Aspects of neutrino masses Jessica Turner UCL 13 December 2019 - - PowerPoint PPT Presentation

SLIDE 1

Jessica Turner

UCL 13 December 2019

Aspects of neutrino masses

SLIDE 2

• Neutrino masses and mixing
• Neutrino masses from gravity, what has been done
• Two ways of solving the SDEs
• Discussions and conclusions
• Neutrino masses from gravity: the Schwinger Dyson approach

Outline

2

• Consequences of neutrino masses

SLIDE 3

Jessica Turner

3

Neutrino Oscillations

  νe νµ ντ   =   Ue1 Ue2 Ue Uµ1 Uµ2 Uµ3 Uτ1 Uτ2 Uτ3     ν1 ν2 ν3  

flavour states PMNS matrix mass states

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W

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`α

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να(t0)

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νβ(t)

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|ν(t)i = e−iHt|ν(0)i = αe−iE1t|ν1i + βe−iE2t|ν2i + γe−iE3t|ν3i

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P (να → νβ) = sin2 (2θ) sin2

• ∆m2

ijL

• 2E

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mixing angle parametrises misalignment of bases mass splitting baseline
 distance between production and detection Energy of neutrino

Ei ' E + m2

i

E = ) Ei Ej ' ∆m2

ij

2E

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In the simplified two neutrino case:

UmνU † = mνdiag

UP MNS = U †

eUν

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3

SLIDE 4

Jessica Turner

• Neutrinos have (non-degenerate) masses
• Neutrinos mix i.e. PMNS matrix is a non-identity matrix

leptonic mixing quark mixing

  1 c23 s23 −s23 c23     c13 s13e−iδ 1 −s13eiδ c13     c12 s12 −s12 c12 1  

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31.61 ≤ θ12() ≤ 36.27

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144 ≤ δ() ≤ 357

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41.1 ≤ θ23() ≤ 51.3

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8.22 ≤ θ13() ≤ 8.98

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• If neutrinos Dirac fermions, PMNS: 3 mixing angles + 1 phase

nu-fit data 4.1

4

SLIDE 5

Jessica Turner

leptonic mixing quark mixing

• If neutrinos Majorana fermions, PMNS: 3 mixing angles + 3 phase

nu-fit data 4.1

U =   1 c23 s23 −s23 c23     c13 s13e−iδ 1 −s13eiδ c13     c12 s12 −s12 c12 1     1 ei α21

2

ei α31

2

 

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• Majorana nature of neutrinos not observable at oscillation experiments
• Neutrinos have (non-degenerate) masses
• Neutrinos mix i.e. PMNS matrix is a non-identity matrix

5

SLIDE 6

Neutrinos are ubiquitous but also mysterious

∼ 330 cm−3

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T ∼ 1.95 K

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1305.7513

6

SLIDE 7

Jessica Turner

Atmospheric

νe,µ produced by interaction of cosmic rays with Earth’s atmosphere 15 km

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Discovered by SK in 1998

R µ

e =

Nνµ+Nνµ Nνe+Nνe ≈ 2

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7

Eν ∼ GeV

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SLIDE 8

Jessica Turner

ICECUBE

P (νµ → ντ)

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∆m2 ∼ 2 × 10−3 eV2

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θ ∼ π 4

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SK

Eν ∼ GeV

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8

SLIDE 9

Jessica Turner

ICECUBE

P (νµ → ντ)

<latexit sha1_base64="MKyVsMKL0YSD6Nco0TR/3w/wSM=">ACE3icbZDLSsNAFIYnXmu9RV26CRahuihJFXRZdOygr1AE8JkOmHTiZh5oxSQt/Bja/ixoUibt2482cXhba+sPAz3fO4cz5o4wzBa7bS0tr6yurRc2iptb2zu79t5+U6VaEtogKU9lO8KciZoAxhw2s4kxUnEaSsaXI/rXsqFUvFHQwzGiS4J1jMCAaDQvu07nMaQ9kXOsz9RI98yXp9wFKmD2PmA9ZTdBLaJbfiTuQsGm9mSmimemh/+d2U6IQKIBwr1fHcDIcS2CE01HR14pmAxwj3aMFTihKsgnN42cY0O6TpxK8wQ4E/p7IseJUsMkMp0Jhr6ar43hf7WOhvgyJnINFBpotizR1InXFATpdJSoAPjcFEMvNXh/SxARMjEUTgjd/8qJpViveWaV6e16qXc3iKBDdITKyEMXqIZuUB01EGP6Bm9ojfryXqx3q2PaeuSNZs5QH9kf4Ah8afMg=</latexit>

∆m2 ∼ 2 × 10−3 eV2

<latexit sha1_base64="xegstYIKwovEjKuTOEKGwre1ias=">ACFnicbVDJSgNBEO1xN25Rj14ag+DBhJmJoEdRDx4jmAUySejpVGJj98zQXSOGIV/hxV/x4kERr+LNv7GzHNweFDzeq6KqXphIYdB1P52Z2bn5hcWl5dzK6tr6Rn5zq2biVHOo8ljGuhEyA1JEUEWBEhqJBqZCfXw5mzk129BGxFHVzhIoKVYPxI9wRlaqZMvBucgkVHV9mlghKJ+gEKBoZ7bzorlYXBA4Q7zKA2bPudfMEtuWPQv8SbkgKZotLJfwTdmKcKIuSGdP03ARbGdMouIRhLkgNJIzfsD40LY2YXd3Kxm8N6Z5VurQXa1sR0rH6fSJjypiBCm2nYnhtfnsj8T+vmWLvuJWJKEkRIj5Z1EslxZiOMqJdoYGjHFjCuBb2VsqvmWYcbZI5G4L3+W/pOaXvHLJvzwsnJxO41giO2SX7BOPHJETckEqpEo4uSeP5Jm8OA/Ok/PqvE1aZ5zpzDb5Aef9C2wNnaw=</latexit>

θ ∼ π 4

<latexit sha1_base64="+JuEG6QFb/uRIZ8CMnqhujp0mDg=">ACAHicbVBNS8NAEN3Ur1q/oh48eAkWwVNJakGPRS8eK9gPaELZbDft0t1N2J0IJeTiX/HiQRGv/gxv/hu3bQ7a+mDg8d4M/PChDMNrvtldbWNza3ytuVnd29/QP78Kij41QR2iYxj1UvxJpyJmkbGHDaSxTFIuS0G05uZ373kSrNYvkA04QGAo8kixjBYKSBfeLDmAL2NRN+pDJ/ITlWSMf2FW35s7hrBKvIFVUoDWwv/xhTFJBJRCOte57bgJBhUwmle8VNE0wmeET7hkosqA6y+QO5c26UoRPFypQEZ67+nsiw0HoqQtMpMIz1sjcT/P6KUTXQcZkgKVZLEoSrkDsTNLwxkyRQnwqSGYKGZudcgYmxzAZFYxIXjL6+STr3mXdbq941q86aIo4xO0Rm6QB6Qk10h1qojQjK0TN6RW/Wk/VivVsfi9aSVcwcoz+wPn8AgXGW/Q=</latexit>

Solar

CNO cycle pp chain νe copiously produced by the Sun dominant energy production

SK

Eν ∼ GeV

<latexit sha1_base64="21sbPXE1xrfVKgoZjQjeoVrV6Iw=">AB/3icbVDLSgNBEJz1GeMrKnjxMhgET2E3CnoMiugxgnlANoTZScZMju7zPSKYc3BX/HiQRGv/oY3/8bJ46CJBQ1FVTfdXUEshUHX/XYWFpeWV1Yza9n1jc2t7dzObtVEieZQ4ZGMdD1gBqRQUEGBEuqxBhYGEmpB/3Lk1+5BGxGpOxzE0AxZV4mO4Ayt1MrtX7VSXyVD34iQ+gPmF5DdjK5d2COwadJ96U5MkU5Vbuy29HPAlBIZfMmIbnxthMmUbBJQyzfmIgZrzPutCwVLEQTDMd3z+kR1Zp06kbSmkY/X3RMpCYwZhYDtDhj0z643E/7xGgp3zZipUnCAoPlnUSTFiI7CoG2hgaMcWMK4FvZWyntM42sqwNwZt9eZ5UiwXvpFC8Pc2XLqZxZMgBOSTHxCNnpERuSJlUCeP5Jm8kjfnyXlx3p2PSeuCM53ZI3/gfP4ASeWRg=</latexit>

9

SLIDE 10

Jessica Turner

ICECUBE

P (νµ → ντ)

<latexit sha1_base64="MKyVsMKL0YSD6Nco0TR/3w/wSM=">ACE3icbZDLSsNAFIYnXmu9RV26CRahuihJFXRZdOygr1AE8JkOmHTiZh5oxSQt/Bja/ixoUibt2482cXhba+sPAz3fO4cz5o4wzBa7bS0tr6yurRc2iptb2zu79t5+U6VaEtogKU9lO8KciZoAxhw2s4kxUnEaSsaXI/rXsqFUvFHQwzGiS4J1jMCAaDQvu07nMaQ9kXOsz9RI98yXp9wFKmD2PmA9ZTdBLaJbfiTuQsGm9mSmimemh/+d2U6IQKIBwr1fHcDIcS2CE01HR14pmAxwj3aMFTihKsgnN42cY0O6TpxK8wQ4E/p7IseJUsMkMp0Jhr6ar43hf7WOhvgyJnINFBpotizR1InXFATpdJSoAPjcFEMvNXh/SxARMjEUTgjd/8qJpViveWaV6e16qXc3iKBDdITKyEMXqIZuUB01EGP6Bm9ojfryXqx3q2PaeuSNZs5QH9kf4Ah8afMg=</latexit>

∆m2 ∼ 2 × 10−3 eV2

<latexit sha1_base64="xegstYIKwovEjKuTOEKGwre1ias=">ACFnicbVDJSgNBEO1xN25Rj14ag+DBhJmJoEdRDx4jmAUySejpVGJj98zQXSOGIV/hxV/x4kERr+LNv7GzHNweFDzeq6KqXphIYdB1P52Z2bn5hcWl5dzK6tr6Rn5zq2biVHOo8ljGuhEyA1JEUEWBEhqJBqZCfXw5mzk129BGxFHVzhIoKVYPxI9wRlaqZMvBucgkVHV9mlghKJ+gEKBoZ7bzorlYXBA4Q7zKA2bPudfMEtuWPQv8SbkgKZotLJfwTdmKcKIuSGdP03ARbGdMouIRhLkgNJIzfsD40LY2YXd3Kxm8N6Z5VurQXa1sR0rH6fSJjypiBCm2nYnhtfnsj8T+vmWLvuJWJKEkRIj5Z1EslxZiOMqJdoYGjHFjCuBb2VsqvmWYcbZI5G4L3+W/pOaXvHLJvzwsnJxO41giO2SX7BOPHJETckEqpEo4uSeP5Jm8OA/Ok/PqvE1aZ5zpzDb5Aef9C2wNnaw=</latexit>

θ ∼ π 4

<latexit sha1_base64="+JuEG6QFb/uRIZ8CMnqhujp0mDg=">ACAHicbVBNS8NAEN3Ur1q/oh48eAkWwVNJakGPRS8eK9gPaELZbDft0t1N2J0IJeTiX/HiQRGv/gxv/hu3bQ7a+mDg8d4M/PChDMNrvtldbWNza3ytuVnd29/QP78Kij41QR2iYxj1UvxJpyJmkbGHDaSxTFIuS0G05uZ373kSrNYvkA04QGAo8kixjBYKSBfeLDmAL2NRN+pDJ/ITlWSMf2FW35s7hrBKvIFVUoDWwv/xhTFJBJRCOte57bgJBhUwmle8VNE0wmeET7hkosqA6y+QO5c26UoRPFypQEZ67+nsiw0HoqQtMpMIz1sjcT/P6KUTXQcZkgKVZLEoSrkDsTNLwxkyRQnwqSGYKGZudcgYmxzAZFYxIXjL6+STr3mXdbq941q86aIo4xO0Rm6QB6Qk10h1qojQjK0TN6RW/Wk/VivVsfi9aSVcwcoz+wPn8AgXGW/Q=</latexit>

SK

Eν ∼ GeV

<latexit sha1_base64="21sbPXE1xrfVKgoZjQjeoVrV6Iw=">AB/3icbVDLSgNBEJz1GeMrKnjxMhgET2E3CnoMiugxgnlANoTZScZMju7zPSKYc3BX/HiQRGv/oY3/8bJ46CJBQ1FVTfdXUEshUHX/XYWFpeWV1Yza9n1jc2t7dzObtVEieZQ4ZGMdD1gBqRQUEGBEuqxBhYGEmpB/3Lk1+5BGxGpOxzE0AxZV4mO4Ayt1MrtX7VSXyVD34iQ+gPmF5DdjK5d2COwadJ96U5MkU5Vbuy29HPAlBIZfMmIbnxthMmUbBJQyzfmIgZrzPutCwVLEQTDMd3z+kR1Zp06kbSmkY/X3RMpCYwZhYDtDhj0z643E/7xGgp3zZipUnCAoPlnUSTFiI7CoG2hgaMcWMK4FvZWyntM42sqwNwZt9eZ5UiwXvpFC8Pc2XLqZxZMgBOSTHxCNnpERuSJlUCeP5Jm8kjfnyXlx3p2PSeuCM53ZI3/gfP4ASeWRg=</latexit>

SNO detected solar electron neutrino disappearance

10

SLIDE 11

Jessica Turner

ICECUBE

P (νµ → ντ)

<latexit sha1_base64="MKyVsMKL0YSD6Nco0TR/3w/wSM=">ACE3icbZDLSsNAFIYnXmu9RV26CRahuihJFXRZdOygr1AE8JkOmHTiZh5oxSQt/Bja/ixoUibt2482cXhba+sPAz3fO4cz5o4wzBa7bS0tr6yurRc2iptb2zu79t5+U6VaEtogKU9lO8KciZoAxhw2s4kxUnEaSsaXI/rXsqFUvFHQwzGiS4J1jMCAaDQvu07nMaQ9kXOsz9RI98yXp9wFKmD2PmA9ZTdBLaJbfiTuQsGm9mSmimemh/+d2U6IQKIBwr1fHcDIcS2CE01HR14pmAxwj3aMFTihKsgnN42cY0O6TpxK8wQ4E/p7IseJUsMkMp0Jhr6ar43hf7WOhvgyJnINFBpotizR1InXFATpdJSoAPjcFEMvNXh/SxARMjEUTgjd/8qJpViveWaV6e16qXc3iKBDdITKyEMXqIZuUB01EGP6Bm9ojfryXqx3q2PaeuSNZs5QH9kf4Ah8afMg=</latexit>

∆m2 ∼ 2 × 10−3 eV2

<latexit sha1_base64="xegstYIKwovEjKuTOEKGwre1ias=">ACFnicbVDJSgNBEO1xN25Rj14ag+DBhJmJoEdRDx4jmAUySejpVGJj98zQXSOGIV/hxV/x4kERr+LNv7GzHNweFDzeq6KqXphIYdB1P52Z2bn5hcWl5dzK6tr6Rn5zq2biVHOo8ljGuhEyA1JEUEWBEhqJBqZCfXw5mzk129BGxFHVzhIoKVYPxI9wRlaqZMvBucgkVHV9mlghKJ+gEKBoZ7bzorlYXBA4Q7zKA2bPudfMEtuWPQv8SbkgKZotLJfwTdmKcKIuSGdP03ARbGdMouIRhLkgNJIzfsD40LY2YXd3Kxm8N6Z5VurQXa1sR0rH6fSJjypiBCm2nYnhtfnsj8T+vmWLvuJWJKEkRIj5Z1EslxZiOMqJdoYGjHFjCuBb2VsqvmWYcbZI5G4L3+W/pOaXvHLJvzwsnJxO41giO2SX7BOPHJETckEqpEo4uSeP5Jm8OA/Ok/PqvE1aZ5zpzDb5Aef9C2wNnaw=</latexit>

θ ∼ π 4

<latexit sha1_base64="+JuEG6QFb/uRIZ8CMnqhujp0mDg=">ACAHicbVBNS8NAEN3Ur1q/oh48eAkWwVNJakGPRS8eK9gPaELZbDft0t1N2J0IJeTiX/HiQRGv/gxv/hu3bQ7a+mDg8d4M/PChDMNrvtldbWNza3ytuVnd29/QP78Kij41QR2iYxj1UvxJpyJmkbGHDaSxTFIuS0G05uZ373kSrNYvkA04QGAo8kixjBYKSBfeLDmAL2NRN+pDJ/ITlWSMf2FW35s7hrBKvIFVUoDWwv/xhTFJBJRCOte57bgJBhUwmle8VNE0wmeET7hkosqA6y+QO5c26UoRPFypQEZ67+nsiw0HoqQtMpMIz1sjcT/P6KUTXQcZkgKVZLEoSrkDsTNLwxkyRQnwqSGYKGZudcgYmxzAZFYxIXjL6+STr3mXdbq941q86aIo4xO0Rm6QB6Qk10h1qojQjK0TN6RW/Wk/VivVsfi9aSVcwcoz+wPn8AgXGW/Q=</latexit>

SK

Eν ∼ GeV

<latexit sha1_base64="21sbPXE1xrfVKgoZjQjeoVrV6Iw=">AB/3icbVDLSgNBEJz1GeMrKnjxMhgET2E3CnoMiugxgnlANoTZScZMju7zPSKYc3BX/HiQRGv/oY3/8bJ46CJBQ1FVTfdXUEshUHX/XYWFpeWV1Yza9n1jc2t7dzObtVEieZQ4ZGMdD1gBqRQUEGBEuqxBhYGEmpB/3Lk1+5BGxGpOxzE0AxZV4mO4Ayt1MrtX7VSXyVD34iQ+gPmF5DdjK5d2COwadJ96U5MkU5Vbuy29HPAlBIZfMmIbnxthMmUbBJQyzfmIgZrzPutCwVLEQTDMd3z+kR1Zp06kbSmkY/X3RMpCYwZhYDtDhj0z643E/7xGgp3zZipUnCAoPlnUSTFiI7CoG2hgaMcWMK4FvZWyntM42sqwNwZt9eZ5UiwXvpFC8Pc2XLqZxZMgBOSTHxCNnpERuSJlUCeP5Jm8kjfnyXlx3p2PSeuCM53ZI3/gfP4ASeWRg=</latexit>

P

• νe → νµ/τ
• <latexit sha1_base64="zjHAZMx7AqadKl2LCrLnaF9tok=">ACGHicbVA9SwNBEN3z2/gVtbRZDEJs4p0KWo2lhGMCeRC2NvMJYt7e8furBKO/Awb/4qNhSK2dv4bN/EKjT4YeLw3w8y8KJPCoO9/ejOzc/MLi0vLpZXVtfWN8ubWjUmt5tDgqUx1K2IGpFDQIESWpkGlkQSmtHtxdhv3oE2IlXOMygk7C+ErHgDJ3ULR/UQwkxVkNluzmMQi36A2Rap/d0IoWJPQiR2cLZ75Yrfs2fgP4lQUEqpEC9W/4Ieym3CSjkhnTDvwMOznTKLiEUSm0BjLGb1kf2o4qloDp5JPHRnTPKT0ap9qVQjpRf07kLDFmESuM2E4MNPeWPzPa1uMTzu5UJlFUPx7UWwlxZSOU6I9oYGjHDrCuBbuVsoHTDOLsuSCyGYfvkvuTmsBUe1w6vjytl5EcS2SG7pEoCckLOyCWpkwbh5IE8kRfy6j16z96b9/7dOuMVM9vkF7yPLx2koRA=</latexit>

SNO KamLand

terrestrial 
 source

∆m2 ∼ 7 × 10−5 eV2

<latexit sha1_base64="F24sHeMA47r+GCwMBJqEzrAqog=">ACFnicbVA9SwNBEN3z2/gVtbRZDIKFCXdRiaWohaWC+YBcEvY2k7hk9+7YnRPDkV9h41+xsVDEVuz8N25iCk18MPB4b4aZeUEshUHX/XJmZufmFxaXljMrq2vrG9nNrYqJEs2hzCMZ6VrADEgRQhkFSqjFGpgKJFSD3vnQr96BNiIKb7AfQ0Oxbig6gjO0Uiub9y9AIqOqWaS+EYqWfBQKDPXcZpo/HvgH1Ee4xQqg2axlc25BXcEOk28McmRMa5a2U+/HfFEQYhcMmPqnhtjI2UaBZcwyPiJgZjxHutC3dKQ2dWNdPTWgO5ZpU07kbYVIh2pvydSpozpq8B2Koa3ZtIbiv959Q7J41UhHGCEPKfRZ1EUozoMCPaFho4yr4ljGthb6X8lmnG0SaZsSF4ky9Pk0qx4B0WitdHudOzcRxLZIfskn3ikRI5JZfkipQJw/kibyQV+fReXbenPef1hlnPLN/sD5+AZ3U52z</latexit>

θ ∼ π 6

<latexit sha1_base64="Zt3rH5HPisor20SHBlSjt/1B1dk=">ACAXicbVBNS8NAEN34WetX1IvgZbEInkpSRT0WvXisYD+gCWz3bRLd5OwOxFKiBf/ihcPinj1X3jz37htc9DWBwOP92aYmRckgmtwnG9raXldW29tFHe3Nre2bX39ls6ThVlTRqLWHUCopngEWsCB8E6iWJEBoK1g9HNxG8/MKV5HN3DOG+JIOIh5wSMFLPvRgyIB4mkvshYrQzEt4nl3kPbviVJ0p8CJxC1JBRo9+8vrxzSVLAIqiNZd10nAz4gCTgXLy16qWULoiAxY19CISKb9bPpBjk+M0sdhrExFgKfq74mMSK3HMjCdksBQz3sT8T+vm0J45Wc8SlJgEZ0tClOBIcaTOHCfK0ZBjA0hVHFzK6ZDYnIAE1rZhODOv7xIWrWqe1at3Z1X6tdFHCV0hI7RKXLRJaqjW9RATUTRI3pGr+jNerJerHfrY9a6ZBUzB+gPrM8f3+GXKQ=</latexit>

L ∼ 180 km

<latexit sha1_base64="E+F9md+B1QoMZmb8NmWR9SJGXlY=">AB/nicbVBNS8NAEN34WetXVDx5WSyCBylJFeyx6MWDhwr2A5pQNtNu3Q3CbsTsYSCf8WLB0W8+ju8+W/ctjlo64OBx3szMwLEsE1OM63tbS8srq2Xtgobm5t7+zae/tNHaeKsgaNRazaAdFM8Ig1gINg7UQxIgPBWsHweuK3HpjSPI7uYZQwX5J+xENOCRipax/epL7FYd7wx7wB4hG8px1y45ZWcKvEjcnJRQjnrX/vJ6MU0li4AKonXHdRLwM6KAU8HGRS/VLCF0SPqsY2hEJN+Nj1/jE+M0sNhrExFgKfq74mMSK1HMjCdksBAz3sT8T+vk0JY9TMeJSmwiM4WhanAEONJFrjHFaMgRoYQqri5FdMBUYSCSaxoQnDnX14kzUrZPS9X7i5Ktas8jgI6QsfoFLnoEtXQDaqjBqIoQ8/oFb1ZT9aL9W59zFqXrHzmAP2B9fkD0huUxA=</latexit>

Eνe ∼ O(1) MeV

<latexit sha1_base64="RIdrSx7Ll5Rc9Xq+isFN/usSUvo=">ACHnicbVBSxtBFJ61WjXauq1HL4OhEKGE3ai0x1Ap9CIqmBjIhmV28qKDs7PLzNvSMOwv8eJf8dKDRQRP+m+cTXLQ2A8GPr73vTfvfUkuhcEgePIW3i0uvV9eWa2trX/4uOF/+tw1WaE5dHgmM91LmAEpFHRQoIReroGliYSz5PKgqp/9Bm1Epk5xnMgZedKjARn6KTY3/8Z2yhzjmqAjVRxhbKMjIipVHK8IzaY/KRrgTfY0Q/qA9hG4Z+/WgGUxA35JwRupkhuPYf4iGS9SUMglM6YfBjkOLNMouISyFhUGcsYv2Tn0HVUsBTOwk/NK+sUpQzrKtHsK6UR92WFZasw4TZyz2tjM1yrxf7V+gaPvAytUXiAoPv1oVEiKGa2yokOhgaMcO8K4Fm5Xyi+YZhxdojUXQjh/8lvSbTXD3WbrZK/e/jGLY4VskW3SICH5RtrkFzkmHcLJFbkht+Sfd+39e68+6l1wZv1bJX8B6fAc8fo30=</latexit>

L ∼ 108 km

<latexit sha1_base64="MWfDT6R/sCP7r2phMRTarKVtFbc=">ACAHicbVA9SwNBEN2LXzF+RS0sbBaDYCHhLgqmDNpYWEQwH5A7w95mkyzZvTt258RwXONfsbFQxNafYe/cZNcoYkPBh7vzTAz48E12Db31ZuaXldS2/XtjY3NreKe7uNXUYK8oaNBShavtEM8ED1gAOgrUjxYj0BWv5o6uJ3pgSvMwuINxDxJBgHvc0rASN3iwY2rucSOfZ9U/fUBfYIyUim3WLJLtT4EXiZKSEMtS7xS+3F9JYsgCoIFp3HDsCLyEKOBUsLbixZhGhIzJgHUMDIpn2kukDKT42Sg/3Q2UqADxVf08kRGo9lr7plASGet6biP95nRj6VS/hQRQDC+hsUT8WGEI8SQP3uGIUxNgQhU3t2I6JIpQMJkVTAjO/MuLpFkpO2flyu15qXaZxZFHh+gInSAHXaAaukZ1EAUpegZvaI368l6sd6tj1lrzspm9tEfWJ8/Bm6WDg=</latexit>

11

SLIDE 12

Jessica Turner

Kim, Lasserre, Wang

ICECUBE

P (νµ → ντ)

<latexit sha1_base64="MKyVsMKL0YSD6Nco0TR/3w/wSM=">ACE3icbZDLSsNAFIYnXmu9RV26CRahuihJFXRZdOygr1AE8JkOmHTiZh5oxSQt/Bja/ixoUibt2482cXhba+sPAz3fO4cz5o4wzBa7bS0tr6yurRc2iptb2zu79t5+U6VaEtogKU9lO8KciZoAxhw2s4kxUnEaSsaXI/rXsqFUvFHQwzGiS4J1jMCAaDQvu07nMaQ9kXOsz9RI98yXp9wFKmD2PmA9ZTdBLaJbfiTuQsGm9mSmimemh/+d2U6IQKIBwr1fHcDIcS2CE01HR14pmAxwj3aMFTihKsgnN42cY0O6TpxK8wQ4E/p7IseJUsMkMp0Jhr6ar43hf7WOhvgyJnINFBpotizR1InXFATpdJSoAPjcFEMvNXh/SxARMjEUTgjd/8qJpViveWaV6e16qXc3iKBDdITKyEMXqIZuUB01EGP6Bm9ojfryXqx3q2PaeuSNZs5QH9kf4Ah8afMg=</latexit>

