LOW-SCALE LEPTOGENESIS & HIDDEN-SECTOR BARYOGENESIS
Brian Shuve Testing CPV for Baryogenesis ACFI, UMass Amherst
LOW-SCALE LEPTOGENESIS & HIDDEN-SECTOR BARYOGENESIS Brian Shuve - - PowerPoint PPT Presentation
LOW-SCALE LEPTOGENESIS & HIDDEN-SECTOR BARYOGENESIS Brian Shuve Testing CPV for Baryogenesis ACFI, UMass Amherst OUTLINE Overview of low-scale leptogenesis (~GeV RHNs) CPV and phenomenology of low-scale leptogenesis
Brian Shuve Testing CPV for Baryogenesis ACFI, UMass Amherst
2
3
N
ν
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I
|F|2 ⇠ 10−14 ⇣ mν 0.1 eV ⌘ ⇣ mN GeV ⌘ ✓100 GeV hΦi ◆2
mν ⇠ F 2hΦi2 MN
masses, baryon asymmetry, DM!
Minkowski, PLB 67 (1977); Yanagida Conf. Proc C7902131 (1979); Mohapatra and Senjanovic, PRL 44 (1980)… Asaka, Shaposhnikov hep-ph/0503065, hep-ph/0505013
4
N
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(valid only for )
MN TEW
<latexit sha1_base64="xUBtZbTy5AIYGodokbEBKlvDX5A=">AB+XicbVBNS8NAEN3Ur1q/Uj16WSyCp5KIoN6KInhRKjS20ISw2W7apbubsLtRSuxP8eJBxav/xJv/xm2bg7Y+GHi8N8PMvChlVGnH+bZKS8srq2vl9crG5tb2jl3dvVdJjHxcMIS2YmQIowK4mqGemkiAeMdKOhpcTv/1ApKJaOlRSgKO+oLGFCNtpNCu3oS3fr8PW2HuSw6v2uPQrjl1Zwq4SNyC1ECBZmh/+b0EZ5wIjRlSqus6qQ5yJDXFjIwrfqZIivAQ9UnXUIE4UE+PX0MD43Sg3EiTQkNp+rviRxpUY8Mp0c6YGa9ybif1430/FZkFORZpoIPFsUZwzqBE5ygD0qCdZsZAjCkpbIR4gibA2aVMCO78y4vEO6f1927k1rjokijDPbBATgCLjgFDXANmsADGDyCZ/AK3qwn68V6tz5mrSWrmNkDf2B9/gB/9JMP</latexit><latexit sha1_base64="xUBtZbTy5AIYGodokbEBKlvDX5A=">AB+XicbVBNS8NAEN3Ur1q/Uj16WSyCp5KIoN6KInhRKjS20ISw2W7apbubsLtRSuxP8eJBxav/xJv/xm2bg7Y+GHi8N8PMvChlVGnH+bZKS8srq2vl9crG5tb2jl3dvVdJjHxcMIS2YmQIowK4mqGemkiAeMdKOhpcTv/1ApKJaOlRSgKO+oLGFCNtpNCu3oS3fr8PW2HuSw6v2uPQrjl1Zwq4SNyC1ECBZmh/+b0EZ5wIjRlSqus6qQ5yJDXFjIwrfqZIivAQ9UnXUIE4UE+PX0MD43Sg3EiTQkNp+rviRxpUY8Mp0c6YGa9ybif1430/FZkFORZpoIPFsUZwzqBE5ygD0qCdZsZAjCkpbIR4gibA2aVMCO78y4vEO6f1927k1rjokijDPbBATgCLjgFDXANmsADGDyCZ/AK3qwn68V6tz5mrSWrmNkDf2B9/gB/9JMP</latexit><latexit sha1_base64="xUBtZbTy5AIYGodokbEBKlvDX5A=">AB+XicbVBNS8NAEN3Ur1q/Uj16WSyCp5KIoN6KInhRKjS20ISw2W7apbubsLtRSuxP8eJBxav/xJv/xm2bg7Y+GHi8N8PMvChlVGnH+bZKS8srq2vl9crG5tb2jl3dvVdJjHxcMIS2YmQIowK4mqGemkiAeMdKOhpcTv/1ApKJaOlRSgKO+oLGFCNtpNCu3oS3fr8PW2HuSw6v2uPQrjl1Zwq4SNyC1ECBZmh/+b0EZ5wIjRlSqus6qQ5yJDXFjIwrfqZIivAQ9UnXUIE4UE+PX0MD43Sg3EiTQkNp+rviRxpUY8Mp0c6YGa9ybif1430/FZkFORZpoIPFsUZwzqBE5ygD0qCdZsZAjCkpbIR4gibA2aVMCO78y4vEO6f1927k1rjokijDPbBATgCLjgFDXANmsADGDyCZ/AK3qwn68V6tz5mrSWrmNkDf2B9/gB/9JMP</latexit><latexit sha1_base64="xUBtZbTy5AIYGodokbEBKlvDX5A=">AB+XicbVBNS8NAEN3Ur1q/Uj16WSyCp5KIoN6KInhRKjS20ISw2W7apbubsLtRSuxP8eJBxav/xJv/xm2bg7Y+GHi8N8PMvChlVGnH+bZKS8srq2vl9crG5tb2jl3dvVdJjHxcMIS2YmQIowK4mqGemkiAeMdKOhpcTv/1ApKJaOlRSgKO+oLGFCNtpNCu3oS3fr8PW2HuSw6v2uPQrjl1Zwq4SNyC1ECBZmh/+b0EZ5wIjRlSqus6qQ5yJDXFjIwrfqZIivAQ9UnXUIE4UE+PX0MD43Sg3EiTQkNp+rviRxpUY8Mp0c6YGa9ybif1430/FZkFORZpoIPFsUZwzqBE5ygD0qCdZsZAjCkpbIR4gibA2aVMCO78y4vEO6f1927k1rjokijDPbBATgCLjgFDXANmsADGDyCZ/AK3qwn68V6tz5mrSWrmNkDf2B9/gB/9JMP</latexit>(mass can be below EW scale!)
Fukugita, Yanagida, Phys. Lett. B174 (1986) 45 Akhmedov et al., hep-ph/9803255 Asaka, Shaposhnikov, hep-ph/0505013
5
Lα NI H∗ Lα NI H∗
Lβ NJ H Lβ NJ H
J
FαI
FαJ
F ∗
βJ I
F ∗
βI
e−iωIt
e−iωJt
ωI − ωJ ≈ M 2
I − M 2 J
2T
† † † †
Γ(Lα → Lβ) − Γ(¯ Lα → ¯ Lβ) ∼ Im(F 4) Im h ei(ωI−ωJ)ti
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6
104 105 106 107
0.5 1 time HGeV-1L ImH osc. phase L
Γ(Lα → Lβ) − Γ(¯ Lα → ¯ Lβ) ∼ Im(F 4) Im h ei(ωI−ωJ)ti
<latexit sha1_base64="3QZnK7tu5GvQbWAq/hQXh/xHLqY=">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</latexit><latexit sha1_base64="3QZnK7tu5GvQbWAq/hQXh/xHLqY=">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</latexit><latexit sha1_base64="3QZnK7tu5GvQbWAq/hQXh/xHLqY=">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</latexit><latexit sha1_base64="3QZnK7tu5GvQbWAq/hQXh/xHLqY=">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</latexit>(M 2
3 − M 2 2 )/T ∼ H
asymmetry, not lepton number asymmetry: need re-scattering
Lα NI H∗
7
asymmetry generation and longer integration time
104 105 106 107
0.5 1 time HGeV-1L ImH osc. phase L
7
asymmetry generation and longer integration time
104 105 106 107
0.5 1 time HGeV-1L ImH osc. phase L
asymmetry, but too big = equilibrium! (BAD)
7
asymmetry generation and longer integration time
104 105 106 107
0.5 1 time HGeV-1L ImH osc. phase L
asymmetry, but too big = equilibrium! (BAD)
need flavour-dependent scattering rates!
Lα NI H∗
7
asymmetry generation and longer integration time
104 105 106 107
0.5 1 time HGeV-1L ImH osc. phase L
asymmetry, but too big = equilibrium! (BAD)
need flavour-dependent scattering rates!
Lα NI H∗
Canetti, Shaposhnikov, arXiv:1006.0133; Canetti et al., arXiv:1208.4607; BS, Yavin, arXiv:1401.2459
8
BS, Yavin, arXiv:1401.2459
10-20 10-18 10-16 10-14 10-12 10-10 10-17 10-15 10-13 10-11 10-9 10-7 106 105 104 103 102 time HsecondsL lepton asymmetry » YDL » Temperature HGeVL
Tau Muon Electron Total Regime I
10-20 10-18 10-16 10-14 10-12 10-10 10-17 10-15 10-13 10-11 10-9 10-7 106 105 104 103 102 time HsecondsL lepton asymmetry » YDL » Temperature HGeVL
Tau Muon Electron Total Regime II
mass degeneracy large Yukawa couplings
9
10
FαI = i v Uν √mν R √mN
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<latexit sha1_base64="gTGqWu6gtob8m1HibavTPinYIc=">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</latexit><latexit sha1_base64="gTGqWu6gtob8m1HibavTPinYIc=">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</latexit><latexit sha1_base64="gTGqWu6gtob8m1HibavTPinYIc=">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</latexit>Casas, Ibarra, hep-ph/0103065
10
FαI = i v Uν √mν R √mN
<latexit sha1_base64="QkDThXxI0JhTfVq1t70ujFrWzs=">ACJHicbZDLSsNAFIYn9VbrLerSzWARXJSiKCQlEQ3UgVYwtNCZPpB06mcSZSaGEvIwbX8WNCysu3PgsTi+Ctv4w8PGfczhzfj9mVCrL+jRyc/MLi0v5cLK6tr6hrm59SCjRGDi4IhFou4jSRjlxFUMVKPBUGhz0jN714M67UeEZJG/F71Y9IMUZvTgGKktOWZp5de6iIWdxC8zuAZdAOBcEqztJc5nsTVz4KlYZDzKBbunNL8Me6yTyzaJWtkeAs2BMogomqnjlwWxFOQsIVZkjKhm3FqpkioShmJCu4iSQxwl3UJg2NHIVENtPRlRnc04LBpHQjys4cn9PpCiUsh/6ujNEqiOna0Pzv1ojUcFxM6U8ThTheLwoSBhUERxGBltUEKxYXwPCguq/QtxBOielgy3oEOzpk2fBOSiflO3bw2LlfJGHuyAXbAPbHAEKuAKVIEDMHgCL+ANDIxn49V4Nz7GrTljMrMN/sj4+gZ3faV5</latexit><latexit sha1_base64="QkDThXxI0JhTfVq1t70ujFrWzs=">ACJHicbZDLSsNAFIYn9VbrLerSzWARXJSiKCQlEQ3UgVYwtNCZPpB06mcSZSaGEvIwbX8WNCysu3PgsTi+Ctv4w8PGfczhzfj9mVCrL+jRyc/MLi0v5cLK6tr6hrm59SCjRGDi4IhFou4jSRjlxFUMVKPBUGhz0jN714M67UeEZJG/F71Y9IMUZvTgGKktOWZp5de6iIWdxC8zuAZdAOBcEqztJc5nsTVz4KlYZDzKBbunNL8Me6yTyzaJWtkeAs2BMogomqnjlwWxFOQsIVZkjKhm3FqpkioShmJCu4iSQxwl3UJg2NHIVENtPRlRnc04LBpHQjys4cn9PpCiUsh/6ujNEqiOna0Pzv1ojUcFxM6U8ThTheLwoSBhUERxGBltUEKxYXwPCguq/QtxBOielgy3oEOzpk2fBOSiflO3bw2LlfJGHuyAXbAPbHAEKuAKVIEDMHgCL+ANDIxn49V4Nz7GrTljMrMN/sj4+gZ3faV5</latexit><latexit sha1_base64="QkDThXxI0JhTfVq1t70ujFrWzs=">ACJHicbZDLSsNAFIYn9VbrLerSzWARXJSiKCQlEQ3UgVYwtNCZPpB06mcSZSaGEvIwbX8WNCysu3PgsTi+Ctv4w8PGfczhzfj9mVCrL+jRyc/MLi0v5cLK6tr6hrm59SCjRGDi4IhFou4jSRjlxFUMVKPBUGhz0jN714M67UeEZJG/F71Y9IMUZvTgGKktOWZp5de6iIWdxC8zuAZdAOBcEqztJc5nsTVz4KlYZDzKBbunNL8Me6yTyzaJWtkeAs2BMogomqnjlwWxFOQsIVZkjKhm3FqpkioShmJCu4iSQxwl3UJg2NHIVENtPRlRnc04LBpHQjys4cn9PpCiUsh/6ujNEqiOna0Pzv1ojUcFxM6U8ThTheLwoSBhUERxGBltUEKxYXwPCguq/QtxBOielgy3oEOzpk2fBOSiflO3bw2LlfJGHuyAXbAPbHAEKuAKVIEDMHgCL+ANDIxn49V4Nz7GrTljMrMN/sj4+gZ3faV5</latexit>Uν = c12c13 s12c13 s13e−iδ −s12c23 − c12s23s13eiδ c12c23 − s12s23s13eiδ s23c13 s12s23 − c12c23s13eiδ −c12s23 − s12c23s13eiδ c23c13 eiα1/2 eiα2/2 1
