8CJ08EGMODBzOuZd75kQJZ8YGwac3N7+wuLScWcmurq1vbOa2tmtGpZpilSqudCMCg5xJrFpmOTYSjSAijvWoczH06/eoDVPynYTbAm4lSxmFKyTKvFN7jDIByP4sySckMPS3qDy9bA/KN/kvq/biqYCpaUcjGmGQWJbPdCWUY797HVqMAHagVtsOipBoGn1RkH7/pFT2n6stHvS+iP170YPhDFdEblJAfbOZI/+mUP15w6ZeOzVo/JLUo6fhSnHLfKn/4b/NFLu4A1cyF9ekdaKDWlTMVoVA1Tiojh0Dsq2tEsChU4ixKwXIvms/N/PLKkV8+FJvlhx1Z2TMTJklxyQYxKSU1Iil6RMqoQSJI/kiTx7L96r9+a9j0fnvMnODpmC9/EDwYSjbg=</latexit>

f

<latexit sha1_base64="W0Cd3NqFKV/2uVsCn5yScPns9ik=">ACFXicZVC7SgNBFJ31GeMraqnIoghWyW4stAzaWCZgHhCD3J3c1SHzWGZmhRBSWtkq/koaO7G19hv8CJ08EGMODBzOuZd75kQJZ8YGwac3N7+wuLScWcmurq1vbOa2tmtGpZpilSqudCMCg5xJrFpmOTYSjSAijvWoczH06/eoDVPynYTbAm4lSxmFKyTKvFN7jDIByP4sySckMPS3qDy9bA/KN/kvq/biqYCpaUcjGmGQWJbPdCWUY797HVqMAHagVtsOipBoGn1RkH7/pFT2n6stHvS+iP170YPhDFdEblJAfbOZI/+mUP15w6ZeOzVo/JLUo6fhSnHLfKn/4b/NFLu4A1cyF9ekdaKDWlTMVoVA1Tiojh0Dsq2tEsChU4ixKwXIvms/N/PLKkV8+FJvlhx1Z2TMTJklxyQYxKSU1Iil6RMqoQSJI/kiTx7L96r9+a9j0fnvMnODpmC9/EDwYSjbg=</latexit>

Qf

<latexit sha1_base64="b3nFdM3I7FVdDZDSEGmnoIMHXY=">ACF3icZVC7SgNBFJ31GeMramz+ACrZDcWo2lgm6UYgh3J3cjUPmsczMCiHkE2wVf8TWQhBbSz9EW50kIsYcGDicy/3zIlTzowNgndvanpmdm4+t5BfXFpeWS2srdeMyjTFiCqu9GUMBjmTGFlmOV6mGkHEHC/izsnAv7hBbZiS57abYkNAW7KEUbBOqs2k2ZhOygGQ/iTJPwh20c7H4/PN4uflWbh6qlaCZQWsrBmHoYpLbRA20Z5djPX2UGU6AdaGPdUQkCTaM3jNr3d53S8hOl3ZPWH6p/N3ogjOmK2E0KsNcmv/vPHKi/5tgpmxw2ekymUVJR5eSjPtW+YOP+y2mkVredQSoZi6sT69BA7WunrEIpcg4qaQ4dgzIlrZKAIdOKcGuFCD7rHwfz+TpFYuhvFctVd0xGyJFNskX2SEgOyBE5JRUSEUra5JbckXvwXvyXrzX0eiU97OzQcbgvX0DJw6k0A=</latexit>

γ

<latexit sha1_base64="xCrXyBYaW3OLP43sakS6BcVoAgY=">ACGnicZVC7SgNBFJ31GeMraqnIoghWyW4stAzaWCZgomBCuDu5G8fMY5mZFUJIaW+r+CGp7cTWxm/wI3SiBhzYOBwzr3cMydKODM2CD68mdm5+YXFzFJ2eWV1bT23sVkzKtUq1Rxpa8iMiZxKpluNVohFExPEy6pwN/cs71IYpeWG7CTYEtCWLGQXrpFq9DUJAM7cf5IMR/GkS/pD90s6g8nm/Oyg3c1/1lqKpQGkpB2OuwyCxjR5oyjHfraeGkyAdqCN145KEGgavVHavn/glJYfK+2etP5I/bvRA2FMV0RuUoC9MdmDf+ZQ/TUnTtn4pNFjMktSjq+FKfct8of/t1vMY3U8q4jQDVzYX16AxqodQ1NRChUjZMKimPHgGxpqwRw6BRi7EoBsu8aC/3M01qxXx4lC9WXHWnZIwM2SZ75JCE5JiUyDkpkyqh5JY8kEfy5D17L96r9zYenfF+drbIBLz3b9ckpZk=</latexit>γ <latexit sha1_base64="xCrXyBYaW3OLP43sakS6BcVoAgY=">ACGnicZVC7SgNBFJ31GeMraqnIoghWyW4stAzaWCZgomBCuDu5G8fMY5mZFUJIaW+r+CGp7cTWxm/wI3SiBhzYOBwzr3cMydKODM2CD68mdm5+YXFzFJ2eWV1bT23sVkzKtUq1Rxpa8iMiZxKpluNVohFExPEy6pwN/cs71IYpeWG7CTYEtCWLGQXrpFq9DUJAM7cf5IMR/GkS/pD90s6g8nm/Oyg3c1/1lqKpQGkpB2OuwyCxjR5oyjHfraeGkyAdqCN145KEGgavVHavn/glJYfK+2etP5I/bvRA2FMV0RuUoC9MdmDf+ZQ/TUnTtn4pNFjMktSjq+FKfct8of/t1vMY3U8q4jQDVzYX16AxqodQ1NRChUjZMKimPHgGxpqwRw6BRi7EoBsu8aC/3M01qxXx4lC9WXHWnZIwM2SZ75JCE5JiUyDkpkyqh5JY8kEfy5D17L96r9zYenfF+drbIBLz3b9ckpZk=</latexit>γ <latexit sha1_base64="IoELSitFJaTQ4WT4pr8f01q0csw=">AB7XicbVDLSgNBEJyNrxhfUY9eBoPgKexGQY9BLx4jmAckS+idzCZj5rHMzAphyT948aCIV/Hm3/jJNmDJhY0FXdHdFCWfG+v63V1hb39jcKm6Xdnb39g/Kh0cto1JNaJMornQnAkM5k7RpmeW0k2gKIuK0HY1vZ37iWrDlHywk4SGAoaSxYyAdVKrNwQhoF+u+FV/DrxKgpxUI5Gv/zVGyiSCiot4WBMN/ATG2agLSOcTku91NAEyBiGtOuoBEFNmM2vneIzpwxwrLQrafFc/T2RgTBmIiLXKcCOzLI3E/zuqmNr8OMyS1VJLFojl2Co8ex0PmKbE8okjQDRzt2IyAg3EuoBKLoRg+eV0qpVg4tq7f6yUr/J4yiE3SKzlGArlAd3aEGaiKCHtEzekVvnvJevHfvY9Fa8PKZY/QH3ucPiDmPGQ=</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

e, f

<latexit sha1_base64="iWaQfvkxvh9Rfqbav1n4je9lSjQ=">AB63icbVBNS8NAEJ3Ur1q/qh69LBbBg5SkCnosevFYwX5AG8pmO2mX7iZhdyOU0r/gxYMiXv1D3vw3btoctPXBwO9GWbmBYng2rjut1NYW9/Y3Cpul3Z29/YPyodHLR2nimGTxSJWnYBqFDzCpuFGYCdRSGUgsB2M7zK/YRK8zh6NJMEfUmHEQ85oyaT8IKE/XLFrbpzkFXi5aQCORr98ldvELNUYmSYoFp3PTcx/pQqw5nAWamXakwoG9Mhdi2NqETtT+e3zsiZVQYkjJWtyJC5+ntiSqXWExnYTknNSC97mfif101NeONPeZSkBiO2WBSmgpiYZI+TAVfIjJhYQpni9lbCRlRZmw8JRuCt/zyKmnVqt5ltfZwVanf5nEU4QRO4Rw8uIY63EMDmsBgBM/wCm+OdF6cd+dj0Vpw8plj+APn8wdI+o29</latexit>

e, f

<latexit sha1_base64="iWaQfvkxvh9Rfqbav1n4je9lSjQ=">AB63icbVBNS8NAEJ3Ur1q/qh69LBbBg5SkCnosevFYwX5AG8pmO2mX7iZhdyOU0r/gxYMiXv1D3vw3btoctPXBwO9GWbmBYng2rjut1NYW9/Y3Cpul3Z29/YPyodHLR2nimGTxSJWnYBqFDzCpuFGYCdRSGUgsB2M7zK/YRK8zh6NJMEfUmHEQ85oyaT8IKE/XLFrbpzkFXi5aQCORr98ldvELNUYmSYoFp3PTcx/pQqw5nAWamXakwoG9Mhdi2NqETtT+e3zsiZVQYkjJWtyJC5+ntiSqXWExnYTknNSC97mfif101NeONPeZSkBiO2WBSmgpiYZI+TAVfIjJhYQpni9lbCRlRZmw8JRuCt/zyKmnVqt5ltfZwVanf5nEU4QRO4Rw8uIY63EMDmsBgBM/wCm+OdF6cd+dj0Vpw8plj+APn8wdI+o29</latexit>

f

<latexit sha1_base64="aj1VrWgqSrqkgqJ/bLgtsTmRK/w=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlZtgvV9yqOwdZJV5OKpCj0S9/9QYxSyOUhgmqdzE+NnVBnOBE5LvVRjQtmYDrFrqaQRaj+bHzolZ1YZkDBWtqQhc/X3REYjrSdRYDsjakZ62ZuJ/3nd1ITXfsZlkhqUbLEoTAUxMZl9TQZcITNiYglitbCRtRZmx2ZRsCN7y6ukXat6F9Va87JSv8njKMIJnMI5eHAFdbiDBrSAcIzvMKb8+i8O/Ox6K14OQzx/AHzucPzD+M7g=</latexit>

f

<latexit sha1_base64="aj1VrWgqSrqkgqJ/bLgtsTmRK/w=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlZtgvV9yqOwdZJV5OKpCj0S9/9QYxSyOUhgmqdzE+NnVBnOBE5LvVRjQtmYDrFrqaQRaj+bHzolZ1YZkDBWtqQhc/X3REYjrSdRYDsjakZ62ZuJ/3nd1ITXfsZlkhqUbLEoTAUxMZl9TQZcITNiYglitbCRtRZmx2ZRsCN7y6ukXat6F9Va87JSv8njKMIJnMI5eHAFdbiDBrSAcIzvMKb8+i8O/Ox6K14OQzx/AHzucPzD+M7g=</latexit>
  • after diagonalization, only 1 effective coupling changes with scale
  • known from electroweak to hadronic scales
slide-11
SLIDE 11