∆m2 ∼ 2 × 10−3 eV2

<latexit sha1_base64="xegstYIKwovEjKuTOEKGwre1ias=">ACFnicbVDJSgNBEO1xN25Rj14ag+DBhJmJoEdRDx4jmAUySejpVGJj98zQXSOGIV/hxV/x4kERr+LNv7GzHNweFDzeq6KqXphIYdB1P52Z2bn5hcWl5dzK6tr6Rn5zq2biVHOo8ljGuhEyA1JEUEWBEhqJBqZCfXw5mzk129BGxFHVzhIoKVYPxI9wRlaqZMvBucgkVHV9mlghKJ+gEKBoZ7bzorlYXBA4Q7zKA2bPudfMEtuWPQv8SbkgKZotLJfwTdmKcKIuSGdP03ARbGdMouIRhLkgNJIzfsD40LY2YXd3Kxm8N6Z5VurQXa1sR0rH6fSJjypiBCm2nYnhtfnsj8T+vmWLvuJWJKEkRIj5Z1EslxZiOMqJdoYGjHFjCuBb2VsqvmWYcbZI5G4L3+W/pOaXvHLJvzwsnJxO41giO2SX7BOPHJETckEqpEo4uSeP5Jm8OA/Ok/PqvE1aZ5zpzDb5Aef9C2wNnaw=</latexit>

θ ∼ π 4

<latexit sha1_base64="+JuEG6QFb/uRIZ8CMnqhujp0mDg=">ACAHicbVBNS8NAEN3Ur1q/oh48eAkWwVNJakGPRS8eK9gPaELZbDft0t1N2J0IJeTiX/HiQRGv/gxv/hu3bQ7a+mDg8d4M/PChDMNrvtldbWNza3ytuVnd29/QP78Kij41QR2iYxj1UvxJpyJmkbGHDaSxTFIuS0G05uZ373kSrNYvkA04QGAo8kixjBYKSBfeLDmAL2NRN+pDJ/ITlWSMf2FW35s7hrBKvIFVUoDWwv/xhTFJBJRCOte57bgJBhUwmle8VNE0wmeET7hkosqA6y+QO5c26UoRPFypQEZ67+nsiw0HoqQtMpMIz1sjcT/P6KUTXQcZkgKVZLEoSrkDsTNLwxkyRQnwqSGYKGZudcgYmxzAZFYxIXjL6+STr3mXdbq941q86aIo4xO0Rm6QB6Qk10h1qojQjK0TN6RW/Wk/VivVsfi9aSVcwcoz+wPn8AgXGW/Q=</latexit>

SK

Eν ∼ GeV

<latexit sha1_base64="21sbPXE1xrfVKgoZjQjeoVrV6Iw=">AB/3icbVDLSgNBEJz1GeMrKnjxMhgET2E3CnoMiugxgnlANoTZScZMju7zPSKYc3BX/HiQRGv/oY3/8bJ46CJBQ1FVTfdXUEshUHX/XYWFpeWV1Yza9n1jc2t7dzObtVEieZQ4ZGMdD1gBqRQUEGBEuqxBhYGEmpB/3Lk1+5BGxGpOxzE0AxZV4mO4Ayt1MrtX7VSXyVD34iQ+gPmF5DdjK5d2COwadJ96U5MkU5Vbuy29HPAlBIZfMmIbnxthMmUbBJQyzfmIgZrzPutCwVLEQTDMd3z+kR1Zp06kbSmkY/X3RMpCYwZhYDtDhj0z643E/7xGgp3zZipUnCAoPlnUSTFiI7CoG2hgaMcWMK4FvZWyntM42sqwNwZt9eZ5UiwXvpFC8Pc2XLqZxZMgBOSTHxCNnpERuSJlUCeP5Jm8kjfnyXlx3p2PSeuCM53ZI3/gfP4ASeWRg=</latexit>

P

• νe → νµ/τ
• <latexit sha1_base64="zjHAZMx7AqadKl2LCrLnaF9tok=">ACGHicbVA9SwNBEN3z2/gVtbRZDEJs4p0KWo2lhGMCeRC2NvMJYt7e8furBKO/Awb/4qNhSK2dv4bN/EKjT4YeLw3w8y8KJPCoO9/ejOzc/MLi0vLpZXVtfWN8ubWjUmt5tDgqUx1K2IGpFDQIESWpkGlkQSmtHtxdhv3oE2IlXOMygk7C+ErHgDJ3ULR/UQwkxVkNluzmMQi36A2Rap/d0IoWJPQiR2cLZ75Yrfs2fgP4lQUEqpEC9W/4Ieym3CSjkhnTDvwMOznTKLiEUSm0BjLGb1kf2o4qloDp5JPHRnTPKT0ap9qVQjpRf07kLDFmESuM2E4MNPeWPzPa1uMTzu5UJlFUPx7UWwlxZSOU6I9oYGjHDrCuBbuVsoHTDOLsuSCyGYfvkvuTmsBUe1w6vjytl5EcS2SG7pEoCckLOyCWpkwbh5IE8kRfy6j16z96b9/7dOuMVM9vkF7yPLx2koRA=</latexit>

SNO KamLand

terrestrial 
 source

∆m2 ∼ 7 × 10−5 eV2

<latexit sha1_base64="F24sHeMA47r+GCwMBJqEzrAqog=">ACFnicbVA9SwNBEN3z2/gVtbRZDIKFCXdRiaWohaWC+YBcEvY2k7hk9+7YnRPDkV9h41+xsVDEVuz8N25iCk18MPB4b4aZeUEshUHX/XJmZufmFxaXljMrq2vrG9nNrYqJEs2hzCMZ6VrADEgRQhkFSqjFGpgKJFSD3vnQr96BNiIKb7AfQ0Oxbig6gjO0Uiub9y9AIqOqWaS+EYqWfBQKDPXcZpo/HvgH1Ee4xQqg2axlc25BXcEOk28McmRMa5a2U+/HfFEQYhcMmPqnhtjI2UaBZcwyPiJgZjxHutC3dKQ2dWNdPTWgO5ZpU07kbYVIh2pvydSpozpq8B2Koa3ZtIbiv959Q7J41UhHGCEPKfRZ1EUozoMCPaFho4yr4ljGthb6X8lmnG0SaZsSF4ky9Pk0qx4B0WitdHudOzcRxLZIfskn3ikRI5JZfkipQJw/kibyQV+fReXbenPef1hlnPLN/sD5+AZ3U52z</latexit>

θ ∼ π 6

<latexit sha1_base64="Zt3rH5HPisor20SHBlSjt/1B1dk=">ACAXicbVBNS8NAEN34WetX1IvgZbEInkpSRT0WvXisYD+gCWz3bRLd5OwOxFKiBf/ihcPinj1X3jz37htc9DWBwOP92aYmRckgmtwnG9raXldW29tFHe3Nre2bX39ls6ThVlTRqLWHUCopngEWsCB8E6iWJEBoK1g9HNxG8/MKV5HN3DOG+JIOIh5wSMFLPvRgyIB4mkvshYrQzEt4nl3kPbviVJ0p8CJxC1JBRo9+8vrxzSVLAIqiNZd10nAz4gCTgXLy16qWULoiAxY19CISKb9bPpBjk+M0sdhrExFgKfq74mMSK3HMjCdksBQz3sT8T+vm0J45Wc8SlJgEZ0tClOBIcaTOHCfK0ZBjA0hVHFzK6ZDYnIAE1rZhODOv7xIWrWqe1at3Z1X6tdFHCV0hI7RKXLRJaqjW9RATUTRI3pGr+jNerJerHfrY9a6ZBUzB+gPrM8f3+GXKQ=</latexit>

L ∼ 180 km

<latexit sha1_base64="E+F9md+B1QoMZmb8NmWR9SJGXlY=">AB/nicbVBNS8NAEN34WetXVDx5WSyCBylJFeyx6MWDhwr2A5pQNtNu3Q3CbsTsYSCf8WLB0W8+ju8+W/ctjlo64OBx3szMwLEsE1OM63tbS8srq2Xtgobm5t7+zae/tNHaeKsgaNRazaAdFM8Ig1gINg7UQxIgPBWsHweuK3HpjSPI7uYZQwX5J+xENOCRipax/epL7FYd7wx7wB4hG8px1y45ZWcKvEjcnJRQjnrX/vJ6MU0li4AKonXHdRLwM6KAU8HGRS/VLCF0SPqsY2hEJN+Nj1/jE+M0sNhrExFgKfq74mMSK1HMjCdksBAz3sT8T+vk0JY9TMeJSmwiM4WhanAEONJFrjHFaMgRoYQqri5FdMBUYSCSaxoQnDnX14kzUrZPS9X7i5Ktas8jgI6QsfoFLnoEtXQDaqjBqIoQ8/oFb1ZT9aL9W59zFqXrHzmAP2B9fkD0huUxA=</latexit>

Eνe ∼ O(1) MeV

<latexit sha1_base64="RIdrSx7Ll5Rc9Xq+isFN/usSUvo=">ACHnicbVBSxtBFJ61WjXauq1HL4OhEKGE3ai0x1Ap9CIqmBjIhmV28qKDs7PLzNvSMOwv8eJf8dKDRQRP+m+cTXLQ2A8GPr73vTfvfUkuhcEgePIW3i0uvV9eWa2trX/4uOF/+tw1WaE5dHgmM91LmAEpFHRQoIReroGliYSz5PKgqp/9Bm1Epk5xnMgZedKjARn6KTY3/8Z2yhzjmqAjVRxhbKMjIipVHK8IzaY/KRrgTfY0Q/qA9hG4Z+/WgGUxA35JwRupkhuPYf4iGS9SUMglM6YfBjkOLNMouISyFhUGcsYv2Tn0HVUsBTOwk/NK+sUpQzrKtHsK6UR92WFZasw4TZyz2tjM1yrxf7V+gaPvAytUXiAoPv1oVEiKGa2yokOhgaMcO8K4Fm5Xyi+YZhxdojUXQjh/8lvSbTXD3WbrZK/e/jGLY4VskW3SICH5RtrkFzkmHcLJFbkht+Sfd+39e68+6l1wZv1bJX8B6fAc8fo30=</latexit>

L ∼ 108 km

<latexit sha1_base64="MWfDT6R/sCP7r2phMRTarKVtFbc=">ACAHicbVA9SwNBEN2LXzF+RS0sbBaDYCHhLgqmDNpYWEQwH5A7w95mkyzZvTt258RwXONfsbFQxNafYe/cZNcoYkPBh7vzTAz48E12Db31ZuaXldS2/XtjY3NreKe7uNXUYK8oaNBShavtEM8ED1gAOgrUjxYj0BWv5o6uJ3pgSvMwuINxDxJBgHvc0rASN3iwY2rucSOfZ9U/fUBfYIyUim3WLJLtT4EXiZKSEMtS7xS+3F9JYsgCoIFp3HDsCLyEKOBUsLbixZhGhIzJgHUMDIpn2kukDKT42Sg/3Q2UqADxVf08kRGo9lr7plASGet6biP95nRj6VS/hQRQDC+hsUT8WGEI8SQP3uGIUxNgQhU3t2I6JIpQMJkVTAjO/MuLpFkpO2flyu15qXaZxZFHh+gInSAHXaAaukZ1EAUpegZvaI368l6sd6tj1lrzspm9tEfWJ8/Bm6WDg=</latexit>

Reactor

DAYA,RENO and Double Chooz all use neutrinos produced at reactors

Double Chooz

1711.00588

12

SLIDE 13

Jessica Turner

13

ICECUBE

P (νµ → ντ)

<latexit sha1_base64="MKyVsMKL0YSD6Nco0TR/3w/wSM=">ACE3icbZDLSsNAFIYnXmu9RV26CRahuihJFXRZdOygr1AE8JkOmHTiZh5oxSQt/Bja/ixoUibt2482cXhba+sPAz3fO4cz5o4wzBa7bS0tr6yurRc2iptb2zu79t5+U6VaEtogKU9lO8KciZoAxhw2s4kxUnEaSsaXI/rXsqFUvFHQwzGiS4J1jMCAaDQvu07nMaQ9kXOsz9RI98yXp9wFKmD2PmA9ZTdBLaJbfiTuQsGm9mSmimemh/+d2U6IQKIBwr1fHcDIcS2CE01HR14pmAxwj3aMFTihKsgnN42cY0O6TpxK8wQ4E/p7IseJUsMkMp0Jhr6ar43hf7WOhvgyJnINFBpotizR1InXFATpdJSoAPjcFEMvNXh/SxARMjEUTgjd/8qJpViveWaV6e16qXc3iKBDdITKyEMXqIZuUB01EGP6Bm9ojfryXqx3q2PaeuSNZs5QH9kf4Ah8afMg=</latexit>

∆m2 ∼ 2 × 10−3 eV2

<latexit sha1_base64="xegstYIKwovEjKuTOEKGwre1ias=">ACFnicbVDJSgNBEO1xN25Rj14ag+DBhJmJoEdRDx4jmAUySejpVGJj98zQXSOGIV/hxV/x4kERr+LNv7GzHNweFDzeq6KqXphIYdB1P52Z2bn5hcWl5dzK6tr6Rn5zq2biVHOo8ljGuhEyA1JEUEWBEhqJBqZCfXw5mzk129BGxFHVzhIoKVYPxI9wRlaqZMvBucgkVHV9mlghKJ+gEKBoZ7bzorlYXBA4Q7zKA2bPudfMEtuWPQv8SbkgKZotLJfwTdmKcKIuSGdP03ARbGdMouIRhLkgNJIzfsD40LY2YXd3Kxm8N6Z5VurQXa1sR0rH6fSJjypiBCm2nYnhtfnsj8T+vmWLvuJWJKEkRIj5Z1EslxZiOMqJdoYGjHFjCuBb2VsqvmWYcbZI5G4L3+W/pOaXvHLJvzwsnJxO41giO2SX7BOPHJETckEqpEo4uSeP5Jm8OA/Ok/PqvE1aZ5zpzDb5Aef9C2wNnaw=</latexit>

θ ∼ π 4

<latexit sha1_base64="+JuEG6QFb/uRIZ8CMnqhujp0mDg=">ACAHicbVBNS8NAEN3Ur1q/oh48eAkWwVNJakGPRS8eK9gPaELZbDft0t1N2J0IJeTiX/HiQRGv/gxv/hu3bQ7a+mDg8d4M/PChDMNrvtldbWNza3ytuVnd29/QP78Kij41QR2iYxj1UvxJpyJmkbGHDaSxTFIuS0G05uZ373kSrNYvkA04QGAo8kixjBYKSBfeLDmAL2NRN+pDJ/ITlWSMf2FW35s7hrBKvIFVUoDWwv/xhTFJBJRCOte57bgJBhUwmle8VNE0wmeET7hkosqA6y+QO5c26UoRPFypQEZ67+nsiw0HoqQtMpMIz1sjcT/P6KUTXQcZkgKVZLEoSrkDsTNLwxkyRQnwqSGYKGZudcgYmxzAZFYxIXjL6+STr3mXdbq941q86aIo4xO0Rm6QB6Qk10h1qojQjK0TN6RW/Wk/VivVsfi9aSVcwcoz+wPn8AgXGW/Q=</latexit>

SK

Eν ∼ GeV

<latexit sha1_base64="21sbPXE1xrfVKgoZjQjeoVrV6Iw=">AB/3icbVDLSgNBEJz1GeMrKnjxMhgET2E3CnoMiugxgnlANoTZScZMju7zPSKYc3BX/HiQRGv/oY3/8bJ46CJBQ1FVTfdXUEshUHX/XYWFpeWV1Yza9n1jc2t7dzObtVEieZQ4ZGMdD1gBqRQUEGBEuqxBhYGEmpB/3Lk1+5BGxGpOxzE0AxZV4mO4Ayt1MrtX7VSXyVD34iQ+gPmF5DdjK5d2COwadJ96U5MkU5Vbuy29HPAlBIZfMmIbnxthMmUbBJQyzfmIgZrzPutCwVLEQTDMd3z+kR1Zp06kbSmkY/X3RMpCYwZhYDtDhj0z643E/7xGgp3zZipUnCAoPlnUSTFiI7CoG2hgaMcWMK4FvZWyntM42sqwNwZt9eZ5UiwXvpFC8Pc2XLqZxZMgBOSTHxCNnpERuSJlUCeP5Jm8kjfnyXlx3p2PSeuCM53ZI3/gfP4ASeWRg=</latexit>

P

• νe → νµ/τ
• <latexit sha1_base64="zjHAZMx7AqadKl2LCrLnaF9tok=">ACGHicbVA9SwNBEN3z2/gVtbRZDEJs4p0KWo2lhGMCeRC2NvMJYt7e8furBKO/Awb/4qNhSK2dv4bN/EKjT4YeLw3w8y8KJPCoO9/ejOzc/MLi0vLpZXVtfWN8ubWjUmt5tDgqUx1K2IGpFDQIESWpkGlkQSmtHtxdhv3oE2IlXOMygk7C+ErHgDJ3ULR/UQwkxVkNluzmMQi36A2Rap/d0IoWJPQiR2cLZ75Yrfs2fgP4lQUEqpEC9W/4Ieym3CSjkhnTDvwMOznTKLiEUSm0BjLGb1kf2o4qloDp5JPHRnTPKT0ap9qVQjpRf07kLDFmESuM2E4MNPeWPzPa1uMTzu5UJlFUPx7UWwlxZSOU6I9oYGjHDrCuBbuVsoHTDOLsuSCyGYfvkvuTmsBUe1w6vjytl5EcS2SG7pEoCckLOyCWpkwbh5IE8kRfy6j16z96b9/7dOuMVM9vkF7yPLx2koRA=</latexit>

SNO KamLand

terrestrial 
 source

∆m2 ∼ 7 × 10−5 eV2

<latexit sha1_base64="F24sHeMA47r+GCwMBJqEzrAqog=">ACFnicbVA9SwNBEN3z2/gVtbRZDIKFCXdRiaWohaWC+YBcEvY2k7hk9+7YnRPDkV9h41+xsVDEVuz8N25iCk18MPB4b4aZeUEshUHX/XJmZufmFxaXljMrq2vrG9nNrYqJEs2hzCMZ6VrADEgRQhkFSqjFGpgKJFSD3vnQr96BNiIKb7AfQ0Oxbig6gjO0Uiub9y9AIqOqWaS+EYqWfBQKDPXcZpo/HvgH1Ee4xQqg2axlc25BXcEOk28McmRMa5a2U+/HfFEQYhcMmPqnhtjI2UaBZcwyPiJgZjxHutC3dKQ2dWNdPTWgO5ZpU07kbYVIh2pvydSpozpq8B2Koa3ZtIbiv959Q7J41UhHGCEPKfRZ1EUozoMCPaFho4yr4ljGthb6X8lmnG0SaZsSF4ky9Pk0qx4B0WitdHudOzcRxLZIfskn3ikRI5JZfkipQJw/kibyQV+fReXbenPef1hlnPLN/sD5+AZ3U52z</latexit>

θ ∼ π 6

<latexit sha1_base64="Zt3rH5HPisor20SHBlSjt/1B1dk=">ACAXicbVBNS8NAEN34WetX1IvgZbEInkpSRT0WvXisYD+gCWz3bRLd5OwOxFKiBf/ihcPinj1X3jz37htc9DWBwOP92aYmRckgmtwnG9raXldW29tFHe3Nre2bX39ls6ThVlTRqLWHUCopngEWsCB8E6iWJEBoK1g9HNxG8/MKV5HN3DOG+JIOIh5wSMFLPvRgyIB4mkvshYrQzEt4nl3kPbviVJ0p8CJxC1JBRo9+8vrxzSVLAIqiNZd10nAz4gCTgXLy16qWULoiAxY19CISKb9bPpBjk+M0sdhrExFgKfq74mMSK3HMjCdksBQz3sT8T+vm0J45Wc8SlJgEZ0tClOBIcaTOHCfK0ZBjA0hVHFzK6ZDYnIAE1rZhODOv7xIWrWqe1at3Z1X6tdFHCV0hI7RKXLRJaqjW9RATUTRI3pGr+jNerJerHfrY9a6ZBUzB+gPrM8f3+GXKQ=</latexit>

L ∼ 180 km

<latexit sha1_base64="E+F9md+B1QoMZmb8NmWR9SJGXlY=">AB/nicbVBNS8NAEN34WetXVDx5WSyCBylJFeyx6MWDhwr2A5pQNtNu3Q3CbsTsYSCf8WLB0W8+ju8+W/ctjlo64OBx3szMwLEsE1OM63tbS8srq2Xtgobm5t7+zae/tNHaeKsgaNRazaAdFM8Ig1gINg7UQxIgPBWsHweuK3HpjSPI7uYZQwX5J+xENOCRipax/epL7FYd7wx7wB4hG8px1y45ZWcKvEjcnJRQjnrX/vJ6MU0li4AKonXHdRLwM6KAU8HGRS/VLCF0SPqsY2hEJN+Nj1/jE+M0sNhrExFgKfq74mMSK1HMjCdksBAz3sT8T+vk0JY9TMeJSmwiM4WhanAEONJFrjHFaMgRoYQqri5FdMBUYSCSaxoQnDnX14kzUrZPS9X7i5Ktas8jgI6QsfoFLnoEtXQDaqjBqIoQ8/oFb1ZT9aL9W59zFqXrHzmAP2B9fkD0huUxA=</latexit>

Eνe ∼ O(1) MeV

<latexit sha1_base64="RIdrSx7Ll5Rc9Xq+isFN/usSUvo=">ACHnicbVBSxtBFJ61WjXauq1HL4OhEKGE3ai0x1Ap9CIqmBjIhmV28qKDs7PLzNvSMOwv8eJf8dKDRQRP+m+cTXLQ2A8GPr73vTfvfUkuhcEgePIW3i0uvV9eWa2trX/4uOF/+tw1WaE5dHgmM91LmAEpFHRQoIReroGliYSz5PKgqp/9Bm1Epk5xnMgZedKjARn6KTY3/8Z2yhzjmqAjVRxhbKMjIipVHK8IzaY/KRrgTfY0Q/qA9hG4Z+/WgGUxA35JwRupkhuPYf4iGS9SUMglM6YfBjkOLNMouISyFhUGcsYv2Tn0HVUsBTOwk/NK+sUpQzrKtHsK6UR92WFZasw4TZyz2tjM1yrxf7V+gaPvAytUXiAoPv1oVEiKGa2yokOhgaMcO8K4Fm5Xyi+YZhxdojUXQjh/8lvSbTXD3WbrZK/e/jGLY4VskW3SICH5RtrkFzkmHcLJFbkht+Sfd+39e68+6l1wZv1bJX8B6fAc8fo30=</latexit>

L ∼ 108 km

<latexit sha1_base64="MWfDT6R/sCP7r2phMRTarKVtFbc=">ACAHicbVA9SwNBEN2LXzF+RS0sbBaDYCHhLgqmDNpYWEQwH5A7w95mkyzZvTt258RwXONfsbFQxNafYe/cZNcoYkPBh7vzTAz48E12Db31ZuaXldS2/XtjY3NreKe7uNXUYK8oaNBShavtEM8ED1gAOgrUjxYj0BWv5o6uJ3pgSvMwuINxDxJBgHvc0rASN3iwY2rucSOfZ9U/fUBfYIyUim3WLJLtT4EXiZKSEMtS7xS+3F9JYsgCoIFp3HDsCLyEKOBUsLbixZhGhIzJgHUMDIpn2kukDKT42Sg/3Q2UqADxVf08kRGo9lr7plASGet6biP95nRj6VS/hQRQDC+hsUT8WGEI8SQP3uGIUxNgQhU3t2I6JIpQMJkVTAjO/MuLpFkpO2flyu15qXaZxZFHh+gInSAHXaAaukZ1EAUpegZvaI368l6sd6tj1lrzspm9tEfWJ8/Bm6WDg=</latexit>

1711.00588 Kim, Lasserre, Wang

Double Chooz

P (νe → νe)

<latexit sha1_base64="9ruWs20DpXmD9b2HhCXGh3VzfM=">ACJnicdVDLSgMxFM34tr6qLt0MFkE3ZUYF3QhFNy4r2Ad0hpJ7TBTDIkd5Qy9Gvc+CtuXCgi7vwUM20XPg8EDuecm+SeKBXcoOe9OzOzc/MLi0vLpZXVtfWN8uZW06hM2gwJZRuR9SA4BIayFAO9VAk0hAK7q5KPzWLWjDlbzGYQphQvuSx5xRtFK3fFYPBMS4HyibKi7JA5mNujmMAs37A6Raq7v/zINueJVvTHc38SfkgqZot4tPwc9xbIEJDJBjen4XophTjVyJmBUCjIDKWU3tA8dSyVNwIT5eM2Ru2eVnhsrbY9Ed6x+nchpYswiWwyoTgwP71C/MvrZBifhjmXaYg2eShOBMuKrfozO1xDQzF0BLKNLd/dmAasrQNluyJfg/V/5NmodV/6h6eHVcqZ1P61giO2SX7BOfnJAauSR10iCM3JNH8kxenAfnyXl13ibRGWc6s02+wfn4BHrYqD4=</latexit>

L ∼ km

<latexit sha1_base64="QlWIB9g8BtMfp9nkTDmsdFRTjcw=">AB+HicbVA9SwNBEN3zM8aPnFraLAbBKtxFQcugjYVFBPMBuSPsbTbJkt29Y3dOjEd+iY2FIrb+FDv/jZvkCk18MPB4b4aZeVEiuAHP+3ZWVtfWNzYLW8Xtnd29krt/0DRxqilr0FjEuh0RwRXrAEcBGsnmhEZCdaKRtdTv/XAtOGxuodxwkJBor3OSVgpa5bug0MlzgA9gjZSE6btmreDPgZeLnpIxy1LvuV9CLaSqZAiqIMR3fSyDMiAZOBZsUg9SwhNARGbCOpYpIZsJsdvgEn1ilh/uxtqUAz9TfExmRxoxlZDslgaFZ9Kbif14nhf5lmHGVpMAUnS/qpwJDjKcp4B7XjIYW0Ko5vZWTIdEwo2q6INwV98eZk0qxX/rFK9Oy/XrvI4CugIHaNT5KMLVEM3qI4aiKIUPaNX9OY8OS/Ou/Mxb1x8plD9AfO5w/xmpNH</latexit>

Eνe ∼ O(1) MeV

<latexit sha1_base64="RIdrSx7Ll5Rc9Xq+isFN/usSUvo=">ACHnicbVBSxtBFJ61WjXauq1HL4OhEKGE3ai0x1Ap9CIqmBjIhmV28qKDs7PLzNvSMOwv8eJf8dKDRQRP+m+cTXLQ2A8GPr73vTfvfUkuhcEgePIW3i0uvV9eWa2trX/4uOF/+tw1WaE5dHgmM91LmAEpFHRQoIReroGliYSz5PKgqp/9Bm1Epk5xnMgZedKjARn6KTY3/8Z2yhzjmqAjVRxhbKMjIipVHK8IzaY/KRrgTfY0Q/qA9hG4Z+/WgGUxA35JwRupkhuPYf4iGS9SUMglM6YfBjkOLNMouISyFhUGcsYv2Tn0HVUsBTOwk/NK+sUpQzrKtHsK6UR92WFZasw4TZyz2tjM1yrxf7V+gaPvAytUXiAoPv1oVEiKGa2yokOhgaMcO8K4Fm5Xyi+YZhxdojUXQjh/8lvSbTXD3WbrZK/e/jGLY4VskW3SICH5RtrkFzkmHcLJFbkht+Sfd+39e68+6l1wZv1bJX8B6fAc8fo30=</latexit>