<latexit sha1_base64="aENbOusfC9/al91CRuNRgZdeQ=">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</latexit><latexit sha1_base64="aENbOusfC9/al91CRuNRgZdeQ=">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</latexit><latexit sha1_base64="aENbOusfC9/al91CRuNRgZdeQ=">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</latexit>R = cos ω sin ω − sin ω cos ω
<latexit sha1_base64="gTGqWu6gtob8m1HibavTPinYIc=">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</latexit><latexit sha1_base64="gTGqWu6gtob8m1HibavTPinYIc=">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</latexit><latexit sha1_base64="gTGqWu6gtob8m1HibavTPinYIc=">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</latexit>arg(cos ω) = − tan(Re ω) tanh(Im ω)
<latexit sha1_base64="E9akn8GWAWxU0iMki8WeBJNQbIw=">ACL3icbZBNSyNBEIZ73PUru2rUo5fGIGRBw4wI6kEQPax7U9mokAmhplNJGvtj6O4RwpCftBd/il4UVvG6/8KeOy6akHDy/tU0VvkgpuXRjeBxOfPk9OTc/MVr58nZtfqC4unVmdGYZNpoU2FwlYFxh03En8CI1CDIReJ5cHhb8/AqN5Vr9dMU2xL6ivc4A+etTvV7DKZfj5m2sZbYh290j27EDlQ9luAGRuanOIrXS1iAwV/yQ/4jnWotbITjou9FVIoaKeu4U72Ju5plEpVjAqxtRWHq2jkYx5nAUSXOLKbALqGPLS8VSLTtfHzwiK5p0t72vinHB27rydykNYOZeI7i13tW1aYH7FW5no7ZyrNHOo2MtHvUxQp2mRHu1yg8yJoRfADPe7UjYA8z5jCs+hOjtye9Fc7Ox24hOtmr7B2UaM2SFrJI6icg2SdH5Jg0CSO/yC35TR6C6+AueAyeXlongnJmfxXwZ9n4/upJQ=</latexit><latexit sha1_base64="E9akn8GWAWxU0iMki8WeBJNQbIw=">ACL3icbZBNSyNBEIZ73PUru2rUo5fGIGRBw4wI6kEQPax7U9mokAmhplNJGvtj6O4RwpCftBd/il4UVvG6/8KeOy6akHDy/tU0VvkgpuXRjeBxOfPk9OTc/MVr58nZtfqC4unVmdGYZNpoU2FwlYFxh03En8CI1CDIReJ5cHhb8/AqN5Vr9dMU2xL6ivc4A+etTvV7DKZfj5m2sZbYh290j27EDlQ9luAGRuanOIrXS1iAwV/yQ/4jnWotbITjou9FVIoaKeu4U72Ju5plEpVjAqxtRWHq2jkYx5nAUSXOLKbALqGPLS8VSLTtfHzwiK5p0t72vinHB27rydykNYOZeI7i13tW1aYH7FW5no7ZyrNHOo2MtHvUxQp2mRHu1yg8yJoRfADPe7UjYA8z5jCs+hOjtye9Fc7Ox24hOtmr7B2UaM2SFrJI6icg2SdH5Jg0CSO/yC35TR6C6+AueAyeXlongnJmfxXwZ9n4/upJQ=</latexit><latexit sha1_base64="E9akn8GWAWxU0iMki8WeBJNQbIw=">ACL3icbZBNSyNBEIZ73PUru2rUo5fGIGRBw4wI6kEQPax7U9mokAmhplNJGvtj6O4RwpCftBd/il4UVvG6/8KeOy6akHDy/tU0VvkgpuXRjeBxOfPk9OTc/MVr58nZtfqC4unVmdGYZNpoU2FwlYFxh03En8CI1CDIReJ5cHhb8/AqN5Vr9dMU2xL6ivc4A+etTvV7DKZfj5m2sZbYh290j27EDlQ9luAGRuanOIrXS1iAwV/yQ/4jnWotbITjou9FVIoaKeu4U72Ju5plEpVjAqxtRWHq2jkYx5nAUSXOLKbALqGPLS8VSLTtfHzwiK5p0t72vinHB27rydykNYOZeI7i13tW1aYH7FW5no7ZyrNHOo2MtHvUxQp2mRHu1yg8yJoRfADPe7UjYA8z5jCs+hOjtye9Fc7Ox24hOtmr7B2UaM2SFrJI6icg2SdH5Jg0CSO/yC35TR6C6+AueAyeXlongnJmfxXwZ9n4/upJQ=</latexit>Casas, Ibarra, hep-ph/0103065
11
Im ω
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<latexit sha1_base64="FPLD0uglSgrhd+iEabgcb56Pl4=">AB+3icbZDNSsNAFIUn9a/Wv2iXboJFcFKIoK6EIpuXFYwtCEMpnctEMnkzAzEUKor+LGhYpbX8Sdb+O0zUJbDwx8nHsv984JUkalsu1vo7Kyura+Ud2sbW3v7O6Z+wcPMskEAZckLBG9AEtglIOrqGLQSwXgOGDQDcY303r3EYSkCb9XeQp+jIecRpRgpa2BWfdA4Su76TW9EJhGL6UDs2G37JmsZXBKaKBSnYH5YUJyWLgijAsZd+xU+UXWChKGExqXiYhxWSMh9DXyHEM0i9mx0+sY+2EVpQI/biyZu7viQLHUuZxoDtjrEZysTY1/6v1MxVd+AXlaAk/miKGOWSqxpElZIBRDFcg2YCKpvtcgIC0yUzqumQ3AWv7wM7mnrsuXcnTXa12UaVXSIjtAJctA5aqNb1EuIihHz+gVvRlPxovxbnzMWytGOVNHf2R8/gDUPpPM</latexit><latexit sha1_base64="FPLD0uglSgrhd+iEabgcb56Pl4=">AB+3icbZDNSsNAFIUn9a/Wv2iXboJFcFKIoK6EIpuXFYwtCEMpnctEMnkzAzEUKor+LGhYpbX8Sdb+O0zUJbDwx8nHsv984JUkalsu1vo7Kyura+Ud2sbW3v7O6Z+wcPMskEAZckLBG9AEtglIOrqGLQSwXgOGDQDcY303r3EYSkCb9XeQp+jIecRpRgpa2BWfdA4Su76TW9EJhGL6UDs2G37JmsZXBKaKBSnYH5YUJyWLgijAsZd+xU+UXWChKGExqXiYhxWSMh9DXyHEM0i9mx0+sY+2EVpQI/biyZu7viQLHUuZxoDtjrEZysTY1/6v1MxVd+AXlaAk/miKGOWSqxpElZIBRDFcg2YCKpvtcgIC0yUzqumQ3AWv7wM7mnrsuXcnTXa12UaVXSIjtAJctA5aqNb1EuIihHz+gVvRlPxovxbnzMWytGOVNHf2R8/gDUPpPM</latexit><latexit sha1_base64="FPLD0uglSgrhd+iEabgcb56Pl4=">AB+3icbZDNSsNAFIUn9a/Wv2iXboJFcFKIoK6EIpuXFYwtCEMpnctEMnkzAzEUKor+LGhYpbX8Sdb+O0zUJbDwx8nHsv984JUkalsu1vo7Kyura+Ud2sbW3v7O6Z+wcPMskEAZckLBG9AEtglIOrqGLQSwXgOGDQDcY303r3EYSkCb9XeQp+jIecRpRgpa2BWfdA4Su76TW9EJhGL6UDs2G37JmsZXBKaKBSnYH5YUJyWLgijAsZd+xU+UXWChKGExqXiYhxWSMh9DXyHEM0i9mx0+sY+2EVpQI/biyZu7viQLHUuZxoDtjrEZysTY1/6v1MxVd+AXlaAk/miKGOWSqxpElZIBRDFcg2YCKpvtcgIC0yUzqumQ3AWv7wM7mnrsuXcnTXa12UaVXSIjtAJctA5aqNb1EuIihHz+gVvRlPxovxbnzMWytGOVNHf2R8/gDUPpPM</latexit><latexit sha1_base64="FPLD0uglSgrhd+iEabgcb56Pl4=">AB+3icbZDNSsNAFIUn9a/Wv2iXboJFcFKIoK6EIpuXFYwtCEMpnctEMnkzAzEUKor+LGhYpbX8Sdb+O0zUJbDwx8nHsv984JUkalsu1vo7Kyura+Ud2sbW3v7O6Z+wcPMskEAZckLBG9AEtglIOrqGLQSwXgOGDQDcY303r3EYSkCb9XeQp+jIecRpRgpa2BWfdA4Su76TW9EJhGL6UDs2G37JmsZXBKaKBSnYH5YUJyWLgijAsZd+xU+UXWChKGExqXiYhxWSMh9DXyHEM0i9mx0+sY+2EVpQI/biyZu7viQLHUuZxoDtjrEZysTY1/6v1MxVd+AXlaAk/miKGOWSqxpElZIBRDFcg2YCKpvtcgIC0yUzqumQ3AWv7wM7mnrsuXcnTXa12UaVXSIjtAJctA5aqNb1EuIihHz+gVvRlPxovxbnzMWytGOVNHf2R8/gDUPpPM</latexit>|F|2 ∼ mνmN v2 e2|Im ω|
<latexit sha1_base64="bDn2n7jPO4GI+DaqplfApJ+j4TY=">ACJHicbVBNSwMxEM36bf2qevQSLIHKbtFUMFDURC9iIK1QrdsulsDU2yS5ItlO3+GS/+FS8eVDx48beY1h60+mDg8d4M/PChDNtXPfDmZqemZ2bX1gsLC2vrK4V1zdudZwqCjUa81jdhUQDZxJqhkOd4kCIkIO9bB7OvTrPVCaxfLG9BNoCtKRLGKUGCsFxePB2aBVwb5mAvuRIjQTgS9TLILPOu1Krm/B62sMvAFMfdKZBfCKn4soEMGeVAsuWV3BPyXeGNSQmNcBcVXvx3TVIA0lBOtG56bmGZGlGUQ17wUw0JoV3SgYalkgjQzWz0ZY53rNLGUaxsSYNH6s+JjAit+yK0ncNj9aQ3FP/zGqmJDpsZk0lqQNLvRVHKsYnxMDLcZgqo4X1LCFXM3orpPbFZGRtswYbgTb78l9Qq5aOyd71fqp6M01hAW2gb7SIPHaAqOkdXqIYoekBP6AW9Oo/Os/PmvH+3TjnjmU30C87nF70Gpao=</latexit><latexit sha1_base64="bDn2n7jPO4GI+DaqplfApJ+j4TY=">ACJHicbVBNSwMxEM36bf2qevQSLIHKbtFUMFDURC9iIK1QrdsulsDU2yS5ItlO3+GS/+FS8eVDx48beY1h60+mDg8d4M/PChDNtXPfDmZqemZ2bX1gsLC2vrK4V1zdudZwqCjUa81jdhUQDZxJqhkOd4kCIkIO9bB7OvTrPVCaxfLG9BNoCtKRLGKUGCsFxePB2aBVwb5mAvuRIjQTgS9TLILPOu1Krm/B62sMvAFMfdKZBfCKn4soEMGeVAsuWV3BPyXeGNSQmNcBcVXvx3TVIA0lBOtG56bmGZGlGUQ17wUw0JoV3SgYalkgjQzWz0ZY53rNLGUaxsSYNH6s+JjAit+yK0ncNj9aQ3FP/zGqmJDpsZk0lqQNLvRVHKsYnxMDLcZgqo4X1LCFXM3orpPbFZGRtswYbgTb78l9Qq5aOyd71fqp6M01hAW2gb7SIPHaAqOkdXqIYoekBP6AW9Oo/Os/PmvH+3TjnjmU30C87nF70Gpao=</latexit><latexit sha1_base64="bDn2n7jPO4GI+DaqplfApJ+j4TY=">ACJHicbVBNSwMxEM36bf2qevQSLIHKbtFUMFDURC9iIK1QrdsulsDU2yS5ItlO3+GS/+FS8eVDx48beY1h60+mDg8d4M/PChDNtXPfDmZqemZ2bX1gsLC2vrK4V1zdudZwqCjUa81jdhUQDZxJqhkOd4kCIkIO9bB7OvTrPVCaxfLG9BNoCtKRLGKUGCsFxePB2aBVwb5mAvuRIjQTgS9TLILPOu1Krm/B62sMvAFMfdKZBfCKn4soEMGeVAsuWV3BPyXeGNSQmNcBcVXvx3TVIA0lBOtG56bmGZGlGUQ17wUw0JoV3SgYalkgjQzWz0ZY53rNLGUaxsSYNH6s+JjAit+yK0ncNj9aQ3FP/zGqmJDpsZk0lqQNLvRVHKsYnxMDLcZgqo4X1LCFXM3orpPbFZGRtswYbgTb78l9Qq5aOyd71fqp6M01hAW2gb7SIPHaAqOkdXqIYoekBP6AW9Oo/Os/PmvH+3TjnjmU30C87nF70Gpao=</latexit><latexit sha1_base64="bDn2n7jPO4GI+DaqplfApJ+j4TY=">ACJHicbVBNSwMxEM36bf2qevQSLIHKbtFUMFDURC9iIK1QrdsulsDU2yS5ItlO3+GS/+FS8eVDx48beY1h60+mDg8d4M/PChDNtXPfDmZqemZ2bX1gsLC2vrK4V1zdudZwqCjUa81jdhUQDZxJqhkOd4kCIkIO9bB7OvTrPVCaxfLG9BNoCtKRLGKUGCsFxePB2aBVwb5mAvuRIjQTgS9TLILPOu1Krm/B62sMvAFMfdKZBfCKn4soEMGeVAsuWV3BPyXeGNSQmNcBcVXvx3TVIA0lBOtG56bmGZGlGUQ17wUw0JoV3SgYalkgjQzWz0ZY53rNLGUaxsSYNH6s+JjAit+yK0ncNj9aQ3FP/zGqmJDpsZk0lqQNLvRVHKsYnxMDLcZgqo4X1LCFXM3orpPbFZGRtswYbgTb78l9Qq5aOyd71fqp6M01hAW2gb7SIPHaAqOkdXqIYoekBP6AW9Oo/Os/PmvH+3TjnjmU30C87nF70Gpao=</latexit>approximate lepton number symmetry