11

  • after diagonalization, only 1 effective coupling changes with scale
  • known from electroweak to hadronic scales
  • integrate out top at Z scale
  • only one EFT coupling

ν ? e e ν

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f

<latexit sha1_base64="W0Cd3NqFKV/2uVsCn5yScPns9ik=">ACFXicZVC7SgNBFJ31GeMraqnIoghWyW4stAzaWCZgHhCD3J3c1SHzWGZmhRBSWtkq/koaO7G19hv8CJ08EGMODBzOuZd75kQJZ8YGwac3N7+wuLScWcmurq1vbOa2tmtGpZpilSqudCMCg5xJrFpmOTYSjSAijvWoczH06/eoDVPynYTbAm4lSxmFKyTKvFN7jDIByP4sySckMPS3qDy9bA/KN/kvq/biqYCpaUcjGmGQWJbPdCWUY797HVqMAHagVtsOipBoGn1RkH7/pFT2n6stHvS+iP170YPhDFdEblJAfbOZI/+mUP15w6ZeOzVo/JLUo6fhSnHLfKn/4b/NFLu4A1cyF9ekdaKDWlTMVoVA1Tiojh0Dsq2tEsChU4ixKwXIvms/N/PLKkV8+FJvlhx1Z2TMTJklxyQYxKSU1Iil6RMqoQSJI/kiTx7L96r9+a9j0fnvMnODpmC9/EDwYSjbg=</latexit>

f

<latexit sha1_base64="W0Cd3NqFKV/2uVsCn5yScPns9ik=">ACFXicZVC7SgNBFJ31GeMraqnIoghWyW4stAzaWCZgHhCD3J3c1SHzWGZmhRBSWtkq/koaO7G19hv8CJ08EGMODBzOuZd75kQJZ8YGwac3N7+wuLScWcmurq1vbOa2tmtGpZpilSqudCMCg5xJrFpmOTYSjSAijvWoczH06/eoDVPynYTbAm4lSxmFKyTKvFN7jDIByP4sySckMPS3qDy9bA/KN/kvq/biqYCpaUcjGmGQWJbPdCWUY797HVqMAHagVtsOipBoGn1RkH7/pFT2n6stHvS+iP170YPhDFdEblJAfbOZI/+mUP15w6ZeOzVo/JLUo6fhSnHLfKn/4b/NFLu4A1cyF9ekdaKDWlTMVoVA1Tiojh0Dsq2tEsChU4ixKwXIvms/N/PLKkV8+FJvlhx1Z2TMTJklxyQYxKSU1Iil6RMqoQSJI/kiTx7L96r9+a9j0fnvMnODpmC9/EDwYSjbg=</latexit>

Qf

<latexit sha1_base64="b3nFdM3I7FVdDZDSEGmnoIMHXY=">ACF3icZVC7SgNBFJ31GeMramz+ACrZDcWo2lgm6UYgh3J3cjUPmsczMCiHkE2wVf8TWQhBbSz9EW50kIsYcGDicy/3zIlTzowNgndvanpmdm4+t5BfXFpeWS2srdeMyjTFiCqu9GUMBjmTGFlmOV6mGkHEHC/izsnAv7hBbZiS57abYkNAW7KEUbBOqs2k2ZhOygGQ/iTJPwh20c7H4/PN4uflWbh6qlaCZQWsrBmHoYpLbRA20Z5djPX2UGU6AdaGPdUQkCTaM3jNr3d53S8hOl3ZPWH6p/N3ogjOmK2E0KsNcmv/vPHKi/5tgpmxw2ekymUVJR5eSjPtW+YOP+y2mkVredQSoZi6sT69BA7WunrEIpcg4qaQ4dgzIlrZKAIdOKcGuFCD7rHwfz+TpFYuhvFctVd0xGyJFNskX2SEgOyBE5JRUSEUra5JbckXvwXvyXrzX0eiU97OzQcbgvX0DJw6k0A=</latexit>

γ

<latexit sha1_base64="xCrXyBYaW3OLP43sakS6BcVoAgY=">ACGnicZVC7SgNBFJ31GeMraqnIoghWyW4stAzaWCZgomBCuDu5G8fMY5mZFUJIaW+r+CGp7cTWxm/wI3SiBhzYOBwzr3cMydKODM2CD68mdm5+YXFzFJ2eWV1bT23sVkzKtUq1Rxpa8iMiZxKpluNVohFExPEy6pwN/cs71IYpeWG7CTYEtCWLGQXrpFq9DUJAM7cf5IMR/GkS/pD90s6g8nm/Oyg3c1/1lqKpQGkpB2OuwyCxjR5oyjHfraeGkyAdqCN145KEGgavVHavn/glJYfK+2etP5I/bvRA2FMV0RuUoC9MdmDf+ZQ/TUnTtn4pNFjMktSjq+FKfct8of/t1vMY3U8q4jQDVzYX16AxqodQ1NRChUjZMKimPHgGxpqwRw6BRi7EoBsu8aC/3M01qxXx4lC9WXHWnZIwM2SZ75JCE5JiUyDkpkyqh5JY8kEfy5D17L96r9zYenfF+drbIBLz3b9ckpZk=</latexit>
  • αs becomes too strong
  • hadronic physics down to 140 MeV
  • theory with leptons:
  • ne unknown coupling
  • integrate out GeV particles

changes with scale

  • PDG running for α, αs
  • perator mixing

MZ

<latexit sha1_base64="Z982f1amNq6H5eUnLkLx+QwIM0k=">AB6nicdVDLSsNAFJ3UV62vquDGzWApuApJa027K3XjRmjRPrANZTKdtEMnD2YmQgn9BDcuFHr1r/wC9y58VuctCpW8MCFwzn3cu89TsiokIbxrqWldW19LrmY3Nre2d7O5eSwQRx6SJAxbwjoMEYdQnTUklI52QE+Q5jLSd8Vnit28IFzTwr+QkJLaHhj51KUZSZcX/et+NmfohYpVMUvQ0I3SdmyElKonJpFaOrGDLnqQeODvtRe6/3sW28Q4MgjvsQMCdE1jVDaMeKSYkamV4kSIjwGA1JV1EfeUTY8ezUKcwrZQDdgKvyJZypvydi5Akx8RzV6SE5Epn8HzNRf8yFVdIt2zH1w0gSH83uRGDMoDJ43BAOcGSTRBmFN1LMQjxBGWKh4Vwven8H/SKuhmUS80VBo1MEcaHIjcAxMYIEqOAd10AQYDMEtuAcPGtPutEftad6a0r5m9sECtOdPWH+Rrw=</latexit>

mb

<latexit sha1_base64="agrK2VR1EhHFgJtKJUwzKJ7C/lw=">AB6nicdVDLSsNAFJ3UV62vquDGzWApuApJak27K3XjskX7gDaUyXTSDp08mJkIJfQT3LhQxK1b/8IvcOfGb3HSqljBAxcO59zLvfe4EaNCGsa7lZXVvfyG7mtrZ3dvfy+wdtEcYckxYOWci7LhKE0YC0JWMdCNOkO8y0nEnF6nfuSFc0DC4ltOIOD4aBdSjGEklXfkDd5AvGLpVtatmGRq6UT6r2HZKrOq5WYKmbsxRqB01P+hL/bUxyL/1hyGOfRJIzJAQPdOIpJMgLilmZJbrx4JECE/QiPQUDZBPhJPMT53BolKG0Au5qkDCufp7IkG+EFPfVZ0+kmORK/4xU/XHXFolvYqT0CKJQnwYpMXMyhDmD4Oh5QTLNlUEYQ5VcdCPEYcYaniUSF8fwr/J21LN0u61VRp1MECWXAMTsApMIENauASNEALYDACt+AePGhMu9MetadFa0b7mjkES9CePwGVX5HX</latexit>

<latexit sha1_base64="v4U/eD7i/qLVzUQOx/ARY9cjvOs=">AB7XicdVDLSsNAFJ3UV62vquDGzWApuApJak27K3XjsgX7gDaUyXTSjp08mJkIJfQf3LhQxK0r/8IvcOfGb3HSqljBAxcO59zLvfe4EaNCGsa7lZXVvfyG7mtrZ3dvfy+wdtEcYckxYOWci7LhKE0YC0JWMdCNOkO8y0nEnF6nfuSFc0DC4ktOIOD4aBdSjGEkltf1BX6J4kC8YulW1q2YZGrpRPqvYdkqs6rlZgqZuzFGoHTU/6Ev9tTHIv/WHIY59EkjMkBA904ikyAuKWZkluvHgkQIT9CI9BQNkE+Ek8yvncGiUobQC7mqQMK5+nsiQb4QU9VnT6SY5Er/jFT9cdcWiW9ipPQIolCfBikxczKEOY/g6HlBMs2VQRhDlVx0I8RhxhqRJSIXx/Cv8nbUs3S7rVGnUwQJZcAxOwCkwgQ1q4BI0QAtgcA1uwT140ELtTnvUnhatGe1r5hAsQXv+BPQMkzk=</latexit>

mc

<latexit sha1_base64="xguVl6SeAwFNaqUcbQMSi6cKV5E=">AB6nicdVDLSsNAFJ3UV62vquDGzWApuApJak27K3XjskX7gDaUyXTSDp08mJkIJfQT3LhQxK1b/8IvcOfGb3HSqljBAxcO59zLvfe4EaNCGsa7lZXVvfyG7mtrZ3dvfy+wdtEcYckxYOWci7LhKE0YC0JWMdCNOkO8y0nEnF6nfuSFc0DC4ltOIOD4aBdSjGEklXfkDPMgXDN2q2lWzDA3dKJ9VbDslVvXcLEFTN+Yo1I6aH/Sl/toY5N/6wxDHPgkZkiInmlE0kQlxQzMsv1Y0EihCdoRHqKBsgnwknmp85gUSlD6IVcVSDhXP09kSBfiKnvqk4fybHIFf+YqfpjLq2SXsVJaBDFkgR4scmLGZQhTB+HQ8oJlmyqCMKcqmMhHiOsFTxqBC+P4X/k7almyXdaqo06mCBLDgGJ+AUmMAGNXAJGqAFMBiBW3APHjSm3WmP2tOiNaN9zRyCJWjPn5bjkdg=</latexit>