θ ∼ π 20

<latexit sha1_base64="/pTNyQCTc4sp0js5EW6C/uBPYxU=">ACAnicbVBNS8NAEN3Ur1q/op7Ey2IRPJWkCnosevFYwX5AE8pmu2mX7iZhdyKUELz4V7x4UMSrv8Kb/8Ztm4O2Ph4vDfDzLwgEVyD43xbpZXVtfWN8mZla3tnd8/eP2jrOFWUtWgsYtUNiGaCR6wFHATrJoRGQjWCcY3U7/zwJTmcXQPk4T5kgwjHnJKwEh9+8iDEQPiaS6xFypCMy/heVZ38r5dWrODHiZuAWpogLNv3lDWKaShYBFUTrnusk4GdEAaeC5RUv1SwhdEyGrGdoRCTfjZ7IcenRhngMFamIsAz9fdERqTWExmYTklgpBe9qfif10shvPIzHiUpsIjOF4WpwBDjaR54wBWjICaGEKq4uRXTETFBgEmtYkJwF19eJu16zT2v1e8uqo3rIo4yOkYn6Ay56BI10C1qohai6BE9o1f0Zj1ZL9a79TFvLVnFzCH6A+vzB1EGl18=</latexit>

1711.00588

SLIDE 14

Jessica Turner

14

ICECUBE

P (νµ → ντ)

<latexit sha1_base64="MKyVsMKL0YSD6Nco0TR/3w/wSM=">ACE3icbZDLSsNAFIYnXmu9RV26CRahuihJFXRZdOygr1AE8JkOmHTiZh5oxSQt/Bja/ixoUibt2482cXhba+sPAz3fO4cz5o4wzBa7bS0tr6yurRc2iptb2zu79t5+U6VaEtogKU9lO8KciZoAxhw2s4kxUnEaSsaXI/rXsqFUvFHQwzGiS4J1jMCAaDQvu07nMaQ9kXOsz9RI98yXp9wFKmD2PmA9ZTdBLaJbfiTuQsGm9mSmimemh/+d2U6IQKIBwr1fHcDIcS2CE01HR14pmAxwj3aMFTihKsgnN42cY0O6TpxK8wQ4E/p7IseJUsMkMp0Jhr6ar43hf7WOhvgyJnINFBpotizR1InXFATpdJSoAPjcFEMvNXh/SxARMjEUTgjd/8qJpViveWaV6e16qXc3iKBDdITKyEMXqIZuUB01EGP6Bm9ojfryXqx3q2PaeuSNZs5QH9kf4Ah8afMg=</latexit>

∆m2 ∼ 2 × 10−3 eV2

<latexit sha1_base64="xegstYIKwovEjKuTOEKGwre1ias=">ACFnicbVDJSgNBEO1xN25Rj14ag+DBhJmJoEdRDx4jmAUySejpVGJj98zQXSOGIV/hxV/x4kERr+LNv7GzHNweFDzeq6KqXphIYdB1P52Z2bn5hcWl5dzK6tr6Rn5zq2biVHOo8ljGuhEyA1JEUEWBEhqJBqZCfXw5mzk129BGxFHVzhIoKVYPxI9wRlaqZMvBucgkVHV9mlghKJ+gEKBoZ7bzorlYXBA4Q7zKA2bPudfMEtuWPQv8SbkgKZotLJfwTdmKcKIuSGdP03ARbGdMouIRhLkgNJIzfsD40LY2YXd3Kxm8N6Z5VurQXa1sR0rH6fSJjypiBCm2nYnhtfnsj8T+vmWLvuJWJKEkRIj5Z1EslxZiOMqJdoYGjHFjCuBb2VsqvmWYcbZI5G4L3+W/pOaXvHLJvzwsnJxO41giO2SX7BOPHJETckEqpEo4uSeP5Jm8OA/Ok/PqvE1aZ5zpzDb5Aef9C2wNnaw=</latexit>

θ ∼ π 4

<latexit sha1_base64="+JuEG6QFb/uRIZ8CMnqhujp0mDg=">ACAHicbVBNS8NAEN3Ur1q/oh48eAkWwVNJakGPRS8eK9gPaELZbDft0t1N2J0IJeTiX/HiQRGv/gxv/hu3bQ7a+mDg8d4M/PChDMNrvtldbWNza3ytuVnd29/QP78Kij41QR2iYxj1UvxJpyJmkbGHDaSxTFIuS0G05uZ373kSrNYvkA04QGAo8kixjBYKSBfeLDmAL2NRN+pDJ/ITlWSMf2FW35s7hrBKvIFVUoDWwv/xhTFJBJRCOte57bgJBhUwmle8VNE0wmeET7hkosqA6y+QO5c26UoRPFypQEZ67+nsiw0HoqQtMpMIz1sjcT/P6KUTXQcZkgKVZLEoSrkDsTNLwxkyRQnwqSGYKGZudcgYmxzAZFYxIXjL6+STr3mXdbq941q86aIo4xO0Rm6QB6Qk10h1qojQjK0TN6RW/Wk/VivVsfi9aSVcwcoz+wPn8AgXGW/Q=</latexit>

SK

Eν ∼ GeV

<latexit sha1_base64="21sbPXE1xrfVKgoZjQjeoVrV6Iw=">AB/3icbVDLSgNBEJz1GeMrKnjxMhgET2E3CnoMiugxgnlANoTZScZMju7zPSKYc3BX/HiQRGv/oY3/8bJ46CJBQ1FVTfdXUEshUHX/XYWFpeWV1Yza9n1jc2t7dzObtVEieZQ4ZGMdD1gBqRQUEGBEuqxBhYGEmpB/3Lk1+5BGxGpOxzE0AxZV4mO4Ayt1MrtX7VSXyVD34iQ+gPmF5DdjK5d2COwadJ96U5MkU5Vbuy29HPAlBIZfMmIbnxthMmUbBJQyzfmIgZrzPutCwVLEQTDMd3z+kR1Zp06kbSmkY/X3RMpCYwZhYDtDhj0z643E/7xGgp3zZipUnCAoPlnUSTFiI7CoG2hgaMcWMK4FvZWyntM42sqwNwZt9eZ5UiwXvpFC8Pc2XLqZxZMgBOSTHxCNnpERuSJlUCeP5Jm8kjfnyXlx3p2PSeuCM53ZI3/gfP4ASeWRg=</latexit>

P

• νe → νµ/τ
• <latexit sha1_base64="zjHAZMx7AqadKl2LCrLnaF9tok=">ACGHicbVA9SwNBEN3z2/gVtbRZDEJs4p0KWo2lhGMCeRC2NvMJYt7e8furBKO/Awb/4qNhSK2dv4bN/EKjT4YeLw3w8y8KJPCoO9/ejOzc/MLi0vLpZXVtfWN8ubWjUmt5tDgqUx1K2IGpFDQIESWpkGlkQSmtHtxdhv3oE2IlXOMygk7C+ErHgDJ3ULR/UQwkxVkNluzmMQi36A2Rap/d0IoWJPQiR2cLZ75Yrfs2fgP4lQUEqpEC9W/4Ieym3CSjkhnTDvwMOznTKLiEUSm0BjLGb1kf2o4qloDp5JPHRnTPKT0ap9qVQjpRf07kLDFmESuM2E4MNPeWPzPa1uMTzu5UJlFUPx7UWwlxZSOU6I9oYGjHDrCuBbuVsoHTDOLsuSCyGYfvkvuTmsBUe1w6vjytl5EcS2SG7pEoCckLOyCWpkwbh5IE8kRfy6j16z96b9/7dOuMVM9vkF7yPLx2koRA=</latexit>

SNO KamLand

terrestrial 
 source

∆m2 ∼ 7 × 10−5 eV2

<latexit sha1_base64="F24sHeMA47r+GCwMBJqEzrAqog=">ACFnicbVA9SwNBEN3z2/gVtbRZDIKFCXdRiaWohaWC+YBcEvY2k7hk9+7YnRPDkV9h41+xsVDEVuz8N25iCk18MPB4b4aZeUEshUHX/XJmZufmFxaXljMrq2vrG9nNrYqJEs2hzCMZ6VrADEgRQhkFSqjFGpgKJFSD3vnQr96BNiIKb7AfQ0Oxbig6gjO0Uiub9y9AIqOqWaS+EYqWfBQKDPXcZpo/HvgH1Ee4xQqg2axlc25BXcEOk28McmRMa5a2U+/HfFEQYhcMmPqnhtjI2UaBZcwyPiJgZjxHutC3dKQ2dWNdPTWgO5ZpU07kbYVIh2pvydSpozpq8B2Koa3ZtIbiv959Q7J41UhHGCEPKfRZ1EUozoMCPaFho4yr4ljGthb6X8lmnG0SaZsSF4ky9Pk0qx4B0WitdHudOzcRxLZIfskn3ikRI5JZfkipQJw/kibyQV+fReXbenPef1hlnPLN/sD5+AZ3U52z</latexit>

θ ∼ π 6

<latexit sha1_base64="Zt3rH5HPisor20SHBlSjt/1B1dk=">ACAXicbVBNS8NAEN34WetX1IvgZbEInkpSRT0WvXisYD+gCWz3bRLd5OwOxFKiBf/ihcPinj1X3jz37htc9DWBwOP92aYmRckgmtwnG9raXldW29tFHe3Nre2bX39ls6ThVlTRqLWHUCopngEWsCB8E6iWJEBoK1g9HNxG8/MKV5HN3DOG+JIOIh5wSMFLPvRgyIB4mkvshYrQzEt4nl3kPbviVJ0p8CJxC1JBRo9+8vrxzSVLAIqiNZd10nAz4gCTgXLy16qWULoiAxY19CISKb9bPpBjk+M0sdhrExFgKfq74mMSK3HMjCdksBQz3sT8T+vm0J45Wc8SlJgEZ0tClOBIcaTOHCfK0ZBjA0hVHFzK6ZDYnIAE1rZhODOv7xIWrWqe1at3Z1X6tdFHCV0hI7RKXLRJaqjW9RATUTRI3pGr+jNerJerHfrY9a6ZBUzB+gPrM8f3+GXKQ=</latexit>

L ∼ 180 km

<latexit sha1_base64="E+F9md+B1QoMZmb8NmWR9SJGXlY=">AB/nicbVBNS8NAEN34WetXVDx5WSyCBylJFeyx6MWDhwr2A5pQNtNu3Q3CbsTsYSCf8WLB0W8+ju8+W/ctjlo64OBx3szMwLEsE1OM63tbS8srq2Xtgobm5t7+zae/tNHaeKsgaNRazaAdFM8Ig1gINg7UQxIgPBWsHweuK3HpjSPI7uYZQwX5J+xENOCRipax/epL7FYd7wx7wB4hG8px1y45ZWcKvEjcnJRQjnrX/vJ6MU0li4AKonXHdRLwM6KAU8HGRS/VLCF0SPqsY2hEJN+Nj1/jE+M0sNhrExFgKfq74mMSK1HMjCdksBAz3sT8T+vk0JY9TMeJSmwiM4WhanAEONJFrjHFaMgRoYQqri5FdMBUYSCSaxoQnDnX14kzUrZPS9X7i5Ktas8jgI6QsfoFLnoEtXQDaqjBqIoQ8/oFb1ZT9aL9W59zFqXrHzmAP2B9fkD0huUxA=</latexit>

Eνe ∼ O(1) MeV

<latexit sha1_base64="RIdrSx7Ll5Rc9Xq+isFN/usSUvo=">ACHnicbVBSxtBFJ61WjXauq1HL4OhEKGE3ai0x1Ap9CIqmBjIhmV28qKDs7PLzNvSMOwv8eJf8dKDRQRP+m+cTXLQ2A8GPr73vTfvfUkuhcEgePIW3i0uvV9eWa2trX/4uOF/+tw1WaE5dHgmM91LmAEpFHRQoIReroGliYSz5PKgqp/9Bm1Epk5xnMgZedKjARn6KTY3/8Z2yhzjmqAjVRxhbKMjIipVHK8IzaY/KRrgTfY0Q/qA9hG4Z+/WgGUxA35JwRupkhuPYf4iGS9SUMglM6YfBjkOLNMouISyFhUGcsYv2Tn0HVUsBTOwk/NK+sUpQzrKtHsK6UR92WFZasw4TZyz2tjM1yrxf7V+gaPvAytUXiAoPv1oVEiKGa2yokOhgaMcO8K4Fm5Xyi+YZhxdojUXQjh/8lvSbTXD3WbrZK/e/jGLY4VskW3SICH5RtrkFzkmHcLJFbkht+Sfd+39e68+6l1wZv1bJX8B6fAc8fo30=</latexit>

L ∼ 108 km

<latexit sha1_base64="MWfDT6R/sCP7r2phMRTarKVtFbc=">ACAHicbVA9SwNBEN2LXzF+RS0sbBaDYCHhLgqmDNpYWEQwH5A7w95mkyzZvTt258RwXONfsbFQxNafYe/cZNcoYkPBh7vzTAz48E12Db31ZuaXldS2/XtjY3NreKe7uNXUYK8oaNBShavtEM8ED1gAOgrUjxYj0BWv5o6uJ3pgSvMwuINxDxJBgHvc0rASN3iwY2rucSOfZ9U/fUBfYIyUim3WLJLtT4EXiZKSEMtS7xS+3F9JYsgCoIFp3HDsCLyEKOBUsLbixZhGhIzJgHUMDIpn2kukDKT42Sg/3Q2UqADxVf08kRGo9lr7plASGet6biP95nRj6VS/hQRQDC+hsUT8WGEI8SQP3uGIUxNgQhU3t2I6JIpQMJkVTAjO/MuLpFkpO2flyu15qXaZxZFHh+gInSAHXaAaukZ1EAUpegZvaI368l6sd6tj1lrzspm9tEfWJ8/Bm6WDg=</latexit>

1711.00588 Kim, Lasserre, Wang

Double Chooz

P (νe → νe)

<latexit sha1_base64="9ruWs20DpXmD9b2HhCXGh3VzfM=">ACJnicdVDLSgMxFM34tr6qLt0MFkE3ZUYF3QhFNy4r2Ad0hpJ7TBTDIkd5Qy9Gvc+CtuXCgi7vwUM20XPg8EDuecm+SeKBXcoOe9OzOzc/MLi0vLpZXVtfWN8uZW06hM2gwJZRuR9SA4BIayFAO9VAk0hAK7q5KPzWLWjDlbzGYQphQvuSx5xRtFK3fFYPBMS4HyibKi7JA5mNujmMAs37A6Raq7v/zINueJVvTHc38SfkgqZot4tPwc9xbIEJDJBjen4XophTjVyJmBUCjIDKWU3tA8dSyVNwIT5eM2Ru2eVnhsrbY9Ed6x+nchpYswiWwyoTgwP71C/MvrZBifhjmXaYg2eShOBMuKrfozO1xDQzF0BLKNLd/dmAasrQNluyJfg/V/5NmodV/6h6eHVcqZ1P61giO2SX7BOfnJAauSR10iCM3JNH8kxenAfnyXl13ibRGWc6s02+wfn4BHrYqD4=</latexit>

L ∼ km

<latexit sha1_base64="QlWIB9g8BtMfp9nkTDmsdFRTjcw=">AB+HicbVA9SwNBEN3zM8aPnFraLAbBKtxFQcugjYVFBPMBuSPsbTbJkt29Y3dOjEd+iY2FIrb+FDv/jZvkCk18MPB4b4aZeVEiuAHP+3ZWVtfWNzYLW8Xtnd29krt/0DRxqilr0FjEuh0RwRXrAEcBGsnmhEZCdaKRtdTv/XAtOGxuodxwkJBor3OSVgpa5bug0MlzgA9gjZSE6btmreDPgZeLnpIxy1LvuV9CLaSqZAiqIMR3fSyDMiAZOBZsUg9SwhNARGbCOpYpIZsJsdvgEn1ilh/uxtqUAz9TfExmRxoxlZDslgaFZ9Kbif14nhf5lmHGVpMAUnS/qpwJDjKcp4B7XjIYW0Ko5vZWTIdEwo2q6INwV98eZk0qxX/rFK9Oy/XrvI4CugIHaNT5KMLVEM3qI4aiKIUPaNX9OY8OS/Ou/Mxb1x8plD9AfO5w/xmpNH</latexit>

Eνe ∼ O(1) MeV

<latexit sha1_base64="RIdrSx7Ll5Rc9Xq+isFN/usSUvo=">ACHnicbVBSxtBFJ61WjXauq1HL4OhEKGE3ai0x1Ap9CIqmBjIhmV28qKDs7PLzNvSMOwv8eJf8dKDRQRP+m+cTXLQ2A8GPr73vTfvfUkuhcEgePIW3i0uvV9eWa2trX/4uOF/+tw1WaE5dHgmM91LmAEpFHRQoIReroGliYSz5PKgqp/9Bm1Epk5xnMgZedKjARn6KTY3/8Z2yhzjmqAjVRxhbKMjIipVHK8IzaY/KRrgTfY0Q/qA9hG4Z+/WgGUxA35JwRupkhuPYf4iGS9SUMglM6YfBjkOLNMouISyFhUGcsYv2Tn0HVUsBTOwk/NK+sUpQzrKtHsK6UR92WFZasw4TZyz2tjM1yrxf7V+gaPvAytUXiAoPv1oVEiKGa2yokOhgaMcO8K4Fm5Xyi+YZhxdojUXQjh/8lvSbTXD3WbrZK/e/jGLY4VskW3SICH5RtrkFzkmHcLJFbkht+Sfd+39e68+6l1wZv1bJX8B6fAc8fo30=</latexit>

θ ∼ π 20

<latexit sha1_base64="/pTNyQCTc4sp0js5EW6C/uBPYxU=">ACAnicbVBNS8NAEN3Ur1q/op7Ey2IRPJWkCnosevFYwX5AE8pmu2mX7iZhdyKUELz4V7x4UMSrv8Kb/8Ztm4O2Ph4vDfDzLwgEVyD43xbpZXVtfWN8mZla3tnd8/eP2jrOFWUtWgsYtUNiGaCR6wFHATrJoRGQjWCcY3U7/zwJTmcXQPk4T5kgwjHnJKwEh9+8iDEQPiaS6xFypCMy/heVZ38r5dWrODHiZuAWpogLNv3lDWKaShYBFUTrnusk4GdEAaeC5RUv1SwhdEyGrGdoRCTfjZ7IcenRhngMFamIsAz9fdERqTWExmYTklgpBe9qfif10shvPIzHiUpsIjOF4WpwBDjaR54wBWjICaGEKq4uRXTETFBgEmtYkJwF19eJu16zT2v1e8uqo3rIo4yOkYn6Ay56BI10C1qohai6BE9o1f0Zj1ZL9a79TFvLVnFzCH6A+vzB1EGl18=</latexit>

1711.00588

Accelerator

295km

(Tokai) JAERI Super Kamiokande KEK Tokyo

T2K

L ∼ 735 km

<latexit sha1_base64="32xkMZr78eSsg2wGevTQZ2R2ZE=">AB/XicbVDJSgNBEO2JW4zbuNy8NAbBg4SZRInHoBcPHiKYBTJD6Ol0kibdM0N3jRiH4K948aCIV/Dm39jZzlo4oOCx3tVNULYsE1OM63lVlaXldy67nNja3tnfs3b26jhJFWY1GIlLNgGgmeMhqwEGwZqwYkYFgjWBwNfYb90xpHoV3MIyZL0kv5F1OCRipbR/ceJpLXC6de6cesAdIB3LUtvNOwZkALxJ3RvJohmrb/vI6EU0kC4EKonXLdWLwU6KAU8FGOS/RLCZ0QHqsZWhIJN+Orl+hI+N0sHdSJkKAU/U3xMpkVoPZWA6JYG+nvfG4n9eK4HuhZ/yME6AhXS6qJsIDBEeR4E7XDEKYmgIoYqbWzHtE0UomMByJgR3/uVFUi8W3FKheHuWr1zO4siQ3SETpCLyqiCrlEV1RBFj+gZvaI368l6sd6tj2lrxprN7KM/sD5/AIGBlKA=</latexit>

L ∼ 295 km

<latexit sha1_base64="ZKDgP91HNed8Ud8Vn49FkaTfJKo=">AB/HicbVBNS8NAEN3Ur1q/oj16CRbBg5SkKuqt6MWDhwr2A5pQNtNu3Q3CbsTMYT6V7x4UMSrP8Sb/8Ztm4O2Ph4vDfDzDw/5kyBbX8bhaXldW14npY3Nre8fc3WupKJGENknEI9nxsaKchbQJDjtxJi4XPa9kfXE7/9QKViUXgPaUw9gQchCxjBoKWeWb51FRO1yzP32AX6CNlIjHtmxa7aU1iLxMlJBeVo9Mwvtx+RNAQCMdKdR07Bi/DEhjhdFxyE0VjTEZ4QLuahlhQ5WXT48fWoVb6VhBJXSFYU/X3RIaFUqnwdafAMFTz3kT8z+smEFx4GQvjBGhIZouChFsQWZMkrD6TlABPNcFEMn2rRYZYgI6r5IOwZl/eZG0alXnpFq7O63Ur/I4imgfHaAj5KBzVEc3qIGaiKAUPaNX9GY8GS/Gu/Exay0Y+UwZ/YHx+QMptJR3</latexit>

Eν ∼ O(100) MeV

<latexit sha1_base64="bADgT7iKOwh3+mHht3iFWRvVOvo=">ACEXicbVA9SwNBEN3z2/gVtbRZDEIECXdR0DIogo2oYGIgF8LeZhKX7O0du3NiO4v2PhXbCwUsbWz89+4iSk08cHA470ZuYFsRQGXfLmZqemZ2bX1jMLS2vrK7l1zdqJko0hyqPZKTrATMghYIqCpRQjzWwMJBwE/ROBv7NHWgjInWN/RiaIesq0RGcoZVa+eJpK/VkvlGhNQPGd5yJtOLrOi57q6/5yPcY3oOtayVL7gldwg6SbwRKZARLlv5T78d8SQEhVwyYxqeG2MzZRoFl5Dl/MRAzHiPdaFhqWIhmGY6/CijO1Zp06kbSmkQ/X3RMpCY/phYDsHN5txbyD+5zUS7Bw1U6HiBEHxn0WdRFKM6CAe2hYaOMq+JYxrYW+l/JZpxtGmLMheOMvT5JaueTtl8pXB4XK8SiOBbJFtkmReOSQVMgZuSRVwskDeSIv5NV5dJ6dN+f9p3XKGc1skj9wPr4Bq9yc5w=</latexit>

MINOS NOVA

L ∼ 810 km

<latexit sha1_base64="NafEtgWOZwP7D0/oK1D3WH2AlrY=">AB/XicbVDLSsNAFJ3UV62v+Ni5GSyCylJFey6MaFiwr2AU0pk+mkHTqThJkbsYbir7hxoYhb/8Odf+O0zUJbD1w4nHMv97jx4JrcJxvK7e0vLK6l8vbGxube/Yu3sNHSWKsjqNRKRaPtFM8JDVgYNgrVgxIn3Bmv7wauI375nSPArvYBSzjiT9kAecEjBS1z648TSXuOI63qkH7AHSoRx37aJTcqbAi8TNSBFlqHXtL68X0USyEKgWrdJ4ZOShRwKti4CWaxYQOSZ+1DQ2JZLqTq8f42Oj9HAQKVMh4Kn6eyIlUuR9E2nJDQ895E/M9rJxBUOikP4wRYSGeLgkRgiPAkCtzjilEQI0MIVdzciumAKELBFYwIbjzLy+SRrnknpXKt+fF6mUWRx4doiN0glx0garoGtVQHVH0iJ7RK3qznqwX6936mLXmrGxmH/2B9fkDeCeUmg=</latexit>

Eν ∼ O(1) GeV

<latexit sha1_base64="q3ocSPB0G/ju9oU13NWtLCvkK8=">ACD3icbVDLSgNBEJz1GeMr6tHLYFAiSNhVQY+iN6MYB6QDWF20olDZmeXmV4xLPsHXvwVLx4U8erVm3/jJObgq6ChqOqmuyuIpTDouh/OxOTU9Mxsbi4/v7C4tFxYWa2ZKNEcqjySkW4EzIAUCqoUEIj1sDCQEI96J8M/foNaCMidYWDGFoh6ynRFZyhldqFrdN26qsk840IqR8yvOZMphdZydv2d3yEW0zPoJa1C0W37I5A/xJvTIpkjEq78O53Ip6EoJBLZkzTc2NspUyj4BKyvJ8YiBnvsx40LVUsBNKR/9kdNMqHdqNtC2FdKR+n0hZaMwgDGzn8GLz2xuK/3nNBLuHrVSoOEFQ/GtRN5EUIzoMh3aEBo5yYAnjWthbKb9mnG0EeZtCN7vl/+S2m7Z2yvXu4Xj47HceTIOtkgJeKRA3JEzkmFVAknd+SBPJFn595dF6c16/WCWc8s0Z+wHn7BK6LnG0=</latexit>

0106019

SLIDE 15

Jessica Turner

15

ICECUBE

P (νµ → ντ)

<latexit sha1_base64="MKyVsMKL0YSD6Nco0TR/3w/wSM=">ACE3icbZDLSsNAFIYnXmu9RV26CRahuihJFXRZdOygr1AE8JkOmHTiZh5oxSQt/Bja/ixoUibt2482cXhba+sPAz3fO4cz5o4wzBa7bS0tr6yurRc2iptb2zu79t5+U6VaEtogKU9lO8KciZoAxhw2s4kxUnEaSsaXI/rXsqFUvFHQwzGiS4J1jMCAaDQvu07nMaQ9kXOsz9RI98yXp9wFKmD2PmA9ZTdBLaJbfiTuQsGm9mSmimemh/+d2U6IQKIBwr1fHcDIcS2CE01HR14pmAxwj3aMFTihKsgnN42cY0O6TpxK8wQ4E/p7IseJUsMkMp0Jhr6ar43hf7WOhvgyJnINFBpotizR1InXFATpdJSoAPjcFEMvNXh/SxARMjEUTgjd/8qJpViveWaV6e16qXc3iKBDdITKyEMXqIZuUB01EGP6Bm9ojfryXqx3q2PaeuSNZs5QH9kf4Ah8afMg=</latexit>