BS, Yavin, arXiv:1401.2459 Shaposhnikov, hep-ph/0605047
12
U`N = F`Nv mN
<latexit sha1_base64="wG1VZOH91wbn+TSjTkIRw0WHYM=">ACDXicbVBNS8NAEN3Ur1q/oh69LJaCp5KIoB6EoiCeSgVjC0Im+2mXbqbhN1NoYT8Ai/+FS8eVLx69+a/cdsG1NYHA4/3ZpiZFySMSmVZX0ZpaXlda28XtnY3NreMXf37mWcCkwcHLNYdAIkCaMRcRVjHQSQRAPGkHw6uJ3x4RIWkc3alxQjyO+hENKUZKS75Zc/zMJYzBZg4voBsKhLPrH2mUZ9xv5r5ZterWFHCR2AWpgIt3/x0ezFOYkUZkjKrm0lysuQUBQzklfcVJIE4SHqk6mEeJEetn0nRzWtNKDYSx0RQpO1d8TGeJSjnmgOzlSAznvTcT/vG6qwjMvo1GSKhLh2aIwZVDFcJIN7FBsGJjTRAWVN8K8QDpSJROsKJDsOdfXiTOcf28bt+eVBuXRplcAOwRGwSlogBvQAg7A4AE8gRfwajwaz8ab8T5rLRnFzD74A+PjG4T7m10=</latexit><latexit sha1_base64="wG1VZOH91wbn+TSjTkIRw0WHYM=">ACDXicbVBNS8NAEN3Ur1q/oh69LJaCp5KIoB6EoiCeSgVjC0Im+2mXbqbhN1NoYT8Ai/+FS8eVLx69+a/cdsG1NYHA4/3ZpiZFySMSmVZX0ZpaXlda28XtnY3NreMXf37mWcCkwcHLNYdAIkCaMRcRVjHQSQRAPGkHw6uJ3x4RIWkc3alxQjyO+hENKUZKS75Zc/zMJYzBZg4voBsKhLPrH2mUZ9xv5r5ZterWFHCR2AWpgIt3/x0ezFOYkUZkjKrm0lysuQUBQzklfcVJIE4SHqk6mEeJEetn0nRzWtNKDYSx0RQpO1d8TGeJSjnmgOzlSAznvTcT/vG6qwjMvo1GSKhLh2aIwZVDFcJIN7FBsGJjTRAWVN8K8QDpSJROsKJDsOdfXiTOcf28bt+eVBuXRplcAOwRGwSlogBvQAg7A4AE8gRfwajwaz8ab8T5rLRnFzD74A+PjG4T7m10=</latexit><latexit sha1_base64="wG1VZOH91wbn+TSjTkIRw0WHYM=">ACDXicbVBNS8NAEN3Ur1q/oh69LJaCp5KIoB6EoiCeSgVjC0Im+2mXbqbhN1NoYT8Ai/+FS8eVLx69+a/cdsG1NYHA4/3ZpiZFySMSmVZX0ZpaXlda28XtnY3NreMXf37mWcCkwcHLNYdAIkCaMRcRVjHQSQRAPGkHw6uJ3x4RIWkc3alxQjyO+hENKUZKS75Zc/zMJYzBZg4voBsKhLPrH2mUZ9xv5r5ZterWFHCR2AWpgIt3/x0ezFOYkUZkjKrm0lysuQUBQzklfcVJIE4SHqk6mEeJEetn0nRzWtNKDYSx0RQpO1d8TGeJSjnmgOzlSAznvTcT/vG6qwjMvo1GSKhLh2aIwZVDFcJIN7FBsGJjTRAWVN8K8QDpSJROsKJDsOdfXiTOcf28bt+eVBuXRplcAOwRGwSlogBvQAg7A4AE8gRfwajwaz8ab8T5rLRnFzD74A+PjG4T7m10=</latexit><latexit sha1_base64="wG1VZOH91wbn+TSjTkIRw0WHYM=">ACDXicbVBNS8NAEN3Ur1q/oh69LJaCp5KIoB6EoiCeSgVjC0Im+2mXbqbhN1NoYT8Ai/+FS8eVLx69+a/cdsG1NYHA4/3ZpiZFySMSmVZX0ZpaXlda28XtnY3NreMXf37mWcCkwcHLNYdAIkCaMRcRVjHQSQRAPGkHw6uJ3x4RIWkc3alxQjyO+hENKUZKS75Zc/zMJYzBZg4voBsKhLPrH2mUZ9xv5r5ZterWFHCR2AWpgIt3/x0ezFOYkUZkjKrm0lysuQUBQzklfcVJIE4SHqk6mEeJEetn0nRzWtNKDYSx0RQpO1d8TGeJSjnmgOzlSAznvTcT/vG6qwjMvo1GSKhLh2aIwZVDFcJIN7FBsGJjTRAWVN8K8QDpSJROsKJDsOdfXiTOcf28bt+eVBuXRplcAOwRGwSlogBvQAg7A4AE8gRfwajwaz8ab8T5rLRnFzD74A+PjG4T7m10=</latexit>N να sin θα
N
U`N
<latexit sha1_base64="gys9MhNypyS1DvV0amMzt2Jnyw=">AB/nicbVDLSsNAFJ34rPVFdy4GSyCq5KIoO6KblxJBWMLTQiTyU07dPJgZiKUmIW/4saFilu/w51/4zTNQlsPXDic+/cucdPOZPKNL+NhcWl5ZXV2lp9fWNza7uxs3svk0xQsGnCE9HziQTOYrAVUx6qQAS+Ry6/uhq4ncfQEiWxHdqnIbkUHMQkaJ0pLX2HfKN3IBQYFtL3eAc3xTeI2m2TJL4HliVaSJKnS8xpcTJDSLIFaUEyn7lpkqNydCMcqhqDuZhJTQERlAX9OYRCDdvNxd4COtBDhMhK5Y4VL9PZGTSMpx5OvOiKihnPUm4n9eP1PhuZuzOM0UxHS6KMw4VgmehIEDJoAqPtaEUMH0XzEdEkGo0pHVdQjW7MnzxD5pXbSs29Nm+7JKo4YO0CE6RhY6Q210jTrIRhQ9omf0it6MJ+PFeDc+pq0LRjWzh/7A+PwBWE6V3A=</latexit><latexit sha1_base64="gys9MhNypyS1DvV0amMzt2Jnyw=">AB/nicbVDLSsNAFJ34rPVFdy4GSyCq5KIoO6KblxJBWMLTQiTyU07dPJgZiKUmIW/4saFilu/w51/4zTNQlsPXDic+/cucdPOZPKNL+NhcWl5ZXV2lp9fWNza7uxs3svk0xQsGnCE9HziQTOYrAVUx6qQAS+Ry6/uhq4ncfQEiWxHdqnIbkUHMQkaJ0pLX2HfKN3IBQYFtL3eAc3xTeI2m2TJL4HliVaSJKnS8xpcTJDSLIFaUEyn7lpkqNydCMcqhqDuZhJTQERlAX9OYRCDdvNxd4COtBDhMhK5Y4VL9PZGTSMpx5OvOiKihnPUm4n9eP1PhuZuzOM0UxHS6KMw4VgmehIEDJoAqPtaEUMH0XzEdEkGo0pHVdQjW7MnzxD5pXbSs29Nm+7JKo4YO0CE6RhY6Q210jTrIRhQ9omf0it6MJ+PFeDc+pq0LRjWzh/7A+PwBWE6V3A=</latexit><latexit sha1_base64="gys9MhNypyS1DvV0amMzt2Jnyw=">AB/nicbVDLSsNAFJ34rPVFdy4GSyCq5KIoO6KblxJBWMLTQiTyU07dPJgZiKUmIW/4saFilu/w51/4zTNQlsPXDic+/cucdPOZPKNL+NhcWl5ZXV2lp9fWNza7uxs3svk0xQsGnCE9HziQTOYrAVUx6qQAS+Ry6/uhq4ncfQEiWxHdqnIbkUHMQkaJ0pLX2HfKN3IBQYFtL3eAc3xTeI2m2TJL4HliVaSJKnS8xpcTJDSLIFaUEyn7lpkqNydCMcqhqDuZhJTQERlAX9OYRCDdvNxd4COtBDhMhK5Y4VL9PZGTSMpx5OvOiKihnPUm4n9eP1PhuZuzOM0UxHS6KMw4VgmehIEDJoAqPtaEUMH0XzEdEkGo0pHVdQjW7MnzxD5pXbSs29Nm+7JKo4YO0CE6RhY6Q210jTrIRhQ9omf0it6MJ+PFeDc+pq0LRjWzh/7A+PwBWE6V3A=</latexit><latexit sha1_base64="gys9MhNypyS1DvV0amMzt2Jnyw=">AB/nicbVDLSsNAFJ34rPVFdy4GSyCq5KIoO6KblxJBWMLTQiTyU07dPJgZiKUmIW/4saFilu/w51/4zTNQlsPXDic+/cucdPOZPKNL+NhcWl5ZXV2lp9fWNza7uxs3svk0xQsGnCE9HziQTOYrAVUx6qQAS+Ry6/uhq4ncfQEiWxHdqnIbkUHMQkaJ0pLX2HfKN3IBQYFtL3eAc3xTeI2m2TJL4HliVaSJKnS8xpcTJDSLIFaUEyn7lpkqNydCMcqhqDuZhJTQERlAX9OYRCDdvNxd4COtBDhMhK5Y4VL9PZGTSMpx5OvOiKihnPUm4n9eP1PhuZuzOM0UxHS6KMw4VgmehIEDJoAqPtaEUMH0XzEdEkGo0pHVdQjW7MnzxD5pXbSs29Nm+7JKo4YO0CE6RhY6Q210jTrIRhQ9omf0it6MJ+PFeDc+pq0LRjWzh/7A+PwBWE6V3A=</latexit>Z
N
νµ
N
µ± W ⌥ ΓN ∼ |VµN|2G2
FM 5 N
µ Ds N θ2
µ
νµ
see e.g., Gorbunov and Shaposhnikov, arXiv:0705.1729; Atre, Han, Pascoli, Zhang, arXiv:0901.3589; Deppisch, Dev, Pilaftsis, arXiv:1502.06541
13
100 101
mN (GeV)
10−13 10−12 10−11 10−10 10−9 10−8 10−7 10−6 10−5 10−4
|UµN|2 ILC NA62 LBNE/DUNE SHiP CEPC FCC-ee MATHUSLA HL-LHC (W/Z) MATHUSLA HL-LHC (B/D-Meson) MATHUSLA FCC-hh (Standard) (W/Z) MATHUSLA FCC-hh (Forward) (W/Z) BBN Neutrino Osc. (n = 2) Leptogenesis (n = 2) Current Exp. Limits
Drewes, Mohapatra, BS (ed.), “Theory Motivation for LLPs: Neutrino Masses”, MATHUSLA theory case
14
W +
µ+
N
µ+
e−
¯ νe
Izaguirre, BS, arXiv:1504.02470 (GeV)
1 10
2
10
3
10
(GeV)
N
m
5 −
10
4 −
10
3 −
10
2 −
10
1 −
10 1
2
|
N µ
|V
95% CL upper limits Expected 2 std. deviation ± 1 std. deviation ± Observed decays prompt N Observed, DELPHI prompt DELPHI long-lived CMS 8 TeV ATLAS
CMS
(13 TeV)
35.9 fb
2 vs. m
(left) and V
2 vs. m
(right) planes.
CMS, arXiv:1802.02965
14
W +
µ+
N
µ+
e−
¯ νe
Izaguirre, BS, arXiv:1504.02470 (GeV)
1 10
2
10
3
10
(GeV)
N
m
5 −
10
4 −
10
3 −
10
2 −
10
1 −
10 1
2
|
N µ
|V
95% CL upper limits Expected 2 std. deviation ± 1 std. deviation ± Observed decays prompt N Observed, DELPHI prompt DELPHI long-lived CMS 8 TeV ATLAS
CMS
(13 TeV)
35.9 fb
2 vs. m
(left) and V
2 vs. m
(right) planes.
CMS, arXiv:1802.02965
displaced search can target this region
15
direct CP-violating decays!