<latexit sha1_base64="wrky59xaKSyqQlBuf9qS2sZUBs=">AB7HicdVDLSsNAFJ3UV62vquDGzWApuApJqrbuSt24bMG0hTaUyXTSDp1MwsxEKHf4MaFIm7d+Rd+gTs3fovTh2IFD1w4nHMv97jx4xKZVkfRmZldW19I7uZ29re2d3L7x80ZQITFwcsUi0fSQJo5y4ipG2rEgKPQZafmjq6nfuiVC0ojfqHFMvBANOA0oRkpLbtjrxrSXL1imNQO0TKdyXrbPNLGcywu7BO2FVageNT7pa+2t3su/d/sRTkLCFWZIyo5txcpLkVAUMzLJdRNJYoRHaEA6mnIUEumls2MnsKiVPgwioYsrOFN/T6QolHIc+rozRGoc8U/5lT9MZdWqaDipZTHiSIczcFCYMqgtPXYZ8KghUba4KwoPpYiIdIKx0QDqE70/h/6TpmHbJdBo6jRqYIwuOwQk4BTYogyq4BnXgAgwouAMP4NHgxr3xZDzPWzPGYuYQLMF4+QLrLpKZ</latexit>

Running to low scales

f

<latexit sha1_base64="W0Cd3NqFKV/2uVsCn5yScPns9ik=">ACFXicZVC7SgNBFJ31GeMraqnIoghWyW4stAzaWCZgHhCD3J3c1SHzWGZmhRBSWtkq/koaO7G19hv8CJ08EGMODBzOuZd75kQJZ8YGwac3N7+wuLScWcmurq1vbOa2tmtGpZpilSqudCMCg5xJrFpmOTYSjSAijvWoczH06/eoDVPynYTbAm4lSxmFKyTKvFN7jDIByP4sySckMPS3qDy9bA/KN/kvq/biqYCpaUcjGmGQWJbPdCWUY797HVqMAHagVtsOipBoGn1RkH7/pFT2n6stHvS+iP170YPhDFdEblJAfbOZI/+mUP15w6ZeOzVo/JLUo6fhSnHLfKn/4b/NFLu4A1cyF9ekdaKDWlTMVoVA1Tiojh0Dsq2tEsChU4ixKwXIvms/N/PLKkV8+FJvlhx1Z2TMTJklxyQYxKSU1Iil6RMqoQSJI/kiTx7L96r9+a9j0fnvMnODpmC9/EDwYSjbg=</latexit>

f

<latexit sha1_base64="W0Cd3NqFKV/2uVsCn5yScPns9ik=">ACFXicZVC7SgNBFJ31GeMraqnIoghWyW4stAzaWCZgHhCD3J3c1SHzWGZmhRBSWtkq/koaO7G19hv8CJ08EGMODBzOuZd75kQJZ8YGwac3N7+wuLScWcmurq1vbOa2tmtGpZpilSqudCMCg5xJrFpmOTYSjSAijvWoczH06/eoDVPynYTbAm4lSxmFKyTKvFN7jDIByP4sySckMPS3qDy9bA/KN/kvq/biqYCpaUcjGmGQWJbPdCWUY797HVqMAHagVtsOipBoGn1RkH7/pFT2n6stHvS+iP170YPhDFdEblJAfbOZI/+mUP15w6ZeOzVo/JLUo6fhSnHLfKn/4b/NFLu4A1cyF9ekdaKDWlTMVoVA1Tiojh0Dsq2tEsChU4ixKwXIvms/N/PLKkV8+FJvlhx1Z2TMTJklxyQYxKSU1Iil6RMqoQSJI/kiTx7L96r9+a9j0fnvMnODpmC9/EDwYSjbg=</latexit>

Qf

<latexit sha1_base64="b3nFdM3I7FVdDZDSEGmnoIMHXY=">ACF3icZVC7SgNBFJ31GeMramz+ACrZDcWo2lgm6UYgh3J3cjUPmsczMCiHkE2wVf8TWQhBbSz9EW50kIsYcGDicy/3zIlTzowNgndvanpmdm4+t5BfXFpeWS2srdeMyjTFiCqu9GUMBjmTGFlmOV6mGkHEHC/izsnAv7hBbZiS57abYkNAW7KEUbBOqs2k2ZhOygGQ/iTJPwh20c7H4/PN4uflWbh6qlaCZQWsrBmHoYpLbRA20Z5djPX2UGU6AdaGPdUQkCTaM3jNr3d53S8hOl3ZPWH6p/N3ogjOmK2E0KsNcmv/vPHKi/5tgpmxw2ekymUVJR5eSjPtW+YOP+y2mkVredQSoZi6sT69BA7WunrEIpcg4qaQ4dgzIlrZKAIdOKcGuFCD7rHwfz+TpFYuhvFctVd0xGyJFNskX2SEgOyBE5JRUSEUra5JbckXvwXvyXrzX0eiU97OzQcbgvX0DJw6k0A=</latexit>

γ

<latexit sha1_base64="xCrXyBYaW3OLP43sakS6BcVoAgY=">ACGnicZVC7SgNBFJ31GeMraqnIoghWyW4stAzaWCZgomBCuDu5G8fMY5mZFUJIaW+r+CGp7cTWxm/wI3SiBhzYOBwzr3cMydKODM2CD68mdm5+YXFzFJ2eWV1bT23sVkzKtUq1Rxpa8iMiZxKpluNVohFExPEy6pwN/cs71IYpeWG7CTYEtCWLGQXrpFq9DUJAM7cf5IMR/GkS/pD90s6g8nm/Oyg3c1/1lqKpQGkpB2OuwyCxjR5oyjHfraeGkyAdqCN145KEGgavVHavn/glJYfK+2etP5I/bvRA2FMV0RuUoC9MdmDf+ZQ/TUnTtn4pNFjMktSjq+FKfct8of/t1vMY3U8q4jQDVzYX16AxqodQ1NRChUjZMKimPHgGxpqwRw6BRi7EoBsu8aC/3M01qxXx4lC9WXHWnZIwM2SZ75JCE5JiUyDkpkyqh5JY8kEfy5D17L96r9zYenfF+drbIBLz3b9ckpZk=</latexit>γ <latexit sha1_base64="xCrXyBYaW3OLP43sakS6BcVoAgY=">ACGnicZVC7SgNBFJ31GeMraqnIoghWyW4stAzaWCZgomBCuDu5G8fMY5mZFUJIaW+r+CGp7cTWxm/wI3SiBhzYOBwzr3cMydKODM2CD68mdm5+YXFzFJ2eWV1bT23sVkzKtUq1Rxpa8iMiZxKpluNVohFExPEy6pwN/cs71IYpeWG7CTYEtCWLGQXrpFq9DUJAM7cf5IMR/GkS/pD90s6g8nm/Oyg3c1/1lqKpQGkpB2OuwyCxjR5oyjHfraeGkyAdqCN145KEGgavVHavn/glJYfK+2etP5I/bvRA2FMV0RuUoC9MdmDf+ZQ/TUnTtn4pNFjMktSjq+FKfct8of/t1vMY3U8q4jQDVzYX16AxqodQ1NRChUjZMKimPHgGxpqwRw6BRi7EoBsu8aC/3M01qxXx4lC9WXHWnZIwM2SZ75JCE5JiUyDkpkyqh5JY8kEfy5D17L96r9zYenfF+drbIBLz3b9ckpZk=</latexit>γ <latexit sha1_base64="IoELSitFJaTQ4WT4pr8f01q0csw=">AB7XicbVDLSgNBEJyNrxhfUY9eBoPgKexGQY9BLx4jmAckS+idzCZj5rHMzAphyT948aCIV/Hm3/jJNmDJhY0FXdHdFCWfG+v63V1hb39jcKm6Xdnb39g/Kh0cto1JNaJMornQnAkM5k7RpmeW0k2gKIuK0HY1vZ37iWrDlHywk4SGAoaSxYyAdVKrNwQhoF+u+FV/DrxKgpxUI5Gv/zVGyiSCiot4WBMN/ATG2agLSOcTku91NAEyBiGtOuoBEFNmM2vneIzpwxwrLQrafFc/T2RgTBmIiLXKcCOzLI3E/zuqmNr8OMyS1VJLFojl2Co8ex0PmKbE8okjQDRzt2IyAg3EuoBKLoRg+eV0qpVg4tq7f6yUr/J4yiE3SKzlGArlAd3aEGaiKCHtEzekVvnvJevHfvY9Fa8PKZY/QH3ucPiDmPGQ=</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

Qf

<latexit sha1_base64="iPePgoaDxhFJKE4mHOQWbymQHo=">AB6nicbVBNS8NAEJ34WetX1aOXxSJ4KkV9Fj04rF+wFtKJvtpF262YTdjVBCf4IXD4p49Rd589+4bXPQ1gcDj/dmJkXJIJr47rfztr6xubWdmGnuLu3f3BYOjpu6ThVDJsFrHqBFSj4BKbhuBnUQhjQKB7WB8N/PbT6g0j+WjmSToR3QoecgZNVZ6aPTDfqnsVtw5yCrxclKGHPV+6as3iFkaoTRMUK27npsYP6PKcCZwWuylGhPKxnSIXUsljVD72fzUKTm3yoCEsbIlDZmrvycyGmk9iQLbGVEz0sveTPzP6YmvPEzLpPUoGSLRWEqiInJ7G8y4AqZERNLKFPc3krYiCrKjE2naEPwl9eJa1qxbusVBtX5dptHkcBTuEMLsCDa6jBPdShCQyG8Ayv8OYI58V5dz4WrWtOPnMCf+B8/gAh6I2y</latexit>

e, f

<latexit sha1_base64="iWaQfvkxvh9Rfqbav1n4je9lSjQ=">AB63icbVBNS8NAEJ3Ur1q/qh69LBbBg5SkCnosevFYwX5AG8pmO2mX7iZhdyOU0r/gxYMiXv1D3vw3btoctPXBwO9GWbmBYng2rjut1NYW9/Y3Cpul3Z29/YPyodHLR2nimGTxSJWnYBqFDzCpuFGYCdRSGUgsB2M7zK/YRK8zh6NJMEfUmHEQ85oyaT8IKE/XLFrbpzkFXi5aQCORr98ldvELNUYmSYoFp3PTcx/pQqw5nAWamXakwoG9Mhdi2NqETtT+e3zsiZVQYkjJWtyJC5+ntiSqXWExnYTknNSC97mfif101NeONPeZSkBiO2WBSmgpiYZI+TAVfIjJhYQpni9lbCRlRZmw8JRuCt/zyKmnVqt5ltfZwVanf5nEU4QRO4Rw8uIY63EMDmsBgBM/wCm+OdF6cd+dj0Vpw8plj+APn8wdI+o29</latexit>