∆m2 ∼ 2 × 10−3 eV2

<latexit sha1_base64="xegstYIKwovEjKuTOEKGwre1ias=">ACFnicbVDJSgNBEO1xN25Rj14ag+DBhJmJoEdRDx4jmAUySejpVGJj98zQXSOGIV/hxV/x4kERr+LNv7GzHNweFDzeq6KqXphIYdB1P52Z2bn5hcWl5dzK6tr6Rn5zq2biVHOo8ljGuhEyA1JEUEWBEhqJBqZCfXw5mzk129BGxFHVzhIoKVYPxI9wRlaqZMvBucgkVHV9mlghKJ+gEKBoZ7bzorlYXBA4Q7zKA2bPudfMEtuWPQv8SbkgKZotLJfwTdmKcKIuSGdP03ARbGdMouIRhLkgNJIzfsD40LY2YXd3Kxm8N6Z5VurQXa1sR0rH6fSJjypiBCm2nYnhtfnsj8T+vmWLvuJWJKEkRIj5Z1EslxZiOMqJdoYGjHFjCuBb2VsqvmWYcbZI5G4L3+W/pOaXvHLJvzwsnJxO41giO2SX7BOPHJETckEqpEo4uSeP5Jm8OA/Ok/PqvE1aZ5zpzDb5Aef9C2wNnaw=</latexit>

SK

Eν ∼ GeV

<latexit sha1_base64="21sbPXE1xrfVKgoZjQjeoVrV6Iw=">AB/3icbVDLSgNBEJz1GeMrKnjxMhgET2E3CnoMiugxgnlANoTZScZMju7zPSKYc3BX/HiQRGv/oY3/8bJ46CJBQ1FVTfdXUEshUHX/XYWFpeWV1Yza9n1jc2t7dzObtVEieZQ4ZGMdD1gBqRQUEGBEuqxBhYGEmpB/3Lk1+5BGxGpOxzE0AxZV4mO4Ayt1MrtX7VSXyVD34iQ+gPmF5DdjK5d2COwadJ96U5MkU5Vbuy29HPAlBIZfMmIbnxthMmUbBJQyzfmIgZrzPutCwVLEQTDMd3z+kR1Zp06kbSmkY/X3RMpCYwZhYDtDhj0z643E/7xGgp3zZipUnCAoPlnUSTFiI7CoG2hgaMcWMK4FvZWyntM42sqwNwZt9eZ5UiwXvpFC8Pc2XLqZxZMgBOSTHxCNnpERuSJlUCeP5Jm8kjfnyXlx3p2PSeuCM53ZI3/gfP4ASeWRg=</latexit>

P

• νe → νµ/τ
• <latexit sha1_base64="zjHAZMx7AqadKl2LCrLnaF9tok=">ACGHicbVA9SwNBEN3z2/gVtbRZDEJs4p0KWo2lhGMCeRC2NvMJYt7e8furBKO/Awb/4qNhSK2dv4bN/EKjT4YeLw3w8y8KJPCoO9/ejOzc/MLi0vLpZXVtfWN8ubWjUmt5tDgqUx1K2IGpFDQIESWpkGlkQSmtHtxdhv3oE2IlXOMygk7C+ErHgDJ3ULR/UQwkxVkNluzmMQi36A2Rap/d0IoWJPQiR2cLZ75Yrfs2fgP4lQUEqpEC9W/4Ieym3CSjkhnTDvwMOznTKLiEUSm0BjLGb1kf2o4qloDp5JPHRnTPKT0ap9qVQjpRf07kLDFmESuM2E4MNPeWPzPa1uMTzu5UJlFUPx7UWwlxZSOU6I9oYGjHDrCuBbuVsoHTDOLsuSCyGYfvkvuTmsBUe1w6vjytl5EcS2SG7pEoCckLOyCWpkwbh5IE8kRfy6j16z96b9/7dOuMVM9vkF7yPLx2koRA=</latexit>

SNO KamLand

terrestrial 
 source

∆m2 ∼ 7 × 10−5 eV2

<latexit sha1_base64="F24sHeMA47r+GCwMBJqEzrAqog=">ACFnicbVA9SwNBEN3z2/gVtbRZDIKFCXdRiaWohaWC+YBcEvY2k7hk9+7YnRPDkV9h41+xsVDEVuz8N25iCk18MPB4b4aZeUEshUHX/XJmZufmFxaXljMrq2vrG9nNrYqJEs2hzCMZ6VrADEgRQhkFSqjFGpgKJFSD3vnQr96BNiIKb7AfQ0Oxbig6gjO0Uiub9y9AIqOqWaS+EYqWfBQKDPXcZpo/HvgH1Ee4xQqg2axlc25BXcEOk28McmRMa5a2U+/HfFEQYhcMmPqnhtjI2UaBZcwyPiJgZjxHutC3dKQ2dWNdPTWgO5ZpU07kbYVIh2pvydSpozpq8B2Koa3ZtIbiv959Q7J41UhHGCEPKfRZ1EUozoMCPaFho4yr4ljGthb6X8lmnG0SaZsSF4ky9Pk0qx4B0WitdHudOzcRxLZIfskn3ikRI5JZfkipQJw/kibyQV+fReXbenPef1hlnPLN/sD5+AZ3U52z</latexit>

L ∼ 180 km

<latexit sha1_base64="E+F9md+B1QoMZmb8NmWR9SJGXlY=">AB/nicbVBNS8NAEN34WetXVDx5WSyCBylJFeyx6MWDhwr2A5pQNtNu3Q3CbsTsYSCf8WLB0W8+ju8+W/ctjlo64OBx3szMwLEsE1OM63tbS8srq2Xtgobm5t7+zae/tNHaeKsgaNRazaAdFM8Ig1gINg7UQxIgPBWsHweuK3HpjSPI7uYZQwX5J+xENOCRipax/epL7FYd7wx7wB4hG8px1y45ZWcKvEjcnJRQjnrX/vJ6MU0li4AKonXHdRLwM6KAU8HGRS/VLCF0SPqsY2hEJN+Nj1/jE+M0sNhrExFgKfq74mMSK1HMjCdksBAz3sT8T+vk0JY9TMeJSmwiM4WhanAEONJFrjHFaMgRoYQqri5FdMBUYSCSaxoQnDnX14kzUrZPS9X7i5Ktas8jgI6QsfoFLnoEtXQDaqjBqIoQ8/oFb1ZT9aL9W59zFqXrHzmAP2B9fkD0huUxA=</latexit>

Eνe ∼ O(1) MeV

<latexit sha1_base64="RIdrSx7Ll5Rc9Xq+isFN/usSUvo=">ACHnicbVBSxtBFJ61WjXauq1HL4OhEKGE3ai0x1Ap9CIqmBjIhmV28qKDs7PLzNvSMOwv8eJf8dKDRQRP+m+cTXLQ2A8GPr73vTfvfUkuhcEgePIW3i0uvV9eWa2trX/4uOF/+tw1WaE5dHgmM91LmAEpFHRQoIReroGliYSz5PKgqp/9Bm1Epk5xnMgZedKjARn6KTY3/8Z2yhzjmqAjVRxhbKMjIipVHK8IzaY/KRrgTfY0Q/qA9hG4Z+/WgGUxA35JwRupkhuPYf4iGS9SUMglM6YfBjkOLNMouISyFhUGcsYv2Tn0HVUsBTOwk/NK+sUpQzrKtHsK6UR92WFZasw4TZyz2tjM1yrxf7V+gaPvAytUXiAoPv1oVEiKGa2yokOhgaMcO8K4Fm5Xyi+YZhxdojUXQjh/8lvSbTXD3WbrZK/e/jGLY4VskW3SICH5RtrkFzkmHcLJFbkht+Sfd+39e68+6l1wZv1bJX8B6fAc8fo30=</latexit>

L ∼ 108 km

<latexit sha1_base64="MWfDT6R/sCP7r2phMRTarKVtFbc=">ACAHicbVA9SwNBEN2LXzF+RS0sbBaDYCHhLgqmDNpYWEQwH5A7w95mkyzZvTt258RwXONfsbFQxNafYe/cZNcoYkPBh7vzTAz48E12Db31ZuaXldS2/XtjY3NreKe7uNXUYK8oaNBShavtEM8ED1gAOgrUjxYj0BWv5o6uJ3pgSvMwuINxDxJBgHvc0rASN3iwY2rucSOfZ9U/fUBfYIyUim3WLJLtT4EXiZKSEMtS7xS+3F9JYsgCoIFp3HDsCLyEKOBUsLbixZhGhIzJgHUMDIpn2kukDKT42Sg/3Q2UqADxVf08kRGo9lr7plASGet6biP95nRj6VS/hQRQDC+hsUT8WGEI8SQP3uGIUxNgQhU3t2I6JIpQMJkVTAjO/MuLpFkpO2flyu15qXaZxZFHh+gInSAHXaAaukZ1EAUpegZvaI368l6sd6tj1lrzspm9tEfWJ8/Bm6WDg=</latexit>

1711.00588 Kim, Lasserre, Wang

Double Chooz

P (νe → νe)

<latexit sha1_base64="9ruWs20DpXmD9b2HhCXGh3VzfM=">ACJnicdVDLSgMxFM34tr6qLt0MFkE3ZUYF3QhFNy4r2Ad0hpJ7TBTDIkd5Qy9Gvc+CtuXCgi7vwUM20XPg8EDuecm+SeKBXcoOe9OzOzc/MLi0vLpZXVtfWN8uZW06hM2gwJZRuR9SA4BIayFAO9VAk0hAK7q5KPzWLWjDlbzGYQphQvuSx5xRtFK3fFYPBMS4HyibKi7JA5mNujmMAs37A6Raq7v/zINueJVvTHc38SfkgqZot4tPwc9xbIEJDJBjen4XophTjVyJmBUCjIDKWU3tA8dSyVNwIT5eM2Ru2eVnhsrbY9Ed6x+nchpYswiWwyoTgwP71C/MvrZBifhjmXaYg2eShOBMuKrfozO1xDQzF0BLKNLd/dmAasrQNluyJfg/V/5NmodV/6h6eHVcqZ1P61giO2SX7BOfnJAauSR10iCM3JNH8kxenAfnyXl13ibRGWc6s02+wfn4BHrYqD4=</latexit>

L ∼ km

<latexit sha1_base64="QlWIB9g8BtMfp9nkTDmsdFRTjcw=">AB+HicbVA9SwNBEN3zM8aPnFraLAbBKtxFQcugjYVFBPMBuSPsbTbJkt29Y3dOjEd+iY2FIrb+FDv/jZvkCk18MPB4b4aZeVEiuAHP+3ZWVtfWNzYLW8Xtnd29krt/0DRxqilr0FjEuh0RwRXrAEcBGsnmhEZCdaKRtdTv/XAtOGxuodxwkJBor3OSVgpa5bug0MlzgA9gjZSE6btmreDPgZeLnpIxy1LvuV9CLaSqZAiqIMR3fSyDMiAZOBZsUg9SwhNARGbCOpYpIZsJsdvgEn1ilh/uxtqUAz9TfExmRxoxlZDslgaFZ9Kbif14nhf5lmHGVpMAUnS/qpwJDjKcp4B7XjIYW0Ko5vZWTIdEwo2q6INwV98eZk0qxX/rFK9Oy/XrvI4CugIHaNT5KMLVEM3qI4aiKIUPaNX9OY8OS/Ou/Mxb1x8plD9AfO5w/xmpNH</latexit>

Eνe ∼ O(1) MeV

<latexit sha1_base64="RIdrSx7Ll5Rc9Xq+isFN/usSUvo=">ACHnicbVBSxtBFJ61WjXauq1HL4OhEKGE3ai0x1Ap9CIqmBjIhmV28qKDs7PLzNvSMOwv8eJf8dKDRQRP+m+cTXLQ2A8GPr73vTfvfUkuhcEgePIW3i0uvV9eWa2trX/4uOF/+tw1WaE5dHgmM91LmAEpFHRQoIReroGliYSz5PKgqp/9Bm1Epk5xnMgZedKjARn6KTY3/8Z2yhzjmqAjVRxhbKMjIipVHK8IzaY/KRrgTfY0Q/qA9hG4Z+/WgGUxA35JwRupkhuPYf4iGS9SUMglM6YfBjkOLNMouISyFhUGcsYv2Tn0HVUsBTOwk/NK+sUpQzrKtHsK6UR92WFZasw4TZyz2tjM1yrxf7V+gaPvAytUXiAoPv1oVEiKGa2yokOhgaMcO8K4Fm5Xyi+YZhxdojUXQjh/8lvSbTXD3WbrZK/e/jGLY4VskW3SICH5RtrkFzkmHcLJFbkht+Sfd+39e68+6l1wZv1bJX8B6fAc8fo30=</latexit>

1711.00588

Accelerator

P(νµ → να6=µ)

<latexit sha1_base64="Zj8x4xhvqIi7gPemipfU4+gqgVw=">ACE3icbVA9SwNBEN2LXzF+RS1tDoMQLcJdFLQM2lhGMB+QC2Fus5dbsrt37u4p4ch/sPGv2FgoYmtj579xk1yhiQ8GHu/NMDPjxlV2nG+rdzS8srqWn69sLG5tb1T3N1rqiRmDRwxCLZ9kERgVpaKoZaceSAPcZafnDq4nfuidS0Ujc6lFMuhwGgYUgzZSr3hSL3si6aUeT8aepINQg5TRw0wDFofgCXI3cY97xZJTcawF4mbkRLKUO8Vv7x+hBNOhMYMlOq4Tqy7KUhNMSPjgpcoEgMewoB0DBXAieqm05/G9pFR+nYQSVNC21P190QKXKkR90nBx2qeW8i/ud1Eh1cdFMq4kQTgWeLgoTZOrInAdl9KgnWbGQIYEnNrTYOQLWJsaCcGdf3mRNKsV97RSvTkr1S6zOPLoAB2iMnLROaqha1RHDYTRI3pGr+jNerJerHfrY9as7KZfQH1ucPopWfQw=</latexit>

0.3 0.4 0.5 0.6 0.7 2.5 3.0

Normal hierarchy MINOS+ Preliminary MINOS, MINOS+ combined analysis 68% C.L. 90% C.L. 23

θ

2

sin

0.3 0.4 0.5 0.6 0.7

• 3.0
• 2.5

Inverted hierarchy MINOS+ best fit Neutrino 2016 NOvA 90% C.L. Neutrino 2016 T2K 90% C.L.

)

2

eV

• 3

(10

2 32

m Δ

θ23

<latexit sha1_base64="w4NlNBIJN262JDbFXn0bK9MvVQ=">AB8nicbVBNS8NAEN3Ur1q/qh69LBbBU0laQY9FLx4r2A9oQ9lsJ+3STbsToQS+jO8eFDEq7/Gm/GbZuDtj4YeLw3w8y8IJHCoOt+O4WNza3tneJuaW/4PCofHzSNirVHFpcSaW7ATMgRQwtFCihm2hgUSChE0zu5n7nCbQRKn7EaQJ+xEaxCAVnaKVeH8eAbJDV6rNBueJW3QXoOvFyUiE5moPyV3+oeBpBjFwyY3qem6CfMY2CS5iV+qmBhPEJG0HP0phFYPxscfKMXlhlSEOlbcVIF+rviYxFxkyjwHZGDMdm1ZuL/3m9FMbPxNxkiLEfLkoTCVFRef/06HQwFOLWFcC3sr5WOmGUebUsmG4K2+vE7atapXr9YeriqN2zyOIjkj5+SeOSaNMg9aZIW4USRZ/JK3hx0Xpx352PZWnDymVPyB87nDw7pkRo=</latexit>

∆m2 ∼ 10−3 eV2

<latexit sha1_base64="aQ89CtUXf2P1cYb0+wmIOP12c=">ACDXicbVA9SwNBEN3z2/gVtbRZjIKFhrtE0FLUwlLBRCGXhL3NJC7ZvTt258Rw3B+w8a/YWChia2/nv3ETr9Dog4HezPMzAtiKQy67qczMTk1PTM7N19YWFxaXimurtVNlGgONR7JSF8HzIAUIdRQoITrWANTgYSroH8y9K9uQRsRhZc4iKGpWC8UXcEZWqld3PJPQSKjqlWhvhGKem4r3atm/q6PcIcp1LNWpV0suWV3BPqXeDkpkRzn7eKH34l4oiBELpkxDc+NsZkyjYJLyAp+YiBmvM960LA0ZApMx19k9Ftq3RoN9K2QqQj9edEypQxAxXYTsXwxox7Q/E/r5Fg97CZijBOEL+vaibSIoRHUZDO0IDRzmwhHEt7K2U3zDNONoACzYEb/zlv6ReKXvVcuViv3R0nMcxRzbIJtkhHjkgR+SMnJMa4eSePJn8uI8OE/Oq/P23Trh5DPr5Bec9y8vkZpi</latexit>

T2K 2017

δ ∼ 3π 2

<latexit sha1_base64="8QKJKty9rpqw8wMsegEHeOa4i/w=">ACA3icbVBNS8NAEN34WetX1JteFovgqStoMeiF48V7Ac0oWw2m3bpbhJ2J0IJBS/+FS8eFPHqn/Dmv3Hb5qCtDwYe780wMy9IBdfgON/Wyura+sZmau8vbO7t28fHLZ1kinKWjQRieoGRDPBY9YCDoJ1U8WIDATrBKObqd95YErzJL6Hcp8SQYxjzglYKS+feyFTADBnuYSe5EiNK97KZ/ktUnfrjhVZwa8TNyCVFCBZt/+8sKEZpLFQAXRuc6Kfg5UcCpYJOyl2mWEjoiA9YzNCaSaT+f/TDBZ0YJcZQoUzHgmfp7IidS67EMTKckMNSL3lT8z+tlEF35OY/TDFhM54uiTGBI8DQHLFKIixIYQqbm7FdEhMEGBiK5sQ3MWXl0m7VnXr1drdRaVxXcRQifoFJ0jF12iBrpFTdRCFD2iZ/SK3qwn68V6tz7mrStWMXOE/sD6/AGbkpeA</latexit>

θ23 ∼ π

4

<latexit sha1_base64="OcjugtEvY5sKYywALeJ0DHSWl1M=">ACBnicbVDJSgNBEO1xjXEb9ShCYxD0EmYSQY9RQTxGMAtkhtDT6Uma9Cx01whmJMXf8IP8OJBEa9+gzf/wLNfYGc5aOKDgsd7VTV82LBFVjWpzE3v7C4tJxbya+urW9smlvbdRUlkrIajUQkmx5RTPCQ1YCDYM1YMhJ4gjW8/sXQb9wyqXgU3sAgZm5AuiH3OSWgpba50CPAWmnpXLmKB5gx5eEpk7Ms/Q4a5sFq2iNgGeJPSGFypF1+fX9cFZtmx9OJ6JwEKgijVsq0Y3JRI4FSwLO8kisWE9kmXtTQNScCUm47eyPCBVjrYj6SuEPBI/T2RkCpQeDpzoBAT017Q/E/r5WAf+qmPIwTYCEdL/ITgSHCw0xwh0tGQw0IVRyfSumPaJzAJ1cXodgT78S+qlol0ulq7tQuUcjZFDu2gfHSIbnaAKukJVEMU3aFH9IxejHvjyXg13satc8ZkZgf9gfH+Azh3nKk=</latexit>

θ12 ∼ π

6

<latexit sha1_base64="C4RJUDiT06NpoIOY6NvwnvpMpdY=">ACBnicbVDJSgNBEO2JW4zbqEcRGoOglzATQT1GBfEYwSyQGUJPpydp0rPQXSOEYU5e/Ak/wIsHRbz6Dd78A89+gZ3loIkPCh7vVFVz4sFV2BZn0Zubn5hcSm/XFhZXVvfMDe36ipKJGU1GolINj2imOAhqwEHwZqxZCTwBGt4/Yuh37hlUvEovIFBzNyAdEPuc0pAS21z14EeA9JO7XLmKB5gx5eEpk7Ms/Q4a5tFq2SNgGeJPSHFyqF1+fX9cFZtmx9OJ6JwEKgijVsq0Y3JRI4FSwrOAkisWE9kmXtTQNScCUm47eyPC+VjrYj6SuEPBI/T2RkCpQeDpzoBAT017Q/E/r5WAf+qmPIwTYCEdL/ITgSHCw0xwh0tGQw0IVRyfSumPaJzAJ1cQYdgT78S+rlkn1UKl/bxco5GiOPdtAeOkA2OkEVdIWqIYoukOP6Bm9GPfGk/FqvI1bc8ZkZhv9gfH+AzhSnKk=</latexit>

θ13 ∼ π

20

<latexit sha1_base64="Vuvs7nb52lFIycTahxM6k3y0=">ACB3icbVC7SgNBFJ2Nrxhfq5aCDAZBm7CbFpGBbGMYB6QXcLsZDYZMvtg5q4Qlu1s/Ah/wMZCEVt/wc4/sPYLnDwKTxw4XDOvdx7jxcLrsCyPo3cwuLS8kp+tbC2vrG5ZW7vNFSUSMrqNBKRbHlEMcFDVgcOgrViyUjgCdb0Bhcjv3nLpOJReAPDmLkB6YXc5SAljrmvgN9BqST2pXMUTzAji8JTZ2YZ2nZyjpm0SpZY+B5Yk9JsXpsX59P5zVOuaH041oErAQqCBKtW0rBjclEjgVLCs4iWIxoQPSY21NQxIw5abjPzJ8qJUu9iOpKwQ8Vn9PpCRQah4ujMg0Fez3kj8z2sn4J+6KQ/jBFhIJ4v8RGCI8CgU3OWSURBDTQiVXN+KaZ/oIEBHV9Ah2LMvz5NGuWRXSuVru1g9RxPk0R46QEfIRieoiq5QDdURXfoET2jF+PeDJejbdJa86YzuyiPzDefwCsxJzg</latexit>

SLIDE 16

Jessica Turner

16

Other experiments and future ones

Minerva CX measurement incoming charged pion SBND Liquid argon detectors, beam ~ O(1) GeV

• investigate anomalies eV scale steriles
• neutrino argon cross sections

DUNE JUNO Mass ordering and solar mixing CPV, atmospheric mixing, proton decay, mass ordering…. CPV, atmospheric mixing, proton decay, mass ordering….

SLIDE 17

U =   1 c23 s23 −s23 c23     c13 s13e−iδ 1 −s13eiδ c13     c12 s12 −s12 c12 1     1 ei α21

2

ei α31

2

 

If neutrinos are Majorana there are two additional phases: Observation of neutrinoless double beta decay would indicate the nature of the neutrino.

(A, Z) − → (A, Z + 2) + 2e−(∆L = 2)

The half life of rare decay is proportional to effective Majorana mass:

|mee| = |m1 cos2 θ12 cos2 θ13 + m2 sin2 θ12 cos2 θ13eiα21 + m3 sin2 θ13ei(α31−2δ)|

• ()

||()

IH NH QD GERDA, KamLAND-Zen, EXO, CUORICINO

CUORE, KamLAND-Zen2, SNO+, COBRA, NEXT, nEXO, SUPERNEMO, MAJORANA

Wide range of future experiments: positive signal would mean LNV NDBD can probe neutrino mass

• rdering, absolute mass scale and CPV

phases (in principle).

Majorana neutrinos

17

SLIDE 18

Jessica Turner

18

• How are the masses ordered?
• What are the precise values of the 


mixing angles?

• Is leptonic CP maximally violated?
• What is the mass of the lightest neutrino?

cosmology, many groups see

X mν . 0.2 eV

<latexit sha1_base64="UVXGs1kFNmtq/L6NiKjzQGlPBho=">ACDXicbVA9SwNBEN3z2/gVtbRZjIKFhLsoaCnaWEYwMZA7wt5mou7e8funBiO/AEb/4qNhSK29nb+GzfJFWp8MPB4b4aZeXEqhUXf/Kmpmdm5+YXFktLyura+X1jaZNMsOhwROZmFbMLEihoYECJbRSA0zFEq7i27Ohf3UHxopEX2I/hUixay16gjN0Uqe8E9pMUdXJQ50NQgnWqGoX63RcD9EuMcmoNOueJX/RHoJAkKUiEF6p3yZ9hNeKZAI5fM2nbgpxjlzKDgEgalMLOQMn7LrqHtqGYKbJSPvhnQXad0aS8xrjTSkfpzImfK2r6KXadieGP/ekPxP6+dYe84yoVOMwTNx4t6maSY0GE0tCsMcJR9Rxg3wt1K+Q0zjKMLsORCP6+PEmatWpwUK1dHFZOTos4FsgW2SZ7JCBH5ISckzpE4eyBN5Ia/eo/fsvXnv49Ypr5jZJL/gfXwD6i6bcw=</latexit>

PDG

X mν ≤ 1.1 eV

<latexit sha1_base64="woPLE5Mqc9PzMEinYeZtvYVx6PU=">ACHicbVA9SwNBEN3z2/gVtbRwMQgWEu6ioGXQxlLBRCEXwt5mkizZ3Tt358RwpLTxr9hYKGLrT7Dz37j5KDTxwcDjvRlm5kWJFBZ9/9ubmZ2bX1hcWs6trK6tb+Q3t6o2Tg2HCo9lbG4jZkEKDRUKOE2McBUJOEm6p4P/Jt7MFbE+hp7CdQVa2vREpyhkxr53dCmiqpGFuq0H0q4o0ExCA9DhAfMoNpv5At+0R+CTpNgTApkjMtG/itsxjxVoJFLZm0t8BOsZ8yg4BL6uTC1kDeZW2oOaqZAlvPho/06b5TmrQVG1ca6VD9PZExZW1PRa5TMezYSW8g/ufVUmyd1jOhkxRB89GiViopxnSQCm0KAxlzxHGjXC3Ut5hnF02eVcCMHky9OkWioGR8XS1XGhfDaOY4nskD1yQAJyQsrkglySCuHkTyTV/LmPXkv3rv3MWqd8cYz2+QPvM8fGmKZYw=</latexit>

recent measurement by KATRIN

1909.06048

• Are neutrinos Dirac or Majorana fermions?