" ≡ Γ(N → `−W +∗) − Γ(N → `+W −∗) Γ(N → `−W +∗) + Γ(N → `+W −∗) ∼ ΓN MN ∆M/MN ∆M 2/M 2
N + (Γ/MN)2
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<latexit sha1_base64="UanMY1aYKcj3bc/g+9vdcqSWsbQ=">ACAHicbVDLSsNAFJ34rPUVdSO4GSyCG0tSBHUhFHXhplLB2EIbwmQ6aYdOJmFmIpQN/6KGxcqbv0Md/6NkzYLbT1wuYdz7mXmHj9mVCrL+jbm5hcWl5ZLK+XVtfWNTXNr+15GicDEwRGLRNtHkjDKiaOoYqQdC4JCn5GWP7zM/dYDEZJG/E6NYuKGqM9pQDFSWvLM3e4VYQrBjyHDS+9qWVHebMz6xYVWsMOEvsglRAgaZnfnV7EU5CwhVmSMqObcXKTZFQFDOSlbuJDHCQ9QnHU05Col0/EFGTzQSg8GkdDFRyrvzdSFEo5Cn09GSI1kNeLv7ndRIVnLop5XGiCMeTh4KEQRXBPA7Yo4JgxUaICyo/ivEAyQVjq0sg7Bnj5lji16lnVvj2u1C+KNEpgD+yDQ2CDE1AH16AJHIDBI3gGr+DNeDJejHfjYzI6ZxQ7O+APjM8fTpqVEw=</latexit><latexit sha1_base64="UanMY1aYKcj3bc/g+9vdcqSWsbQ=">ACAHicbVDLSsNAFJ34rPUVdSO4GSyCG0tSBHUhFHXhplLB2EIbwmQ6aYdOJmFmIpQN/6KGxcqbv0Md/6NkzYLbT1wuYdz7mXmHj9mVCrL+jbm5hcWl5ZLK+XVtfWNTXNr+15GicDEwRGLRNtHkjDKiaOoYqQdC4JCn5GWP7zM/dYDEZJG/E6NYuKGqM9pQDFSWvLM3e4VYQrBjyHDS+9qWVHebMz6xYVWsMOEvsglRAgaZnfnV7EU5CwhVmSMqObcXKTZFQFDOSlbuJDHCQ9QnHU05Col0/EFGTzQSg8GkdDFRyrvzdSFEo5Cn09GSI1kNeLv7ndRIVnLop5XGiCMeTh4KEQRXBPA7Yo4JgxUaICyo/ivEAyQVjq0sg7Bnj5lji16lnVvj2u1C+KNEpgD+yDQ2CDE1AH16AJHIDBI3gGr+DNeDJejHfjYzI6ZxQ7O+APjM8fTpqVEw=</latexit><latexit sha1_base64="UanMY1aYKcj3bc/g+9vdcqSWsbQ=">ACAHicbVDLSsNAFJ34rPUVdSO4GSyCG0tSBHUhFHXhplLB2EIbwmQ6aYdOJmFmIpQN/6KGxcqbv0Md/6NkzYLbT1wuYdz7mXmHj9mVCrL+jbm5hcWl5ZLK+XVtfWNTXNr+15GicDEwRGLRNtHkjDKiaOoYqQdC4JCn5GWP7zM/dYDEZJG/E6NYuKGqM9pQDFSWvLM3e4VYQrBjyHDS+9qWVHebMz6xYVWsMOEvsglRAgaZnfnV7EU5CwhVmSMqObcXKTZFQFDOSlbuJDHCQ9QnHU05Col0/EFGTzQSg8GkdDFRyrvzdSFEo5Cn09GSI1kNeLv7ndRIVnLop5XGiCMeTh4KEQRXBPA7Yo4JgxUaICyo/ivEAyQVjq0sg7Bnj5lji16lnVvj2u1C+KNEpgD+yDQ2CDE1AH16AJHIDBI3gGr+DNeDJejHfjYzI6ZxQ7O+APjM8fTpqVEw=</latexit><latexit sha1_base64="UanMY1aYKcj3bc/g+9vdcqSWsbQ=">ACAHicbVDLSsNAFJ34rPUVdSO4GSyCG0tSBHUhFHXhplLB2EIbwmQ6aYdOJmFmIpQN/6KGxcqbv0Md/6NkzYLbT1wuYdz7mXmHj9mVCrL+jbm5hcWl5ZLK+XVtfWNTXNr+15GicDEwRGLRNtHkjDKiaOoYqQdC4JCn5GWP7zM/dYDEZJG/E6NYuKGqM9pQDFSWvLM3e4VYQrBjyHDS+9qWVHebMz6xYVWsMOEvsglRAgaZnfnV7EU5CwhVmSMqObcXKTZFQFDOSlbuJDHCQ9QnHU05Col0/EFGTzQSg8GkdDFRyrvzdSFEo5Cn09GSI1kNeLv7ndRIVnLop5XGiCMeTh4KEQRXBPA7Yo4JgxUaICyo/ivEAyQVjq0sg7Bnj5lji16lnVvj2u1C+KNEpgD+yDQ2CDE1AH16AJHIDBI3gGr+DNeDJejHfjYzI6ZxQ7O+APjM8fTpqVEw=</latexit>(ΓN/MN . 10−12)
<latexit sha1_base64="JrA9qZXfp2WctW8J63y09qJG8Mg=">ACXicbVBNS8NAEN3Ur1q/oh69rBahHqxJEdRb0YNeLBWMLTQxbLbduluEnY3Qgk9e/GvePGg4tV/4M1/47bNQVsfDzem2FmXhAzKpVlfRu5ufmFxaX8cmFldW19w9zcupNRIjBxcMQi0QyQJIyGxFUMdKMBUE8YKQR9C9GfuOBCEmj8FYNYuJx1A1ph2KktOSbuyX3EnGO/Bo8gtd+zWVESk5tK379NCuDA98s2iVrTHgLEzUgQZ6r75bYjnHASKsyQlC3bipWXIqEoZmRYcBNJYoT7qEtamoaIE+ml41eGcF8rbdiJhK5QwbH6eyJFXMoBD3QnR6onp72R+J/XSlTn1EtpGCeKhHiyqJMwqCI4ygW2qSBYsYEmCAuqb4W4hwTCSqdX0CHY0y/PEqdSPivbN8fF6nmWRh7sgD1QAjY4AVwBerARg8gmfwCt6MJ+PFeDc+Jq05I5vZBn9gfP4AIGOYMg=</latexit><latexit sha1_base64="JrA9qZXfp2WctW8J63y09qJG8Mg=">ACXicbVBNS8NAEN3Ur1q/oh69rBahHqxJEdRb0YNeLBWMLTQxbLbduluEnY3Qgk9e/GvePGg4tV/4M1/47bNQVsfDzem2FmXhAzKpVlfRu5ufmFxaX8cmFldW19w9zcupNRIjBxcMQi0QyQJIyGxFUMdKMBUE8YKQR9C9GfuOBCEmj8FYNYuJx1A1ph2KktOSbuyX3EnGO/Bo8gtd+zWVESk5tK379NCuDA98s2iVrTHgLEzUgQZ6r75bYjnHASKsyQlC3bipWXIqEoZmRYcBNJYoT7qEtamoaIE+ml41eGcF8rbdiJhK5QwbH6eyJFXMoBD3QnR6onp72R+J/XSlTn1EtpGCeKhHiyqJMwqCI4ygW2qSBYsYEmCAuqb4W4hwTCSqdX0CHY0y/PEqdSPivbN8fF6nmWRh7sgD1QAjY4AVwBerARg8gmfwCt6MJ+PFeDc+Jq05I5vZBn9gfP4AIGOYMg=</latexit><latexit sha1_base64="JrA9qZXfp2WctW8J63y09qJG8Mg=">ACXicbVBNS8NAEN3Ur1q/oh69rBahHqxJEdRb0YNeLBWMLTQxbLbduluEnY3Qgk9e/GvePGg4tV/4M1/47bNQVsfDzem2FmXhAzKpVlfRu5ufmFxaX8cmFldW19w9zcupNRIjBxcMQi0QyQJIyGxFUMdKMBUE8YKQR9C9GfuOBCEmj8FYNYuJx1A1ph2KktOSbuyX3EnGO/Bo8gtd+zWVESk5tK379NCuDA98s2iVrTHgLEzUgQZ6r75bYjnHASKsyQlC3bipWXIqEoZmRYcBNJYoT7qEtamoaIE+ml41eGcF8rbdiJhK5QwbH6eyJFXMoBD3QnR6onp72R+J/XSlTn1EtpGCeKhHiyqJMwqCI4ygW2qSBYsYEmCAuqb4W4hwTCSqdX0CHY0y/PEqdSPivbN8fF6nmWRh7sgD1QAjY4AVwBerARg8gmfwCt6MJ+PFeDc+Jq05I5vZBn9gfP4AIGOYMg=</latexit><latexit sha1_base64="JrA9qZXfp2WctW8J63y09qJG8Mg=">ACXicbVBNS8NAEN3Ur1q/oh69rBahHqxJEdRb0YNeLBWMLTQxbLbduluEnY3Qgk9e/GvePGg4tV/4M1/47bNQVsfDzem2FmXhAzKpVlfRu5ufmFxaX8cmFldW19w9zcupNRIjBxcMQi0QyQJIyGxFUMdKMBUE8YKQR9C9GfuOBCEmj8FYNYuJx1A1ph2KktOSbuyX3EnGO/Bo8gtd+zWVESk5tK379NCuDA98s2iVrTHgLEzUgQZ6r75bYjnHASKsyQlC3bipWXIqEoZmRYcBNJYoT7qEtamoaIE+ml41eGcF8rbdiJhK5QwbH6eyJFXMoBD3QnR6onp72R+J/XSlTn1EtpGCeKhHiyqJMwqCI4ygW2qSBYsYEmCAuqb4W4hwTCSqdX0CHY0y/PEqdSPivbN8fF6nmWRh7sgD1QAjY4AVwBerARg8gmfwCt6MJ+PFeDc+Jq05I5vZBn9gfP4AIGOYMg=</latexit>Cvetič, Kim, Zamora-Saa, arXiv:1403.2555
16
asymmetry in semileptonic decays
100 101
mN (GeV)
10−13 10−12 10−11 10−10 10−9 10−8 10−7 10−6 10−5 10−4
|UµN|2 ILC NA62 LBNE/DUNE SHiP CEPC FCC-ee MATHUSLA HL-LHC (W/Z) MATHUSLA HL-LHC (B/D-Meson) MATHUSLA FCC-hh (Standard) (W/Z) MATHUSLA FCC-hh (Forward) (W/Z) BBN Neutrino Osc. (n = 2) Leptogenesis (n = 2) Current Exp. Limits
17
backgrounds and be harder to reconstruct N mass peaks
W +
µ+
N
µ+
e−
¯ νe
N → µ+e−νe
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vs.
N → µ−e+¯ νe
<latexit sha1_base64="NjYSoprBxztKB3J5WS8WZtnimM=">ACnicbVBNS8NAEN3Ur1q/oh69LC2CIJZEBPVW9OJKhbaNqw2U7bpZtN2N0oJfTuxb/ixYOKV3+BN/+N24+Dtj4YeLw3w8y8MOFMacf5tnILi0vLK/nVwtr6xuaWvb1zp+JUvBozGNZD4kCzgR4mkO9UQCiUIOtbB/OfJr9yAVi8WtHiTQjEhXsA6jRBspsIvXvmTdniZSxg/Yj9LWEYbWIfZDIjNfpMArvklJ0x8Dxp6SEpqgG9pfjmkagdCUE6UarpPoZkakZpTDsOCnChJC+6QLDUMFiUA1s/EvQ7xvlDbuxNKU0His/p7ISKTUIApNZ0R0T816I/E/r5HqzlkzYyJNQg6WdRJOdYxHgWD20wC1XxgCKGSmVsx7RFJqDbxFUwI7uzL8Q7Lp+X3ZuTUuVimkYe7aEiOkAuOkUVdIWqyEMUPaJn9IrerCfrxXq3PiatOWs6s4v+wPr8AbaEmk=</latexit><latexit sha1_base64="NjYSoprBxztKB3J5WS8WZtnimM=">ACnicbVBNS8NAEN3Ur1q/oh69LC2CIJZEBPVW9OJKhbaNqw2U7bpZtN2N0oJfTuxb/ixYOKV3+BN/+N24+Dtj4YeLw3w8y8MOFMacf5tnILi0vLK/nVwtr6xuaWvb1zp+JUvBozGNZD4kCzgR4mkO9UQCiUIOtbB/OfJr9yAVi8WtHiTQjEhXsA6jRBspsIvXvmTdniZSxg/Yj9LWEYbWIfZDIjNfpMArvklJ0x8Dxp6SEpqgG9pfjmkagdCUE6UarpPoZkakZpTDsOCnChJC+6QLDUMFiUA1s/EvQ7xvlDbuxNKU0His/p7ISKTUIApNZ0R0T816I/E/r5HqzlkzYyJNQg6WdRJOdYxHgWD20wC1XxgCKGSmVsx7RFJqDbxFUwI7uzL8Q7Lp+X3ZuTUuVimkYe7aEiOkAuOkUVdIWqyEMUPaJn9IrerCfrxXq3PiatOWs6s4v+wPr8AbaEmk=</latexit><latexit sha1_base64="NjYSoprBxztKB3J5WS8WZtnimM=">ACnicbVBNS8NAEN3Ur1q/oh69LC2CIJZEBPVW9OJKhbaNqw2U7bpZtN2N0oJfTuxb/ixYOKV3+BN/+N24+Dtj4YeLw3w8y8MOFMacf5tnILi0vLK/nVwtr6xuaWvb1zp+JUvBozGNZD4kCzgR4mkO9UQCiUIOtbB/OfJr9yAVi8WtHiTQjEhXsA6jRBspsIvXvmTdniZSxg/Yj9LWEYbWIfZDIjNfpMArvklJ0x8Dxp6SEpqgG9pfjmkagdCUE6UarpPoZkakZpTDsOCnChJC+6QLDUMFiUA1s/EvQ7xvlDbuxNKU0His/p7ISKTUIApNZ0R0T816I/E/r5HqzlkzYyJNQg6WdRJOdYxHgWD20wC1XxgCKGSmVsx7RFJqDbxFUwI7uzL8Q7Lp+X3ZuTUuVimkYe7aEiOkAuOkUVdIWqyEMUPaJn9IrerCfrxXq3PiatOWs6s4v+wPr8AbaEmk=</latexit><latexit sha1_base64="NjYSoprBxztKB3J5WS8WZtnimM=">ACnicbVBNS8NAEN3Ur1q/oh69LC2CIJZEBPVW9OJKhbaNqw2U7bpZtN2N0oJfTuxb/ixYOKV3+BN/+N24+Dtj4YeLw3w8y8MOFMacf5tnILi0vLK/nVwtr6xuaWvb1zp+JUvBozGNZD4kCzgR4mkO9UQCiUIOtbB/OfJr9yAVi8WtHiTQjEhXsA6jRBspsIvXvmTdniZSxg/Yj9LWEYbWIfZDIjNfpMArvklJ0x8Dxp6SEpqgG9pfjmkagdCUE6UarpPoZkakZpTDsOCnChJC+6QLDUMFiUA1s/EvQ7xvlDbuxNKU0His/p7ISKTUIApNZ0R0T816I/E/r5HqzlkzYyJNQg6WdRJOdYxHgWD20wC1XxgCKGSmVsx7RFJqDbxFUwI7uzL8Q7Lp+X3ZuTUuVimkYe7aEiOkAuOkUVdIWqyEMUPaJn9IrerCfrxXq3PiatOWs6s4v+wPr8AbaEmk=</latexit>Izaguirre, BS, arXiv:1504.02470
18
Challenges with direct observation of CPV:
some contexts
leptogenesis
account for late-time lepton asymmetry for DM production
∆M/MN ∼ 10−15
<latexit sha1_base64="9wtcBTJSxw/LroVnzgOkVhUxsac=">ACAnicbVBNS8NAEN3Ur1q/ot70slgEL9ZEFPVW1IOXSgVjC0Mm+2mXbqbhN2NUELBi3/FiwcVr/4Kb/4bt20O2vpg4PHeDPzgoRqSzr2yjMzM7NLxQXS0vLK6tr5vrGnYxTgYmDYxaLZoAkYTQijqKkWYiCOIBI42gdzH0Gw9ESBpHt6qfEI+jTkRDipHSkm9uZeEKQRrBzX/GrqScmhb9m+fTzwzbJVsUaA08TOSRnkqPvml9uOcpJpDBDUrZsK1FehoSimJFByU0lSRDuoQ5paRohTqSXjX4YwF2tGEYC12RgiP190SGuJR9HuhOjlRXTnpD8T+vlarw1MtolKSKRHi8KEwZVDEcBgLbVBCsWF8ThAXVt0LcRQJhpWMr6RDsyZeniXNYOavYN0fl6nmeRhFsgx2wB2xwAqrgCtSBAzB4BM/gFbwZT8aL8W58jFsLRj6zCf7A+PwBRbqVjg=</latexit><latexit sha1_base64="9wtcBTJSxw/LroVnzgOkVhUxsac=">ACAnicbVBNS8NAEN3Ur1q/ot70slgEL9ZEFPVW1IOXSgVjC0Mm+2mXbqbhN2NUELBi3/FiwcVr/4Kb/4bt20O2vpg4PHeDPzgoRqSzr2yjMzM7NLxQXS0vLK6tr5vrGnYxTgYmDYxaLZoAkYTQijqKkWYiCOIBI42gdzH0Gw9ESBpHt6qfEI+jTkRDipHSkm9uZeEKQRrBzX/GrqScmhb9m+fTzwzbJVsUaA08TOSRnkqPvml9uOcpJpDBDUrZsK1FehoSimJFByU0lSRDuoQ5paRohTqSXjX4YwF2tGEYC12RgiP190SGuJR9HuhOjlRXTnpD8T+vlarw1MtolKSKRHi8KEwZVDEcBgLbVBCsWF8ThAXVt0LcRQJhpWMr6RDsyZeniXNYOavYN0fl6nmeRhFsgx2wB2xwAqrgCtSBAzB4BM/gFbwZT8aL8W58jFsLRj6zCf7A+PwBRbqVjg=</latexit><latexit sha1_base64="9wtcBTJSxw/LroVnzgOkVhUxsac=">ACAnicbVBNS8NAEN3Ur1q/ot70slgEL9ZEFPVW1IOXSgVjC0Mm+2mXbqbhN2NUELBi3/FiwcVr/4Kb/4bt20O2vpg4PHeDPzgoRqSzr2yjMzM7NLxQXS0vLK6tr5vrGnYxTgYmDYxaLZoAkYTQijqKkWYiCOIBI42gdzH0Gw9ESBpHt6qfEI+jTkRDipHSkm9uZeEKQRrBzX/GrqScmhb9m+fTzwzbJVsUaA08TOSRnkqPvml9uOcpJpDBDUrZsK1FehoSimJFByU0lSRDuoQ5paRohTqSXjX4YwF2tGEYC12RgiP190SGuJR9HuhOjlRXTnpD8T+vlarw1MtolKSKRHi8KEwZVDEcBgLbVBCsWF8ThAXVt0LcRQJhpWMr6RDsyZeniXNYOavYN0fl6nmeRhFsgx2wB2xwAqrgCtSBAzB4BM/gFbwZT8aL8W58jFsLRj6zCf7A+PwBRbqVjg=</latexit><latexit sha1_base64="9wtcBTJSxw/LroVnzgOkVhUxsac=">ACAnicbVBNS8NAEN3Ur1q/ot70slgEL9ZEFPVW1IOXSgVjC0Mm+2mXbqbhN2NUELBi3/FiwcVr/4Kb/4bt20O2vpg4PHeDPzgoRqSzr2yjMzM7NLxQXS0vLK6tr5vrGnYxTgYmDYxaLZoAkYTQijqKkWYiCOIBI42gdzH0Gw9ESBpHt6qfEI+jTkRDipHSkm9uZeEKQRrBzX/GrqScmhb9m+fTzwzbJVsUaA08TOSRnkqPvml9uOcpJpDBDUrZsK1FehoSimJFByU0lSRDuoQ5paRohTqSXjX4YwF2tGEYC12RgiP190SGuJR9HuhOjlRXTnpD8T+vlarw1MtolKSKRHi8KEwZVDEcBgLbVBCsWF8ThAXVt0LcRQJhpWMr6RDsyZeniXNYOavYN0fl6nmeRhFsgx2wB2xwAqrgCtSBAzB4BM/gFbwZT8aL8W58jFsLRj6zCf7A+PwBRbqVjg=</latexit>Drewes, Garbrecht, arXiv:1206.5537; BS, Yavin, arXiv:1401.2459
19
FαI = i v Uν √mν R √mN
<latexit sha1_base64="QkDThXxI0JhTfVq1t70ujFrWzs=">ACJHicbZDLSsNAFIYn9VbrLerSzWARXJSiKCQlEQ3UgVYwtNCZPpB06mcSZSaGEvIwbX8WNCysu3PgsTi+Ctv4w8PGfczhzfj9mVCrL+jRyc/MLi0v5cLK6tr6hrm59SCjRGDi4IhFou4jSRjlxFUMVKPBUGhz0jN714M67UeEZJG/F71Y9IMUZvTgGKktOWZp5de6iIWdxC8zuAZdAOBcEqztJc5nsTVz4KlYZDzKBbunNL8Me6yTyzaJWtkeAs2BMogomqnjlwWxFOQsIVZkjKhm3FqpkioShmJCu4iSQxwl3UJg2NHIVENtPRlRnc04LBpHQjys4cn9PpCiUsh/6ujNEqiOna0Pzv1ojUcFxM6U8ThTheLwoSBhUERxGBltUEKxYXwPCguq/QtxBOielgy3oEOzpk2fBOSiflO3bw2LlfJGHuyAXbAPbHAEKuAKVIEDMHgCL+ANDIxn49V4Nz7GrTljMrMN/sj4+gZ3faV5</latexit><latexit sha1_base64="QkDThXxI0JhTfVq1t70ujFrWzs=">ACJHicbZDLSsNAFIYn9VbrLerSzWARXJSiKCQlEQ3UgVYwtNCZPpB06mcSZSaGEvIwbX8WNCysu3PgsTi+Ctv4w8PGfczhzfj9mVCrL+jRyc/MLi0v5cLK6tr6hrm59SCjRGDi4IhFou4jSRjlxFUMVKPBUGhz0jN714M67UeEZJG/F71Y9IMUZvTgGKktOWZp5de6iIWdxC8zuAZdAOBcEqztJc5nsTVz4KlYZDzKBbunNL8Me6yTyzaJWtkeAs2BMogomqnjlwWxFOQsIVZkjKhm3FqpkioShmJCu4iSQxwl3UJg2NHIVENtPRlRnc04LBpHQjys4cn9PpCiUsh/6ujNEqiOna0Pzv1ojUcFxM6U8ThTheLwoSBhUERxGBltUEKxYXwPCguq/QtxBOielgy3oEOzpk2fBOSiflO3bw2LlfJGHuyAXbAPbHAEKuAKVIEDMHgCL+ANDIxn49V4Nz7GrTljMrMN/sj4+gZ3faV5</latexit><latexit sha1_base64="QkDThXxI0JhTfVq1t70ujFrWzs=">ACJHicbZDLSsNAFIYn9VbrLerSzWARXJSiKCQlEQ3UgVYwtNCZPpB06mcSZSaGEvIwbX8WNCysu3PgsTi+Ctv4w8PGfczhzfj9mVCrL+jRyc/MLi0v5cLK6tr6hrm59SCjRGDi4IhFou4jSRjlxFUMVKPBUGhz0jN714M67UeEZJG/F71Y9IMUZvTgGKktOWZp5de6iIWdxC8zuAZdAOBcEqztJc5nsTVz4KlYZDzKBbunNL8Me6yTyzaJWtkeAs2BMogomqnjlwWxFOQsIVZkjKhm3FqpkioShmJCu4iSQxwl3UJg2NHIVENtPRlRnc04LBpHQjys4cn9PpCiUsh/6ujNEqiOna0Pzv1ojUcFxM6U8ThTheLwoSBhUERxGBltUEKxYXwPCguq/QtxBOielgy3oEOzpk2fBOSiflO3bw2LlfJGHuyAXbAPbHAEKuAKVIEDMHgCL+ANDIxn49V4Nz7GrTljMrMN/sj4+gZ3faV5</latexit>Uν = c12c13 s12c13 s13e−iδ −s12c23 − c12s23s13eiδ c12c23 − s12s23s13eiδ s23c13 s12s23 − c12c23s13eiδ −c12s23 − s12c23s13eiδ c23c13 eiα1/2 eiα2/2 1
<latexit sha1_base64="aENbOusfC9/al91CRuNRgZdeQ=">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</latexit><latexit sha1_base64="aENbOusfC9/al91CRuNRgZdeQ=">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</latexit><latexit sha1_base64="aENbOusfC9/al91CRuNRgZdeQ=">ADinichVJb9MwFHYTLiUw6OCRF4sKNB5akhRpmxDSBDzwOCTCJjUlctyT1prjRLaDVEX5Mfwl3vg3OJdV6bqJIx3r8/m+c/GR45wzpV378Cy791/8HD4yHn85ODps9Hh8x8qKySFgGY8k5cxUcCZgEAzeEyl0DSmMNFfPW5i9+gVQsE9/1JodFSlaCJYwSbULR4eB3EIWi+BhySPRGMOKiZJISTZVSmtHBqVnl/V56zCb7Dav84q+FlOWLgErkVhs5kK/Jn1aQtoJrLVn6tNiVoX6z+I26Ztr3p1JdP+oVuy92ZGfGO8badnJCEMtuK04o2Wqt3965sKYM4fmaRN47vy7lNm7GrUGP9q/pjqrd67XqOkWjsTt1G8P7wOvAGHV2Ho3+hMuMFikITlRau65uV6YopRDuYFhYKc0CuygrmBgqSgFmXzlyr82kSWOMmkcaFxE+1nlCRVapPGRpkSvVY3uTp4GzcvdHKyKJnICw2Cto2SgmOd4fpj4iWTQDXfGECoZGZWTNdEqrN93XMErybT94HgT89nXrf3o/PnXbGKX6BU6Qh46RmfoKzpHAaLW0Jpax9aJfWDP7FP7Qyu1Bl3OC7Rj9pd/tjoZCg=</latexit>typically non-zero
δ + (α1 + α2)/2 = ±π/2
<latexit sha1_base64="nxC/02Zphz+dJCnHw6T/h2pXOKM=">ACEXicbZBPSwJBGMZn7Z/ZP6tjlyEJFEF3JagOgdSlo0GbgrvIu+Oog7O7w8xsIOJn6NJX6dKhomu3bn2bRt1DaQ8M/Hje9+Wd9wkEZ0rb9reVWVldW9/Ibua2tnd29/L7B/cqTiShLol5LFsBKMpZRF3NKctISmEAafNYHg9rTcfqFQsju70SFA/hH7EeoyANlYnX/K6lGvAZVz0gIsBdJxyCrVStYvsSdCT7BqrZMv2BV7JrwMTgoFlKrRyX953ZgkIY04aBU27GF9scgNSOcTnJeoqgAMoQ+bRuMIKTKH89OmuAT43RxL5bmRrP3N8TYwiVGoWB6QxBD9RibWr+V2snunfuj1kEk0jMl/USzjWMZ7mg7tMUqL5yAQycxfMRmABKJNijkTgrN48jK4tcpFxbk9LdSv0jSy6AgdoyJy0BmqoxvUQC4i6BE9o1f0Zj1ZL9a79TFvzVjpzCH6I+vzB2Mkmvg=</latexit><latexit sha1_base64="nxC/02Zphz+dJCnHw6T/h2pXOKM=">ACEXicbZBPSwJBGMZn7Z/ZP6tjlyEJFEF3JagOgdSlo0GbgrvIu+Oog7O7w8xsIOJn6NJX6dKhomu3bn2bRt1DaQ8M/Hje9+Wd9wkEZ0rb9reVWVldW9/Ibua2tnd29/L7B/cqTiShLol5LFsBKMpZRF3NKctISmEAafNYHg9rTcfqFQsju70SFA/hH7EeoyANlYnX/K6lGvAZVz0gIsBdJxyCrVStYvsSdCT7BqrZMv2BV7JrwMTgoFlKrRyX953ZgkIY04aBU27GF9scgNSOcTnJeoqgAMoQ+bRuMIKTKH89OmuAT43RxL5bmRrP3N8TYwiVGoWB6QxBD9RibWr+V2snunfuj1kEk0jMl/USzjWMZ7mg7tMUqL5yAQycxfMRmABKJNijkTgrN48jK4tcpFxbk9LdSv0jSy6AgdoyJy0BmqoxvUQC4i6BE9o1f0Zj1ZL9a79TFvzVjpzCH6I+vzB2Mkmvg=</latexit><latexit sha1_base64="nxC/02Zphz+dJCnHw6T/h2pXOKM=">ACEXicbZBPSwJBGMZn7Z/ZP6tjlyEJFEF3JagOgdSlo0GbgrvIu+Oog7O7w8xsIOJn6NJX6dKhomu3bn2bRt1DaQ8M/Hje9+Wd9wkEZ0rb9reVWVldW9/Ibua2tnd29/L7B/cqTiShLol5LFsBKMpZRF3NKctISmEAafNYHg9rTcfqFQsju70SFA/hH7EeoyANlYnX/K6lGvAZVz0gIsBdJxyCrVStYvsSdCT7BqrZMv2BV7JrwMTgoFlKrRyX953ZgkIY04aBU27GF9scgNSOcTnJeoqgAMoQ+bRuMIKTKH89OmuAT43RxL5bmRrP3N8TYwiVGoWB6QxBD9RibWr+V2snunfuj1kEk0jMl/USzjWMZ7mg7tMUqL5yAQycxfMRmABKJNijkTgrN48jK4tcpFxbk9LdSv0jSy6AgdoyJy0BmqoxvUQC4i6BE9o1f0Zj1ZL9a79TFvzVjpzCH6I+vzB2Mkmvg=</latexit><latexit sha1_base64="nxC/02Zphz+dJCnHw6T/h2pXOKM=">ACEXicbZBPSwJBGMZn7Z/ZP6tjlyEJFEF3JagOgdSlo0GbgrvIu+Oog7O7w8xsIOJn6NJX6dKhomu3bn2bRt1DaQ8M/Hje9+Wd9wkEZ0rb9reVWVldW9/Ibua2tnd29/L7B/cqTiShLol5LFsBKMpZRF3NKctISmEAafNYHg9rTcfqFQsju70SFA/hH7EeoyANlYnX/K6lGvAZVz0gIsBdJxyCrVStYvsSdCT7BqrZMv2BV7JrwMTgoFlKrRyX953ZgkIY04aBU27GF9scgNSOcTnJeoqgAMoQ+bRuMIKTKH89OmuAT43RxL5bmRrP3N8TYwiVGoWB6QxBD9RibWr+V2snunfuj1kEk0jMl/USzjWMZ7mg7tMUqL5yAQycxfMRmABKJNijkTgrN48jK4tcpFxbk9LdSv0jSy6AgdoyJy0BmqoxvUQC4i6BE9o1f0Zj1ZL9a79TFvzVjpzCH6I+vzB2Mkmvg=</latexit>20
typically non-zero
0.5 1.0 1.5
1.5 ¥10-10 GHm Æ N+L ê GHt Æ N+L YDB
BS, Yavin, arXiv:1401.2459
21
1 10 100 1000 104 10-14 10-13 10-12 10-11 10-10 coshH 2 Im w L » YDB » 1 10 100 1000 104 10-17 10-16 10-15 10-14 10-13 10-12 G HGeVL
electron muon tau Regime I Regime II Regime III
α1 + α2 = −π/2
<latexit sha1_base64="q9bUR7+rYovPwrJ4HAImgca3wc=">ACAnicbZBPS8MwGMZT/875r+pNL8EhCOJsh6AehKEXjxOsG6ylpFm6haVpSFJhlIEXv4oXDype/RTe/DZmWw+6+UDgx/O+L2/eJxKMKu0439bc/MLi0nJpby6tr6xaW9t36s0k5h4OGWpbEVIEUY58TVjLSEJCiJGlG/etRvflApKIpv9MDQYIEdTmNKUbaWKG96yMmeih0jwqowUt47At6UgvtilN1xoKz4BZQAYUaof3ld1KcJYRrzJBSbdcROsiR1BQzMiz7mSIC4T7qkrZBjhKignx8wxAeGKcD41SaxzUcu78ncpQoNUgi05kg3VPTtZH5X62d6fg8yCkXmSYcTxbFGYM6haNAYIdKgjUbGEBYUvNXiHtIqxNbGUTgjt98ix4tepF1b09rdSvijRKYA/sg0PgjNQBzegATyAwSN4Bq/gzXqyXqx362PSOmcVMzvgj6zPH7b6ldM=</latexit><latexit sha1_base64="q9bUR7+rYovPwrJ4HAImgca3wc=">ACAnicbZBPS8MwGMZT/875r+pNL8EhCOJsh6AehKEXjxOsG6ylpFm6haVpSFJhlIEXv4oXDype/RTe/DZmWw+6+UDgx/O+L2/eJxKMKu0439bc/MLi0nJpby6tr6xaW9t36s0k5h4OGWpbEVIEUY58TVjLSEJCiJGlG/etRvflApKIpv9MDQYIEdTmNKUbaWKG96yMmeih0jwqowUt47At6UgvtilN1xoKz4BZQAYUaof3ld1KcJYRrzJBSbdcROsiR1BQzMiz7mSIC4T7qkrZBjhKignx8wxAeGKcD41SaxzUcu78ncpQoNUgi05kg3VPTtZH5X62d6fg8yCkXmSYcTxbFGYM6haNAYIdKgjUbGEBYUvNXiHtIqxNbGUTgjt98ix4tepF1b09rdSvijRKYA/sg0PgjNQBzegATyAwSN4Bq/gzXqyXqx362PSOmcVMzvgj6zPH7b6ldM=</latexit><latexit sha1_base64="q9bUR7+rYovPwrJ4HAImgca3wc=">ACAnicbZBPS8MwGMZT/875r+pNL8EhCOJsh6AehKEXjxOsG6ylpFm6haVpSFJhlIEXv4oXDype/RTe/DZmWw+6+UDgx/O+L2/eJxKMKu0439bc/MLi0nJpby6tr6xaW9t36s0k5h4OGWpbEVIEUY58TVjLSEJCiJGlG/etRvflApKIpv9MDQYIEdTmNKUbaWKG96yMmeih0jwqowUt47At6UgvtilN1xoKz4BZQAYUaof3ld1KcJYRrzJBSbdcROsiR1BQzMiz7mSIC4T7qkrZBjhKignx8wxAeGKcD41SaxzUcu78ncpQoNUgi05kg3VPTtZH5X62d6fg8yCkXmSYcTxbFGYM6haNAYIdKgjUbGEBYUvNXiHtIqxNbGUTgjt98ix4tepF1b09rdSvijRKYA/sg0PgjNQBzegATyAwSN4Bq/gzXqyXqx362PSOmcVMzvgj6zPH7b6ldM=</latexit><latexit sha1_base64="q9bUR7+rYovPwrJ4HAImgca3wc=">ACAnicbZBPS8MwGMZT/875r+pNL8EhCOJsh6AehKEXjxOsG6ylpFm6haVpSFJhlIEXv4oXDype/RTe/DZmWw+6+UDgx/O+L2/eJxKMKu0439bc/MLi0nJpby6tr6xaW9t36s0k5h4OGWpbEVIEUY58TVjLSEJCiJGlG/etRvflApKIpv9MDQYIEdTmNKUbaWKG96yMmeih0jwqowUt47At6UgvtilN1xoKz4BZQAYUaof3ld1KcJYRrzJBSbdcROsiR1BQzMiz7mSIC4T7qkrZBjhKignx8wxAeGKcD41SaxzUcu78ncpQoNUgi05kg3VPTtZH5X62d6fg8yCkXmSYcTxbFGYM6haNAYIdKgjUbGEBYUvNXiHtIqxNbGUTgjt98ix4tepF1b09rdSvijRKYA/sg0PgjNQBzegATyAwSN4Bq/gzXqyXqx362PSOmcVMzvgj6zPH7b6ldM=</latexit>δ = −π/4
<latexit sha1_base64="Y45pXO3lQF+MFWBupspuCkpdRNY=">AB93icbVBNS8NAEN34WetHox69LBbBizWRgnoQil48VjC20ISy2U7apZtN2N0INfSXePGg4tW/4s1/47bNQVsfDzem2FmXphyprTjfFtLyura+uljfLm1vZOxd7de1BJil4NOGJbIdEAWcCPM0h3YqgcQh1Y4vJn4rUeQiXiXo9SCGLSFyxilGgjde2K3wOuCb7CJ37KTutdu+rUnCnwInELUkUFml37y+8lNItBaMqJUh3XSXWQE6kZ5TAu+5mClNAh6UPHUEFiUE+PXyMj4zSw1EiTQmNp+rviZzESo3i0HTGRA/UvDcR/M6mY4ugpyJNMg6GxRlHGsEzxJAfeYBKr5yBCJTO3YjogklBtsiqbENz5lxeJd1a7rLl39WrjukijhA7QITpGLjpHDXSLmshDFGXoGb2iN+vJerHerY9Z65JVzOyjP7A+fwBJ5pG9</latexit><latexit sha1_base64="Y45pXO3lQF+MFWBupspuCkpdRNY=">AB93icbVBNS8NAEN34WetHox69LBbBizWRgnoQil48VjC20ISy2U7apZtN2N0INfSXePGg4tW/4s1/47bNQVsfDzem2FmXphyprTjfFtLyura+uljfLm1vZOxd7de1BJil4NOGJbIdEAWcCPM0h3YqgcQh1Y4vJn4rUeQiXiXo9SCGLSFyxilGgjde2K3wOuCb7CJ37KTutdu+rUnCnwInELUkUFml37y+8lNItBaMqJUh3XSXWQE6kZ5TAu+5mClNAh6UPHUEFiUE+PXyMj4zSw1EiTQmNp+rviZzESo3i0HTGRA/UvDcR/M6mY4ugpyJNMg6GxRlHGsEzxJAfeYBKr5yBCJTO3YjogklBtsiqbENz5lxeJd1a7rLl39WrjukijhA7QITpGLjpHDXSLmshDFGXoGb2iN+vJerHerY9Z65JVzOyjP7A+fwBJ5pG9</latexit><latexit sha1_base64="Y45pXO3lQF+MFWBupspuCkpdRNY=">AB93icbVBNS8NAEN34WetHox69LBbBizWRgnoQil48VjC20ISy2U7apZtN2N0INfSXePGg4tW/4s1/47bNQVsfDzem2FmXphyprTjfFtLyura+uljfLm1vZOxd7de1BJil4NOGJbIdEAWcCPM0h3YqgcQh1Y4vJn4rUeQiXiXo9SCGLSFyxilGgjde2K3wOuCb7CJ37KTutdu+rUnCnwInELUkUFml37y+8lNItBaMqJUh3XSXWQE6kZ5TAu+5mClNAh6UPHUEFiUE+PXyMj4zSw1EiTQmNp+rviZzESo3i0HTGRA/UvDcR/M6mY4ugpyJNMg6GxRlHGsEzxJAfeYBKr5yBCJTO3YjogklBtsiqbENz5lxeJd1a7rLl39WrjukijhA7QITpGLjpHDXSLmshDFGXoGb2iN+vJerHerY9Z65JVzOyjP7A+fwBJ5pG9</latexit><latexit sha1_base64="Y45pXO3lQF+MFWBupspuCkpdRNY=">AB93icbVBNS8NAEN34WetHox69LBbBizWRgnoQil48VjC20ISy2U7apZtN2N0INfSXePGg4tW/4s1/47bNQVsfDzem2FmXphyprTjfFtLyura+uljfLm1vZOxd7de1BJil4NOGJbIdEAWcCPM0h3YqgcQh1Y4vJn4rUeQiXiXo9SCGLSFyxilGgjde2K3wOuCb7CJ37KTutdu+rUnCnwInELUkUFml37y+8lNItBaMqJUh3XSXWQE6kZ5TAu+5mClNAh6UPHUEFiUE+PXyMj4zSw1EiTQmNp+rviZzESo3i0HTGRA/UvDcR/M6mY4ugpyJNMg6GxRlHGsEzxJAfeYBKr5yBCJTO3YjogklBtsiqbENz5lxeJd1a7rLl39WrjukijhA7QITpGLjpHDXSLmshDFGXoGb2iN+vJerHerY9Z65JVzOyjP7A+fwBJ5pG9</latexit>MN = 1 GeV
<latexit sha1_base64="1b+TRzHjemsoQ3x9re5bNENqfF4=">AB/XicbVBPS8MwHE39O+e/qnjyEhyCBxmtCOpBGHrQizLBboOtlDRLt7AkLUkqjDLwq3jxoOLV7+HNb2O69aCbLwQe7/1+5OWFCaNKO863NTe/sLi0XFopr6tb2zaW9sNFacSEw/HLJatECnCqCepqRViIJ4iEjzXBwlfvNRyIVjcWDHibE56gnaEQx0kYK7N3b4O7C7RyZw5HuS5dk8YosCtO1RkDzhK3IBVQoB7YX51ujFNOhMYMKdV2nUT7GZKaYkZG5U6qSILwAPVI21CBOF+No4/gdG6cIoluYKDcfq740McaWGPDSTeUY17eXif1471dGZn1GRpJoIPHkoShnUMcy7gF0qCdZsaAjCkpqsEPeRFibxsqmBHf6y7PEO6eV937k0rtsmijBPbAPjgELjgFNXAD6sADGTgGbyCN+vJerHerY/J6JxV7OyAP7A+fwBXDZSo</latexit><latexit sha1_base64="1b+TRzHjemsoQ3x9re5bNENqfF4=">AB/XicbVBPS8MwHE39O+e/qnjyEhyCBxmtCOpBGHrQizLBboOtlDRLt7AkLUkqjDLwq3jxoOLV7+HNb2O69aCbLwQe7/1+5OWFCaNKO863NTe/sLi0XFopr6tb2zaW9sNFacSEw/HLJatECnCqCepqRViIJ4iEjzXBwlfvNRyIVjcWDHibE56gnaEQx0kYK7N3b4O7C7RyZw5HuS5dk8YosCtO1RkDzhK3IBVQoB7YX51ujFNOhMYMKdV2nUT7GZKaYkZG5U6qSILwAPVI21CBOF+No4/gdG6cIoluYKDcfq740McaWGPDSTeUY17eXif1471dGZn1GRpJoIPHkoShnUMcy7gF0qCdZsaAjCkpqsEPeRFibxsqmBHf6y7PEO6eV937k0rtsmijBPbAPjgELjgFNXAD6sADGTgGbyCN+vJerHerY/J6JxV7OyAP7A+fwBXDZSo</latexit><latexit sha1_base64="1b+TRzHjemsoQ3x9re5bNENqfF4=">AB/XicbVBPS8MwHE39O+e/qnjyEhyCBxmtCOpBGHrQizLBboOtlDRLt7AkLUkqjDLwq3jxoOLV7+HNb2O69aCbLwQe7/1+5OWFCaNKO863NTe/sLi0XFopr6tb2zaW9sNFacSEw/HLJatECnCqCepqRViIJ4iEjzXBwlfvNRyIVjcWDHibE56gnaEQx0kYK7N3b4O7C7RyZw5HuS5dk8YosCtO1RkDzhK3IBVQoB7YX51ujFNOhMYMKdV2nUT7GZKaYkZG5U6qSILwAPVI21CBOF+No4/gdG6cIoluYKDcfq740McaWGPDSTeUY17eXif1471dGZn1GRpJoIPHkoShnUMcy7gF0qCdZsaAjCkpqsEPeRFibxsqmBHf6y7PEO6eV937k0rtsmijBPbAPjgELjgFNXAD6sADGTgGbyCN+vJerHerY/J6JxV7OyAP7A+fwBXDZSo</latexit><latexit sha1_base64="1b+TRzHjemsoQ3x9re5bNENqfF4=">AB/XicbVBPS8MwHE39O+e/qnjyEhyCBxmtCOpBGHrQizLBboOtlDRLt7AkLUkqjDLwq3jxoOLV7+HNb2O69aCbLwQe7/1+5OWFCaNKO863NTe/sLi0XFopr6tb2zaW9sNFacSEw/HLJatECnCqCepqRViIJ4iEjzXBwlfvNRyIVjcWDHibE56gnaEQx0kYK7N3b4O7C7RyZw5HuS5dk8YosCtO1RkDzhK3IBVQoB7YX51ujFNOhMYMKdV2nUT7GZKaYkZG5U6qSILwAPVI21CBOF+No4/gdG6cIoluYKDcfq740McaWGPDSTeUY17eXif1471dGZn1GRpJoIPHkoShnUMcy7gF0qCdZsaAjCkpqsEPeRFibxsqmBHf6y7PEO6eV937k0rtsmijBPbAPjgELjgFNXAD6sADGTgGbyCN+vJerHerY/J6JxV7OyAP7A+fwBXDZSo</latexit>∆M = 10−3 GeV
<latexit sha1_base64="NDd4uOPIVkDgq4pgqlW8oi59McA=">ACnicbVDLSgMxFM3UV62vqks3oUVwoWVGBXUhFBV0I1SwD+jUklv29BkZkgyQhlm78ZfceNCxa1f4M6/MW1nodUTAodz7uXe7yQM6Vt+8vKzMzOzS9kF3NLyura/n1jZoKIkmhSgMeyIZHFHDmQ1UzaERSiDC41D3Bucjv34PUrHAv9XDEFqC9HzWZRoI7XzBfcCuCb4Gp9ix76L9w4Sd9c8QXRfivgSak7X7RL9hj4L3FSUkQpKu38p9sJaCTA15QTpZqOHepWTKRmlEOScyMFIaED0oOmoT4RoFrx+JYEbxulg7uBN/XeKz+7IiJUGoPFM52lFNeyPxP68Z6e5xK2Z+Gnw6WRQN+JYB3gUDO4wCVTzoSGESmZ2xbRPJKHaxJczITjTJ/8l1f3Scm5OSyWz9I0smgLFdAOctARKqMrVEFVRNEDekIv6NV6tJ6tN+t9Upqx0p5N9AvWxzd+m5kJ</latexit><latexit sha1_base64="NDd4uOPIVkDgq4pgqlW8oi59McA=">ACnicbVDLSgMxFM3UV62vqks3oUVwoWVGBXUhFBV0I1SwD+jUklv29BkZkgyQhlm78ZfceNCxa1f4M6/MW1nodUTAodz7uXe7yQM6Vt+8vKzMzOzS9kF3NLyura/n1jZoKIkmhSgMeyIZHFHDmQ1UzaERSiDC41D3Bucjv34PUrHAv9XDEFqC9HzWZRoI7XzBfcCuCb4Gp9ix76L9w4Sd9c8QXRfivgSak7X7RL9hj4L3FSUkQpKu38p9sJaCTA15QTpZqOHepWTKRmlEOScyMFIaED0oOmoT4RoFrx+JYEbxulg7uBN/XeKz+7IiJUGoPFM52lFNeyPxP68Z6e5xK2Z+Gnw6WRQN+JYB3gUDO4wCVTzoSGESmZ2xbRPJKHaxJczITjTJ/8l1f3Scm5OSyWz9I0smgLFdAOctARKqMrVEFVRNEDekIv6NV6tJ6tN+t9Upqx0p5N9AvWxzd+m5kJ</latexit><latexit sha1_base64="NDd4uOPIVkDgq4pgqlW8oi59McA=">ACnicbVDLSgMxFM3UV62vqks3oUVwoWVGBXUhFBV0I1SwD+jUklv29BkZkgyQhlm78ZfceNCxa1f4M6/MW1nodUTAodz7uXe7yQM6Vt+8vKzMzOzS9kF3NLyura/n1jZoKIkmhSgMeyIZHFHDmQ1UzaERSiDC41D3Bucjv34PUrHAv9XDEFqC9HzWZRoI7XzBfcCuCb4Gp9ix76L9w4Sd9c8QXRfivgSak7X7RL9hj4L3FSUkQpKu38p9sJaCTA15QTpZqOHepWTKRmlEOScyMFIaED0oOmoT4RoFrx+JYEbxulg7uBN/XeKz+7IiJUGoPFM52lFNeyPxP68Z6e5xK2Z+Gnw6WRQN+JYB3gUDO4wCVTzoSGESmZ2xbRPJKHaxJczITjTJ/8l1f3Scm5OSyWz9I0smgLFdAOctARKqMrVEFVRNEDekIv6NV6tJ6tN+t9Upqx0p5N9AvWxzd+m5kJ</latexit><latexit sha1_base64="NDd4uOPIVkDgq4pgqlW8oi59McA=">ACnicbVDLSgMxFM3UV62vqks3oUVwoWVGBXUhFBV0I1SwD+jUklv29BkZkgyQhlm78ZfceNCxa1f4M6/MW1nodUTAodz7uXe7yQM6Vt+8vKzMzOzS9kF3NLyura/n1jZoKIkmhSgMeyIZHFHDmQ1UzaERSiDC41D3Bucjv34PUrHAv9XDEFqC9HzWZRoI7XzBfcCuCb4Gp9ix76L9w4Sd9c8QXRfivgSak7X7RL9hj4L3FSUkQpKu38p9sJaCTA15QTpZqOHepWTKRmlEOScyMFIaED0oOmoT4RoFrx+JYEbxulg7uBN/XeKz+7IiJUGoPFM52lFNeyPxP68Z6e5xK2Z+Gnw6WRQN+JYB3gUDO4wCVTzoSGESmZ2xbRPJKHaxJczITjTJ/8l1f3Scm5OSyWz9I0smgLFdAOctARKqMrVEFVRNEDekIv6NV6tJ6tN+t9Upqx0p5N9AvWxzd+m5kJ</latexit>Re ω = π/4
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P(νµ → νe)
<latexit sha1_base64="JLZbVqH/Nl+C9XiIwXpMSaBl6TQ=">ACA3icbVDLSsNAFJ34rPUVdnNYBHqpiQiqLuiG5cVjC0IUymk3boZBLmoZTQhRt/xY0LFbf+hDv/xkmbhbYeuHA4517uvSfKGJXKcb6tpeWV1bX1ykZ1c2t7Z9fe27+TqRaYeDhlqehGSBJGOfEUVYx0M0FQEjHSiUZXhd+5J0LSlN+qcUaCBA04jSlGykihXWs3fK5DP9G+oIOhQkKkD7CQyHFo152mMwVcJG5J6qBEO7S/H6KdUK4wgxJ2XOdTAU5EopiRiZVX0uSITxCA9IzlKOEyCfPjGBR0bpwzgVpriCU/X3RI4SKcdJZDoTpIZy3ivE/7yeVvF5kFOeaU4ni2KNYMqhUisE8FwYqNDUFYUHMrxEMkEFYmt6oJwZ1/eZF4J82LpntzWm9dlmlUQA0cgZwRlogWvQBh7A4BE8g1fwZj1ZL9a79TFrXbLKmQPwB9bnD+cGl9I=</latexit><latexit sha1_base64="JLZbVqH/Nl+C9XiIwXpMSaBl6TQ=">ACA3icbVDLSsNAFJ34rPUVdnNYBHqpiQiqLuiG5cVjC0IUymk3boZBLmoZTQhRt/xY0LFbf+hDv/xkmbhbYeuHA4517uvSfKGJXKcb6tpeWV1bX1ykZ1c2t7Z9fe27+TqRaYeDhlqehGSBJGOfEUVYx0M0FQEjHSiUZXhd+5J0LSlN+qcUaCBA04jSlGykihXWs3fK5DP9G+oIOhQkKkD7CQyHFo152mMwVcJG5J6qBEO7S/H6KdUK4wgxJ2XOdTAU5EopiRiZVX0uSITxCA9IzlKOEyCfPjGBR0bpwzgVpriCU/X3RI4SKcdJZDoTpIZy3ivE/7yeVvF5kFOeaU4ni2KNYMqhUisE8FwYqNDUFYUHMrxEMkEFYmt6oJwZ1/eZF4J82LpntzWm9dlmlUQA0cgZwRlogWvQBh7A4BE8g1fwZj1ZL9a79TFrXbLKmQPwB9bnD+cGl9I=</latexit><latexit sha1_base64="JLZbVqH/Nl+C9XiIwXpMSaBl6TQ=">ACA3icbVDLSsNAFJ34rPUVdnNYBHqpiQiqLuiG5cVjC0IUymk3boZBLmoZTQhRt/xY0LFbf+hDv/xkmbhbYeuHA4517uvSfKGJXKcb6tpeWV1bX1ykZ1c2t7Z9fe27+TqRaYeDhlqehGSBJGOfEUVYx0M0FQEjHSiUZXhd+5J0LSlN+qcUaCBA04jSlGykihXWs3fK5DP9G+oIOhQkKkD7CQyHFo152mMwVcJG5J6qBEO7S/H6KdUK4wgxJ2XOdTAU5EopiRiZVX0uSITxCA9IzlKOEyCfPjGBR0bpwzgVpriCU/X3RI4SKcdJZDoTpIZy3ivE/7yeVvF5kFOeaU4ni2KNYMqhUisE8FwYqNDUFYUHMrxEMkEFYmt6oJwZ1/eZF4J82LpntzWm9dlmlUQA0cgZwRlogWvQBh7A4BE8g1fwZj1ZL9a79TFrXbLKmQPwB9bnD+cGl9I=</latexit><latexit sha1_base64="JLZbVqH/Nl+C9XiIwXpMSaBl6TQ=">ACA3icbVDLSsNAFJ34rPUVdnNYBHqpiQiqLuiG5cVjC0IUymk3boZBLmoZTQhRt/xY0LFbf+hDv/xkmbhbYeuHA4517uvSfKGJXKcb6tpeWV1bX1ykZ1c2t7Z9fe27+TqRaYeDhlqehGSBJGOfEUVYx0M0FQEjHSiUZXhd+5J0LSlN+qcUaCBA04jSlGykihXWs3fK5DP9G+oIOhQkKkD7CQyHFo152mMwVcJG5J6qBEO7S/H6KdUK4wgxJ2XOdTAU5EopiRiZVX0uSITxCA9IzlKOEyCfPjGBR0bpwzgVpriCU/X3RI4SKcdJZDoTpIZy3ivE/7yeVvF5kFOeaU4ni2KNYMqhUisE8FwYqNDUFYUHMrxEMkEFYmt6oJwZ1/eZF4J82LpntzWm9dlmlUQA0cgZwRlogWvQBh7A4BE8g1fwZj1ZL9a79TFrXbLKmQPwB9bnD+cGl9I=</latexit>P(¯ νµ → ¯ νe)
<latexit sha1_base64="vKRn5m15HMaUjk3pudxh+t8E9Q=">AC3icbVDLSgMxFM3UV62vqks3wSLUTZkRQd0V3bisYK3QGUomzbSheQx5KGXoB7jxV9y4UHrD7jzb0zbEbT1QOBwzrnc3BOnjGrj+19eYWFxaXmluFpaW9/Y3Cpv79xoaRUmTSyZVLcx0oRQZqGkZuU0UQjxlpxYOLsd+6I0pTKa7NMCURz1BE4qRcVKnXGlUwxipUNhOyG2oaK9vkFLyHv7I5NCl/Jo/AZwnQU4qIEejU/4MuxJbToTBDGndDvzURBlShmJGRqXQapIiPEA90nZUIE50lE2OGcEDp3RhIpV7wsCJ+nsiQ1zrIY9dkiPT17PeWPzPa1uTnEYZFak1RODposQyaCQcNwO7VBFs2NARhBV1f4W4jxTCxvVXciUEsyfPk+ZR7awWXB1X6ud5G0WwB/ZBFQTgBNTBJWiAJsDgATyBF/DqPXrP3pv3Po0WvHxmF/yB9/ENK0abRA=</latexit><latexit sha1_base64="vKRn5m15HMaUjk3pudxh+t8E9Q=">AC3icbVDLSgMxFM3UV62vqks3wSLUTZkRQd0V3bisYK3QGUomzbSheQx5KGXoB7jxV9y4UHrD7jzb0zbEbT1QOBwzrnc3BOnjGrj+19eYWFxaXmluFpaW9/Y3Cpv79xoaRUmTSyZVLcx0oRQZqGkZuU0UQjxlpxYOLsd+6I0pTKa7NMCURz1BE4qRcVKnXGlUwxipUNhOyG2oaK9vkFLyHv7I5NCl/Jo/AZwnQU4qIEejU/4MuxJbToTBDGndDvzURBlShmJGRqXQapIiPEA90nZUIE50lE2OGcEDp3RhIpV7wsCJ+nsiQ1zrIY9dkiPT17PeWPzPa1uTnEYZFak1RODposQyaCQcNwO7VBFs2NARhBV1f4W4jxTCxvVXciUEsyfPk+ZR7awWXB1X6ud5G0WwB/ZBFQTgBNTBJWiAJsDgATyBF/DqPXrP3pv3Po0WvHxmF/yB9/ENK0abRA=</latexit><latexit sha1_base64="vKRn5m15HMaUjk3pudxh+t8E9Q=">AC3icbVDLSgMxFM3UV62vqks3wSLUTZkRQd0V3bisYK3QGUomzbSheQx5KGXoB7jxV9y4UHrD7jzb0zbEbT1QOBwzrnc3BOnjGrj+19eYWFxaXmluFpaW9/Y3Cpv79xoaRUmTSyZVLcx0oRQZqGkZuU0UQjxlpxYOLsd+6I0pTKa7NMCURz1BE4qRcVKnXGlUwxipUNhOyG2oaK9vkFLyHv7I5NCl/Jo/AZwnQU4qIEejU/4MuxJbToTBDGndDvzURBlShmJGRqXQapIiPEA90nZUIE50lE2OGcEDp3RhIpV7wsCJ+nsiQ1zrIY9dkiPT17PeWPzPa1uTnEYZFak1RODposQyaCQcNwO7VBFs2NARhBV1f4W4jxTCxvVXciUEsyfPk+ZR7awWXB1X6ud5G0WwB/ZBFQTgBNTBJWiAJsDgATyBF/DqPXrP3pv3Po0WvHxmF/yB9/ENK0abRA=</latexit><latexit sha1_base64="vKRn5m15HMaUjk3pudxh+t8E9Q=">AC3icbVDLSgMxFM3UV62vqks3wSLUTZkRQd0V3bisYK3QGUomzbSheQx5KGXoB7jxV9y4UHrD7jzb0zbEbT1QOBwzrnc3BOnjGrj+19eYWFxaXmluFpaW9/Y3Cpv79xoaRUmTSyZVLcx0oRQZqGkZuU0UQjxlpxYOLsd+6I0pTKa7NMCURz1BE4qRcVKnXGlUwxipUNhOyG2oaK9vkFLyHv7I5NCl/Jo/AZwnQU4qIEejU/4MuxJbToTBDGndDvzURBlShmJGRqXQapIiPEA90nZUIE50lE2OGcEDp3RhIpV7wsCJ+nsiQ1zrIY9dkiPT17PeWPzPa1uTnEYZFak1RODposQyaCQcNwO7VBFs2NARhBV1f4W4jxTCxvVXciUEsyfPk+ZR7awWXB1X6ud5G0WwB/ZBFQTgBNTBJWiAJsDgATyBF/DqPXrP3pv3Po0WvHxmF/yB9/ENK0abRA=</latexit>vs.
23
θ
2
sin
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
)
4
/c
2
eV
| (10
32 2
m Δ |
1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 ln L = 2.3) Δ 68%CL (-2 ln L = 4.61) Δ 90%CL (-2 T2K best-fit
T2K Super-K NOvA MINOS+ IceCube
13
θ
2
sin
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
(radians)
CP
δ
1 2 3 Normal Ordering Inverted Ordering ln L = 2.3) Δ 68%CL (-2 ln L = 4.61) Δ 90%CL (-2 Best-fit PDG 2015
T2K, arXiv:1701.00432
23
P(νµ → νe)
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<latexit sha1_base64="vKRn5m15HMaUjk3pudxh+t8E9Q=">AC3icbVDLSgMxFM3UV62vqks3wSLUTZkRQd0V3bisYK3QGUomzbSheQx5KGXoB7jxV9y4UHrD7jzb0zbEbT1QOBwzrnc3BOnjGrj+19eYWFxaXmluFpaW9/Y3Cpv79xoaRUmTSyZVLcx0oRQZqGkZuU0UQjxlpxYOLsd+6I0pTKa7NMCURz1BE4qRcVKnXGlUwxipUNhOyG2oaK9vkFLyHv7I5NCl/Jo/AZwnQU4qIEejU/4MuxJbToTBDGndDvzURBlShmJGRqXQapIiPEA90nZUIE50lE2OGcEDp3RhIpV7wsCJ+nsiQ1zrIY9dkiPT17PeWPzPa1uTnEYZFak1RODposQyaCQcNwO7VBFs2NARhBV1f4W4jxTCxvVXciUEsyfPk+ZR7awWXB1X6ud5G0WwB/ZBFQTgBNTBJWiAJsDgATyBF/DqPXrP3pv3Po0WvHxmF/yB9/ENK0abRA=</latexit><latexit sha1_base64="vKRn5m15HMaUjk3pudxh+t8E9Q=">AC3icbVDLSgMxFM3UV62vqks3wSLUTZkRQd0V3bisYK3QGUomzbSheQx5KGXoB7jxV9y4UHrD7jzb0zbEbT1QOBwzrnc3BOnjGrj+19eYWFxaXmluFpaW9/Y3Cpv79xoaRUmTSyZVLcx0oRQZqGkZuU0UQjxlpxYOLsd+6I0pTKa7NMCURz1BE4qRcVKnXGlUwxipUNhOyG2oaK9vkFLyHv7I5NCl/Jo/AZwnQU4qIEejU/4MuxJbToTBDGndDvzURBlShmJGRqXQapIiPEA90nZUIE50lE2OGcEDp3RhIpV7wsCJ+nsiQ1zrIY9dkiPT17PeWPzPa1uTnEYZFak1RODposQyaCQcNwO7VBFs2NARhBV1f4W4jxTCxvVXciUEsyfPk+ZR7awWXB1X6ud5G0WwB/ZBFQTgBNTBJWiAJsDgATyBF/DqPXrP3pv3Po0WvHxmF/yB9/ENK0abRA=</latexit><latexit sha1_base64="vKRn5m15HMaUjk3pudxh+t8E9Q=">AC3icbVDLSgMxFM3UV62vqks3wSLUTZkRQd0V3bisYK3QGUomzbSheQx5KGXoB7jxV9y4UHrD7jzb0zbEbT1QOBwzrnc3BOnjGrj+19eYWFxaXmluFpaW9/Y3Cpv79xoaRUmTSyZVLcx0oRQZqGkZuU0UQjxlpxYOLsd+6I0pTKa7NMCURz1BE4qRcVKnXGlUwxipUNhOyG2oaK9vkFLyHv7I5NCl/Jo/AZwnQU4qIEejU/4MuxJbToTBDGndDvzURBlShmJGRqXQapIiPEA90nZUIE50lE2OGcEDp3RhIpV7wsCJ+nsiQ1zrIY9dkiPT17PeWPzPa1uTnEYZFak1RODposQyaCQcNwO7VBFs2NARhBV1f4W4jxTCxvVXciUEsyfPk+ZR7awWXB1X6ud5G0WwB/ZBFQTgBNTBJWiAJsDgATyBF/DqPXrP3pv3Po0WvHxmF/yB9/ENK0abRA=</latexit><latexit sha1_base64="vKRn5m15HMaUjk3pudxh+t8E9Q=">AC3icbVDLSgMxFM3UV62vqks3wSLUTZkRQd0V3bisYK3QGUomzbSheQx5KGXoB7jxV9y4UHrD7jzb0zbEbT1QOBwzrnc3BOnjGrj+19eYWFxaXmluFpaW9/Y3Cpv79xoaRUmTSyZVLcx0oRQZqGkZuU0UQjxlpxYOLsd+6I0pTKa7NMCURz1BE4qRcVKnXGlUwxipUNhOyG2oaK9vkFLyHv7I5NCl/Jo/AZwnQU4qIEejU/4MuxJbToTBDGndDvzURBlShmJGRqXQapIiPEA90nZUIE50lE2OGcEDp3RhIpV7wsCJ+nsiQ1zrIY9dkiPT17PeWPzPa1uTnEYZFak1RODposQyaCQcNwO7VBFs2NARhBV1f4W4jxTCxvVXciUEsyfPk+ZR7awWXB1X6ud5G0WwB/ZBFQTgBNTBJWiAJsDgATyBF/DqPXrP3pv3Po0WvHxmF/yB9/ENK0abRA=</latexit>vs.
DUNE CDR, arXiv:1512.06148
π /
CPδ
0.2 0.4 0.6 0.8 1
2χ ∆ = σ 1 2 3 4 5 6 7 8 π /
CPδ
0.2 0.4 0.6 0.8 1
2χ ∆ = σ 1 2 3 4 5 6 7 8
DUNE Sensitivity Normal Hierarchy 300 kt-MW-years = 0.085
13θ 2
2sin = 0.45
23θ
2sin σ 3 σ 5
CDR Reference Design Optimized Designπ /
CPδ
0.2 0.4 0.6 0.8 1
2χ ∆ = σ 1 2 3 4 5 6 7 8 π /
CPδ
0.2 0.4 0.6 0.8 1
2χ ∆ = σ 1 2 3 4 5 6 7 8
DUNE Sensitivity Inverted Hierarchy 300 kt-MW-years = 0.085
13θ 2
2sin = 0.58
23θ
2sin σ 3 σ 5
CDR Reference Design Optimized Design24
additional lepton-number-violating effects
neutrinoless double-beta decay, extract Majorana phases indirectly if we already know other oscillation parameters (seems fraught!)
see e.g., de Gouvêa, Kayser, Mohapatra, hep-ph/0211394
25
neutrino masses γ W W e f2 e f1 e
de . 10−33 e · cm
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26
to neutrinos are larger
BS, Yavin, arXiv:1401.2459
2 5 10 20 50 100 10-14 10-13 10-12 10-11 10-10 10-9 leptophilic VEV HGeVL » YDB »
Leptophilic model Minimal model
couplings in extended Higgs sector
for leptophilic Higgs states
27
28
hidden-sector particles
Nussinov, 1985; Dodelson, Widrow, 1990; Barr, Chivukula, Farhi, 1991; …; Kaplan, Luty, Zurek, 2009; Davoudiasl et al., 2010; Shelton, Zurek, 2010; Buckley, Randall, 2010; McDonald, 2011; Cui, Randall, BS, 2011; Zurek, 2013;……….
29
DM DM B B
baryon number
CP
Cui, Randall, BS, arXiv:1112.2704
30
Cui, Randall, BS, arXiv:1112.2704
DM DM SM baryons B violating decay exotic antibaryon
DM DM SM baryons sterile antibaryons B conserving decay exotic antibaryon
(kinematic effects lead to a suppression of washout processes)
colliders
31
Cui, Randall, BS, arXiv:1112.2704
X X ψ L S1
Q
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ψ
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quark state
ψ
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Cui, Randall, BS, arXiv:1112.2704
the leading contribution to EDM vanishes
loops for non-zero effect
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QL
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33
Cui, Randall, BS, arXiv:1112.2704
decays, typically decays into other hidden-sector particles
ψ
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model are on mψ . 1.5 TeV
<latexit sha1_base64="YlTt1eZkOyqS8c4wag7GZfsHL9Y=">ACnicbVBNS8NAEN3Ur1q/qh69LC2CBwmJKOqt6MVjhaYtNCVstN26W4SdjdCb178a948aDi1V/gzX/jpu1BW9+y8Hhvhpl5YcKZ0o7zbRVWVtfWN4qbpa3tnd298v5BU8WpODRmMeyHRIFnEXgaY5tBMJRIQcWuHoNvdbDyAVi6OGHifQFWQsT6jRBspKFdE4CeKYZ+DUoJ17wT80TRA+lyBrQnATlqmM7U+Bl4s5JFc1RD8pfi+mqYBIU06U6rhOorsZkZpRDpOSnypICB2RAXQMjYgA1c2mt0zwsVF6uB9L8yONp+rvjowIpcYiNJX5jmrRy8X/vE6q+1fdjEVJqiGis0H9lGMd4zwY3GMSqOZjQwiVzOyK6ZBIQrWJr2RCcBdPXibemX1tu/fn1drNPI0iOkIVdIJcdIlq6A7VkYcoekTP6BW9WU/Wi/VufcxKC9a85xD9gfX5A5IKmlM=</latexit><latexit sha1_base64="YlTt1eZkOyqS8c4wag7GZfsHL9Y=">ACnicbVBNS8NAEN3Ur1q/qh69LC2CBwmJKOqt6MVjhaYtNCVstN26W4SdjdCb178a948aDi1V/gzX/jpu1BW9+y8Hhvhpl5YcKZ0o7zbRVWVtfWN4qbpa3tnd298v5BU8WpODRmMeyHRIFnEXgaY5tBMJRIQcWuHoNvdbDyAVi6OGHifQFWQsT6jRBspKFdE4CeKYZ+DUoJ17wT80TRA+lyBrQnATlqmM7U+Bl4s5JFc1RD8pfi+mqYBIU06U6rhOorsZkZpRDpOSnypICB2RAXQMjYgA1c2mt0zwsVF6uB9L8yONp+rvjowIpcYiNJX5jmrRy8X/vE6q+1fdjEVJqiGis0H9lGMd4zwY3GMSqOZjQwiVzOyK6ZBIQrWJr2RCcBdPXibemX1tu/fn1drNPI0iOkIVdIJcdIlq6A7VkYcoekTP6BW9WU/Wi/VufcxKC9a85xD9gfX5A5IKmlM=</latexit><latexit sha1_base64="YlTt1eZkOyqS8c4wag7GZfsHL9Y=">ACnicbVBNS8NAEN3Ur1q/qh69LC2CBwmJKOqt6MVjhaYtNCVstN26W4SdjdCb178a948aDi1V/gzX/jpu1BW9+y8Hhvhpl5YcKZ0o7zbRVWVtfWN4qbpa3tnd298v5BU8WpODRmMeyHRIFnEXgaY5tBMJRIQcWuHoNvdbDyAVi6OGHifQFWQsT6jRBspKFdE4CeKYZ+DUoJ17wT80TRA+lyBrQnATlqmM7U+Bl4s5JFc1RD8pfi+mqYBIU06U6rhOorsZkZpRDpOSnypICB2RAXQMjYgA1c2mt0zwsVF6uB9L8yONp+rvjowIpcYiNJX5jmrRy8X/vE6q+1fdjEVJqiGis0H9lGMd4zwY3GMSqOZjQwiVzOyK6ZBIQrWJr2RCcBdPXibemX1tu/fn1drNPI0iOkIVdIJcdIlq6A7VkYcoekTP6BW9WU/Wi/VufcxKC9a85xD9gfX5A5IKmlM=</latexit><latexit sha1_base64="YlTt1eZkOyqS8c4wag7GZfsHL9Y=">ACnicbVBNS8NAEN3Ur1q/qh69LC2CBwmJKOqt6MVjhaYtNCVstN26W4SdjdCb178a948aDi1V/gzX/jpu1BW9+y8Hhvhpl5YcKZ0o7zbRVWVtfWN4qbpa3tnd298v5BU8WpODRmMeyHRIFnEXgaY5tBMJRIQcWuHoNvdbDyAVi6OGHifQFWQsT6jRBspKFdE4CeKYZ+DUoJ17wT80TRA+lyBrQnATlqmM7U+Bl4s5JFc1RD8pfi+mqYBIU06U6rhOorsZkZpRDpOSnypICB2RAXQMjYgA1c2mt0zwsVF6uB9L8yONp+rvjowIpcYiNJX5jmrRy8X/vE6q+1fdjEVJqiGis0H9lGMd4zwY3GMSqOZjQwiVzOyK6ZBIQrWJr2RCcBdPXibemX1tu/fn1drNPI0iOkIVdIJcdIlq6A7VkYcoekTP6BW9WU/Wi/VufcxKC9a85xD9gfX5A5IKmlM=</latexit>in decays could give more exotic signals in other models
Cui, Sundrum, arXiv:1212.2973; Cui, BS, arXiv:1409.6729
34
coverage: all are needed to close in on low-scale baryogenesis!
baryogenesis
phenomenological predictions
35
36
M(a → b) = x eiφ M(¯ a → ¯ b) = x e−iφ
|M(¯ a → ¯ b)|2 = x2 |M(a → b)|2 = x2 ∆|M|2 = 0
36
M(a → b) = x eiφ M(¯ a → ¯ b) = x e−iφ
|M(¯ a → ¯ b)|2 = x2 |M(a → b)|2 = x2 ∆|M|2 = 0
M(¯ a → ¯ b) = x1 e−iφ + x2 M(a → b) = x1 eiφ + x2
|M(a → b)|2 = x2
1 + x2 2 + 2x1x2 cos φ
|M(¯ a → ¯ b)|2 = x2
1 + x2 2 + 2x1x2 cos φ
∆|M|2 = 0
36
M(a → b) = x eiφ M(¯ a → ¯ b) = x e−iφ
|M(¯ a → ¯ b)|2 = x2 |M(a → b)|2 = x2 ∆|M|2 = 0
M(¯ a → ¯ b) = x1 e−iφ + x2 M(a → b) = x1 eiφ + x2
|M(a → b)|2 = x2
1 + x2 2 + 2x1x2 cos φ
|M(¯ a → ¯ b)|2 = x2
1 + x2 2 + 2x1x2 cos φ
∆|M|2 = 0
M(a → b) = x1 eiφ+iθ + x2 M(¯ a → ¯ b) = x1 e−iφ+iθ + x2
|M(¯ a → ¯ b)|2 = x2
1 + x2 2 + 2x1x2 cos(θ − φ)
|M(a → b)|2 = x2
1 + x2 2 + 2x1x2 cos(θ + φ)
∆|M|2 = −4x1x2 sin φ sin θ
37
much stronger now…)
Cui, Randall, BS, arXiv:1112.2704
Washout 2mX mΨ Viable parameters LHC gluino constraint too strong 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.5 1.0 1.5
mX mS mΨ mS mS 1.5 TeV
2mX mΨ V i a b l e p a r a m e t e r s Washout too strong LHC gluino constraint 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.5 1.0 1.5
mX mS mΨ mS
mS 5 TeV
38
d W W c t g b d ¯ u S1 S2 ψ†
u
ψ†
c
g ¯ c ¯ u
Cui, Randall, BS, arXiv:1112.2704