e, f

<latexit sha1_base64="iWaQfvkxvh9Rfqbav1n4je9lSjQ=">AB63icbVBNS8NAEJ3Ur1q/qh69LBbBg5SkCnosevFYwX5AG8pmO2mX7iZhdyOU0r/gxYMiXv1D3vw3btoctPXBwO9GWbmBYng2rjut1NYW9/Y3Cpul3Z29/YPyodHLR2nimGTxSJWnYBqFDzCpuFGYCdRSGUgsB2M7zK/YRK8zh6NJMEfUmHEQ85oyaT8IKE/XLFrbpzkFXi5aQCORr98ldvELNUYmSYoFp3PTcx/pQqw5nAWamXakwoG9Mhdi2NqETtT+e3zsiZVQYkjJWtyJC5+ntiSqXWExnYTknNSC97mfif101NeONPeZSkBiO2WBSmgpiYZI+TAVfIjJhYQpni9lbCRlRZmw8JRuCt/zyKmnVqt5ltfZwVanf5nEU4QRO4Rw8uIY63EMDmsBgBM/wCm+OdF6cd+dj0Vpw8plj+APn8wdI+o29</latexit>

f

<latexit sha1_base64="aj1VrWgqSrqkgqJ/bLgtsTmRK/w=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlZtgvV9yqOwdZJV5OKpCj0S9/9QYxSyOUhgmqdzE+NnVBnOBE5LvVRjQtmYDrFrqaQRaj+bHzolZ1YZkDBWtqQhc/X3REYjrSdRYDsjakZ62ZuJ/3nd1ITXfsZlkhqUbLEoTAUxMZl9TQZcITNiYglitbCRtRZmx2ZRsCN7y6ukXat6F9Va87JSv8njKMIJnMI5eHAFdbiDBrSAcIzvMKb8+i8O/Ox6K14OQzx/AHzucPzD+M7g=</latexit>

f

<latexit sha1_base64="aj1VrWgqSrqkgqJ/bLgtsTmRK/w=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlZtgvV9yqOwdZJV5OKpCj0S9/9QYxSyOUhgmqdzE+NnVBnOBE5LvVRjQtmYDrFrqaQRaj+bHzolZ1YZkDBWtqQhc/X3REYjrSdRYDsjakZ62ZuJ/3nd1ITXfsZlkhqUbLEoTAUxMZl9TQZcITNiYglitbCRtRZmx2ZRsCN7y6ukXat6F9Va87JSv8njKMIJnMI5eHAFdbiDBrSAcIzvMKb8+i8O/Ox6K14OQzx/AHzucPzD+M7g=</latexit>

cνee

L

: 2.387 → 2.397 cνµe

L

: −0.912 → −0.902 cR : 0.758 → 0.768

<latexit sha1_base64="ui46y8rTeDx5BzE1XM+Gw2w4oWg=">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</latexit>
slide-12
SLIDE 12

12

Virtual QED corrections. Vertex

  • given in terms of QED form factors at one loop

ν e e ν

<latexit sha1_base64="oNfCjRrq8zoJemqLbd02P0qnjCg=">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</latexit>
  • factorizable in limit of small electron mass:
  • infrared divergence cancels with radiation of real soft photon
  • up to suppressed by neutrino mass terms:

f2 = 0

<latexit sha1_base64="pN81ytukdAcieUPy0ivP2sOLO8c=">ACG3icZVC7SgNBFJ31bXxFLRUZFMEq2Y2FNoJoYxnBGEFDuDu5q8POY5mZFUJI6QfYKv5HejuxtfAb/AidJCJGDwczrmXe+bEmeDWheF7MDY+MTk1PTNbmJtfWFwqLq+cW50bhjWmhTYXMVgUXGHNcSfwIjMIMhZYj9Pjvl+/RWO5VmeunWFDwrXiCWfgvFRPmhV6QMNmcSshQPQ/yT6JluH673Tj7uNXrVZ/LxqaZLVI4JsPYyCjPX6IBxnAnsFq5yixmwFK7x0lMFEm2jM4jbpdteadFEG/+UowP190YHpLVtGftJCe7GFrb/mH31xw5ZL9RoerLHeo2PBSkgvqNO1/nra4QeZE2xNghvuwlN2AeZ8RSMRyjXrpbIWmFpQLeO0BAFpOcG2kqC6vrHobz/yXmlFO2WKqe+uiMyxAxZI5tkh0RkjxySE1IlNcJISu7JA3kMnoLn4CV4HY6OBd87q2QEwdsXwBSk6A=</latexit>

γ

<latexit sha1_base64="xCrXyBYaW3OLP43sakS6BcVoAgY=">ACGnicZVC7SgNBFJ31GeMraqnIoghWyW4stAzaWCZgomBCuDu5G8fMY5mZFUJIaW+r+CGp7cTWxm/wI3SiBhzYOBwzr3cMydKODM2CD68mdm5+YXFzFJ2eWV1bT23sVkzKtUq1Rxpa8iMiZxKpluNVohFExPEy6pwN/cs71IYpeWG7CTYEtCWLGQXrpFq9DUJAM7cf5IMR/GkS/pD90s6g8nm/Oyg3c1/1lqKpQGkpB2OuwyCxjR5oyjHfraeGkyAdqCN145KEGgavVHavn/glJYfK+2etP5I/bvRA2FMV0RuUoC9MdmDf+ZQ/TUnTtn4pNFjMktSjq+FKfct8of/t1vMY3U8q4jQDVzYX16AxqodQ1NRChUjZMKimPHgGxpqwRw6BRi7EoBsu8aC/3M01qxXx4lC9WXHWnZIwM2SZ75JCE5JiUyDkpkyqh5JY8kEfy5D17L96r9zYenfF+drbIBLz3b9ckpZk=</latexit>

ω

<latexit sha1_base64="mY78qiwNE1T7O8QPSAdCIylXWdc=">AB7XicdVDLSgNBEJz1GeMr6tHLYBA8LbubaJb0IvHCOYByRJmJ7PJmHksM7NCPkHLx4U8er/ePNvnE0iqGhBQ1HVTXdXlDCqjed9OCura+sbm7mt/PbO7t5+4eCwpWqMGliyaTqREgTRgVpGmoY6SKIB4x0o7GV5nfvidKUyluzSQhIUdDQWOKkbFSqyc5GaJ+oei5Qa3qlWrQc73zcrVSyUhQu/BL0He9OYpgiUa/8N4bSJxyIgxmSOu7yUmnCJlKGZklu+lmiQIj9GQdC0ViBMdTufXzuCpVQYwlsqWMHCufp+YIq71hEe2kyMz0r+9TPzL6YmroZTKpLUEIEXi+KUQSNh9jocUEWwYRNLEFbU3grxCmEjQ0ob0P4+hT+T1qB65fc4KZcrF8u48iBY3ACzoAPKqAOrkEDNAEGd+ABPIFnRzqPzovzumhdcZYzR+AHnLdPCeiPcg=</latexit>

q = k − k0

<latexit sha1_base64="Rmyp5DNqzYjYiy0FzdxvVYnfOSw=">AB8XicdVDLSsNAFJ34rPVdelmsIhuDElabsQim5cVrAPbEOZTCftkMkzkyEvoXblwo4ta/cefOGkrqOiBC4dz7uXe7yYUaks68NYWFxaXlnNreXNza3tgs7uy0ZJQKTJo5YJDoekoRTpqKkY6sSAo9Bhpe8Fl5rfviZA04jdqHBM3RENOfYqR0tLtHTyHATyBwVG/ULRMp1a1SjVomdZpuVqpZMSpndklaJvWFEUwR6NfeO8NIpyEhCvMkJRd24qVmyKhKGZku8lksQIB2hIupyFBLptOLJ/BQKwPoR0IXV3Cqfp9IUSjlOPR0Z4jUSP72MvEvr5sov+qmlMeJIhzPFvkJgyqC2ftwQAXBio01QVhQfSvEIyQVjqkvA7h61P4P2k5pl0ynetysX4xjyMH9sEBOAY2qIA6uAIN0AQYcPAnsCzIY1H48V4nbUuGPOZPfADxtsnjyWPjQ=</latexit>

Q2 = −q2

<latexit sha1_base64="zfIZ3QK7pbyNxoUAnKAogJXgBV4=">AB8nicdVDLSsNAFJ3UV62vqks3g0VwY0jSatuFUHTjsgX7gDQtk+mkHTrJxJmJUEo/w40LRdz6Ne78GydtBRU9cOFwzr3ce48fMyqVZX0YmZXVtfWN7GZua3tndy+/f9CSPBGYNDFnXHR8JAmjEWkqhjpxIKg0Gek7Y+vU79T4SkPLpVk5h4IRpGNKAYKS25jZ4DL+EZvOs5/XzBMp1qxSpWoWVa56VKuZwSp3phF6FtWnMUwBL1fv69O+A4CUmkMENSurYVK2+KhKYkVmum0gSIzxGQ+JqGqGQSG86P3kGT7QygAEXuiIF5+r3iSkKpZyEvu4MkRrJ314q/uW5iQoq3pRGcaJIhBeLgoRBxWH6PxQbBiE0QFlTfCvEICYSVTimnQ/j6FP5PWo5pF02nUSrUrpZxZMEROAanwAZlUAM3oA6aAMOHsATeDaU8Wi8GK+L1oyxnDkEP2C8fQI1l4/r</latexit>

neutrino energy momentum transfer

k

<latexit sha1_base64="cmyaryMraYXyn/+TA2PdYGXmgRY=">AB6HicdVDLSgMxFM3UV62vqks3wSK4GjLTatd0Y3LFuwD2qFk0kwbm8kMSUYoQ7/AjQtF3PpJ7vwbM20FT1w4XDOvdx7jx9zpjRCH1ZubX1jcyu/XdjZ3ds/KB4edVSUSELbJOKR7PlYUc4EbWumOe3FkuLQ57TrT68zv3tPpWKRuNWzmHohHgsWMIK1kVrTYbGEbLdeQ+U6RDa6qNSq1Yy49UunDB0bLVACKzSHxfBKCJSIUmHCvVd1CsvRLzQin8IgUTGZIrHtG+owCFVXro4dA7PjDKCQSRNCQ0X6veJFIdKzULfdIZYT9RvLxP/8vqJDmpeykScaCrIclGQcKgjmH0NR0xSovnMEwkM7dCMsESE2yKZgQvj6F/5Oaztl21VSo2rVRx5cAJOwTlwQBU0wA1ogjYgIH8ASerTvr0XqxXpetOWs1cwx+wHr7BEw8jUY=</latexit>

k0

<latexit sha1_base64="UNd/V2aiCUTntqFcKGA78/fVO0g=">AB6XicdVDLSgMxFM3UV62vqks3wSK6GjJte2u6MZlFfuAdiZNOGyWSGJCOUoX/gxoUibv0jd/6NmbaCih64cDjnXu69x4s5UxqhDyu3srq2vpHfLGxt7+zuFfcPOipKJKFtEvFI9jysKGeCtjXTnPZiSXHocdr1gqvM795TqVgk7vQ0pm6Ix4L5jGBtpNvgdFgsIbvcqKNKAyIbnVfrtVpGyo0LpwIdG81RAku0hsX3wSgiSUiFJhwr1XdQrN0US80Ip7PCIFE0xiTAY9o3VOCQKjedXzqDJ0YZQT+SpoSGc/X7RIpDpahZzpDrCfqt5eJf3n9RPt1N2UiTjQVZLHITzjUEczehiMmKdF8agmkplbIZlgiYk24RMCF+fwv9Jp2w7Fbt8Uy01L5dx5MEROAZnwAE10ATXoAXagAfPIAn8GwF1qP1Yr0uWnPWcuYQ/ID19gmsp413</latexit>