We do know neutrinos are significantly lighter than other SM fermions

SLIDE 19

Neutrino Masses

• Write a Dirac mass term analogous to other SM fermions

type-I SS type-II SS type-III SS

N νL H νL H H H νL νL ∆ νL H νL H Σ

Minkowski, Yanagida, Glashow, Gell-Mann, Ramond, Slansky, Mohapatra, Senjanovic Ma, Roy, Senjanovic, Hambye

fermionic
 singlet scalar
 triplet fermionic
 triplet

−Ld=5 = λL.HL.H M

<latexit sha1_base64="xnt1PyU6jDkHNbgobOvtM/tgvK0=">ACFnicbVDLSgMxFM3UV62vqks3wSK46TBTFd0Uim6qFDBPqBThkwm04ZmHiQZoYT5Cjf+ihsXirgVd/6N6WOhrQcuHM659yb3eAmjQlrWt5FbWV1b38hvFra2d3b3ivsHbRGnHJMWjlnMux4ShNGItCSVjHQTlDoMdLxRjcTv/NAuKBxdC/HCemHaBDRgGIkteQWy2UnRHKIEVONzFV+9SKDVegwvcFHTsARVg2zDnVl6jZziyXLtKaAy8SekxKYo+kWvxw/xmlIokZEqJnW4nsK8QlxYxkBScVJEF4hAakp2mEQiL6anpWBk+04sMg5roiCafq7wmFQiHGoac7JzeIRW8i/uf1Uhlc9RWNklSCM8eClIGZQwnGUGfcoIlG2uCMKf6rxAPkc5C6iQLOgR78eRl0q6Y9plZuTsv1a7nceTBETgGp8AGl6AG6qAJWgCDR/AMXsGb8WS8GO/Gx6w1Z8xnDsEfGJ8/i3aeWA=</latexit>

Magg, Wetterich, Lazarides, Shafi. Mohapatra, Senjanovic, Schecter, Valle

mν = Y 2

ν v2

MN ∼ 0.1 eV

L = −YνNLH − 1 2N CMNN ✓ 0 mD mT

D

MN ◆

19

SLIDE 20

Neutrino Masses

• Write a Dirac mass term analogous to other SM fermions

type-I SS type-II SS type-III SS

N νL H νL H H H νL νL ∆ νL H νL H Σ

Minkowski, Yanagida, Glashow, Gell-Mann, Ramond, Slansky, Mohapatra, Senjanovic Ma, Roy, Senjanovic, Hambye

fermionic
 singlet scalar
 triplet fermionic
 triplet

−Ld=5 = λL.HL.H M

<latexit sha1_base64="xnt1PyU6jDkHNbgobOvtM/tgvK0=">ACFnicbVDLSgMxFM3UV62vqks3wSK46TBTFd0Uim6qFDBPqBThkwm04ZmHiQZoYT5Cjf+ihsXirgVd/6N6WOhrQcuHM659yb3eAmjQlrWt5FbWV1b38hvFra2d3b3ivsHbRGnHJMWjlnMux4ShNGItCSVjHQTlDoMdLxRjcTv/NAuKBxdC/HCemHaBDRgGIkteQWy2UnRHKIEVONzFV+9SKDVegwvcFHTsARVg2zDnVl6jZziyXLtKaAy8SekxKYo+kWvxw/xmlIokZEqJnW4nsK8QlxYxkBScVJEF4hAakp2mEQiL6anpWBk+04sMg5roiCafq7wmFQiHGoac7JzeIRW8i/uf1Uhlc9RWNklSCM8eClIGZQwnGUGfcoIlG2uCMKf6rxAPkc5C6iQLOgR78eRl0q6Y9plZuTsv1a7nceTBETgGp8AGl6AG6qAJWgCDR/AMXsGb8WS8GO/Gx6w1Z8xnDsEfGJ8/i3aeWA=</latexit>

Magg, Wetterich, Lazarides, Shafi. Mohapatra, Senjanovic, Schecter, Valle

• radiative models
• Extra dimensions

review: 1706.08524 review: 0411194

Babu, Leung, Bhattacharya, Wudka, Gouvea, Jenkins, Kobach, Ma Arkani-Hamed, Dimopoulos, Dvali, March-Russell higher dimensional bulk 4D brane wave functions

20

SLIDE 21

Leptogenesis via Decays

N

Decay asymmetry from interference between tree and loop level diagrams

CP-violation weak sphalerons

Decay Asymmetry

Fukugida, Yanagida

Ni H L Ni H L H L Ni L H L H Nj

Yνi Yνi

Yνj

Covi, Roulet, Vissani

• ccurs at T ~ M

✏i = Γi − Γi Γi + Γi

<latexit sha1_base64="yJFk9BUEuFKo4+dHUb9kdcv1iYk=">ACOnicbVDNS8MwHE39nPOr6tFLcAiCONop6EUYetDjBu4D1jLSLN3CkrYkqTBK/y4v/hXePHjxoIhX/wDTrfix7UHg8d7vJfk9L2JUKst6NhYWl5ZXVgtrxfWNza1tc2e3KcNYNLAIQtF20OSMBqQhqKkXYkCOIeIy1veJ35rXsiJA2DOzWKiMtRP6A+xUhpqWvWHRJyjRNaHrp+ALhxLlBnKMuhSdOqLPZ1T9aCtNf/3iOn3bNklW2xoCzxM5JCeSodc0npxfimJNAYak7NhWpNwECUxI2nRiSWJEB6iPuloGiBOpJuMV0/hoVZ60A+FPoGCY/VvIkFcyhH39CRHaiCnvUyc53Vi5V+4CQ2iWJEATx7yYwZVCLMeY8KghUbaYKwoPqvEA+Qrk/ptou6BHt65VnSrJTt03KlflaqXuV1FMA+OABHwAbnoApuQ0AYP4AW8gXfj0Xg1PozPyeiCkWf2wD8YX9/+qK9Y</latexit>

lepton 
 asymmetry baryon 
 asymmetry

Calculation does not usually include finite density temperature effects

B-L conserving

21

SLIDE 22

Basic Mechanism

Washout and Scattering processes

L H N L H N L H† N L H t Q

inverse Decays ΔL=2 ΔL=1

Parameters of theory Kinetic Equations

Yν

<latexit sha1_base64="ixoxAGvyXYmzonWhDh9pJ6KYTUg=">AB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8cK9kPaUDbTbt0swm7E6GE/gvHhTx6u/x5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmltfWNzq7xd2dnd2z+oHh61TZxqxlslrHuBtRwKRvoUDJu4nmNAok7wST29zvPHFtRKwecJpwP6IjJULBKFqp8zjI+iqdDao1t+7OQVaJV5AaFGgOql/9YczSiCtkhrT89wE/YxqFEzyWaWfGp5QNqEj3rNU0YgbP5ufOyNnVhmSMNa2FJK5+nsio5Ex0yiwnRHFsVn2cvE/r5dieO1nQiUpcsUWi8JUEoxJ/jsZCs0ZyqklGlhbyVsTDVlaBOq2BC85ZdXSfui7rl17/6y1rgp4ijDCZzCOXhwBQ24gya0gMEnuEV3pzEeXHenY9Fa8kpZo7hD5zPH4iYj68=</latexit><latexit sha1_base64="ixoxAGvyXYmzonWhDh9pJ6KYTUg=">AB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8cK9kPaUDbTbt0swm7E6GE/gvHhTx6u/x5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmltfWNzq7xd2dnd2z+oHh61TZxqxlslrHuBtRwKRvoUDJu4nmNAok7wST29zvPHFtRKwecJpwP6IjJULBKFqp8zjI+iqdDao1t+7OQVaJV5AaFGgOql/9YczSiCtkhrT89wE/YxqFEzyWaWfGp5QNqEj3rNU0YgbP5ufOyNnVhmSMNa2FJK5+nsio5Ex0yiwnRHFsVn2cvE/r5dieO1nQiUpcsUWi8JUEoxJ/jsZCs0ZyqklGlhbyVsTDVlaBOq2BC85ZdXSfui7rl17/6y1rgp4ijDCZzCOXhwBQ24gya0gMEnuEV3pzEeXHenY9Fa8kpZo7hD5zPH4iYj68=</latexit><latexit sha1_base64="ixoxAGvyXYmzonWhDh9pJ6KYTUg=">AB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8cK9kPaUDbTbt0swm7E6GE/gvHhTx6u/x5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmltfWNzq7xd2dnd2z+oHh61TZxqxlslrHuBtRwKRvoUDJu4nmNAok7wST29zvPHFtRKwecJpwP6IjJULBKFqp8zjI+iqdDao1t+7OQVaJV5AaFGgOql/9YczSiCtkhrT89wE/YxqFEzyWaWfGp5QNqEj3rNU0YgbP5ufOyNnVhmSMNa2FJK5+nsio5Ex0yiwnRHFsVn2cvE/r5dieO1nQiUpcsUWi8JUEoxJ/jsZCs0ZyqklGlhbyVsTDVlaBOq2BC85ZdXSfui7rl17/6y1rgp4ijDCZzCOXhwBQ24gya0gMEnuEV3pzEeXHenY9Fa8kpZo7hD5zPH4iYj68=</latexit><latexit sha1_base64="ixoxAGvyXYmzonWhDh9pJ6KYTUg=">AB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8cK9kPaUDbTbt0swm7E6GE/gvHhTx6u/x5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmltfWNzq7xd2dnd2z+oHh61TZxqxlslrHuBtRwKRvoUDJu4nmNAok7wST29zvPHFtRKwecJpwP6IjJULBKFqp8zjI+iqdDao1t+7OQVaJV5AaFGgOql/9YczSiCtkhrT89wE/YxqFEzyWaWfGp5QNqEj3rNU0YgbP5ufOyNnVhmSMNa2FJK5+nsio5Ex0yiwnRHFsVn2cvE/r5dieO1nQiUpcsUWi8JUEoxJ/jsZCs0ZyqklGlhbyVsTDVlaBOq2BC85ZdXSfui7rl17/6y1rgp4ijDCZzCOXhwBQ24gya0gMEnuEV3pzEeXHenY9Fa8kpZo7hD5zPH4iYj68=</latexit>

dnNi dz = − Di(nNi − neq

Ni),

dnB−L dz =

3

X

i=1

⇣ ✏(i)Di(nNi − neq

Ni) − WinB−L

⌘ .

<latexit sha1_base64="9URGgYgDjncd2qzcUB6lrdHjk0=">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</latexit>

source sink

ηB

<latexit sha1_base64="DW5/tEzLdEphA6uQL4K5ZM/xw2A=">AB7XicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMdSLx4r2FpoQ9lsN+3azSbsToQS+h+8eFDEq/Hm/GbZuDtj4YeLw3w8y8IJHCoOt+O4W19Y3NreJ2aWd3b/+gfHjUNnGqGW+xWMa6E1DpVC8hQIl7ySa0yiQ/CEY38z8hyeujYjVPU4S7kd0qEQoGEUrtXscab/RL1fcqjsHWSVeTiqQo9kvf/UGMUsjrpBJakzXcxP0M6pRMmnpV5qeELZmA51JFI278bH7tlJxZUDCWNtSObq74mMRsZMosB2RhRHZtmbif953RTDaz8TKkmRK7ZYFKaSYExmr5OB0JyhnFhCmRb2VsJGVFOGNqCSDcFbfnmVtGtV76Jau7us1Bt5HEU4gVM4Bw+uoA630IQWMHiEZ3iFNyd2Xpx352PRWnDymWP4A+fzB0ukjvE=</latexit>

22

SLIDE 23

5 7 9 11 μeγ ℓγ μeqq 102 104 106 108 1010 1012 1014 T [GeV]

• Λ
• λ
• λ

current future

LFV 0νββ

EW scale LHC reach

23

~1014 GeV ~50 GeV ~107 GeV ~105 GeV ~ 0.1 GeV ~ eV

Leptogenesis via

• scillations

Resonant Leptogenesis Minimal Leptogenesis Flavour effects can lower the scale

• small neutrino masses ⟺ BAU
• minimal: 2RHN
• neutrino data, NDBD, LFV and LNV, cosmology

in meson decays, collider searches

• small neutrino masses ⟺ BAU
• minimal: 2RHN
• Easily embedded in GUT

models

• falsifiable
• Can induce the EW scale
• Scale too high can exacerbate
• Higgs fine tuning
• RHNs too heavy to produce

Akmedov, Rubakov, Smirnov, Hernandez, Kekic, Lopez-Pavon, Racker, Salvado, Drewes,Garbcreht, Klaric, Gueter

Pilaftsis, Underwood, Millington, Teresi

image taken from 1609.09069 (Drewes, Garbrecht, Klaric, Gueter)

0.5 1 5 10 50 10-13 10-11 10-9 10-7 10-5 M [GeV] U

2

SHiP FCC-ee(W) F C C

• e

e ( B ) N A 6 2 Belle II LHC T2K BAU (upper bound) BAU (lower bound) disfavoured by global constraints

image taken from 1503.04825 (Deppisch, Harz, Hirsch,Huang, Pas)

23

SLIDE 24

Half time summary

• Neutrinos masses are much smaller than other SM fermions
• Neutrinos could be their own anti-particles
• This possibility opens up the possibility neutrino masses may be

connected to the BAU.

• This seems to hint they may acquire their mass in a completely

different way from other fermions.

• We will consider the plausibility of a rather exotic neutrino mass

model….

SLIDE 25

25

Neutrino Masses from gravity

Dvali & Funcke (1602.03191) Logic: make an analogue of gravity with QCD At energies below ΛQCD ∼ 300 MeV

<latexit sha1_base64="rSaYsxOtELyKtby7ujO0CuZ2M=">ACE3icbVC7SgNBFJ2N7/iKWtoMBkFEwq4KWgZjYaGgYKQDWF29q4ZMvtg5q4Ylv0HG3/FxkIRWxs7/8bJo9DEAwOHc87lzj1eIoVG2/62ClPTM7Nz8wvFxaXldXS2npDx6niUOexjNWtxzRIEUEdBUq4TRSw0JNw43Vrf/mHpQWcXSNvQRaIbuLRCA4QyO1S7vuQn7rJ25CA+YXdVO85y6WoT0wLapuzeUL6CRt0tlu2IPQCeJMyJlMsJlu/Tl+jFPQ4iQS6Z107ETbGVMoeAS8qKbakgY7I7aBoasRB0KxvclNto/g0iJV5EdKB+nsiY6HWvdAzyZBhR497fE/r5licNzKRJSkCBEfLgpSTGm/YKoLxRwlD1DGFfC/JXyDlOMo6mxaEpwxk+eJI39inNQ2b86LFdPRnXMk02yRXaIQ45IlZyRS1InDySZ/JK3qwn68V6tz6G0YI1mtkgf2B9/gDPBp15</latexit>

quarks confine into hadrons u, d, s are light relative to c, b and t so approximate flavour symmetry Once confinement occurs, relevant d.o.f baryons and mesons hqqi

<latexit sha1_base64="VI2KPRBLsatplJgs8wt0Co7zSnM=">ACBnicbVDNS8MwHE3n15xfVY8iBIfgabRT0OPQi8cJ7gPWMtIs3cLSpEtSYZSdvPivePGgiFf/Bm/+N6ZdD7r5IPB47/2S/F4QM6q043xbpZXVtfWN8mZla3tnd8/eP2grkUhMWlgwIbsBUoRTlqaka6sSQoChjpBObzO8EKmo4Pd6GhM/QkNOQ4qRNlLfPvY4kNGoCdMLslncwm0JO52rerTs3JAZeJW5AqKNDs21/eQOAkIlxjhpTquU6s/RJTEjs4qXKBIjPEZD0jOUo4goP83XmMFTowxgKQ5XMNc/T2RokipaRSYZIT0SC16mfif10t0eOWnlMeJhzPHwoTBrWAWSdwQCXBmk0NQVhS81eIR0girE1zFVOCu7jyMmnXa+5rX53UW1cF3WUwRE4AWfABZegAW5BE7QABo/gGbyCN+vJerHerY95tGQVM4fgD6zPH8LGmU8=</latexit>

Ground state break symmetry

U(3)A × U(3)V → U(3)V

<latexit sha1_base64="0vVWBltTFLWBsfmUp4lzau/2kaY=">ACFHicbVDLSgMxFM3UV62vUZdugkWoCGWmFXRZdeOygn1AOwyZNG1DM5MhuaOUoR/hxl9x40IRty7c+TemD0FbDwROzrmXe+8JYsE1OM6XlVlaXldy67nNja3tnfs3b26lomirEalkKoZEM0Ej1gNOAjWjBUjYSBYIxhcjf3GHVOay+gWhjHzQtKLeJdTAkby7ZNaoXzspxcj3AYeMo0n/zpuK97rA1FK3uMfzbfzTtGZAC8Sd0byaIaqb3+2O5ImIYuACqJ1y3Vi8FKigFPBRrl2olM6ID0WMvQiJgFvHRy1AgfGaWDu1KZFwGeqL87UhJqPQwDUxkS6Ot5byz+57US6J57KY/iBFhEp4O6icAg8Tgh3OGKURBDQwhV3OyKaZ8oQsHkmDMhuPMnL5J6qeiWi6Wb03zlchZHFh2gQ1RALjpDFXSNqiGKHpAT+gFvVqP1rP1Zr1PSzPWrGcf/YH18Q0+jJvN</latexit>

U(3)A × U(3)V

<latexit sha1_base64="ERCRGxN9GjrJwMcayEpWXYH0zWI=">ACAHicbVDLSsNAFJ34rPUVdeHCzWAR6qYkraDLqhuXFUxbaEOYTCft0MmDmRuhG78FTcuFHrZ7jzb5ymWjrgYFz7mXO/f4ieAKLOvbWFldW9/YLG2Vt3d29/bNg8O2ilNJmUNjEcuTxQTPGIOcBCsm0hGQl+wj+nfmdRyYVj6MHmCTMDckw4gGnBLTkmcdOtXHuZdT3AceMoXzuo09s2LVrBx4mdgFqaACLc/86g9imoYsAiqIUj3bSsDNiAROBZuW+6liCaFjMmQ9TSOil7lZfsAUn2lgINY6hcBztXfExkJlZqEvu4MCYzUojcT/N6KQRXbsajJAUW0fmiIBUYjxLAw+4ZBTERBNCJd/xXREJKGgMyvrEOzFk5dJu16zG7X6/UWleVPEUIn6BRVkY0uURPdoRZyEVT9Ixe0ZvxZLwY78bHvHXFKGaO0B8Ynz+NIJRy</latexit>

1(η0) + 8(π, η, K)

<latexit sha1_base64="3GBuJUG+leYWA3vxKOx0/pvKGQ=">ACB3icbVDLSgNBEJz1GeMr6lGQwSAkGMJuFMwx6EXwEsE8ILuG2UlvMmT2wcysEJbcvPgrXjwo4tVf8ObfOEn2oIkFDUVN91dbsSZVKb5bSwtr6yurWc2sptb2zu7ub39pgxjQaFBQx6KtkskcBZAQzHFoR0JIL7LoeUOryZ+6wGEZGFwp0YROD7pB8xjlCgtdXNHVsEGRe7tSDAfivgUVwt2xEoTsXRT7ObyZtmcAi8SKyV5lKLezX3ZvZDGPgSKciJlxzIj5SREKEY5jLN2LCEidEj60NE0ID5IJ5n+McYnWulhLxS6AoWn6u+JhPhSjnxXd/pEDeS8NxH/8zqx8qpOwoIoVhDQ2SIv5liFeBIK7jEBVPGRJoQKpm/FdEAEoUpHl9UhWPMvL5JmpWydlSu35/naZRpHBh2iY1RAFrpANXSN6qiBKHpEz+gVvRlPxovxbnzMWpeMdOYA/YHx+QOHdpcs</latexit>

quark confinement spontaneously breaks symmetry

Broken symmetry contains U(1)A and an SU(3) part which are broken and via Goldstone’s theorem give

SLIDE 26

26

Neutrino Masses from gravity

is heavy relative to the other mesons as its mass gets raised due to non-perturbative QCD effects.

η0

<latexit sha1_base64="V7VPqmo9vBjmQE6fA1FgpJfCRQ=">AB8nicbVDLSgNBEJyNrxhfUY9eBoPgKexGQY9BLx4jmAfsrmF20psMmX0w0yuEJZ/hxYMiXv0ab/6Nk2QPmljQUFR1090VpFJotO1vq7S2vrG5Vd6u7Ozu7R9UD486OskUhzZPZKJ6AdMgRQxtFCihlypgUSChG4xvZ373CZQWSfyAkxT8iA1jEQrO0EiuB8gevVSJCPrVml2356CrxClIjRo9atf3iDhWQxcsm0dh07RT9nCgWXMK14mYaU8TEbgmtozCLQfj4/eUrPjDKgYaJMxUjn6u+JnEVaT6LAdEYMR3rZm4n/eW6G4bWfizjNEGK+WBRmkmJCZ/TgVDAU4MYVwJcyvlI6YR5NSxYTgL+8SjqNunNRb9xf1po3RxlckJOyTlxyBVpkjvSIm3CSUKeySt5s9B6sd6tj0VrySpmjskfWJ8/blaRWQ=</latexit>

π0

<latexit sha1_base64="fqldkpycfYrpmbFIkb5Tpj7C5n0=">ACA3icbVDLSgNBEJz1GeMr6k0vg0HwFHajoMegF48RzAOSGYnvcmQ2QczvWpYFrz4K148KOLVn/Dm3zjZ5KCJBQ1FVf0dLmRFBpt+9taWFxaXlnNreXNza3tgs7u3UdxopDjYcyVE2XaZAigBoKlNCMFDfldBwh5djv3EHSoswuMFRB2f9QPhCc7QSN3CfhvhAbN3kvuBQEiTdiRuEztNu4WiXbIz0HniTEmRTFHtFr7avZDHPgTIJdO65dgRdhKmUHAJab4da4gYH7I+tAwNmA+6k2S7U3pklB71QmUqQJqpvycS5ms98l3T6TMc6FlvLP7ntWL0zjuJCKIYIeCTRV4sKYZ0HAjtCQUc5cgQxpUwf6V8wBTjaGLmxCc2ZPnSb1ck5K5evTYuViGkeOHJBDckwckYq5IpUSY1w8kieySt5s56sF+vd+pi0LljTmT3yB9bnD5GYmL8=</latexit>

π0

<latexit sha1_base64="yeuY+rWbud3iBcz0UpFHcJaKv/M=">AB7nicbVBNSwMxEJ3Ur1q/qh69BIvgqexWQY9FLx4r2A9o15JNs21oNhuSrFCW/gvHhTx6u/x5r8xbfegrQ8GHu/NMDMvVIb63nfqLC2vrG5Vdwu7ezu7R+UD49aJk1ZU2aiER3QmKY4JI1LbeCdZRmJA4Fa4fj25nfmLa8EQ+2IliQUyGkecEukdk/x8yb9sVr+rNgVeJn5MK5Gj0y1+9QULTmElLBTGm63vKBhnRlPBpqVeapgidEyGrOuoJDEzQTY/d4rPnDLAUaJdSYvn6u+JjMTGTOLQdcbEjsyNxP/87qpja6DjEuVWibpYlGUCmwTPsdD7hm1IqJI4Rq7m7FdEQ0odYlVHIh+Msvr5JWrepfVGv3l5X6TR5HEU7gFM7Bhyuowx0oAkUxvAMr/CGFHpB7+hj0VpA+cwx/AH6/AE7EI9/</latexit>

π+

<latexit sha1_base64="x0EiuV86i60GNjn94cwR6rcHgk=">AB7nicbVBNSwMxEJ31s9avqkcvwSIQtmtgh6LXjxWsB/QriWbZtvQbBKSrFCW/gvHhTx6u/x5r8xbfegrQ8GHu/NMDMvUpwZ6/vf3srq2vrGZmGruL2zu7dfOjhsGplqQhtEcqnbETaUM0EblO20pTnESctqLR7dRvPVFtmBQPdqxomOCBYDEj2Dqp1VXsMTuf9Eplv+LPgJZJkJMy5Kj3Sl/dviRpQoUlHBvTCXxlwxrywink2I3NVRhMsID2nFU4ISaMJudO0GnTumjWGpXwqKZ+nsiw4kx4yRynQm2Q7PoTcX/vE5q4+swY0KlgoyXxSnHFmJpr+jPtOUWD52BPN3K2IDLHGxLqEi6EYPHlZdKsVoKLSvX+sly7yeMowDGcwBkEcAU1uIM6NIDACJ7hFd485b14797HvHXFy2eO4A+8zx8zd496</latexit>

π−

<latexit sha1_base64="Jih6+5KE8ZUr0UvWuPiA2fGVFj8=">AB7nicbVBNSwMxEJ31s9avqkcvwSJ4sexWQY9FLx4r2A9o15JNs21oNglJVihLf4QXD4p49fd489+YtnvQ1gcDj/dmJkXKc6M9f1vb2V1bX1js7BV3N7Z3dsvHRw2jUw1oQ0iudTtCBvKmaANynbaUpTiJOW9Hoduq3nqg2TIoHO1Y0TPBAsJgRbJ3U6ir2mJ1PeqWyX/FnQMskyEkZctR7pa9uX5I0ocISjo3pBL6yYa1ZYTSbGbGqowGeEB7TgqcEJNmM3OnaBTp/RLUrYdFM/T2R4cSYcRK5zgTboVn0puJ/Xie18XWYMaFSwWZL4pTjqxE09Rn2lKLB87golm7lZEhlhjYl1CRdCsPjyMmlWK8FpXp/Wa7d5HEU4BhO4AwCuIa3EdGkBgBM/wCm+e8l68d+9j3ri5TNH8Afe5w82gY98</latexit>

K0

<latexit sha1_base64="PmuTFgCzevbtMbq/qa8BA+U+JlU=">AB6nicbVDLSgNBEOyNrxhfUY9eBoPgKexGQY9BL4KXiOYByRpmJ5NkyOzsMtMrhCWf4MWDIl79Im/+jZNkD5pY0FBUdPdFcRSGHTdbye3srq2vpHfLGxt7+zuFfcPGiZKNON1FslItwJquBSK1Gg5K1YcxoGkjeD0fXUbz5xbUSkHnAcz+kAyX6glG0v3to9stltyOwNZJl5GSpCh1i1+dXoRS0KukElqTNtzY/RTqlEwySeFTmJ4TNmIDnjbUkVDbvx0duqEnFilR/qRtqWQzNTfEykNjRmHge0MKQ7NojcV/PaCfYv/VSoOEGu2HxRP5EIzL9m/SE5gzl2BLKtLC3EjakmjK06RsCN7iy8ukUSl7Z+XK3XmpepXFkYcjOIZT8OACqnADNagDgwE8wyu8OdJ5cd6dj3lrzslmDuEPnM8fxViNdQ=</latexit>

K0

<latexit sha1_base64="tr0X1phvWwhldmCKsqj1XYJmqQs=">AB9XicbVDLSgMxFL3js9ZX1aWbYBFclZkq6LoRnBTwT6gnZMmlDM8mQZJQy9D/cuFDErf/izr8x085CWw8EDufcw705QcyZNq7aysrq1vbBa2its7u3v7pYPDpaJIrRBJeqHWBNORO0YZjhtB0riqOA01Ywvsn81iNVmknxYCYx9SM8FCxkBsr9brSmlk2veu5036p7FbcGdAy8XJShz1fumrO5AkiagwhGOtO54bGz/FyjDC6bTYTSNMRnjIe1YKnBEtZ/Orp6iU6sMUCiVfcKgmfo7keJI60kU2MkIm5Fe9DLxP6+TmPDKT5mIE0MFmS8KE46MRFkFaMAUJYZPLMFEMXsrIiOsMDG2qKItwVv8jJpViveaV6f1GuXed1FOAYTuAMPLiEGtxCHRpAQMEzvMKb8+S8O/Ox3x0xckzR/AHzucPp5ySmw=</latexit>

K+

<latexit sha1_base64="+I9N9tUB1RN9WnwEWp3FnUj+1ME=">AB6nicbVDLSgNBEOz1GeMr6tHLYBAEIexGQY9BL4KXiOYByRpmJ5NkyOzsMtMrhCWf4MWDIl79Im/+jZNkD5pY0FBUdPdFcRSGHTdb2dpeWV1bT23kd/c2t7ZLezt102UaMZrLJKRbgbUcCkUr6FAyZux5jQMJG8Ew+uJ3ji2ohIPeAo5n5I+0r0BKNopfvbx9NOoeiW3CnIvEyUoQM1U7hq92NWBJyhUxSY1qeG6OfUo2CST7OtxPDY8qGtM9blioacuOn01PH5NgqXdKLtC2FZKr+nkhpaMwoDGxnSHFg5r2J+J/XSrB36adCxQlyxWaLeokGJHJ36QrNGcoR5ZQpoW9lbAB1ZShTSdvQ/DmX14k9XLJOyuV786LlasjhwcwhGcgAcXUIEbqEINGPThGV7hzZHOi/PufMxal5xs5gD+wPn8Ab3EjXA=</latexit>

K−

<latexit sha1_base64="dEJQ3nRxij/RxnarycyHsk0Vc=">AB6nicbVDLSgNBEOz1GeMr6tHLYBC8GHajoMegF8FLRPOAZA2zk0kyZHZ2mekVwpJP8OJBEa9+kTf/xkmyB0saCiqunuCmIpDLrut7O0vLK6tp7byG9ube/sFvb26yZKNOM1FslINwNquBSK1Cg5M1YcxoGkjeC4fXEbzxbUSkHnAUcz+kfSV6glG0v3t42mnUHRL7hRkXgZKUKGaqfw1e5GLAm5QiapMS3PjdFPqUbBJB/n24nhMWVD2uctSxUNufHT6aljcmyVLulF2pZCMlV/T6Q0NGYUBrYzpDgw895E/M9rJdi79FOh4gS5YrNFvUQSjMjkb9IVmjOUI0so08LeStiAasrQpO3IXjzLy+SernknZXKd+fFylUWRw4O4QhOwIMLqMANVKEGDPrwDK/w5kjnxXl3PmatS042cwB/4Hz+AMDMjXI=</latexit>

η

<latexit sha1_base64="jpVdjwnRsHnjvYQzwTGHXHUPFLk=">AB63icbVBNS8NAEJ34WetX1aOXxSJ4KkV9Fj04rGC/YA2lM120y7d3YTdiVBC/4IXD4p49Q9589+YtDlo64OBx3szMwLYiksu63s7a+sbm1Xdop7+7tHxWjo7bNkoM4y0Wych0A2q5FJq3UKDk3dhwqgLJO8HkLvc7T9xYEelHnMbcV3SkRSgYxVzqc6SDStWtuXOQVeIVpAoFmoPKV38YsURxjUxSa3ueG6OfUoOCST4r9xPLY8omdMR7GdVUceun81tn5DxThiSMTFYayVz9PZFSZe1UBVmnoji2y14u/uf1Egxv/FToOEGu2WJRmEiCEckfJ0NhOEM5zQhlRmS3EjamhjLM4ilnIXjL6+Sdr3mXdbqD1fVxm0RwlO4QwuwINraMA9NKEFDMbwDK/w5ijnxXl3Phata04xcwJ/4Hz+Aowjw=</latexit>

not to scale ;)

(1602.03191)

SLIDE 27

27

Neutrino Masses from gravity

is heavy relative to the other mesons and its mass gets raised due to non-perturbative QCD effects.

η0

<latexit sha1_base64="V7VPqmo9vBjmQE6fA1FgpJfCRQ=">AB8nicbVDLSgNBEJyNrxhfUY9eBoPgKexGQY9BLx4jmAfsrmF20psMmX0w0yuEJZ/hxYMiXv0ab/6Nk2QPmljQUFR1090VpFJotO1vq7S2vrG5Vd6u7Ozu7R9UD486OskUhzZPZKJ6AdMgRQxtFCihlypgUSChG4xvZ373CZQWSfyAkxT8iA1jEQrO0EiuB8gevVSJCPrVml2356CrxClIjRo9atf3iDhWQxcsm0dh07RT9nCgWXMK14mYaU8TEbgmtozCLQfj4/eUrPjDKgYaJMxUjn6u+JnEVaT6LAdEYMR3rZm4n/eW6G4bWfizjNEGK+WBRmkmJCZ/TgVDAU4MYVwJcyvlI6YR5NSxYTgL+8SjqNunNRb9xf1po3RxlckJOyTlxyBVpkjvSIm3CSUKeySt5s9B6sd6tj0VrySpmjskfWJ8/blaRWQ=</latexit>

π0

<latexit sha1_base64="fqldkpycfYrpmbFIkb5Tpj7C5n0=">ACA3icbVDLSgNBEJz1GeMr6k0vg0HwFHajoMegF48RzAOSGYnvcmQ2QczvWpYFrz4K148KOLVn/Dm3zjZ5KCJBQ1FVf0dLmRFBpt+9taWFxaXlnNreXNza3tgs7u3UdxopDjYcyVE2XaZAigBoKlNCMFDfldBwh5djv3EHSoswuMFRB2f9QPhCc7QSN3CfhvhAbN3kvuBQEiTdiRuEztNu4WiXbIz0HniTEmRTFHtFr7avZDHPgTIJdO65dgRdhKmUHAJab4da4gYH7I+tAwNmA+6k2S7U3pklB71QmUqQJqpvycS5ms98l3T6TMc6FlvLP7ntWL0zjuJCKIYIeCTRV4sKYZ0HAjtCQUc5cgQxpUwf6V8wBTjaGLmxCc2ZPnSb1ck5K5evTYuViGkeOHJBDckwckYq5IpUSY1w8kieySt5s56sF+vd+pi0LljTmT3yB9bnD5GYmL8=</latexit>

π0

<latexit sha1_base64="yeuY+rWbud3iBcz0UpFHcJaKv/M=">AB7nicbVBNSwMxEJ3Ur1q/qh69BIvgqexWQY9FLx4r2A9o15JNs21oNhuSrFCW/gvHhTx6u/x5r8xbfegrQ8GHu/NMDMvVIb63nfqLC2vrG5Vdwu7ezu7R+UD49aJk1ZU2aiER3QmKY4JI1LbeCdZRmJA4Fa4fj25nfmLa8EQ+2IliQUyGkecEukdk/x8yb9sVr+rNgVeJn5MK5Gj0y1+9QULTmElLBTGm63vKBhnRlPBpqVeapgidEyGrOuoJDEzQTY/d4rPnDLAUaJdSYvn6u+JjMTGTOLQdcbEjsyNxP/87qpja6DjEuVWibpYlGUCmwTPsdD7hm1IqJI4Rq7m7FdEQ0odYlVHIh+Msvr5JWrepfVGv3l5X6TR5HEU7gFM7Bhyuowx0oAkUxvAMr/CGFHpB7+hj0VpA+cwx/AH6/AE7EI9/</latexit>

π+

<latexit sha1_base64="x0EiuV86i60GNjn94cwR6rcHgk=">AB7nicbVBNSwMxEJ31s9avqkcvwSIQtmtgh6LXjxWsB/QriWbZtvQbBKSrFCW/gvHhTx6u/x5r8xbfegrQ8GHu/NMDMvUpwZ6/vf3srq2vrGZmGruL2zu7dfOjhsGplqQhtEcqnbETaUM0EblO20pTnESctqLR7dRvPVFtmBQPdqxomOCBYDEj2Dqp1VXsMTuf9Eplv+LPgJZJkJMy5Kj3Sl/dviRpQoUlHBvTCXxlwxrywink2I3NVRhMsID2nFU4ISaMJudO0GnTumjWGpXwqKZ+nsiw4kx4yRynQm2Q7PoTcX/vE5q4+swY0KlgoyXxSnHFmJpr+jPtOUWD52BPN3K2IDLHGxLqEi6EYPHlZdKsVoKLSvX+sly7yeMowDGcwBkEcAU1uIM6NIDACJ7hFd485b14797HvHXFy2eO4A+8zx8zd496</latexit>

π−

<latexit sha1_base64="Jih6+5KE8ZUr0UvWuPiA2fGVFj8=">AB7nicbVBNSwMxEJ31s9avqkcvwSJ4sexWQY9FLx4r2A9o15JNs21oNglJVihLf4QXD4p49fd489+YtnvQ1gcDj/dmJkXKc6M9f1vb2V1bX1js7BV3N7Z3dsvHRw2jUw1oQ0iudTtCBvKmaANynbaUpTiJOW9Hoduq3nqg2TIoHO1Y0TPBAsJgRbJ3U6ir2mJ1PeqWyX/FnQMskyEkZctR7pa9uX5I0ocISjo3pBL6yYa1ZYTSbGbGqowGeEB7TgqcEJNmM3OnaBTp/RLUrYdFM/T2R4cSYcRK5zgTboVn0puJ/Xie18XWYMaFSwWZL4pTjqxE09Rn2lKLB87golm7lZEhlhjYl1CRdCsPjyMmlWK8FpXp/Wa7d5HEU4BhO4AwCuIa3EdGkBgBM/wCm+e8l68d+9j3ri5TNH8Afe5w82gY98</latexit>

K0

<latexit sha1_base64="PmuTFgCzevbtMbq/qa8BA+U+JlU=">AB6nicbVDLSgNBEOyNrxhfUY9eBoPgKexGQY9BL4KXiOYByRpmJ5NkyOzsMtMrhCWf4MWDIl79Im/+jZNkD5pY0FBUdPdFcRSGHTdbye3srq2vpHfLGxt7+zuFfcPGiZKNON1FslItwJquBSK1Gg5K1YcxoGkjeD0fXUbz5xbUSkHnAcz+kAyX6glG0v3to9stltyOwNZJl5GSpCh1i1+dXoRS0KukElqTNtzY/RTqlEwySeFTmJ4TNmIDnjbUkVDbvx0duqEnFilR/qRtqWQzNTfEykNjRmHge0MKQ7NojcV/PaCfYv/VSoOEGu2HxRP5EIzL9m/SE5gzl2BLKtLC3EjakmjK06RsCN7iy8ukUSl7Z+XK3XmpepXFkYcjOIZT8OACqnADNagDgwE8wyu8OdJ5cd6dj3lrzslmDuEPnM8fxViNdQ=</latexit>

K0

<latexit sha1_base64="tr0X1phvWwhldmCKsqj1XYJmqQs=">AB9XicbVDLSgMxFL3js9ZX1aWbYBFclZkq6LoRnBTwT6gnZMmlDM8mQZJQy9D/cuFDErf/izr8x085CWw8EDufcw705QcyZNq7aysrq1vbBa2its7u3v7pYPDpaJIrRBJeqHWBNORO0YZjhtB0riqOA01Ywvsn81iNVmknxYCYx9SM8FCxkBsr9brSmlk2veu5036p7FbcGdAy8XJShz1fumrO5AkiagwhGOtO54bGz/FyjDC6bTYTSNMRnjIe1YKnBEtZ/Orp6iU6sMUCiVfcKgmfo7keJI60kU2MkIm5Fe9DLxP6+TmPDKT5mIE0MFmS8KE46MRFkFaMAUJYZPLMFEMXsrIiOsMDG2qKItwVv8jJpViveaV6f1GuXed1FOAYTuAMPLiEGtxCHRpAQMEzvMKb8+S8O/Ox3x0xckzR/AHzucPp5ySmw=</latexit>

K+

<latexit sha1_base64="+I9N9tUB1RN9WnwEWp3FnUj+1ME=">AB6nicbVDLSgNBEOz1GeMr6tHLYBAEIexGQY9BL4KXiOYByRpmJ5NkyOzsMtMrhCWf4MWDIl79Im/+jZNkD5pY0FBUdPdFcRSGHTdb2dpeWV1bT23kd/c2t7ZLezt102UaMZrLJKRbgbUcCkUr6FAyZux5jQMJG8Ew+uJ3ji2ohIPeAo5n5I+0r0BKNopfvbx9NOoeiW3CnIvEyUoQM1U7hq92NWBJyhUxSY1qeG6OfUo2CST7OtxPDY8qGtM9blioacuOn01PH5NgqXdKLtC2FZKr+nkhpaMwoDGxnSHFg5r2J+J/XSrB36adCxQlyxWaLeokGJHJ36QrNGcoR5ZQpoW9lbAB1ZShTSdvQ/DmX14k9XLJOyuV786LlasjhwcwhGcgAcXUIEbqEINGPThGV7hzZHOi/PufMxal5xs5gD+wPn8Ab3EjXA=</latexit>

K−

<latexit sha1_base64="dEJQ3nRxij/RxnarycyHsk0Vc=">AB6nicbVDLSgNBEOz1GeMr6tHLYBC8GHajoMegF8FLRPOAZA2zk0kyZHZ2mekVwpJP8OJBEa9+kTf/xkmyB0saCiqunuCmIpDLrut7O0vLK6tp7byG9ube/sFvb26yZKNOM1FslINwNquBSK1Cg5M1YcxoGkjeC4fXEbzxbUSkHnAUcz+kfSV6glG0v3t42mnUHRL7hRkXgZKUKGaqfw1e5GLAm5QiapMS3PjdFPqUbBJB/n24nhMWVD2uctSxUNufHT6aljcmyVLulF2pZCMlV/T6Q0NGYUBrYzpDgw895E/M9rJdi79FOh4gS5YrNFvUQSjMjkb9IVmjOUI0so08LeStiAasrQpO3IXjzLy+SernknZXKd+fFylUWRw4O4QhOwIMLqMANVKEGDPrwDK/w5kjnxXl3PmatS042cwB/4Hz+AMDMjXI=</latexit>

η

<latexit sha1_base64="jpVdjwnRsHnjvYQzwTGHXHUPFLk=">AB63icbVBNS8NAEJ34WetX1aOXxSJ4KkV9Fj04rGC/YA2lM120y7d3YTdiVBC/4IXD4p49Q9589+YtDlo64OBx3szMwLYiksu63s7a+sbm1Xdop7+7tHxWjo7bNkoM4y0Wych0A2q5FJq3UKDk3dhwqgLJO8HkLvc7T9xYEelHnMbcV3SkRSgYxVzqc6SDStWtuXOQVeIVpAoFmoPKV38YsURxjUxSa3ueG6OfUoOCST4r9xPLY8omdMR7GdVUceun81tn5DxThiSMTFYayVz9PZFSZe1UBVmnoji2y14u/uf1Egxv/FToOEGu2WJRmEiCEckfJ0NhOEM5zQhlRmS3EjamhjLM4ilnIXjL6+Sdr3mXdbqD1fVxm0RwlO4QwuwINraMA9NKEFDMbwDK/w5ijnxXl3Phata04xcwJ/4Hz+Aowjw=</latexit>

not to scale ;)

η0

<latexit sha1_base64="V7VPqmo9vBjmQE6fA1FgpJfCRQ=">AB8nicbVDLSgNBEJyNrxhfUY9eBoPgKexGQY9BLx4jmAfsrmF20psMmX0w0yuEJZ/hxYMiXv0ab/6Nk2QPmljQUFR1090VpFJotO1vq7S2vrG5Vd6u7Ozu7R9UD486OskUhzZPZKJ6AdMgRQxtFCihlypgUSChG4xvZ373CZQWSfyAkxT8iA1jEQrO0EiuB8gevVSJCPrVml2356CrxClIjRo9atf3iDhWQxcsm0dh07RT9nCgWXMK14mYaU8TEbgmtozCLQfj4/eUrPjDKgYaJMxUjn6u+JnEVaT6LAdEYMR3rZm4n/eW6G4bWfizjNEGK+WBRmkmJCZ/TgVDAU4MYVwJcyvlI6YR5NSxYTgL+8SjqNunNRb9xf1po3RxlckJOyTlxyBVpkjvSIm3CSUKeySt5s9B6sd6tj0VrySpmjskfWJ8/blaRWQ=</latexit>

(1602.03191)

∼ 548 MeV

<latexit sha1_base64="yxGl4gGFhaKy45eoNd4rVXsBV/s=">AB/XicbVDJSgNBEO2JWxy3uNy8NAbBg4QZF8xFDHrxIkQwMZAJoadTMY09C901YhyCvyKIB0W8+gnevYh/YyfxoNEHBY/3qiq58dSaHScTyszNj4xOZWdtmdm5+YXcotLVR0likOFRzJSNZ9pkCKECgqUIsVsMCXcO5fHvX98ytQWkThGXZjaATsIhRtwRkaqZlb8bQI6O5O0dv0EK4xPYFqr5nLOwVnAPqXuN8kf/Bm78f3H3a5mXv3WhFPAgiRS6Z13XVibKRMoeASeraXaIgZv2QXUDc0ZAHoRjq4vkfXjdKi7UiZCpEO1J8TKQu07ga+6QwYdvSo1xf/8+oJtouNVIRxghDy4aJ2IilGtB8FbQkFHGXEMaVMLdS3mGKcTSB2SYEd/Tlv6S6VXC3C1unbr50SIbIklWyRjaIS/ZIiRyTMqkQTm7IHXkT9at9WA9Wy/D1oz1PbNMfsF6/QK6rZfE</latexit>

∼ 958 MeV

<latexit sha1_base64="8sBjOYeCeE6dTIpDuLt/NoL4bws=">AB/XicbVDLSgNBEJyNr7i+4uPmZTAIHiTsKmI8iEvXoQIJgayIcxOmZw9sFMrxiX4K8I4kERr36Cdy/i3zhJPGi0oKGo6qa7y4+l0Og4n1ZmbHxicio7bc/Mzs0v5BaXqjpKFIcKj2Skaj7TIEUIFRQoRYrYIEv4dy/POr751egtIjCM+zG0AjYRSjagjM0UjO34mkR0L2dorfpIVxjegLVXjOXdwrOAPQvcb9J/uDN3o/vP+xyM/futSKeBAil0zruvE2EiZQsEl9Gwv0RAzfskuoG5oyALQjXRwfY+uG6VF25EyFSIdqD8nUhZo3Q180xkw7OhRry/+59UTbBcbqQjBCHkw0XtRFKMaD8K2hIKOMquIYwrYW6lvMU42gCs0I7ujLf0l1q+BuF7ZO3XzpkAyRJatkjWwQl+ySEjkmZVIhnNyQO/JInqxb68F6tl6GrRnre2aZ/IL1+gXChpfJ</latexit>

∼ 495 MeV

<latexit sha1_base64="gb01+nu3XT0fFG3Co0yUzU8MCqk=">AB/XicbVDJSgNBEO2J+7jF5ealMQgeJMy4oB5E0YsXIYJZIBNCT6eSNPYsdNeIcQj+iAeFPHqJ3j3Iv6NncSDGh8UPN6roqeH0uh0XE+rczI6Nj4xOSUPT0zOzefXVgs6ShRHIo8kpGq+EyDFCEUaCESqyABb6Esn950vPLV6C0iMIL7MRQC1grFE3BGRqpnl32tAjo9v6Ot+EhXGN6BqVuPZtz8k4fdJi43yR3+GYfxPcfdqGefcaEU8CJFLpnXVdWKspUyh4BK6tpdoiBm/ZC2oGhqyAHQt7V/fpWtGadBmpEyFSPvqz4mUBVp3At90Bgzb+q/XE/zqgk292qpCOMEIeSDRc1EUoxoLwraEAo4yo4hjCthbqW8zRTjaAKzTQju35eHSWkz727lN8/d3NExGWCSrJBVsk5cskuOyCkpkCLh5IbckUfyZN1aD9az9TJozVjfM0vkF6zXL7xAl8U=</latexit>

∼ 135 MeV

<latexit sha1_base64="AHTaHS3Y2QomDm+pRwABpCckXc=">AB/XicbVDJSgNBEO1xd9zicvPSGAQPEmYSRC+i6MWLoGAWyITQ06kTXoWumvEOAR/RAPinj1E7x7Ef/GTuJBEx8UPN6roqeH0uh0XG+rInJqemZ2bl5e2FxaXkls7pW0lGiOBR5JCNV8ZkGKUIokAJlVgBC3wJZb9z2vfL16C0iMIr7MZQC1grFE3BGRqpntnwtAioW9jzdj2EG0zPodSrZ7JOzhmAjhP3h2SP3u3D+OHTvqhnPrxGxJMAQuSaV1nRhrKVMouISe7SUaYsY7rAVQ0MWgK6lg+t7dNsoDdqMlKkQ6UD9PZGyQOtu4JvOgGFbj3p98T+vmDzoJaKME4Qj5c1EwkxYj2o6ANoYCj7BrCuBLmVsrbTDGOJjDbhOCOvjxOSvmcW8jlL93s8QkZYo5ski2yQ1yT47JGbkgRcLJLbknT+TZurMerRfrdg6Yf3MrJM/sN6+Aa4kl7w=</latexit>

SLIDE 28

28

Neutrino Masses from gravity

is heavy relative to the other mesons and its mass gets raised due to non-perturbative QCD effects.

η0

<latexit sha1_base64="V7VPqmo9vBjmQE6fA1FgpJfCRQ=">AB8nicbVDLSgNBEJyNrxhfUY9eBoPgKexGQY9BLx4jmAfsrmF20psMmX0w0yuEJZ/hxYMiXv0ab/6Nk2QPmljQUFR1090VpFJotO1vq7S2vrG5Vd6u7Ozu7R9UD486OskUhzZPZKJ6AdMgRQxtFCihlypgUSChG4xvZ373CZQWSfyAkxT8iA1jEQrO0EiuB8gevVSJCPrVml2356CrxClIjRo9atf3iDhWQxcsm0dh07RT9nCgWXMK14mYaU8TEbgmtozCLQfj4/eUrPjDKgYaJMxUjn6u+JnEVaT6LAdEYMR3rZm4n/eW6G4bWfizjNEGK+WBRmkmJCZ/TgVDAU4MYVwJcyvlI6YR5NSxYTgL+8SjqNunNRb9xf1po3RxlckJOyTlxyBVpkjvSIm3CSUKeySt5s9B6sd6tj0VrySpmjskfWJ8/blaRWQ=</latexit>

π0

<latexit sha1_base64="fqldkpycfYrpmbFIkb5Tpj7C5n0=">ACA3icbVDLSgNBEJz1GeMr6k0vg0HwFHajoMegF48RzAOSGYnvcmQ2QczvWpYFrz4K148KOLVn/Dm3zjZ5KCJBQ1FVf0dLmRFBpt+9taWFxaXlnNreXNza3tgs7u3UdxopDjYcyVE2XaZAigBoKlNCMFDfldBwh5djv3EHSoswuMFRB2f9QPhCc7QSN3CfhvhAbN3kvuBQEiTdiRuEztNu4WiXbIz0HniTEmRTFHtFr7avZDHPgTIJdO65dgRdhKmUHAJab4da4gYH7I+tAwNmA+6k2S7U3pklB71QmUqQJqpvycS5ms98l3T6TMc6FlvLP7ntWL0zjuJCKIYIeCTRV4sKYZ0HAjtCQUc5cgQxpUwf6V8wBTjaGLmxCc2ZPnSb1ck5K5evTYuViGkeOHJBDckwckYq5IpUSY1w8kieySt5s56sF+vd+pi0LljTmT3yB9bnD5GYmL8=</latexit>

π0

<latexit sha1_base64="yeuY+rWbud3iBcz0UpFHcJaKv/M=">AB7nicbVBNSwMxEJ3Ur1q/qh69BIvgqexWQY9FLx4r2A9o15JNs21oNhuSrFCW/gvHhTx6u/x5r8xbfegrQ8GHu/NMDMvVIb63nfqLC2vrG5Vdwu7ezu7R+UD49aJk1ZU2aiER3QmKY4JI1LbeCdZRmJA4Fa4fj25nfmLa8EQ+2IliQUyGkecEukdk/x8yb9sVr+rNgVeJn5MK5Gj0y1+9QULTmElLBTGm63vKBhnRlPBpqVeapgidEyGrOuoJDEzQTY/d4rPnDLAUaJdSYvn6u+JjMTGTOLQdcbEjsyNxP/87qpja6DjEuVWibpYlGUCmwTPsdD7hm1IqJI4Rq7m7FdEQ0odYlVHIh+Msvr5JWrepfVGv3l5X6TR5HEU7gFM7Bhyuowx0oAkUxvAMr/CGFHpB7+hj0VpA+cwx/AH6/AE7EI9/</latexit>

π+

<latexit sha1_base64="x0EiuV86i60GNjn94cwR6rcHgk=">AB7nicbVBNSwMxEJ31s9avqkcvwSIQtmtgh6LXjxWsB/QriWbZtvQbBKSrFCW/gvHhTx6u/x5r8xbfegrQ8GHu/NMDMvUpwZ6/vf3srq2vrGZmGruL2zu7dfOjhsGplqQhtEcqnbETaUM0EblO20pTnESctqLR7dRvPVFtmBQPdqxomOCBYDEj2Dqp1VXsMTuf9Eplv+LPgJZJkJMy5Kj3Sl/dviRpQoUlHBvTCXxlwxrywink2I3NVRhMsID2nFU4ISaMJudO0GnTumjWGpXwqKZ+nsiw4kx4yRynQm2Q7PoTcX/vE5q4+swY0KlgoyXxSnHFmJpr+jPtOUWD52BPN3K2IDLHGxLqEi6EYPHlZdKsVoKLSvX+sly7yeMowDGcwBkEcAU1uIM6NIDACJ7hFd485b14797HvHXFy2eO4A+8zx8zd496</latexit>

π−

<latexit sha1_base64="Jih6+5KE8ZUr0UvWuPiA2fGVFj8=">AB7nicbVBNSwMxEJ31s9avqkcvwSJ4sexWQY9FLx4r2A9o15JNs21oNglJVihLf4QXD4p49fd489+YtnvQ1gcDj/dmJkXKc6M9f1vb2V1bX1js7BV3N7Z3dsvHRw2jUw1oQ0iudTtCBvKmaANynbaUpTiJOW9Hoduq3nqg2TIoHO1Y0TPBAsJgRbJ3U6ir2mJ1PeqWyX/FnQMskyEkZctR7pa9uX5I0ocISjo3pBL6yYa1ZYTSbGbGqowGeEB7TgqcEJNmM3OnaBTp/RLUrYdFM/T2R4cSYcRK5zgTboVn0puJ/Xie18XWYMaFSwWZL4pTjqxE09Rn2lKLB87golm7lZEhlhjYl1CRdCsPjyMmlWK8FpXp/Wa7d5HEU4BhO4AwCuIa3EdGkBgBM/wCm+e8l68d+9j3ri5TNH8Afe5w82gY98</latexit>

K0

<latexit sha1_base64="PmuTFgCzevbtMbq/qa8BA+U+JlU=">AB6nicbVDLSgNBEOyNrxhfUY9eBoPgKexGQY9BL4KXiOYByRpmJ5NkyOzsMtMrhCWf4MWDIl79Im/+jZNkD5pY0FBUdPdFcRSGHTdbye3srq2vpHfLGxt7+zuFfcPGiZKNON1FslItwJquBSK1Gg5K1YcxoGkjeD0fXUbz5xbUSkHnAcz+kAyX6glG0v3to9stltyOwNZJl5GSpCh1i1+dXoRS0KukElqTNtzY/RTqlEwySeFTmJ4TNmIDnjbUkVDbvx0duqEnFilR/qRtqWQzNTfEykNjRmHge0MKQ7NojcV/PaCfYv/VSoOEGu2HxRP5EIzL9m/SE5gzl2BLKtLC3EjakmjK06RsCN7iy8ukUSl7Z+XK3XmpepXFkYcjOIZT8OACqnADNagDgwE8wyu8OdJ5cd6dj3lrzslmDuEPnM8fxViNdQ=</latexit>

K0

<latexit sha1_base64="tr0X1phvWwhldmCKsqj1XYJmqQs=">AB9XicbVDLSgMxFL3js9ZX1aWbYBFclZkq6LoRnBTwT6gnZMmlDM8mQZJQy9D/cuFDErf/izr8x085CWw8EDufcw705QcyZNq7aysrq1vbBa2its7u3v7pYPDpaJIrRBJeqHWBNORO0YZjhtB0riqOA01Ywvsn81iNVmknxYCYx9SM8FCxkBsr9brSmlk2veu5036p7FbcGdAy8XJShz1fumrO5AkiagwhGOtO54bGz/FyjDC6bTYTSNMRnjIe1YKnBEtZ/Orp6iU6sMUCiVfcKgmfo7keJI60kU2MkIm5Fe9DLxP6+TmPDKT5mIE0MFmS8KE46MRFkFaMAUJYZPLMFEMXsrIiOsMDG2qKItwVv8jJpViveaV6f1GuXed1FOAYTuAMPLiEGtxCHRpAQMEzvMKb8+S8O/Ox3x0xckzR/AHzucPp5ySmw=</latexit>

K+

<latexit sha1_base64="+I9N9tUB1RN9WnwEWp3FnUj+1ME=">AB6nicbVDLSgNBEOz1GeMr6tHLYBAEIexGQY9BL4KXiOYByRpmJ5NkyOzsMtMrhCWf4MWDIl79Im/+jZNkD5pY0FBUdPdFcRSGHTdb2dpeWV1bT23kd/c2t7ZLezt102UaMZrLJKRbgbUcCkUr6FAyZux5jQMJG8Ew+uJ3ji2ohIPeAo5n5I+0r0BKNopfvbx9NOoeiW3CnIvEyUoQM1U7hq92NWBJyhUxSY1qeG6OfUo2CST7OtxPDY8qGtM9blioacuOn01PH5NgqXdKLtC2FZKr+nkhpaMwoDGxnSHFg5r2J+J/XSrB36adCxQlyxWaLeokGJHJ36QrNGcoR5ZQpoW9lbAB1ZShTSdvQ/DmX14k9XLJOyuV786LlasjhwcwhGcgAcXUIEbqEINGPThGV7hzZHOi/PufMxal5xs5gD+wPn8Ab3EjXA=</latexit>

K−

<latexit sha1_base64="dEJQ3nRxij/RxnarycyHsk0Vc=">AB6nicbVDLSgNBEOz1GeMr6tHLYBC8GHajoMegF8FLRPOAZA2zk0kyZHZ2mekVwpJP8OJBEa9+kTf/xkmyB0saCiqunuCmIpDLrut7O0vLK6tp7byG9ube/sFvb26yZKNOM1FslINwNquBSK1Cg5M1YcxoGkjeC4fXEbzxbUSkHnAUcz+kfSV6glG0v3t42mnUHRL7hRkXgZKUKGaqfw1e5GLAm5QiapMS3PjdFPqUbBJB/n24nhMWVD2uctSxUNufHT6aljcmyVLulF2pZCMlV/T6Q0NGYUBrYzpDgw895E/M9rJdi79FOh4gS5YrNFvUQSjMjkb9IVmjOUI0so08LeStiAasrQpO3IXjzLy+SernknZXKd+fFylUWRw4O4QhOwIMLqMANVKEGDPrwDK/w5kjnxXl3PmatS042cwB/4Hz+AMDMjXI=</latexit>

η

<latexit sha1_base64="jpVdjwnRsHnjvYQzwTGHXHUPFLk=">AB63icbVBNS8NAEJ34WetX1aOXxSJ4KkV9Fj04rGC/YA2lM120y7d3YTdiVBC/4IXD4p49Q9589+YtDlo64OBx3szMwLYiksu63s7a+sbm1Xdop7+7tHxWjo7bNkoM4y0Wych0A2q5FJq3UKDk3dhwqgLJO8HkLvc7T9xYEelHnMbcV3SkRSgYxVzqc6SDStWtuXOQVeIVpAoFmoPKV38YsURxjUxSa3ueG6OfUoOCST4r9xPLY8omdMR7GdVUceun81tn5DxThiSMTFYayVz9PZFSZe1UBVmnoji2y14u/uf1Egxv/FToOEGu2WJRmEiCEckfJ0NhOEM5zQhlRmS3EjamhjLM4ilnIXjL6+Sdr3mXdbqD1fVxm0RwlO4QwuwINraMA9NKEFDMbwDK/w5ijnxXl3Phata04xcwJ/4Hz+Aowjw=</latexit>

not to scale ;)

η0

<latexit sha1_base64="V7VPqmo9vBjmQE6fA1FgpJfCRQ=">AB8nicbVDLSgNBEJyNrxhfUY9eBoPgKexGQY9BLx4jmAfsrmF20psMmX0w0yuEJZ/hxYMiXv0ab/6Nk2QPmljQUFR1090VpFJotO1vq7S2vrG5Vd6u7Ozu7R9UD486OskUhzZPZKJ6AdMgRQxtFCihlypgUSChG4xvZ373CZQWSfyAkxT8iA1jEQrO0EiuB8gevVSJCPrVml2356CrxClIjRo9atf3iDhWQxcsm0dh07RT9nCgWXMK14mYaU8TEbgmtozCLQfj4/eUrPjDKgYaJMxUjn6u+JnEVaT6LAdEYMR3rZm4n/eW6G4bWfizjNEGK+WBRmkmJCZ/TgVDAU4MYVwJcyvlI6YR5NSxYTgL+8SjqNunNRb9xf1po3RxlckJOyTlxyBVpkjvSIm3CSUKeySt5s9B6sd6tj0VrySpmjskfWJ8/blaRWQ=</latexit>

QCD instantons (semi- classical solution)

t' Hooft 1976

(1602.03191)

1/NC effects

Witten 1979 Veneziano 1979

SLIDE 29

29

Neutrino Masses from gravity

is heavy relative to the other mesons and its mass gets raised due to non-perturbative QCD effects.

η0

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π0

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π0

<latexit sha1_base64="yeuY+rWbud3iBcz0UpFHcJaKv/M=">AB7nicbVBNSwMxEJ3Ur1q/qh69BIvgqexWQY9FLx4r2A9o15JNs21oNhuSrFCW/gvHhTx6u/x5r8xbfegrQ8GHu/NMDMvVIb63nfqLC2vrG5Vdwu7ezu7R+UD49aJk1ZU2aiER3QmKY4JI1LbeCdZRmJA4Fa4fj25nfmLa8EQ+2IliQUyGkecEukdk/x8yb9sVr+rNgVeJn5MK5Gj0y1+9QULTmElLBTGm63vKBhnRlPBpqVeapgidEyGrOuoJDEzQTY/d4rPnDLAUaJdSYvn6u+JjMTGTOLQdcbEjsyNxP/87qpja6DjEuVWibpYlGUCmwTPsdD7hm1IqJI4Rq7m7FdEQ0odYlVHIh+Msvr5JWrepfVGv3l5X6TR5HEU7gFM7Bhyuowx0oAkUxvAMr/CGFHpB7+hj0VpA+cwx/AH6/AE7EI9/</latexit>

π+

<latexit sha1_base64="x0EiuV86i60GNjn94cwR6rcHgk=">AB7nicbVBNSwMxEJ31s9avqkcvwSIQtmtgh6LXjxWsB/QriWbZtvQbBKSrFCW/gvHhTx6u/x5r8xbfegrQ8GHu/NMDMvUpwZ6/vf3srq2vrGZmGruL2zu7dfOjhsGplqQhtEcqnbETaUM0EblO20pTnESctqLR7dRvPVFtmBQPdqxomOCBYDEj2Dqp1VXsMTuf9Eplv+LPgJZJkJMy5Kj3Sl/dviRpQoUlHBvTCXxlwxrywink2I3NVRhMsID2nFU4ISaMJudO0GnTumjWGpXwqKZ+nsiw4kx4yRynQm2Q7PoTcX/vE5q4+swY0KlgoyXxSnHFmJpr+jPtOUWD52BPN3K2IDLHGxLqEi6EYPHlZdKsVoKLSvX+sly7yeMowDGcwBkEcAU1uIM6NIDACJ7hFd485b14797HvHXFy2eO4A+8zx8zd496</latexit>

π−

<latexit sha1_base64="Jih6+5KE8ZUr0UvWuPiA2fGVFj8=">AB7nicbVBNSwMxEJ31s9avqkcvwSJ4sexWQY9FLx4r2A9o15JNs21oNglJVihLf4QXD4p49fd489+YtnvQ1gcDj/dmJkXKc6M9f1vb2V1bX1js7BV3N7Z3dsvHRw2jUw1oQ0iudTtCBvKmaANynbaUpTiJOW9Hoduq3nqg2TIoHO1Y0TPBAsJgRbJ3U6ir2mJ1PeqWyX/FnQMskyEkZctR7pa9uX5I0ocISjo3pBL6yYa1ZYTSbGbGqowGeEB7TgqcEJNmM3OnaBTp/RLUrYdFM/T2R4cSYcRK5zgTboVn0puJ/Xie18XWYMaFSwWZL4pTjqxE09Rn2lKLB87golm7lZEhlhjYl1CRdCsPjyMmlWK8FpXp/Wa7d5HEU4BhO4AwCuIa3EdGkBgBM/wCm+e8l68d+9j3ri5TNH8Afe5w82gY98</latexit>

K0

<latexit sha1_base64="PmuTFgCzevbtMbq/qa8BA+U+JlU=">AB6nicbVDLSgNBEOyNrxhfUY9eBoPgKexGQY9BL4KXiOYByRpmJ5NkyOzsMtMrhCWf4MWDIl79Im/+jZNkD5pY0FBUdPdFcRSGHTdbye3srq2vpHfLGxt7+zuFfcPGiZKNON1FslItwJquBSK1Gg5K1YcxoGkjeD0fXUbz5xbUSkHnAcz+kAyX6glG0v3to9stltyOwNZJl5GSpCh1i1+dXoRS0KukElqTNtzY/RTqlEwySeFTmJ4TNmIDnjbUkVDbvx0duqEnFilR/qRtqWQzNTfEykNjRmHge0MKQ7NojcV/PaCfYv/VSoOEGu2HxRP5EIzL9m/SE5gzl2BLKtLC3EjakmjK06RsCN7iy8ukUSl7Z+XK3XmpepXFkYcjOIZT8OACqnADNagDgwE8wyu8OdJ5cd6dj3lrzslmDuEPnM8fxViNdQ=</latexit>

K0

<latexit sha1_base64="tr0X1phvWwhldmCKsqj1XYJmqQs=">AB9XicbVDLSgMxFL3js9ZX1aWbYBFclZkq6LoRnBTwT6gnZMmlDM8mQZJQy9D/cuFDErf/izr8x085CWw8EDufcw705QcyZNq7aysrq1vbBa2its7u3v7pYPDpaJIrRBJeqHWBNORO0YZjhtB0riqOA01Ywvsn81iNVmknxYCYx9SM8FCxkBsr9brSmlk2veu5036p7FbcGdAy8XJShz1fumrO5AkiagwhGOtO54bGz/FyjDC6bTYTSNMRnjIe1YKnBEtZ/Orp6iU6sMUCiVfcKgmfo7keJI60kU2MkIm5Fe9DLxP6+TmPDKT5mIE0MFmS8KE46MRFkFaMAUJYZPLMFEMXsrIiOsMDG2qKItwVv8jJpViveaV6f1GuXed1FOAYTuAMPLiEGtxCHRpAQMEzvMKb8+S8O/Ox3x0xckzR/AHzucPp5ySmw=</latexit>

K+

<latexit sha1_base64="+I9N9tUB1RN9WnwEWp3FnUj+1ME=">AB6nicbVDLSgNBEOz1GeMr6tHLYBAEIexGQY9BL4KXiOYByRpmJ5NkyOzsMtMrhCWf4MWDIl79Im/+jZNkD5pY0FBUdPdFcRSGHTdb2dpeWV1bT23kd/c2t7ZLezt102UaMZrLJKRbgbUcCkUr6FAyZux5jQMJG8Ew+uJ3ji2ohIPeAo5n5I+0r0BKNopfvbx9NOoeiW3CnIvEyUoQM1U7hq92NWBJyhUxSY1qeG6OfUo2CST7OtxPDY8qGtM9blioacuOn01PH5NgqXdKLtC2FZKr+nkhpaMwoDGxnSHFg5r2J+J/XSrB36adCxQlyxWaLeokGJHJ36QrNGcoR5ZQpoW9lbAB1ZShTSdvQ/DmX14k9XLJOyuV786LlasjhwcwhGcgAcXUIEbqEINGPThGV7hzZHOi/PufMxal5xs5gD+wPn8Ab3EjXA=</latexit>

K−

<latexit sha1_base64="dEJQ3nRxij/RxnarycyHsk0Vc=">AB6nicbVDLSgNBEOz1GeMr6tHLYBC8GHajoMegF8FLRPOAZA2zk0kyZHZ2mekVwpJP8OJBEa9+kTf/xkmyB0saCiqunuCmIpDLrut7O0vLK6tp7byG9ube/sFvb26yZKNOM1FslINwNquBSK1Cg5M1YcxoGkjeC4fXEbzxbUSkHnAUcz+kfSV6glG0v3t42mnUHRL7hRkXgZKUKGaqfw1e5GLAm5QiapMS3PjdFPqUbBJB/n24nhMWVD2uctSxUNufHT6aljcmyVLulF2pZCMlV/T6Q0NGYUBrYzpDgw895E/M9rJdi79FOh4gS5YrNFvUQSjMjkb9IVmjOUI0so08LeStiAasrQpO3IXjzLy+SernknZXKd+fFylUWRw4O4QhOwIMLqMANVKEGDPrwDK/w5kjnxXl3PmatS042cwB/4Hz+AMDMjXI=</latexit>

η

<latexit sha1_base64="jpVdjwnRsHnjvYQzwTGHXHUPFLk=">AB63icbVBNS8NAEJ34WetX1aOXxSJ4KkV9Fj04rGC/YA2lM120y7d3YTdiVBC/4IXD4p49Q9589+YtDlo64OBx3szMwLYiksu63s7a+sbm1Xdop7+7tHxWjo7bNkoM4y0Wych0A2q5FJq3UKDk3dhwqgLJO8HkLvc7T9xYEelHnMbcV3SkRSgYxVzqc6SDStWtuXOQVeIVpAoFmoPKV38YsURxjUxSa3ueG6OfUoOCST4r9xPLY8omdMR7GdVUceun81tn5DxThiSMTFYayVz9PZFSZe1UBVmnoji2y14u/uf1Egxv/FToOEGu2WJRmEiCEckfJ0NhOEM5zQhlRmS3EjamhjLM4ilnIXjL6+Sdr3mXdbqD1fVxm0RwlO4QwuwINraMA9NKEFDMbwDK/w5ijnxXl3Phata04xcwJ/4Hz+Aowjw=</latexit>

not to scale ;)

η0

<latexit sha1_base64="V7VPqmo9vBjmQE6fA1FgpJfCRQ=">AB8nicbVDLSgNBEJyNrxhfUY9eBoPgKexGQY9BLx4jmAfsrmF20psMmX0w0yuEJZ/hxYMiXv0ab/6Nk2QPmljQUFR1090VpFJotO1vq7S2vrG5Vd6u7Ozu7R9UD486OskUhzZPZKJ6AdMgRQxtFCihlypgUSChG4xvZ373CZQWSfyAkxT8iA1jEQrO0EiuB8gevVSJCPrVml2356CrxClIjRo9atf3iDhWQxcsm0dh07RT9nCgWXMK14mYaU8TEbgmtozCLQfj4/eUrPjDKgYaJMxUjn6u+JnEVaT6LAdEYMR3rZm4n/eW6G4bWfizjNEGK+WBRmkmJCZ/TgVDAU4MYVwJcyvlI6YR5NSxYTgL+8SjqNunNRb9xf1po3RxlckJOyTlxyBVpkjvSIm3CSUKeySt5s9B6sd6tj0VrySpmjskfWJ8/blaRWQ=</latexit>

QCD instantons (semi- classical solution) 1/NC effects

t' Hooft 1976 Witten 1979 Veneziano 1979

L ⊃ θ ˜ GG

<latexit sha1_base64="7gZDVw3KMKrAiLw9Z0wvT8saA5o=">AC3icbVA9SwNBEN2LXzF+RS1tFoNgFe6ioGXQIhYWEcwH5ELY20ySJXsf7M4J4Uhv41+xsVDE1j9g579xL7lCEx8MPN6bYWaeF0mh0ba/rdzK6tr6Rn6zsLW9s7tX3D9o6jBWHBo8lKFqe0yDFAE0UKCEdqSA+Z6Elje+Tv3WAygtwuAeJxF0fTYMxEBwhkbqFY9dn+GIM5ncTl0dRxrQxREgc1HIPiS1a1XLNlewa6TJyMlEiGeq/45fZDHvsQIJdM645jR9hNmELBJUwLbqwhYnzMhtAxNGA+6G4y+2VKT4zSp4NQmQqQztTfEwnztZ74nulML9eLXir+53ViHFx2ExFEMULA54sGsaQY0jQY2hcKOMqJIYwrYW6lfMQU42jiK5gQnMWXl0mzUnbOypW781L1KosjT47IMTklDrkgVXJD6qRBOHkz+SVvFlP1ov1bn3MW3NWNnNI/sD6/AFg5Zvj</latexit>

physical due to
 these NP effects

(1602.03191)

∂µJµ

5 = ˜

GG

<latexit sha1_base64="icEFbcgQqUh7tigtPLWJY0EDmQ=">AC3icbVDLSsNAFJ3UV62vqEs3Q4vgqiRV0Y1QdFxVcE+oIlhMpm0QyeTMDMRSujejb/ixoUibv0Bd/6Nk7YLbT0w+Gce7n3Hj9hVCrL+jYKS8srq2vF9dLG5tb2jrm715ZxKjBp4ZjFousjSRjlpKWoYqSbCIin5GOP7zK/c4DEZLG/E6NEuJGqM9pSDFSWvLMspMgoShinhOl8OZe/94pvIDQUZQFJGuMG5ZsarWBHCR2DNSATM0PfPLCWKcRoQrzJCUPdtKlJvlczAj45KTSpIgPER90tOUo4hIN5vcMoaHWglgGAv9uIT9XdHhiIpR5GvKyOkBnLey8X/vF6qwnM3ozxJFeF4OihMGVQxzIOBARUEKzbSBGFB9a4QD5BAWOn4SjoEe/7kRdKuVe3jau32pFK/nMVRBAegDI6ADc5AHVyDJmgBDB7BM3gFb8aT8WK8Gx/T0oIx69kHf2B8/gCJoU</latexit>

current is not conserved U(1)A is anomalous from NP effects

SLIDE 30

Neutrino Masses from Gravity

Assume gravity has a theta term: LG ⊃ θG ˜

RR

<latexit sha1_base64="Eqw3fFR2EIR2TojxTdMhWMaSkwc=">ACE3icbVC7SgNBFJ2NrxhfUubxSCIRdiNgpZBCy0sYjAPyC7L7OQmGTL7YOauEJb9Bxt/xcZCEVsbO/GyaPQxAMDh3Pu5c45fiy4Qsv6NnJLyura/n1wsbm1vZOcXevqaJEMmiwSESy7VMFgofQI4C2rEGvgCWv7wauy3HkAqHoX3OIrBDWg/5D3OKGrJK54AcUBoyK9zbz0OnNUEitABweAdCIgF1I61ndK5asjWBuUjsGSmRGWpe8cvpRiwJIEQmqFId24rRTalEzgRkBSdREFM2pH3oaBrSAJSbTjJl5pFWumYvkvqFaE7U3xspDZQaBb6eHCdQ895Y/M/rJNi7cFMexglCyKaHeokwMTLHBZldLoGhGlCmeT6ryYbUEkZ6hoLugR7PvIiaVbK9m5cndWql7O6siTA3JIjolNzkmV3JAaRBGHskzeSVvxpPxYrwbH9PRnDHb2Sd/YHz+A4un4U=</latexit>

They postulate neutrinos have zero bare mass. They can condense via NP gravitational effects and use SDA in analogue with QCD: (1602.03191) One massive GB analogous to eta prime and remainder massless

νν = hννi = veiφ = ) ΛG ⇠ v ⇠ mν ⇠ νν

<latexit sha1_base64="E/vG5Fc8sUvR+l9t/VR86ud5o9s=">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</latexit>

Neutrinos acquire mass from their NP coupling to neutrino condensate. small neutrino masses from this gravitational term triggers neutrino condensate and introduces an infrared gravitational scale.

θ

<latexit sha1_base64="XSnmv7Q3htaBkjl1qDUiNLnL28=">AB7XicbZC7SgNBFIZn4y2ut6ilzWAQrMJuLQRgzaWEcwFkiXMTmaTMbMzy8xZISx5BxsLRWwsfBR7G/FtnFwKTfxh4OP/z2HOWEiuAHP+3ZyS8srq2v5dXdjc2t7p7C7Vzcq1ZTVqBJKN0NimOCS1YCDYM1EMxKHgjXCwdU4b9wzbiStzBMWBCTnuQRpwSsVW9DnwHpFIpeyZsIL4I/g+LFh3uevH251U7hs91VNI2ZBCqIMS3fSyDIiAZOBRu57dSwhNAB6bGWRUliZoJsMu0IH1mniyOl7ZOAJ+7vjozExgzj0FbGBPpmPhub/2WtFKzIOMySYFJOv0oSgUGhcer4y7XjIYWiBUczsrpn2iCQV7INcewZ9feRHq5ZJ/UirfeMXKJZoqjw7QITpGPjpFXSNqiGKLpD+gJPTvKeXRenNdpac6Z9eyjP3LefwAE25Jp</latexit>

analogous to 𝝡QCD free parameter Riemann tensor

U(3)V × U(3)A → U(1)3

<latexit sha1_base64="rPv5WT+a5RlP9YK4+rJ/7hlFsU=">ACEHicbVC7TgJBFJ3F+ILtbSZQIwQE7ILhZarNpaYyCNhkcwOA0yYfWTmroZs+AQb45/YWGiMraUdf+OwUCh4knOPefe3LnHDQVXYJoTI7Wyura+kd7MbG3v7O5l9w/qKogkZTUaiEA2XaKY4D6rAQfBmqFkxHMFa7jDq6nfuGdS8cC/hVHI2h7p+7zHKQEtdbIntUKl2InrYwe4xROygtH8v4AiJTBg1as4l2lk82bJTMBXibWnOTtnHP6PLFH1U72+kGNPKYD1QpVqWGUI7JhI4FWycSLFQkKHpM9amvpEb2/HyUFjfKyVLu4FUj8fcKL+noiJp9TIc3WnR2CgFr2p+J/XiqB3o65H0bAfDpb1IsEhgBP08FdLhkFMdKEUMn1XzEdEko6AwzOgRr8eRlUi+XrEqpfGPl7Us0QxodoRwqIAudIRtdoyqIYoe0Qt6Q+/Gk/FqfBifs9aUMZ85RH9gfP0AoKaeCw=</latexit>

1(ην) + 14(φ)

<latexit sha1_base64="RNjRQRlKCyXGFNgTnoBb5xtvUVk=">AB/XicbVDLSsNAFJ3UV62v+Ni5GVqElkJqDLoBuXFewDmhAm02k7dDIJMxMhuJP+AFuXCji1v9w179x+lho64ELh3Pu5d57gphRqSxrYuTW1jc2t/LbhZ3dvf0D8/CoJaNEYNLEYtEJ0CSMpJU1HFSCcWBIUBI+1gdDP12w9ESBrxe5XGxAvRgNM+xUhpyTdP7LJLFPJdnlSq9kXZjYe04pslq2bNAFeJvSAlp+hWnydO2vDNb7cX4SQkXGpOzaVqy8DAlFMSPjgptIEiM8QgPS1ZSjkEgvm10/hmda6cF+JHRxBWfq74kMhVKmYaA7Q6SGctmbiv953UT1r7yM8jhRhOP5on7CoIrgNArYo4JgxVJNEBZU3wrxEAmElQ6soEOwl19eJa16zT6v1e/sknMN5siDU1AEZWCDS+CAW9ATYDBI3gBb+DdeDJejQ/jc96aMxYzx+APjK8fJkaWtw=</latexit>

pseudo Goldstone bosons

30

SLIDE 31

Neutrino Masses from Gravity

1909.04675 With Gabriela Barenboim (Valencia) and Ye-Ling Zhou (Southampton)

q p µν q p µν p, ρ q, σ µν

τ µν

1 (p, q) = iκ

8 [(q − p)µγν + (q − p)νγµ − 2ηµν(q / − p /)]

<latexit sha1_base64="mKJwKidr7faDRHG3TSAmAMauqM=">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</latexit>

τ µν

2 (p, q) = iκ

2 [pµqν + pνqµ − ηµνp · q]

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τ µνρσ

3

(p, q) = iκ[−Pµνρσ − 1 2ηµνpσqρ + ησρ(pµqν + pνqµ) + 1 2(ηµσpνqρ + ηνσpρqµ + ηνρpσqµ + ηµρpνqσ)]

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Pµνρσ = 1 2(ηµρηνσ + ηµσηνρ − ηµνηρσ)

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κ = √ 32πG

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G = 1 M 2

P l

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• We treat gravity as an EFT similar to Donoghue see 9405057v1 for

a review. Start with flat metric and perturb around it, gravity non- Abelian gauge theory with spin-2 gauge boson.

31

gµν → ηµν + κhµν

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SLIDE 32

Neutrino Masses from Gravity

1909.04675 With Gabriela Barenboim (Valencia) and Ye-Ling Zhou (Southampton)

q p µν q p µν p, ρ q, σ µν

τ µν

1 (p, q) = iκ

8 [(q − p)µγν + (q − p)νγµ − 2ηµν(q / − p /)]

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τ µν

2 (p, q) = iκ

2 [pµqν + pνqµ − ηµνp · q]

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τ µνρσ

3

(p, q) = iκ[−Pµνρσ − 1 2ηµνpσqρ + ησρ(pµqν + pνqµ) + 1 2(ηµσpνqρ + ηνσpρqµ + ηνρpσqµ + ηµρpνqσ)]

<latexit sha1_base64="6LXo5LsN476vlWV7CNYcCtiITQM=">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</latexit>

Pµνρσ = 1 2(ηµρηνσ + ηµσηνρ − ηµνηρσ)

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κ = √ 32πG

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G = 1 M 2

P l

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This 2 is often missing in the literature, it should be there! It makes a difference! Problem comes from embedding fermions (spinorial indices) into GR.

32

• We treat gravity as an EFT similar to Donoghue see 9405057v1 for

a review. Start with flat metric and perturb around it, gravity non- Abelian gauge theory with spin-2 gauge boson.

gµν → ηµν + κhµν

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SLIDE 33

• SDE are an infinite tower of integral coupled equations which

relate the Green’s functions of a theory to each other.

• We have to choose some truncation skim. For us this is one

loop improved.

• This allows us to derive a neutrino gap equation.
• “Gravity triggered neutrino condensates” (1009.2504) used

SDEs as a means of studying RH neutrino condensation. We revisit this paper and calculation techniques for light neutrinos.

• Here RHN are heavy and light neutrinos get mass from type-I
• ss. RHN condensate can drive inflation (0811.2998)

33

SLIDE 34

Neutrino Masses from Gravity

S0

F (p) =

i p / − Σ(p) = i α(p2)p / − β(p2)

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Apply Schwinger-Dyson equation to find non-trivial vacuum.

mF = β(p2)/α(p2)

<latexit sha1_base64="JjYXF+w1S9iLQRI5Ic8VvReRc=">ACA3icbZDLSgMxFIYz9VbrbdSdboJFqJs6UwXdCEVBXFawF+iMQyZN29BkJiQZoQwFN76KGxeKuPUl3Pk2pu0stPWHwMd/zuHk/KFgVGnH+bZyC4tLyv51cLa+sbmlr2901BxIjGp45jFshUiRiNSF1TzUhLSIJ4yEgzHFyN680HIhWNozs9FMTnqBfRLsVIGyuw93hwfeGFRKOSuK8cHXuIif6UA7volJ2J4Dy4GRBplpgf3mdGCecRBozpFTbdYT2UyQ1xYyMCl6iEB4gHqkbTBCnCg/ndwgofG6cBuLM2LNJy4vydSxJUa8tB0cqT7arY2Nv+rtRPdPfdTGolEkwhPF3UTBnUMx4HADpUEazY0gLCk5q8Q95FEWJvYCiYEd/bkeWhUyu5JuXJ7WqxeZnHkwT4ACXgjNQBTegBuoAg0fwDF7Bm/VkvVjv1se0NWdlM7vgj6zPH47oli0=</latexit>

Assume neutrino has zero valued bare mass and Dirac fermion.

p k p p − k

Leading self-energy correction

−iΣ(p) = Z d4k (2π)4 τ µν

1 (p, −k)S0 F (k)Gµνρσ(p − k)τ ρσ 1 (k, −p)

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undressed graviton propagator graviton-fermion-fermion vertex

34

SLIDE 35

Neutrino Masses from Gravity

S0

F (p) =

i p / − Σ(p) = i α(p2)p / − β(p2)

<latexit sha1_base64="T15ERxePQ1OJLTr5qKT2qZtWDmw=">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</latexit>

Apply Schwinger-Dyson equation to find non-trivial vacuum.

mF = β(p2)/α(p2)

<latexit sha1_base64="JjYXF+w1S9iLQRI5Ic8VvReRc=">ACA3icbZDLSgMxFIYz9VbrbdSdboJFqJs6UwXdCEVBXFawF+iMQyZN29BkJiQZoQwFN76KGxeKuPUl3Pk2pu0stPWHwMd/zuHk/KFgVGnH+bZyC4tLyv51cLa+sbmlr2901BxIjGp45jFshUiRiNSF1TzUhLSIJ4yEgzHFyN680HIhWNozs9FMTnqBfRLsVIGyuw93hwfeGFRKOSuK8cHXuIif6UA7volJ2J4Dy4GRBplpgf3mdGCecRBozpFTbdYT2UyQ1xYyMCl6iEB4gHqkbTBCnCg/ndwgofG6cBuLM2LNJy4vydSxJUa8tB0cqT7arY2Nv+rtRPdPfdTGolEkwhPF3UTBnUMx4HADpUEazY0gLCk5q8Q95FEWJvYCiYEd/bkeWhUyu5JuXJ7WqxeZnHkwT4ACXgjNQBTegBuoAg0fwDF7Bm/VkvVjv1se0NWdlM7vgj6zPH47oli0=</latexit>

p k p p − k

Taking the appropriate Dirac trace

α(p2) = 1 − 1 4p2 tr(p /Σ(p)) β(p2) = 1 4tr(Σ(p)) .

<latexit sha1_base64="Wu65OpVbI+cuY0um/5d41d/lF8w=">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</latexit>

Assume neutrino has zero valued bare mass and Dirac fermion.

35

SLIDE 36

Neutrino Masses from Gravity

S0

F (p) =

i p / − Σ(p) = i α(p2)p / − β(p2)

<latexit sha1_base64="T15ERxePQ1OJLTr5qKT2qZtWDmw=">ACSXicbVDLS8MwHE43H3O+ph69RIe4HRztFPQiDAXxOJl7wDpnmqVrWNqGJBVG6b/nxZs3/wcvHhTxZPY4zM1fCHx8jzw+hzMqlWm+Gan0vLKamYtu76xubWd29ltyDASmNRxyELRcpAkjAakrqhipMUFQb7DSNMZXI/05hMRkobBvRpy0vFRP6AuxUhpqpt7rB13bwq8C+h7QqEY5rE3D4YL8mQ9OAJtGu07yNtSmZdNmLc0+xDubgQcIiaKAns5vJmyRwPXATWFOTBdKrd3KvdC3Hk0BhfZ5sWyZXnRgJRTEjSdaOJOEID1CftDUMkE9kJx43kcAjzfSgGwq9AwXH7GwiRr6UQ9/RTh8pT85rI/I/rR0p96IT04BHigR4cpEbMahCOKoV9qgWLGhBgLqt8KsYd0VUqXn9UlWPNfXgSNcsk6LZXvzvKVq2kdGbAPDkEBWOAcVMAtqI6wOAZvINP8GW8GB/Gt/EzsaMaWYP/JlU+heqoa6s</latexit>

Apply Schwinger-Dyson equation to find non-trivial vacuum.

mF = β(p2)/α(p2)

<latexit sha1_base64="JjYXF+w1S9iLQRI5Ic8VvReRc=">ACA3icbZDLSgMxFIYz9VbrbdSdboJFqJs6UwXdCEVBXFawF+iMQyZN29BkJiQZoQwFN76KGxeKuPUl3Pk2pu0stPWHwMd/zuHk/KFgVGnH+bZyC4tLyv51cLa+sbmlr2901BxIjGp45jFshUiRiNSF1TzUhLSIJ4yEgzHFyN680HIhWNozs9FMTnqBfRLsVIGyuw93hwfeGFRKOSuK8cHXuIif6UA7volJ2J4Dy4GRBplpgf3mdGCecRBozpFTbdYT2UyQ1xYyMCl6iEB4gHqkbTBCnCg/ndwgofG6cBuLM2LNJy4vydSxJUa8tB0cqT7arY2Nv+rtRPdPfdTGolEkwhPF3UTBnUMx4HADpUEazY0gLCk5q8Q95FEWJvYCiYEd/bkeWhUyu5JuXJ7WqxeZnHkwT4ACXgjNQBTegBuoAg0fwDF7Bm/VkvVjv1se0NWdlM7vgj6zPH47oli0=</latexit>

p k p p − k

β(p2) = 0 ∀p

<latexit sha1_base64="7IWtSf4bCTpTcTO0jFO9r3JjMxo=">ACBXicbVDLSgMxFM3UV62vUZe6CBahQikzVdCNUHTjsoJ9QGcsmThmYyIckIZejGjb/ixoUibv0Hd/6NaTsLbT1w4XDOvdx7TyAYVdpxvq3c0vLK6lp+vbCxubW9Y+/uNVWcSEwaOGaxbAdIEUY5aWiqGWkLSVAUMNIKhtcTv/VApKIxv9MjQfwI9TkNKUbaSF370AuIRiVxXz2Bl9Dxyl4ZemEsEWNQdO2iU3GmgIvEzUgRZKh37S+vF+MkIlxjhpTquI7QfoqkpiRcFLFBEID1GfdAzlKCLKT6dfjOGxUXrQ7DbFNZyqvydSFCk1igLTGSE9UPeRPzP6yQ6vPBTykWiCcezRWHCoI7hJBLYo5JgzUaGICypuRXiAZIaxNcwYTgzr+8SJrVintaqd6eFWtXWRx5cACOQAm4BzUwA2ogwbA4BE8g1fwZj1ZL9a79TFrzVnZzD74A+vzBwHxlk=</latexit>

α(p2) = 1 − i2πG Z d4k (2π)4 α(k2) α2(k2)k2 − β2(k2) ⇥ 2(k · p)2 + 4k2p2 + 3k · p(k2 + p2) ⇤ p2(p − k)2

<latexit sha1_base64="UOKDuI4PRfZgWSs0iKWaLwTowLw=">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</latexit>

Assume neutrino has zero valued bare mass and Dirac fermion.

36

SLIDE 37

Neutrino Masses from Gravity

S0

F (p) =

i p / − Σ(p) = i α(p2)p / − β(p2)

<latexit sha1_base64="T15ERxePQ1OJLTr5qKT2qZtWDmw=">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</latexit>

Apply Schwinger-Dyson equation to find non-trivial vacuum.

mF = β(p2)/α(p2)

<latexit sha1_base64="JjYXF+w1S9iLQRI5Ic8VvReRc=">ACA3icbZDLSgMxFIYz9VbrbdSdboJFqJs6UwXdCEVBXFawF+iMQyZN29BkJiQZoQwFN76KGxeKuPUl3Pk2pu0stPWHwMd/zuHk/KFgVGnH+bZyC4tLyv51cLa+sbmlr2901BxIjGp45jFshUiRiNSF1TzUhLSIJ4yEgzHFyN680HIhWNozs9FMTnqBfRLsVIGyuw93hwfeGFRKOSuK8cHXuIif6UA7volJ2J4Dy4GRBplpgf3mdGCecRBozpFTbdYT2UyQ1xYyMCl6iEB4gHqkbTBCnCg/ndwgofG6cBuLM2LNJy4vydSxJUa8tB0cqT7arY2Nv+rtRPdPfdTGolEkwhPF3UTBnUMx4HADpUEazY0gLCk5q8Q95FEWJvYCiYEd/bkeWhUyu5JuXJ7WqxeZnHkwT4ACXgjNQBTegBuoAg0fwDF7Bm/VkvVjv1se0NWdlM7vgj6zPH47oli0=</latexit>

Assume neutrino has zero valued bare mass. Leading contribution from undressed graviton propagator is vanishing. Need to dress graviton.

p k p p − k

β(p2) = 0 ∀p

<latexit sha1_base64="7IWtSf4bCTpTcTO0jFO9r3JjMxo=">ACBXicbVDLSgMxFM3UV62vUZe6CBahQikzVdCNUHTjsoJ9QGcsmThmYyIckIZejGjb/ixoUibv0Hd/6NaTsLbT1w4XDOvdx7TyAYVdpxvq3c0vLK6lp+vbCxubW9Y+/uNVWcSEwaOGaxbAdIEUY5aWiqGWkLSVAUMNIKhtcTv/VApKIxv9MjQfwI9TkNKUbaSF370AuIRiVxXz2Bl9Dxyl4ZemEsEWNQdO2iU3GmgIvEzUgRZKh37S+vF+MkIlxjhpTquI7QfoqkpiRcFLFBEID1GfdAzlKCLKT6dfjOGxUXrQ7DbFNZyqvydSFCk1igLTGSE9UPeRPzP6yQ6vPBTykWiCcezRWHCoI7hJBLYo5JgzUaGICypuRXiAZIaxNcwYTgzr+8SJrVintaqd6eFWtXWRx5cACOQAm4BzUwA2ogwbA4BE8g1fwZj1ZL9a79TFrzVnZzD74A+vzBwHxlk=</latexit>

α(p2) = 1 − i2πG Z d4k (2π)4 α(k2) α2(k2)k2 − β2(k2) ⇥ 2(k · p)2 + 4k2p2 + 3k · p(k2 + p2) ⇤ p2(p − k)2

<latexit sha1_base64="UOKDuI4PRfZgWSs0iKWaLwTowLw=">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</latexit>

no mass dynamically induced if graviton is undressed

37

SLIDE 38

Neutrino Masses from Gravity

S0

F (p) =

i p / − Σ(p) = i α(p2)p / − β(p2)

<latexit sha1_base64="T15ERxePQ1OJLTr5qKT2qZtWDmw=">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</latexit>

Apply Schwinger-Dyson equation to find non-trivial vacuum.

mF = β(p2)/α(p2)

<latexit sha1_base64="JjYXF+w1S9iLQRI5Ic8VvReRc=">ACA3icbZDLSgMxFIYz9VbrbdSdboJFqJs6UwXdCEVBXFawF+iMQyZN29BkJiQZoQwFN76KGxeKuPUl3Pk2pu0stPWHwMd/zuHk/KFgVGnH+bZyC4tLyv51cLa+sbmlr2901BxIjGp45jFshUiRiNSF1TzUhLSIJ4yEgzHFyN680HIhWNozs9FMTnqBfRLsVIGyuw93hwfeGFRKOSuK8cHXuIif6UA7volJ2J4Dy4GRBplpgf3mdGCecRBozpFTbdYT2UyQ1xYyMCl6iEB4gHqkbTBCnCg/ndwgofG6cBuLM2LNJy4vydSxJUa8tB0cqT7arY2Nv+rtRPdPfdTGolEkwhPF3UTBnUMx4HADpUEazY0gLCk5q8Q95FEWJvYCiYEd/bkeWhUyu5JuXJ7WqxeZnHkwT4ACXgjNQBTegBuoAg0fwDF7Bm/VkvVjv1se0NWdlM7vgj6zPH47oli0=</latexit>

Assume neutrino has zero valued bare mass. Leading contribution from undressed graviton propagator is vanishing. Need to dress graviton.

k p p p − k Π

p k p p − k

G0

µνρσ(p − k) → Gµνρσ(p − k) + Gµναβ(p − k)Παβ,γδ(p − k)Gρσγδ(p − k)

<latexit sha1_base64="jK18pCbhw8XhoRjcd6aBDZFUHw=">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</latexit>

38

SLIDE 39

Neutrino Masses from Gravity

S0

F (p) =

i p / − Σ(p) = i α(p2)p / − β(p2)

<latexit sha1_base64="T15ERxePQ1OJLTr5qKT2qZtWDmw=">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</latexit>

Apply Schwinger-Dyson equation to find non-trivial vacuum.

mF = β(p2)/α(p2)

<latexit sha1_base64="JjYXF+w1S9iLQRI5Ic8VvReRc=">ACA3icbZDLSgMxFIYz9VbrbdSdboJFqJs6UwXdCEVBXFawF+iMQyZN29BkJiQZoQwFN76KGxeKuPUl3Pk2pu0stPWHwMd/zuHk/KFgVGnH+bZyC4tLyv51cLa+sbmlr2901BxIjGp45jFshUiRiNSF1TzUhLSIJ4yEgzHFyN680HIhWNozs9FMTnqBfRLsVIGyuw93hwfeGFRKOSuK8cHXuIif6UA7volJ2J4Dy4GRBplpgf3mdGCecRBozpFTbdYT2UyQ1xYyMCl6iEB4gHqkbTBCnCg/ndwgofG6cBuLM2LNJy4vydSxJUa8tB0cqT7arY2Nv+rtRPdPfdTGolEkwhPF3UTBnUMx4HADpUEazY0gLCk5q8Q95FEWJvYCiYEd/bkeWhUyu5JuXJ7WqxeZnHkwT4ACXgjNQBTegBuoAg0fwDF7Bm/VkvVjv1se0NWdlM7vgj6zPH47oli0=</latexit>

Assume neutrino has zero valued bare mass. Leading contribution from undressed graviton propagator is vanishing. Need to dress graviton.

k p p p − k Π

q = p − k l q − l q

Vacuum polarisations Π

<latexit sha1_base64="B0x7MCsgzQJFWgV+qsHeT62F0C0=">AB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7Qe0oWy2m3bpZhN2J0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekEh0HW/ncLa+sbmVnG7tLO7t39QPjxqmTjVjDdZLGPdCajhUijeRIGSdxLNaRI3g7GtzO/cS1EbF6xEnC/YgOlQgFo2ilh15D9MsVt+rOQVaJl5MK5Gj0y1+9QczSiCtkhrT9dwE/YxqFEzyamXGp5QNqZD3rVU0YgbP5ufOiVnVhmQMNa2FJK5+nsio5ExkyiwnRHFkVn2ZuJ/XjfF8NrPhEpS5IotFoWpJBiT2d9kIDRnKCeWUKaFvZWwEdWUoU2nZEPwl9eJa1a1buo1u4vK/WbPI4inMApnIMHV1CHO2hAExgM4Rle4c2Rzovz7nwsWgtOPnMf+B8/gAga42x</latexit>

fermion scalar graviton GB

t’ Hooft and Veltman 1974

39

SLIDE 40

Neutrino Masses from Gravity

Rotate to Euclidean space and rescale momenta:

α(p2

E) =

1 − 2πG Z d4kE (2π)4 α(k2

E)

α2(k2

E)k2 E + β2(k2 E)

⇥ 2(kE · pE)2 + 4k2

Ep2 E + 3kE · pE(k2 E + p2 E)

⇤ p2

E(pE − kE)2

β(p2

E) =

−8G2 Z d4kE (2π)4 β(k2

E)

α2(k2

E)k2 E + β2(k2 E)

" A(kE + pE)2−B

• p2

E − k2 E

2 8(pE − kE)2 # log  µ2 (pE − kE)2

• <latexit sha1_base64="yKGg4yau3OG8cISBIJ2jaYOcTI=">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</latexit>

x = p2

E

Λ2 y = k2

E

Λ2

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α(x) = 1 − GΛ2 (2π)2 Z 1 dy yα(y) yα2(x) + β2(y)K(x, y) β(x) = 8G2Λ4 (2π)3 Z 1 dy yβ(y) yα2(y) + β2(y)L(x, y)

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Kernels UV cutoff

40

SLIDE 41

0.00 0.25 0.50 0.75 1.00 x 0.00 0.25 0.50 0.75 1.00 y

K (x, y)

2 4 6 8 10 12 0.00 0.25 0.50 0.75 1.00 x 0.00 0.25 0.50 0.75 1.00 y

LA (x, y)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.00 0.25 0.50 0.75 1.00 x 0.00 0.25 0.50 0.75 1.00 y

LB (x, y)

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.00 0.25 0.50 0.75 1.00 x 0.00 0.25 0.50 0.75 1.00 y

L (x, y)

0.2 0.4 0.6 0.8 1.0 1.2

41

Kernel structure

Rotate to Euclidean space, rescale momentum

α(x) = 1 − GΛ2 (2π)2 Z 1 dy yα(y) yα2(x) + β2(y)K(x, y) , β(x) = 8G2Λ4 (2π)3 Z 1 dy yβ(y) yα2(y) + β2(y)L(x, y) .

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rescaled p momentum rescaled k momentum L(x, y) = ALA(x, y) + BLB(x, y)

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41

SLIDE 42

0.00 0.25 0.50 0.75 1.00 x 0.00 0.25 0.50 0.75 1.00 y

K (x, y)

2 4 6 8 10 12 0.00 0.25 0.50 0.75 1.00 x 0.00 0.25 0.50 0.75 1.00 y

LA (x, y)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.00 0.25 0.50 0.75 1.00 x 0.00 0.25 0.50 0.75 1.00 y

LB (x, y)

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.00 0.25 0.50 0.75 1.00 x 0.00 0.25 0.50 0.75 1.00 y

L (x, y)

0.2 0.4 0.6 0.8 1.0 1.2

42

Kernel structure

Rotate to Euclidean space, rescale momentum

α(x) = 1 − GΛ2 (2π)2 Z 1 dy yα(y) yα2(x) + β2(y)K(x, y) , β(x) = 8G2Λ4 (2π)3 Z 1 dy yβ(y) yα2(y) + β2(y)L(x, y) .

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rescaled p momentum rescaled k momentum L(x, y) = ALA(x, y) + BLB(x, y)

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QCD L(0, 0) 6= 0

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x = y = 0

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gravity L(0, 0) = 0

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x = y = 0

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d-wave interaction due to spin 2 nature of graviton

42 42

SLIDE 43

Use two methods to solve SDEs using two well known methods

• 1. Solve equations iteratively and apply extrapolation
• 2. Make informed Ansatz of the kernel and check for


self consistency of non-trivial vacuum.

43

SLIDE 44

Solving SD Equation - Extrapolation

α(i+1)(x) =1 − GΛ2 (2π)2 Z 1 dy yα(i)(y) yα(i)2(x) + β(i)2(y) K(x, y) β(i+1)(x) =8(GΛ2)2 (2π)3 Z 1 dy yβ(i)(y) yα(i)2(y) + β(i)2(y) L(x, y) .

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α(0)(x) = c1 , β(0)(x) = c2

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Start with two trial functions

tolerance ≡ β(i+1)(x) β(i)(x) − 1

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Solution (true non-trivial vacuum) is not sensitive to trial function value

• r tolerance value.

This method allows us to find the NP non-trivial vacuum.

44

SLIDE 45

Solving SD Equation - Extrapolation

• 1. Choose a value of GΛ2, A, B, tolerance and trial function values.
• 2. Subdivide the x-interval [xIR, 1] into n bins, where xIR is infrared bound-

ary of the theory.

• 3. Iteratively solve SDE for each bin.
• 4. For each bin calculate the tolerance and summate this measure over all

bins.

• 5. Require the tolerance to be close to 0.0. For example, for GΛ2 = 1.0,

A = 50.0 and B = 43.5 we choose a tolerance of 10−6.

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50 100 150 200 (GΛ2)A 10−1 100 101 β(0)2

β(0) ≈ 10−29 for Λ ≈ Mpl

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mν = β(0)

α(0)Λ

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Requires beyond SM particle content to support the condensate even if scale is high, also we are tuning around chiral preserving point.

neutrino masses live down here

GΛ2 = ⇒ A & 23

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45

SLIDE 46

Solving SD Equation - Ansatz

10−15 10−14 10−13 10−12 10−11 10−10 x 0.0 0.2 0.4 0.6 0.8 1.0 y

L (x, y)

0.2 0.4 0.6 0.8

Take quenched limit for simplicity i.e α ≈ 1

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β depends on L(x,y). This kernel is flat in the x-direction even for tiny momentum. Make Ansatz that β is a step function

• f magnitude ‘a’.

β(x) = 8(GΛ2)2 (2π)3 Z 1 aydy a2 + y LA(x, y)

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ALA(x, y) BLB(x, y)

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Solve SDE for this Ansatz

10−9 10−7 10−5 10−3 10−1 x 1 2 3 4 5 6 7 β(x) ×10−6

a = 10−5, GΛ2 = 1.0

As before the mass can be tuned but this this approach it is tuned via ‘a’.

concerned with the deep IR neutrino mass

Checks for self-consistency of postulated form 


• f β with kernel structure.

far infrared region of the kernel

46

SLIDE 47

Summary

• Neutrinos are unique amongst the Standard Model (SM) fermions in the

tininess of their mass, the weakness of their interactions and their capacity to be their own anti-particles. Such features suggest neutrinos acquire their mass in a different way from the quarks and charged leptons.

• Neutrino masses from gravity is an intriguing idea and we have made a

first calculational attempt at exploring this possibility.

• An interesting feature is new d.o.fs are necessary to provide finite

support to the condensate even if it occurs at a very high scale. SM + gravity is not sufficient unless there are large ED which lowers Planck scale.

• However a high level of fine-tuning is required if the Planck scale is at

~1019 GeV.

• As gravity does not discriminate between the neutrinos, they are mass

degenerate, one needs some additional mechanism to induce a mass splitting.

47

SLIDE 48

Thank you for your attention

48

SLIDE 49

49

Back up slides - the action

Sg = Z d4x√−g( 1 4πGR + Lm)

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Lm = Dµφ∗gµνDνφ + i 2 ⇥ ¯ ψγaeµ

aDµψ + (Dµ ¯

ψ)γaeµ

aψ

⇤ − 1 4gµνgρσFµρFνσ

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where Fµν = DµAν − DνAµ and Dµ denotes the covariant derivative with respect to the gravitational field and gauge fields, and eµ

a is the vierbein to shift

frame to the local Minkowski flat frame.

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gµν → ηµν + κhµν

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Perturb the metric, the classical gravitational field is fixed at zero.

Graviton propagator : Gµνρσ(p) = iPµνρσ p2

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Pµνρσ = 1 2(ηµρηνσ + ηµσηνρ − ηµνηρσ)

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SLIDE 50

50

Back up slides - kernel structure

K(x, y) = 1 x Z π sin2 θdθ2xy cos2 θ + 4xy + 3√xy(x + y) cos θ x + y − 2√xy cos θ L(x, y) = Z π sin2 θdθ  A (x + y + 2√xy cos θ) − B (x − y)2 8(x + y − 2√xy cos θ)

• ×log [x + y − 2√xy cos θ]

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K(x, y) = π x (x + y)3 − [(x + y)2 + 2xy]|x − y| 2xy , LA(x, y) = π 12 ⇢5(x2 + y2) − 5(x + y)|x − y| − 6xy (x + y) + |x − y| − 6(x + y) log (x + y) + |x − y| 2

• ,

LB(x, y) = π 8 (x − y)2 xy ( (x + y) − |x − y| 2 −(x + y) + |x − y| 2 log (x + y) + |x − y| 2

• + |x − y| log(|x − y|)

) ,

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SLIDE 51

51

Back up slides -regularisarion procedure

• Simplest procedure is cutoff regularisation. At energies above the cutoff

the neutrino is massless and condensate dissolves.

• It has it’s ugly features, we agree: lack of Lorentz covariance, but is

numerically convenient and used frequently in QED and QCD SDE.

• For QED it has been demonstrated the qualitative difference is not

significant so we proceed, see e.g. 9410286 or 9604402

SLIDE 52

52

massless fermions and symmetries

L = iΨjγµ∂µΨj

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Ψ → e−i τ

2 φΨ

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vector transformation

Ψ → ei τ

2 φΨ

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iΨj∂µΨj

transformation

− − − − − − − − − →

vector

iΨj∂µΨj

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Ψ → e−iγ5 τ

2 φΨ

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axial transformation

Ψ → eiγ5 τ

2 φΨ

<latexit sha1_base64="5k2rBpAz6Qa9XKdVIPSoJODk0=">ACMnicbVBNaxsxFNQmaZu4H3GbYy+iptCT2XVj0qNpLu3NhfoDLNe8lbW2sLRapLctZtnflEt/SGH5pBQcs2PiOzsobYzIBhm3vD0Js6UdBiGf4O9/YMnT58dHtWev3j56rj+k3fmdxy0eNGTuMwQklU9FDiUoMytAx0oM4sX5yh/8FNZJk37HZSbGmapTCQH9NKk/pUZb6/SBes6WTIrZ3MEa80vKn4Uks1Aa5i0WKBFwhL4tWybK5H91MTuqNsBmuQXdJVJEGqdCd1P+wqeG5FilyBc6NojDcQEWJVeirLHciQz4AmZi5GkKWrhxsT65pO+9MqWJsf6lSNfq/4kCtHNLHftJDTh3295KfMwb5Zh8GhcyzXIUKX9YlOSKoqGr/uhUWsFRLT0BbqX/K+Vz8OWgb7nmS4i2T94l/VYz+thsfztdD5XdRySt+Qd+UAickY65Avpkh7h5IJckmtyE/wOroJ/we3D6F5QZU7IBoK7e2ASrU=</latexit>

iΨjγµ∂µΨj

transformation

− − − − − − − − − →

axial

iΨjγµ∂µΨj

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δL = mΨΨ

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is not invariant under axial symmetry transformation