¯ eγµγ5e → α π ⇥ f1

  • Q2

− f2

  • Q2⇤

¯ eγµγ5e

<latexit sha1_base64="/STCrurfYaxQpCoDkfxvFBQjnRU=">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</latexit>

¯ eγµe → α π ¯ e  f1

  • Q2

γµ + f2

  • Q2 iσµνqν

2m

  • e
<latexit sha1_base64="B6I6QG2VvLKSexPh4CH8zWtZV4=">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</latexit>

γ

<latexit sha1_base64="IoELSitFJaTQ4WT4pr8f01q0csw=">AB7XicbVDLSgNBEJyNrxhfUY9eBoPgKexGQY9BLx4jmAckS+idzCZj5rHMzAphyT948aCIV/Hm3/jJNmDJhY0FXdHdFCWfG+v63V1hb39jcKm6Xdnb39g/Kh0cto1JNaJMornQnAkM5k7RpmeW0k2gKIuK0HY1vZ37iWrDlHywk4SGAoaSxYyAdVKrNwQhoF+u+FV/DrxKgpxUI5Gv/zVGyiSCiot4WBMN/ATG2agLSOcTku91NAEyBiGtOuoBEFNmM2vneIzpwxwrLQrafFc/T2RgTBmIiLXKcCOzLI3E/zuqmNr8OMyS1VJLFojl2Co8ex0PmKbE8okjQDRzt2IyAg3EuoBKLoRg+eV0qpVg4tq7f6yUr/J4yiE3SKzlGArlAd3aEGaiKCHtEzekVvnvJevHfvY9Fa8PKZY/QH3ucPiDmPGQ=</latexit>

e

<latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>

e

<latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>
slide-13
SLIDE 13

13

Virtual QED corrections. Fermion loop

  • sum over all particles with corresponding couplings
  • given in terms of photon vacuum polarization

ν ? e e ν

<latexit sha1_base64="62PY9jMj5nB0TpZKRdxb4+FpdY=">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</latexit>
  • charged fermions contribute to elastic scattering at one loop:

f

<latexit sha1_base64="W0Cd3NqFKV/2uVsCn5yScPns9ik=">ACFXicZVC7SgNBFJ31GeMraqnIoghWyW4stAzaWCZgHhCD3J3c1SHzWGZmhRBSWtkq/koaO7G19hv8CJ08EGMODBzOuZd75kQJZ8YGwac3N7+wuLScWcmurq1vbOa2tmtGpZpilSqudCMCg5xJrFpmOTYSjSAijvWoczH06/eoDVPynYTbAm4lSxmFKyTKvFN7jDIByP4sySckMPS3qDy9bA/KN/kvq/biqYCpaUcjGmGQWJbPdCWUY797HVqMAHagVtsOipBoGn1RkH7/pFT2n6stHvS+iP170YPhDFdEblJAfbOZI/+mUP15w6ZeOzVo/JLUo6fhSnHLfKn/4b/NFLu4A1cyF9ekdaKDWlTMVoVA1Tiojh0Dsq2tEsChU4ixKwXIvms/N/PLKkV8+FJvlhx1Z2TMTJklxyQYxKSU1Iil6RMqoQSJI/kiTx7L96r9+a9j0fnvMnODpmC9/EDwYSjbg=</latexit>

f

<latexit sha1_base64="W0Cd3NqFKV/2uVsCn5yScPns9ik=">ACFXicZVC7SgNBFJ31GeMraqnIoghWyW4stAzaWCZgHhCD3J3c1SHzWGZmhRBSWtkq/koaO7G19hv8CJ08EGMODBzOuZd75kQJZ8YGwac3N7+wuLScWcmurq1vbOa2tmtGpZpilSqudCMCg5xJrFpmOTYSjSAijvWoczH06/eoDVPynYTbAm4lSxmFKyTKvFN7jDIByP4sySckMPS3qDy9bA/KN/kvq/biqYCpaUcjGmGQWJbPdCWUY797HVqMAHagVtsOipBoGn1RkH7/pFT2n6stHvS+iP170YPhDFdEblJAfbOZI/+mUP15w6ZeOzVo/JLUo6fhSnHLfKn/4b/NFLu4A1cyF9ekdaKDWlTMVoVA1Tiojh0Dsq2tEsChU4ixKwXIvms/N/PLKkV8+FJvlhx1Z2TMTJklxyQYxKSU1Iil6RMqoQSJI/kiTx7L96r9+a9j0fnvMnODpmC9/EDwYSjbg=</latexit>

cf = − α 2π Qf ⇣ cf

L + cf R

⌘ Π

  • Q2, mf
  • <latexit sha1_base64="LzqPq+cany7uJU7vtSv+cYIKNo=">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</latexit>
  • adds vector contribution:

Qf

<latexit sha1_base64="b3nFdM3I7FVdDZDSEGmnoIMHXY=">ACF3icZVC7SgNBFJ31GeMramz+ACrZDcWo2lgm6UYgh3J3cjUPmsczMCiHkE2wVf8TWQhBbSz9EW50kIsYcGDicy/3zIlTzowNgndvanpmdm4+t5BfXFpeWS2srdeMyjTFiCqu9GUMBjmTGFlmOV6mGkHEHC/izsnAv7hBbZiS57abYkNAW7KEUbBOqs2k2ZhOygGQ/iTJPwh20c7H4/PN4uflWbh6qlaCZQWsrBmHoYpLbRA20Z5djPX2UGU6AdaGPdUQkCTaM3jNr3d53S8hOl3ZPWH6p/N3ogjOmK2E0KsNcmv/vPHKi/5tgpmxw2ekymUVJR5eSjPtW+YOP+y2mkVredQSoZi6sT69BA7WunrEIpcg4qaQ4dgzIlrZKAIdOKcGuFCD7rHwfz+TpFYuhvFctVd0xGyJFNskX2SEgOyBE5JRUSEUra5JbckXvwXvyXrzX0eiU97OzQcbgvX0DJw6k0A=</latexit>

γ

<latexit sha1_base64="xCrXyBYaW3OLP43sakS6BcVoAgY=">ACGnicZVC7SgNBFJ31GeMraqnIoghWyW4stAzaWCZgomBCuDu5G8fMY5mZFUJIaW+r+CGp7cTWxm/wI3SiBhzYOBwzr3cMydKODM2CD68mdm5+YXFzFJ2eWV1bT23sVkzKtUq1Rxpa8iMiZxKpluNVohFExPEy6pwN/cs71IYpeWG7CTYEtCWLGQXrpFq9DUJAM7cf5IMR/GkS/pD90s6g8nm/Oyg3c1/1lqKpQGkpB2OuwyCxjR5oyjHfraeGkyAdqCN145KEGgavVHavn/glJYfK+2etP5I/bvRA2FMV0RuUoC9MdmDf+ZQ/TUnTtn4pNFjMktSjq+FKfct8of/t1vMY3U8q4jQDVzYX16AxqodQ1NRChUjZMKimPHgGxpqwRw6BRi7EoBsu8aC/3M01qxXx4lC9WXHWnZIwM2SZ75JCE5JiUyDkpkyqh5JY8kEfy5D17L96r9zYenfF+drbIBLz3b9ckpZk=</latexit>
  • fermion-dependent correction:

Lf

eff = −¯

νγµPLν · ¯ fγµ(cf

LPL + cf RPR)f

<latexit sha1_base64="C+peCmdSzTxTCnFrc0eX/rDwOBQ=">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</latexit>

cf ¯ νγµPLν · ¯ eγµe

<latexit sha1_base64="4kSiXITi8HIHanw7aSQtIfuLfcY=">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</latexit>

γ

<latexit sha1_base64="xCrXyBYaW3OLP43sakS6BcVoAgY=">ACGnicZVC7SgNBFJ31GeMraqnIoghWyW4stAzaWCZgomBCuDu5G8fMY5mZFUJIaW+r+CGp7cTWxm/wI3SiBhzYOBwzr3cMydKODM2CD68mdm5+YXFzFJ2eWV1bT23sVkzKtUq1Rxpa8iMiZxKpluNVohFExPEy6pwN/cs71IYpeWG7CTYEtCWLGQXrpFq9DUJAM7cf5IMR/GkS/pD90s6g8nm/Oyg3c1/1lqKpQGkpB2OuwyCxjR5oyjHfraeGkyAdqCN145KEGgavVHavn/glJYfK+2etP5I/bvRA2FMV0RuUoC9MdmDf+ZQ/TUnTtn4pNFjMktSjq+FKfct8of/t1vMY3U8q4jQDVzYX16AxqodQ1NRChUjZMKimPHgGxpqwRw6BRi7EoBsu8aC/3M01qxXx4lC9WXHWnZIwM2SZ75JCE5JiUyDkpkyqh5JY8kEfy5D17L96r9zYenfF+drbIBLz3b9ckpZk=</latexit>γ <latexit sha1_base64="IoELSitFJaTQ4WT4pr8f01q0csw=">AB7XicbVDLSgNBEJyNrxhfUY9eBoPgKexGQY9BLx4jmAckS+idzCZj5rHMzAphyT948aCIV/Hm3/jJNmDJhY0FXdHdFCWfG+v63V1hb39jcKm6Xdnb39g/Kh0cto1JNaJMornQnAkM5k7RpmeW0k2gKIuK0HY1vZ37iWrDlHywk4SGAoaSxYyAdVKrNwQhoF+u+FV/DrxKgpxUI5Gv/zVGyiSCiot4WBMN/ATG2agLSOcTku91NAEyBiGtOuoBEFNmM2vneIzpwxwrLQrafFc/T2RgTBmIiLXKcCOzLI3E/zuqmNr8OMyS1VJLFojl2Co8ex0PmKbE8okjQDRzt2IyAg3EuoBKLoRg+eV0qpVg4tq7f6yUr/J4yiE3SKzlGArlAd3aEGaiKCHtEzekVvnvJevHfvY9Fa8PKZY/QH3ucPiDmPGQ=</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

e

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e

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?

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Qf

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f

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f

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slide-14
SLIDE 14

Neutrino Energy GeV 1 2 3 4 5 6 7 8 9 10 POT at 1300 km

20

/GeV/10

2

flux/m ν

7

10

8

10

9

10

10

10

µ

ν

µ

ν

e

ν

e

ν

14

Main theoretical uncertainty

  • momentum transfer is suppressed by electron mass:
  • description in terms of quarks is questionable:

DUNE, CDR (2015)

ν ? e e ν

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flux

  • hadronic correction is unknown: estimate in model with quarks

≲ 3 % correction

γ

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Q2 < 2mω . 0.007 GeV2

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γ

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ν

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e

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?

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ν

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e

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slide-15
SLIDE 15

15

Uncertainty-free measurements

  • virtual-loop scale is well below muon mass:
  • only electrons in theory
  • one independent low-energy coupling cR

Q2 < 2mω . 0.007 GeV2

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effective field theory description:

slide-16
SLIDE 16

16

Uncertainty-free measurements

  • virtual-loop scale is well below muon mass:
  • only electrons in theory
  • one independent low-energy coupling cR

fix unknown coupling cR from various distributions measure spin asymmetry

complementary measurement statistical significance

  • only one coupling has to be fixed

Q2 < 2mω . 0.007 GeV2

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effective field theory description: what can we do?

  • n polarised electron target
slide-17
SLIDE 17

17

Low-energy frontier

  • application to solar neutrinos and reactor antineutrinos
slide-18
SLIDE 18

18

Bremsstrahlung

ν e e ν γ

<latexit sha1_base64="Vyvx3X5jZYZEWvFnX/w4toSEXes=">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</latexit>

ν e e ν γ

<latexit sha1_base64="dJ9TbxvWZzUMjNlXRKSHuWpzD0=">ADtHicfVJb9owFA6k2zp2Kd0e92K1VJo2BAkE2j0gse1lj50SiUSIc5AQvbiWxnHYr4F3vdD+uv2Rxoy03rkRx9/s53Lj45Ycqo0o5zWyrbB0+ePjt8Xnx8tXro+rxmyuVZJLAgCQskdchVsCogIGmsF1KgHzkMEwnH0t/MOfIBVNxA89TyHgeCJoTAnWhofl/74IUyoyGOYC47FAlWQMT8GyY1gFOTnDcepo07Dcxa56ywvXnFZ6YAB0TK5ATwbFT0MaSnvVYdMRwC69VqQd5ptJYxFyZB10QW2LmPf7ROd13nXqemyc1naQr2tMygjmJG016MmYIg9ZBm9l2C3nrN+zLNPzSRtFx6l3zWeQ1X2S1PZ9nrTIYZP/9Bj/n1wdM5N6ezmYmj/BnGPj9kFED39jXD0tRlEY2gfuHTjtn/gf9/25fj6l8/SkjGQWjCsFIj10l1kGOpKWGmMT9TkGIywxMYGSgwBxXkyz1aoDPDRChOpDlCoyW7GZFjrtSch0bJsZ6qytmOs2AfnFuldHwR5FSkmQZBVpXijCGdoGIrUSl2SM2NwATSU2ziEyxESb3d1qoTlQhmomDGYKi0jqhGOGZ82Nibm789kHV62G260vpvRfbFWdmi9s06s95ZrnVt965t1aQ0sUj4ofyi3y57dtX2b2LCSlkt3MW+tLbPFP8moF8w=</latexit>
  • soft Bremsstrahlung:

Eγ < ε

<latexit sha1_base64="cMkFYIcuF60jAI+3Ol70HflPtg=">AB/3icdVBNS0JBFJ1nX2ZfVtCmzZAErR7vqaVCymClgb5ASpy3zjq4Mx7j5l5gpiL/kqbFkW07W+06980Tw0q6sCFwzn3cu89XsiZ0o7zYSWldW15LrqY3Nre2d9O5eTQWRJLRKAh7IhgeKcubTqma0YoKQiP07o3vIz9+ohKxQL/Vo9D2hbQ91mPEdBG6qQPrjqtPgB+By3RiBpqBiPjYxjZ0tFJ1fCju2c5ouFQkypTM3h13bmSGDFqh0u+tbkAiQX1NOCjVdJ1QtycgNSOcTlOtSNEQyBD6tGmoD4Kq9mR2/xQfG6WLe4E05Ws8U79PTEAoNRae6RSgB+q3F4t/ec1I94rtCfPDSFOfzBf1Io51gOMwcJdJSjQfGwJEMnMrJgOQLSJLGVC+PoU/09qWdvN2dmbfKZ8sYgjiQ7RETpBLiqgMrpGFVRFBN2hB/SEnq1769F6sV7nrQlrMbOPfsB6+wTJ+JX8</latexit>

dσνe→νeγ

LO

= δsdσνe→νe

LO

<latexit sha1_base64="J76R9WMuv7NIChHWeohyj2V94m4=">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</latexit>

2

e

<latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

e

<latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

γ

<latexit sha1_base64="IoELSitFJaTQ4WT4pr8f01q0csw=">AB7XicbVDLSgNBEJyNrxhfUY9eBoPgKexGQY9BLx4jmAckS+idzCZj5rHMzAphyT948aCIV/Hm3/jJNmDJhY0FXdHdFCWfG+v63V1hb39jcKm6Xdnb39g/Kh0cto1JNaJMornQnAkM5k7RpmeW0k2gKIuK0HY1vZ37iWrDlHywk4SGAoaSxYyAdVKrNwQhoF+u+FV/DrxKgpxUI5Gv/zVGyiSCiot4WBMN/ATG2agLSOcTku91NAEyBiGtOuoBEFNmM2vneIzpwxwrLQrafFc/T2RgTBmIiLXKcCOzLI3E/zuqmNr8OMyS1VJLFojl2Co8ex0PmKbE8okjQDRzt2IyAg3EuoBKLoRg+eV0qpVg4tq7f6yUr/J4yiE3SKzlGArlAd3aEGaiKCHtEzekVvnvJevHfvY9Fa8PKZY/QH3ucPiDmPGQ=</latexit>

γ

<latexit sha1_base64="IoELSitFJaTQ4WT4pr8f01q0csw=">AB7XicbVDLSgNBEJyNrxhfUY9eBoPgKexGQY9BLx4jmAckS+idzCZj5rHMzAphyT948aCIV/Hm3/jJNmDJhY0FXdHdFCWfG+v63V1hb39jcKm6Xdnb39g/Kh0cto1JNaJMornQnAkM5k7RpmeW0k2gKIuK0HY1vZ37iWrDlHywk4SGAoaSxYyAdVKrNwQhoF+u+FV/DrxKgpxUI5Gv/zVGyiSCiot4WBMN/ATG2agLSOcTku91NAEyBiGtOuoBEFNmM2vneIzpwxwrLQrafFc/T2RgTBmIiLXKcCOzLI3E/zuqmNr8OMyS1VJLFojl2Co8ex0PmKbE8okjQDRzt2IyAg3EuoBKLoRg+eV0qpVg4tq7f6yUr/J4yiE3SKzlGArlAd3aEGaiKCHtEzekVvnvJevHfvY9Fa8PKZY/QH3ucPiDmPGQ=</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

e

<latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>

e

<latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>
slide-19
SLIDE 19

19

Bremsstrahlung

  • exactly calculable radiation

Ram (1967) Aoiki, Hioki, Kawabe, Konuma and Muta (1980)

ν e e ν γ

<latexit sha1_base64="Vyvx3X5jZYZEWvFnX/w4toSEXes=">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</latexit>

ν e e ν γ

<latexit sha1_base64="dJ9TbxvWZzUMjNlXRKSHuWpzD0=">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</latexit>
  • soft Bremsstrahlung:

Eγ < ε

<latexit sha1_base64="cMkFYIcuF60jAI+3Ol70HflPtg=">AB/3icdVBNS0JBFJ1nX2ZfVtCmzZAErR7vqaVCymClgb5ASpy3zjq4Mx7j5l5gpiL/kqbFkW07W+06980Tw0q6sCFwzn3cu89XsiZ0o7zYSWldW15LrqY3Nre2d9O5eTQWRJLRKAh7IhgeKcubTqma0YoKQiP07o3vIz9+ohKxQL/Vo9D2hbQ91mPEdBG6qQPrjqtPgB+By3RiBpqBiPjYxjZ0tFJ1fCju2c5ouFQkypTM3h13bmSGDFqh0u+tbkAiQX1NOCjVdJ1QtycgNSOcTlOtSNEQyBD6tGmoD4Kq9mR2/xQfG6WLe4E05Ws8U79PTEAoNRae6RSgB+q3F4t/ec1I94rtCfPDSFOfzBf1Io51gOMwcJdJSjQfGwJEMnMrJgOQLSJLGVC+PoU/09qWdvN2dmbfKZ8sYgjiQ7RETpBLiqgMrpGFVRFBN2hB/SEnq1769F6sV7nrQlrMbOPfsB6+wTJ+JX8</latexit>
  • integration technique
  • EW correction
  • electron energy spectrum and numerically total

Aoiki and Hioki (1981)

  • electron energy spectrum and EW, small m

Sarantakos, Sirlin and Marciano (1982)

  • electromagnetic energy spectrum and total

Bardin and Dokuchaeva (1983-1985)

  • numerically electron and electromagnetic spectra

Passera (2000)

dσνe→νeγ

LO

= δsdσνe→νe

LO

<latexit sha1_base64="J76R9WMuv7NIChHWeohyj2V94m4=">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</latexit>

2

  • soft-photon correction

Lee and Sirlin (1964)

e

<latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

e

<latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

γ

<latexit sha1_base64="IoELSitFJaTQ4WT4pr8f01q0csw=">AB7XicbVDLSgNBEJyNrxhfUY9eBoPgKexGQY9BLx4jmAckS+idzCZj5rHMzAphyT948aCIV/Hm3/jJNmDJhY0FXdHdFCWfG+v63V1hb39jcKm6Xdnb39g/Kh0cto1JNaJMornQnAkM5k7RpmeW0k2gKIuK0HY1vZ37iWrDlHywk4SGAoaSxYyAdVKrNwQhoF+u+FV/DrxKgpxUI5Gv/zVGyiSCiot4WBMN/ATG2agLSOcTku91NAEyBiGtOuoBEFNmM2vneIzpwxwrLQrafFc/T2RgTBmIiLXKcCOzLI3E/zuqmNr8OMyS1VJLFojl2Co8ex0PmKbE8okjQDRzt2IyAg3EuoBKLoRg+eV0qpVg4tq7f6yUr/J4yiE3SKzlGArlAd3aEGaiKCHtEzekVvnvJevHfvY9Fa8PKZY/QH3ucPiDmPGQ=</latexit>

γ

<latexit sha1_base64="IoELSitFJaTQ4WT4pr8f01q0csw=">AB7XicbVDLSgNBEJyNrxhfUY9eBoPgKexGQY9BLx4jmAckS+idzCZj5rHMzAphyT948aCIV/Hm3/jJNmDJhY0FXdHdFCWfG+v63V1hb39jcKm6Xdnb39g/Kh0cto1JNaJMornQnAkM5k7RpmeW0k2gKIuK0HY1vZ37iWrDlHywk4SGAoaSxYyAdVKrNwQhoF+u+FV/DrxKgpxUI5Gv/zVGyiSCiot4WBMN/ATG2agLSOcTku91NAEyBiGtOuoBEFNmM2vneIzpwxwrLQrafFc/T2RgTBmIiLXKcCOzLI3E/zuqmNr8OMyS1VJLFojl2Co8ex0PmKbE8okjQDRzt2IyAg3EuoBKLoRg+eV0qpVg4tq7f6yUr/J4yiE3SKzlGArlAd3aEGaiKCHtEzekVvnvJevHfvY9Fa8PKZY/QH3ucPiDmPGQ=</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

e

<latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>

e

<latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>
slide-20
SLIDE 20

20

  • dramatic difference in radiative corrections

MS

<latexit sha1_base64="mkpRabcheDQVQtMx4RdWfJv5DxM=">AB/3icbVBLS8NAGNzUV62vqODFS7AInkpSBT0WvXgRKtoHNKFstpt26T7C7kYoMQf/ihcPinj1b3jz37hpc9DWgYVhZr7dbyeMKVHadb+t0tLyupaeb2ysbm1vWPv7rWVSCTCLSokN0QKkwJxy1NMXdWGLIQo74fgq9zsPWCoi+L2exDhgcMhJRBDURurbBz6DeiRZ6gsTy29Jb+6yrG9X3Zo7hbNIvIJUQYFm3/7yBwIlDHONKFSq57mxDlIoNUEUZxU/UTiGaAyHuGcohwyrIJ3unznHRhk4kZDmcO1M1d8TKWRKTVhokvm2at7Lxf+8XqKjiyAlPE405mj2UJRQRwsnL8MZEImRphNDIJLE7OqgEZQaVNZxZTgzX95kbTrNe+0Vr89qzYuizrK4BAcgRPgXPQANegCVoAgUfwDF7Bm/VkvVjv1scsWrKmX3wB9bnDwgnlsA=</latexit>

δ = dσνe→νeγ

LO

+ dσνe→νe

NLO

− dσνe→νe

LO

dσνe→νe

LO

<latexit sha1_base64="EiH/9QMckiIRde7D5OQ+HljY96k=">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</latexit>

Electron vs electromagnetic (EM) spectra

  • relative correction depends on scale μ: mc ≤ μ ≤ mb

e, ω = 1 GeV e, ω = 10 GeV EM, ω = 1 GeV EM, ω = 10 GeV νμe νμe δ, % −10 −5 E/ω 0.2 0.4 0.6 0.8 1.0

slide-21
SLIDE 21

21

  • dramatic difference in radiative corrections: cut dependence

Electron vs electromagnetic (EM) spectra

  • resulting spectrum:

e, ω = 1 GeV e, ω = 10 GeV EM, ω = 1 GeV EM, ω = 10 GeV νμe νμe 1042 dσ/ dE, cm2 GeV-1 1.0 1.5 2.0 2.5 103 X, GeV 0.2 0.4 0.6 0.8 1.0

X = 2m ✓ 1 − ¯ E ω ◆ ≈

¯ E=Ee

Eeθ2

e

<latexit sha1_base64="T+KEXKXyESeiCDd9CH+8AKM+XM=">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</latexit>
slide-22
SLIDE 22

22

  • analytical form for finite and small electron mass

Bremsstrahlung cross sections

Ee, θe

<latexit sha1_base64="FtgJ2NL9+Y2eiM9V59ZHTqU+M=">AB9HicbVDLSgNBEJz1GeMr6tHLYBA8SNiNgh6DIniMYB6QLMvspDcZMvtwpjcQlnyHFw+KePVjvPk3TpI9aGJBQ1HVTXeXn0ih0ba/rZXVtfWNzcJWcXtnd2+/dHDY1HGqODR4LGPV9pkGKSJoEAJ7UQBC30JLX94O/VbI1BaxNEjhNwQ9aPRCA4QyO5dx6c0y4OAJkHXqlsV+wZ6DJxclImOepe6avbi3kaQoRcMq07jp2gmzGFgkuYFLuphoTxIetDx9CIhaDdbHb0hJ4apUeDWJmKkM7U3xMZC7Ueh7pDBkO9KI3Ff/zOikG124moiRFiPh8UZBKijGdJkB7QgFHOTaEcSXMrZQPmGIcTU5FE4Kz+PIyaVYrzkWl+nBZrt3kcRTIMTkhZ8QhV6RG7kmdNAgnT+SZvJI3a2S9WO/Wx7x1xcpnjsgfWJ8/6SORiw=</latexit>

EEM, θe

<latexit sha1_base64="vsLXTK1orHQhxi6nprHX07d6fxk=">ACAHicbVDJSgNBEO1xjXGLevDgpTEIHiTMREGPQl4ESKYBTLD0NOpJE16FrprhDk4q948aCIVz/Dm39jZzlo4oOCx3tVNULEik02va3tbS8srq2ntvIb25t7+wW9vYbOk4VhzqPZaxaAdMgRQR1FCihlShgYSChGQxuxn7zEZQWcfSAwS8kPUi0RWcoZH8wmHVd0OGfRVm1bvRGXWxD8h8AtFu2RPQBeJMyNFMkPNL3y5nZinIUTIJdO67dgJehlTKLiEUd5NSMD1gP2oZGLATtZMHRvTEKB3ajZWpCOlE/T2RsVDrYRiYzvGxet4bi/957RS7V14moiRFiPh0UTeVFGM6ToN2hAKOcmgI40qYWynvM8U4mszyJgRn/uVF0iXnPNS+f6iWLmexZEjR+SYnBKHXJIKuSU1UiecjMgzeSVv1pP1Yr1bH9PWJWs2c0D+wPr8ATjElio=</latexit>

Ee, Eγ

<latexit sha1_base64="RgM5lCxwvYAHv9opTNStsxt5Vk=">AB9HicbVBNSwMxEM3Wr1q/qh69BIvgQcpuFfRYlILHCvYD2mWZTbNtaJdk2yhlP4OLx4U8eqP8ea/MW3oK0PBh7vzTAzL0w408Z1v53c2vrG5lZ+u7Czu7d/UDw8auo4VYQ2SMxj1Q5BU84kbRhmOG0nioIOW2Fw7uZ3xpRpVksH804ob6AvmQRI2Cs5NcCeoFrQbcPQkBQLldw68SryMlFCGelD86vZikgoqDeGgdcdzE+NPQBlGOJ0WuqmCZAh9GnHUgmCan8yP3qKz6zSw1GsbEmD5+rviQkIrcitJ0CzEAvezPxP6+TmujGnzCZpIZKslgUpRybGM8SwD2mKDF8bAkQxeytmAxATE2p4INwVt+eZU0K2Xvslx5uCpVb7M48ugEnaJz5KFrVEX3qI4aiKAn9Ixe0Zszcl6cd+dj0Zpzsplj9AfO5w+acZFY</latexit>

Eγ, θγ

<latexit sha1_base64="OBvFbuX962F6uHlPVHbE6THviY=">ACAHicbVA9SwNBEN3zM8avqIWFzWIQLCTcRUHLoAiWEcwH5I4wt9kS3bvjt05IYQ0/hUbC0Vs/Rl2/hs3yRWa+GDg7Xsz7MwLEykMu63s7S8srq2ntvIb25t7+wW9vbrJk414zUWy1g3QzBciojXUKDkzURzUKHkjXBwM/Ebj1wbEUcPOEx4oKAXia5gFZqFw5v234PlIz6mOfI2TPdqHoltwp6CLxMlIkGartwpfiVmqeIRMgjEtz0wGIFGwSQf5/3U8ATYAHq8ZWkEiptgND1gTE+s0qHdWNuKkE7V3xMjUMYMVWg7FWDfzHsT8T+vlWL3KhiJKEmR2z2UTeVFGM6SYN2hOYM5dASYFrYXSnrgwaGNrO8DcGbP3mR1Msl7xUvr8oVq6zOHLkiByTU+KRS1Ihd6RKaoSRMXkmr+TNeXJenHfnY9a65GQzB+QPnM8fE5WFA=</latexit>

<latexit sha1_base64="kzJinyETJ1X0xmXaGvJuV4RjulE=">AB73icbVBNS8NAEJ34WetX1aOXxSJ4KkV9FgUwWMF+wFtKJPtpl26m8TdjVBC/4QXD4p49e9489+4bXPQ1gcDj/dmJkXJIJr47rfzsrq2vrGZmGruL2zu7dfOjhs6jhVlDVoLGLVDlAzwSPWMNwI1k4UQxkI1gpGN1O/9cSU5nH0YMYJ8yUOIh5yisZK7dted4BSYq9UdivuDGSZeDkpQ456r/TV7c0lSwyVKDWHc9NjJ+hMpwKNil2U80SpCMcsI6lEUqm/Wx274ScWqVPwljZigyZqb8nMpRaj2VgOyWaoV70puJ/Xic14ZWf8ShJDYvofFGYCmJiMn2e9Lli1IixJUgVt7cSOkSF1NiIijYEb/HlZdKsVrzSvX+oly7zuMowDGcwBl4cAk1uIM6NICgGd4hTfn0Xlx3p2PeuKk8cwR84nz/O04/R</latexit>

Ee

<latexit sha1_base64="ymTyJKhG5hxuDLBJtdibv8GfZAw=">AB6nicbVBNS8NAEJ34WetX1aOXxSJ4KkV9FgUwWNF+wFtKJvtpF262YTdjVBCf4IXD4p49Rd589+4bXPQ1gcDj/dmJkXJIJr47rfzsrq2vrGZmGruL2zu7dfOjhs6jhVDBsFrFqB1Sj4BIbhuB7UQhjQKBrWB0M/VbT6g0j+WjGSfoR3QgecgZNVZ6uO1hr1R2K+4MZJl4OSlDjnqv9NXtxyNUBomqNYdz02Mn1FlOBM4KXZTjQlIzrAjqWSRqj9bHbqhJxapU/CWNmShszU3xMZjbQeR4HtjKgZ6kVvKv7ndVITXvkZl0lqUL5ojAVxMRk+jfpc4XMiLElClubyVsSBVlxqZTtCF4iy8vk2a14p1XqvcX5dp1HkcBjuEzsCDS6jBHdShAQwG8Ayv8OYI58V5dz7mrStOPnMEf+B8/gAOHI2l</latexit>

EEM

<latexit sha1_base64="1gGHqDTS3DPLUvaB3fB7NigdmD0=">AB9HicbVDLSgMxFL1TX7W+qi7dBIvgqsxUQZdFKbgRKtgHtEPJpGkbmTGJFMoQ7/DjQtF3Pox7vwbM+0stPVA4HDOvdyTE0ScaeO6305ubX1jcyu/XdjZ3ds/KB4eNXUYK0IbJOShagdYU84kbRhmOG1HimIRcNoKxrep35pQpVkoH80or7AQ8kGjGBjJb/W6wpsRkoktftZr1hy+4caJV4GSlBhnqv+NXthyQWVBrCsdYdz42Mn2BlGOF0VujGmkaYjPGQdiyVWFDtJ/PQM3RmlT4ahMo+adBc/b2RYKH1VAR2Mo2ol71U/M/rxGZw7SdMRrGhkiwODWKOTIjSBlCfKUoMn1qCiWI2KyIjrDAxtqeCLcFb/vIqaVbK3kW58nBZqt5kdeThBE7hHDy4gircQR0aQOAJnuEV3pyJ8+K8Ox+L0ZyT7RzDHzifP7vGkhM=</latexit>

total cross section

EEM, θν

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  • distributions under consideration:

Ee, Eγ, θe

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  • O. T. and Richard Hill (2019)

e ν γ

<latexit sha1_base64="MKkgRKiOFG1qxH24TtEu/xYb4mY=">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</latexit>e <latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>

γ

<latexit sha1_base64="IoELSitFJaTQ4WT4pr8f01q0csw=">AB7XicbVDLSgNBEJyNrxhfUY9eBoPgKexGQY9BLx4jmAckS+idzCZj5rHMzAphyT948aCIV/Hm3/jJNmDJhY0FXdHdFCWfG+v63V1hb39jcKm6Xdnb39g/Kh0cto1JNaJMornQnAkM5k7RpmeW0k2gKIuK0HY1vZ37iWrDlHywk4SGAoaSxYyAdVKrNwQhoF+u+FV/DrxKgpxUI5Gv/zVGyiSCiot4WBMN/ATG2agLSOcTku91NAEyBiGtOuoBEFNmM2vneIzpwxwrLQrafFc/T2RgTBmIiLXKcCOzLI3E/zuqmNr8OMyS1VJLFojl2Co8ex0PmKbE8okjQDRzt2IyAg3EuoBKLoRg+eV0qpVg4tq7f6yUr/J4yiE3SKzlGArlAd3aEGaiKCHtEzekVvnvJevHfvY9Fa8PKZY/QH3ucPiDmPGQ=</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>
slide-23
SLIDE 23

23

Conclusions

best tool to constrain neutrino flux

  • EFT of neutrino-electron and neutrino-quark scattering (μ ≳ mc):

left- and right-handed couplings at subpermille level

  • energy spectra and bremsstrahlung cross sections:

new and known results in analytical form

  • main source of uncertainty and how to avoid it:

loops with hadrons at low energy and momentum transfer

  • all results will be available to experimental collaborations soon

ν e e ν

<latexit sha1_base64="GkESPxKba7qd8chOZu8CwF70w=">ADU3ichVPLbtNAFB0nPEqgNIUlm1EfEhKRY7chzYJKATYsi0TaSrEVjSfXySjGWtmTLGs/AV/wNewBbHot7CAcVK1SzElTw6Oufch65nopQzbTzv2qnV791/8HDrUePxk+2nO83dZ+daZorCgEou1WVENHAmYGCY4XCZKiBJxOEimr0v9YvPoDST4pPJUwgTMhEsZpQYS412nTdBMmihykRAxw1sI4hBJdYwDIu63kt/Nqe86K3wJ0S/9/Wrdr0VF69VUpenRqVQvHnKWnMeEawqJzl7RabLNP526Eqs3AF2MdHa+1rHMQiOygoh27PavBKn/idv/Nr9UKQIxvlzVq7ntWLANXgX8D9vt7wauv1/38bNT8E4wlzRIQhnKi9dD3UhMWRBlGue0cZBpSQmdkAkMLBUlAh8XiN8/xoWXGOJbKfsLgBbuaUZBE6zyJrDMhZqobhxtiyd6Ka61M3AsLJtLMgKDLTnHGsZG4vDR4zBRQw3MLCFXMDovplChCjb1ayO0B9pSbclhpokYKyMTwsmsvbIxf3M/VXB+5PrH7tFHu7p3aBlb6AXaQy+Rj05QH31AZ2iAqPN+e78cH7WftV+1+0rWVprzk3Oc7QW9e2/FbL9tA=</latexit> e <latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>

e

<latexit sha1_base64="Pna6fdTWgvUMdKOvBzHgjCOl/o=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlJvbLFbfqzkFWiZeTCuRo9MtfvUHM0gilYJq3fXcxPgZVYzgdNSL9WYUDamQ+xaKmE2s/mh07JmVUGJIyVLWnIXP09kdFI60kU2M6ImpFe9mbif143NeG1n3GZpAYlWywKU0FMTGZfkwFXyIyYWEKZ4vZWwkZUWZsNiUbgrf8ip16reRbXWvKzUb/I4inACp3AOHlxBHe6gAS1gPAMr/DmPDovzrvzsWgtOPnMfyB8/kDyruM7Q=</latexit>

ν

<latexit sha1_base64="Q5QBoJHXaSX6KvHmV3PNna1aMJc=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2k3bpZhN2N0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZLGLVCahGwSU2DTcCO4lCGgUC28H4dua3n1BpHstHM0nQj+hQ8pAzaqz0JNpv1xq+4cZJV4OalAjka/NUbxCyNUBomqNZdz02Mn1FlOBM4LfVSjQlYzrErqWSRqj9bH7qlJxZUDCWNmShszV3xMZjbSeRIHtjKgZ6WVvJv7ndVMTXvsZl0lqULFojAVxMRk9jcZcIXMiIklClubyVsRBVlxqZTsiF4y+vklat6l1Ua/eXlfpNHkcRTuAUzsGDK6jDHTSgCQyG8Ayv8OYI58V5dz4WrQUnzmGP3A+fwBgMY3b</latexit>
slide-24
SLIDE 24

Thanks for your attention !!!

24

slide-25
SLIDE 25

25

Flux determination in DUNE

according to H. Duyang et al., arXiv: 1902.09480v2 (2019)

relative normalization

¯ νµ mode

<latexit sha1_base64="+/8RZpy1gX4af3ZNgfdepIas=">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</latexit>

νµ mode

<latexit sha1_base64="xRgzvwdiE6tNWl0XZ2Opuz6yNAU=">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</latexit>

νµe− → νµe−

<latexit sha1_base64="rEGye8gOatOP5eq+SKM0h6KV4MU=">ACMXicZVDLSitBEO3xdTW+cnXplENyYzcaGLuxAEcSMoGhWcMdR0arSZfgzdPRdCyMKvcav4Ne7ErQs/QTuJiNEDafPqaKqTloIbl0YPgVj4xOTU3+mZyqzc/MLi9W/S2dWl4Zhk2mhzUKFgVX2HTcCbwoDIJMBZ6n+V7fP/+PxnKtTl2nwETCteIZ+C81KquxKpsxbKkeLVJY6fpt3+ruhbWwgHobxJ9krVdenjylif7R63qe9zWrJSoHBNg7WUFi7pgnGcCexV4tJiASyHa7z0VIFEm3QHR/ToulfaNPGP+XoQP3e0QVpbUemvlKCu7GV9R9mX/0yR0a5bCfpclWUDhUbTspKQf21/UhomxtkTnQ8AWa4X5ayGzDAnA9uZIV603qprgXmFlTbOC1BQF7PsKMkqJ5PLPqZz29y1qhFW7XGsY/uHxlimqyQVbJBIrJNdskBOSJNwsgtuSP35CF4DJ6C5+BlWDoWfPYskxErx+Z8Kzg</latexit>

¯ νµp → µ+n

<latexit sha1_base64="Tan4MJlZPaCF/6QMxhvnxveUBzo=">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</latexit>

¯ νµp → µ+pπ−

<latexit sha1_base64="jkvukzuoPQeCILqYwQ10zsEdU=">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</latexit>

νµp → µ−pπ+

<latexit sha1_base64="iv127kfbxrSHK8XgBXjg9bP0x0=">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</latexit>
  • neutrino-electron scattering plays a role of additional constraint
  • determination of neutrino fluxes:
  • νe is required for absolute normalization of νμ component
  • ne of the main goals of Near Detector
slide-26
SLIDE 26

26

  • 1-3 % difference at low recoil energy

Experimental energy spectrum

DUNE e, νμ e, νμ e, νe e, νe e EM, νμ EM, νμ EM, νe EM, νe EM 1042 dσ/ dE, cm2 GeV-1 1.0 2.0 0.5 1.5 2.5 E, GeV 1 2 3 4 5 6 7 8 9 10

  • average over beam flux and sum over flavors: