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Cosmic Neutrino Searches as Dark Matter Detectors David McKeen KEK Theory Meeting December 6, 2018

Cosmic Neutrino Searches as Dark Matter Detectors · Cosmic Neutrino Searches as Dark Matter Detectors David McKeen KEK Theory Meeting December 6, 2018

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Page 1: Cosmic Neutrino Searches as Dark Matter Detectors · Cosmic Neutrino Searches as Dark Matter Detectors David McKeen KEK Theory Meeting December 6, 2018

Cosmic Neutrino Searches as Dark Matter Detectors

David McKeen

KEK Theory Meeting December 6, 2018

Page 2: Cosmic Neutrino Searches as Dark Matter Detectors · Cosmic Neutrino Searches as Dark Matter Detectors David McKeen KEK Theory Meeting December 6, 2018

!2

Let’s start with a plot

Page 3: Cosmic Neutrino Searches as Dark Matter Detectors · Cosmic Neutrino Searches as Dark Matter Detectors David McKeen KEK Theory Meeting December 6, 2018

!2

Let’s start with a plot

🤔🤔🤔

What about here?

🤔🤔🤔

Page 4: Cosmic Neutrino Searches as Dark Matter Detectors · Cosmic Neutrino Searches as Dark Matter Detectors David McKeen KEK Theory Meeting December 6, 2018

!2

Let’s start with a plot

🤔🤔🤔

What about here?

🤔🤔🤔

Similar work by Cui, Pospelov, Pradler; Heeck

Page 5: Cosmic Neutrino Searches as Dark Matter Detectors · Cosmic Neutrino Searches as Dark Matter Detectors David McKeen KEK Theory Meeting December 6, 2018

PlanHow this gap can be populated

What cosmological observations tell us about these possibilities

How the gap can be probed

Page 6: Cosmic Neutrino Searches as Dark Matter Detectors · Cosmic Neutrino Searches as Dark Matter Detectors David McKeen KEK Theory Meeting December 6, 2018

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!4

How could this gap be populated?

L � ��LHN � yN��+ h.c. ! ��v⌫N � yN��+ h.c.

Dark Matter decay:

Odd under e.g. Z2, lightest is stable

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Imagine degeneracy in dark sector

Heavy state, e.g. 𝜙, could be metastable, decay to neutrinos

E⌫ ' (m� �m�)adecayatoday

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Neutrinos redshift until today

Page 7: Cosmic Neutrino Searches as Dark Matter Detectors · Cosmic Neutrino Searches as Dark Matter Detectors David McKeen KEK Theory Meeting December 6, 2018

!5

Let’s make it even simpler(Some of the) Dark Matter weakly coupled to

neutrinos, similar to majoron

This state decays to (only) neutrinos

Again, neutrinos redshift until today

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E⌫ ' mJ

2

adecayatoday

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What sort of flux can we imagine?

Lint = �g

2J⌫⌫ + h.c.

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⌧J =32⇡

|g|2mJ= 2.10⇥ 109 yr

����10�15

g

����2 ✓

eV

mJ

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Page 8: Cosmic Neutrino Searches as Dark Matter Detectors · Cosmic Neutrino Searches as Dark Matter Detectors David McKeen KEK Theory Meeting December 6, 2018

!6

Constraints on this scenarioRoughly speaking there are three possibilities

for DM lifetime 𝜏N (two are interesting)

0. Before BBN 𝜏J≲1 s: neutrinos thermalize, no effect 1. After BBN, before recombination 1 s≲𝜏J≲4×105 yr:

neutrinos contribute to 𝑁eff measured in CMB 2. After recombination 𝜏J≳4×105 yr: 𝐽 acts as

decaying DM component, affects CMB

Page 9: Cosmic Neutrino Searches as Dark Matter Detectors · Cosmic Neutrino Searches as Dark Matter Detectors David McKeen KEK Theory Meeting December 6, 2018

!7

Number densitiesAssuming that 𝐽 is nonrelativisitic before decay, its number density is

nJ(t) = ⌦J⇢cr,0mJ

⇣a0a

⌘3e�t/⌧J

=62.5

cm3

✓⌦J/⌦dm

0.05

◆✓eV

mJ

◆⇣a0a

⌘3e�t/⌧

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The number density of the neutrinos from 𝐽 is then dn⌫

dt+ 3Hn⌫ =

2nJ

⌧J<latexit sha1_base64="ZgGO3Rfr7i26ceaNqiOXf7uXI6k=">AAACJHicbVDLSgMxFM34rPVVdekmWARBkJkqKIhQdFNcVbCt0ClDJpNpQzOZIbkjlGE+xo2/4saFD1y48VtM21nUx4GQwznnktzjJ4JrsO1Pa25+YXFpubRSXl1b39isbG23dZwqylo0FrG684lmgkvWAg6C3SWKkcgXrOMPr8Z+554pzWN5C6OE9SLSlzzklICRvMq5GypCs8AFLgKGpefKNM8CyA+PG7PaxTRXk951nrlAUnN7lap9ZE+A/xKnIFVUoOlV3twgpmnEJFBBtO46dgK9jCjgVLC87KaaJYQOSZ91DZUkYrqXTZbM8b5RAhzGyhwJeKLOTmQk0noU+SYZERjo395Y/M/rphCe9TIukxSYpNOHwlRgiPG4MRxwxSiIkSGEKm7+iumAmDbA9Fo2JTi/V/5L2rUjx/Cbk2r9sqijhHbRHjpADjpFddRATdRCFD2gJ/SCXq1H69l6tz6m0TmrmNlBP2B9fQMgWqW0</latexit><latexit sha1_base64="ZgGO3Rfr7i26ceaNqiOXf7uXI6k=">AAACJHicbVDLSgMxFM34rPVVdekmWARBkJkqKIhQdFNcVbCt0ClDJpNpQzOZIbkjlGE+xo2/4saFD1y48VtM21nUx4GQwznnktzjJ4JrsO1Pa25+YXFpubRSXl1b39isbG23dZwqylo0FrG684lmgkvWAg6C3SWKkcgXrOMPr8Z+554pzWN5C6OE9SLSlzzklICRvMq5GypCs8AFLgKGpefKNM8CyA+PG7PaxTRXk951nrlAUnN7lap9ZE+A/xKnIFVUoOlV3twgpmnEJFBBtO46dgK9jCjgVLC87KaaJYQOSZ91DZUkYrqXTZbM8b5RAhzGyhwJeKLOTmQk0noU+SYZERjo395Y/M/rphCe9TIukxSYpNOHwlRgiPG4MRxwxSiIkSGEKm7+iumAmDbA9Fo2JTi/V/5L2rUjx/Cbk2r9sqijhHbRHjpADjpFddRATdRCFD2gJ/SCXq1H69l6tz6m0TmrmNlBP2B9fQMgWqW0</latexit><latexit sha1_base64="ZgGO3Rfr7i26ceaNqiOXf7uXI6k=">AAACJHicbVDLSgMxFM34rPVVdekmWARBkJkqKIhQdFNcVbCt0ClDJpNpQzOZIbkjlGE+xo2/4saFD1y48VtM21nUx4GQwznnktzjJ4JrsO1Pa25+YXFpubRSXl1b39isbG23dZwqylo0FrG684lmgkvWAg6C3SWKkcgXrOMPr8Z+554pzWN5C6OE9SLSlzzklICRvMq5GypCs8AFLgKGpefKNM8CyA+PG7PaxTRXk951nrlAUnN7lap9ZE+A/xKnIFVUoOlV3twgpmnEJFBBtO46dgK9jCjgVLC87KaaJYQOSZ91DZUkYrqXTZbM8b5RAhzGyhwJeKLOTmQk0noU+SYZERjo395Y/M/rphCe9TIukxSYpNOHwlRgiPG4MRxwxSiIkSGEKm7+iumAmDbA9Fo2JTi/V/5L2rUjx/Cbk2r9sqijhHbRHjpADjpFddRATdRCFD2gJ/SCXq1H69l6tz6m0TmrmNlBP2B9fQMgWqW0</latexit><latexit sha1_base64="ZgGO3Rfr7i26ceaNqiOXf7uXI6k=">AAACJHicbVDLSgMxFM34rPVVdekmWARBkJkqKIhQdFNcVbCt0ClDJpNpQzOZIbkjlGE+xo2/4saFD1y48VtM21nUx4GQwznnktzjJ4JrsO1Pa25+YXFpubRSXl1b39isbG23dZwqylo0FrG684lmgkvWAg6C3SWKkcgXrOMPr8Z+554pzWN5C6OE9SLSlzzklICRvMq5GypCs8AFLgKGpefKNM8CyA+PG7PaxTRXk951nrlAUnN7lap9ZE+A/xKnIFVUoOlV3twgpmnEJFBBtO46dgK9jCjgVLC87KaaJYQOSZ91DZUkYrqXTZbM8b5RAhzGyhwJeKLOTmQk0noU+SYZERjo395Y/M/rphCe9TIukxSYpNOHwlRgiPG4MRxwxSiIkSGEKm7+iumAmDbA9Fo2JTi/V/5L2rUjx/Cbk2r9sqijhHbRHjpADjpFddRATdRCFD2gJ/SCXq1H69l6tz6m0TmrmNlBP2B9fQMgWqW0</latexit>

n⌫(t) =2⌦J⇢cr,0

mJ

1� e�t/⌧J

a3

=125

cm3

✓⌦J/⌦dm

0.05

◆✓eV

mJ

◆1� e�t/⌧J

a3<latexit sha1_base64="CYvEVVLJAR6qSbBhhChCjjWakyc=">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</latexit><latexit sha1_base64="CYvEVVLJAR6qSbBhhChCjjWakyc=">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</latexit><latexit sha1_base64="CYvEVVLJAR6qSbBhhChCjjWakyc=">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</latexit><latexit sha1_base64="CYvEVVLJAR6qSbBhhChCjjWakyc=">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</latexit>

)<latexit sha1_base64="wpk/zjynGmYSy0lRI+eU5+ZY+O4=">AAAB8nicbZBNS8NAEIYn9avWr6pHL4tF8FQSEfRY9OKxiq2FNJTNdtMu3WTD7kQpoT/DiwdFvPprvPlv3LY5aOsLCw/vzLAzb5hKYdB1v53Syura+kZ5s7K1vbO7V90/aBuVacZbTEmlOyE1XIqEt1Cg5J1UcxqHkj+Eo+tp/eGRayNUco/jlAcxHSQiEoyitfzunRgMkWqtnnrVmlt3ZyLL4BVQg0LNXvWr21csi3mCTFJjfM9NMcipRsEkn1S6meEpZSM64L7FhMbcBPls5Qk5sU6fRErblyCZub8nchobM45D2xlTHJrF2tT8r+ZnGF0GuUjSDHnC5h9FmSSoyPR+0heaM5RjC5RpYXclbEg1ZWhTqtgQvMWTl6F9Vvcs357XGldFHGU4gmM4BQ8uoAE30IQWMFDwDK/w5qDz4rw7H/PWklPMHMIfOZ8/kR2RbQ==</latexit><latexit sha1_base64="wpk/zjynGmYSy0lRI+eU5+ZY+O4=">AAAB8nicbZBNS8NAEIYn9avWr6pHL4tF8FQSEfRY9OKxiq2FNJTNdtMu3WTD7kQpoT/DiwdFvPprvPlv3LY5aOsLCw/vzLAzb5hKYdB1v53Syura+kZ5s7K1vbO7V90/aBuVacZbTEmlOyE1XIqEt1Cg5J1UcxqHkj+Eo+tp/eGRayNUco/jlAcxHSQiEoyitfzunRgMkWqtnnrVmlt3ZyLL4BVQg0LNXvWr21csi3mCTFJjfM9NMcipRsEkn1S6meEpZSM64L7FhMbcBPls5Qk5sU6fRErblyCZub8nchobM45D2xlTHJrF2tT8r+ZnGF0GuUjSDHnC5h9FmSSoyPR+0heaM5RjC5RpYXclbEg1ZWhTqtgQvMWTl6F9Vvcs357XGldFHGU4gmM4BQ8uoAE30IQWMFDwDK/w5qDz4rw7H/PWklPMHMIfOZ8/kR2RbQ==</latexit><latexit sha1_base64="wpk/zjynGmYSy0lRI+eU5+ZY+O4=">AAAB8nicbZBNS8NAEIYn9avWr6pHL4tF8FQSEfRY9OKxiq2FNJTNdtMu3WTD7kQpoT/DiwdFvPprvPlv3LY5aOsLCw/vzLAzb5hKYdB1v53Syura+kZ5s7K1vbO7V90/aBuVacZbTEmlOyE1XIqEt1Cg5J1UcxqHkj+Eo+tp/eGRayNUco/jlAcxHSQiEoyitfzunRgMkWqtnnrVmlt3ZyLL4BVQg0LNXvWr21csi3mCTFJjfM9NMcipRsEkn1S6meEpZSM64L7FhMbcBPls5Qk5sU6fRErblyCZub8nchobM45D2xlTHJrF2tT8r+ZnGF0GuUjSDHnC5h9FmSSoyPR+0heaM5RjC5RpYXclbEg1ZWhTqtgQvMWTl6F9Vvcs357XGldFHGU4gmM4BQ8uoAE30IQWMFDwDK/w5qDz4rw7H/PWklPMHMIfOZ8/kR2RbQ==</latexit><latexit sha1_base64="wpk/zjynGmYSy0lRI+eU5+ZY+O4=">AAAB8nicbZBNS8NAEIYn9avWr6pHL4tF8FQSEfRY9OKxiq2FNJTNdtMu3WTD7kQpoT/DiwdFvPprvPlv3LY5aOsLCw/vzLAzb5hKYdB1v53Syura+kZ5s7K1vbO7V90/aBuVacZbTEmlOyE1XIqEt1Cg5J1UcxqHkj+Eo+tp/eGRayNUco/jlAcxHSQiEoyitfzunRgMkWqtnnrVmlt3ZyLL4BVQg0LNXvWr21csi3mCTFJjfM9NMcipRsEkn1S6meEpZSM64L7FhMbcBPls5Qk5sU6fRErblyCZub8nchobM45D2xlTHJrF2tT8r+ZnGF0GuUjSDHnC5h9FmSSoyPR+0heaM5RjC5RpYXclbEg1ZWhTqtgQvMWTl6F9Vvcs357XGldFHGU4gmM4BQ8uoAE30IQWMFDwDK/w5qDz4rw7H/PWklPMHMIfOZ8/kR2RbQ==</latexit>

Page 10: Cosmic Neutrino Searches as Dark Matter Detectors · Cosmic Neutrino Searches as Dark Matter Detectors David McKeen KEK Theory Meeting December 6, 2018

!8

1. Decays before recombinationEnergy density in neutrinos from 𝐽 is important quantity here

d⇢⌫

dt+ 4H ⇢⌫ =

mJnJ

⌧J<latexit sha1_base64="/Opzt/S53klO3UdCDHKXeuZH4ls=">AAACK3icbVDLSgMxFM34rPVVdekmWARBkBkp6EYodVO6qmBroVOGTCbThmYyQ3JHKMP8jxt/xYUufODW/zB9LGzrgZDDOeeS3OMngmuw7U9rZXVtfWOzsFXc3tnd2y8dHLZ1nCrKWjQWser4RDPBJWsBB8E6iWIk8gV78Ie3Y//hkSnNY3kPo4T1ItKXPOSUgJG8Us0NFaFZ4AIXAXPVIPZcmeZZAPl5pT6v3kyzkdfA0mvkmQskNbdXKtsX9gR4mTgzUkYzNL3SqxvENI2YBCqI1l3HTqCXEQWcCpYX3VSzhNAh6bOuoZJETPeyya45PjVKgMNYmSMBT9S/ExmJtB5FvklGBAZ60RuL/3ndFMLrXsZlkgKTdPpQmAoMMR4XhwOuGAUxMoRQxc1fMR0QUwiYeoumBGdx5WXSvrxwDL+rlKu1WR0FdIxO0Bly0BWqojpqohai6Am9oHf0YT1bb9aX9T2NrlizmSM0B+vnF7+cqS0=</latexit><latexit sha1_base64="/Opzt/S53klO3UdCDHKXeuZH4ls=">AAACK3icbVDLSgMxFM34rPVVdekmWARBkBkp6EYodVO6qmBroVOGTCbThmYyQ3JHKMP8jxt/xYUufODW/zB9LGzrgZDDOeeS3OMngmuw7U9rZXVtfWOzsFXc3tnd2y8dHLZ1nCrKWjQWser4RDPBJWsBB8E6iWIk8gV78Ie3Y//hkSnNY3kPo4T1ItKXPOSUgJG8Us0NFaFZ4AIXAXPVIPZcmeZZAPl5pT6v3kyzkdfA0mvkmQskNbdXKtsX9gR4mTgzUkYzNL3SqxvENI2YBCqI1l3HTqCXEQWcCpYX3VSzhNAh6bOuoZJETPeyya45PjVKgMNYmSMBT9S/ExmJtB5FvklGBAZ60RuL/3ndFMLrXsZlkgKTdPpQmAoMMR4XhwOuGAUxMoRQxc1fMR0QUwiYeoumBGdx5WXSvrxwDL+rlKu1WR0FdIxO0Bly0BWqojpqohai6Am9oHf0YT1bb9aX9T2NrlizmSM0B+vnF7+cqS0=</latexit><latexit sha1_base64="/Opzt/S53klO3UdCDHKXeuZH4ls=">AAACK3icbVDLSgMxFM34rPVVdekmWARBkBkp6EYodVO6qmBroVOGTCbThmYyQ3JHKMP8jxt/xYUufODW/zB9LGzrgZDDOeeS3OMngmuw7U9rZXVtfWOzsFXc3tnd2y8dHLZ1nCrKWjQWser4RDPBJWsBB8E6iWIk8gV78Ie3Y//hkSnNY3kPo4T1ItKXPOSUgJG8Us0NFaFZ4AIXAXPVIPZcmeZZAPl5pT6v3kyzkdfA0mvkmQskNbdXKtsX9gR4mTgzUkYzNL3SqxvENI2YBCqI1l3HTqCXEQWcCpYX3VSzhNAh6bOuoZJETPeyya45PjVKgMNYmSMBT9S/ExmJtB5FvklGBAZ60RuL/3ndFMLrXsZlkgKTdPpQmAoMMR4XhwOuGAUxMoRQxc1fMR0QUwiYeoumBGdx5WXSvrxwDL+rlKu1WR0FdIxO0Bly0BWqojpqohai6Am9oHf0YT1bb9aX9T2NrlizmSM0B+vnF7+cqS0=</latexit><latexit sha1_base64="/Opzt/S53klO3UdCDHKXeuZH4ls=">AAACK3icbVDLSgMxFM34rPVVdekmWARBkBkp6EYodVO6qmBroVOGTCbThmYyQ3JHKMP8jxt/xYUufODW/zB9LGzrgZDDOeeS3OMngmuw7U9rZXVtfWOzsFXc3tnd2y8dHLZ1nCrKWjQWser4RDPBJWsBB8E6iWIk8gV78Ie3Y//hkSnNY3kPo4T1ItKXPOSUgJG8Us0NFaFZ4AIXAXPVIPZcmeZZAPl5pT6v3kyzkdfA0mvkmQskNbdXKtsX9gR4mTgzUkYzNL3SqxvENI2YBCqI1l3HTqCXEQWcCpYX3VSzhNAh6bOuoZJETPeyya45PjVKgMNYmSMBT9S/ExmJtB5FvklGBAZ60RuL/3ndFMLrXsZlkgKTdPpQmAoMMR4XhwOuGAUxMoRQxc1fMR0QUwiYeoumBGdx5WXSvrxwDL+rlKu1WR0FdIxO0Bly0BWqojpqohai6Am9oHf0YT1bb9aX9T2NrlizmSM0B+vnF7+cqS0=</latexit>

⇢⌫⇢�

���trec�t�⌧J

=

p⇡

2

⌦J

⌦�

r⌧Jtr

= 0.154

✓⌦J

⌦dm

◆r⌧J

103 yr= 0.23�Ne↵

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)<latexit sha1_base64="wpk/zjynGmYSy0lRI+eU5+ZY+O4=">AAAB8nicbZBNS8NAEIYn9avWr6pHL4tF8FQSEfRY9OKxiq2FNJTNdtMu3WTD7kQpoT/DiwdFvPprvPlv3LY5aOsLCw/vzLAzb5hKYdB1v53Syura+kZ5s7K1vbO7V90/aBuVacZbTEmlOyE1XIqEt1Cg5J1UcxqHkj+Eo+tp/eGRayNUco/jlAcxHSQiEoyitfzunRgMkWqtnnrVmlt3ZyLL4BVQg0LNXvWr21csi3mCTFJjfM9NMcipRsEkn1S6meEpZSM64L7FhMbcBPls5Qk5sU6fRErblyCZub8nchobM45D2xlTHJrF2tT8r+ZnGF0GuUjSDHnC5h9FmSSoyPR+0heaM5RjC5RpYXclbEg1ZWhTqtgQvMWTl6F9Vvcs357XGldFHGU4gmM4BQ8uoAE30IQWMFDwDK/w5qDz4rw7H/PWklPMHMIfOZ8/kR2RbQ==</latexit><latexit sha1_base64="wpk/zjynGmYSy0lRI+eU5+ZY+O4=">AAAB8nicbZBNS8NAEIYn9avWr6pHL4tF8FQSEfRY9OKxiq2FNJTNdtMu3WTD7kQpoT/DiwdFvPprvPlv3LY5aOsLCw/vzLAzb5hKYdB1v53Syura+kZ5s7K1vbO7V90/aBuVacZbTEmlOyE1XIqEt1Cg5J1UcxqHkj+Eo+tp/eGRayNUco/jlAcxHSQiEoyitfzunRgMkWqtnnrVmlt3ZyLL4BVQg0LNXvWr21csi3mCTFJjfM9NMcipRsEkn1S6meEpZSM64L7FhMbcBPls5Qk5sU6fRErblyCZub8nchobM45D2xlTHJrF2tT8r+ZnGF0GuUjSDHnC5h9FmSSoyPR+0heaM5RjC5RpYXclbEg1ZWhTqtgQvMWTl6F9Vvcs357XGldFHGU4gmM4BQ8uoAE30IQWMFDwDK/w5qDz4rw7H/PWklPMHMIfOZ8/kR2RbQ==</latexit><latexit sha1_base64="wpk/zjynGmYSy0lRI+eU5+ZY+O4=">AAAB8nicbZBNS8NAEIYn9avWr6pHL4tF8FQSEfRY9OKxiq2FNJTNdtMu3WTD7kQpoT/DiwdFvPprvPlv3LY5aOsLCw/vzLAzb5hKYdB1v53Syura+kZ5s7K1vbO7V90/aBuVacZbTEmlOyE1XIqEt1Cg5J1UcxqHkj+Eo+tp/eGRayNUco/jlAcxHSQiEoyitfzunRgMkWqtnnrVmlt3ZyLL4BVQg0LNXvWr21csi3mCTFJjfM9NMcipRsEkn1S6meEpZSM64L7FhMbcBPls5Qk5sU6fRErblyCZub8nchobM45D2xlTHJrF2tT8r+ZnGF0GuUjSDHnC5h9FmSSoyPR+0heaM5RjC5RpYXclbEg1ZWhTqtgQvMWTl6F9Vvcs357XGldFHGU4gmM4BQ8uoAE30IQWMFDwDK/w5qDz4rw7H/PWklPMHMIfOZ8/kR2RbQ==</latexit><latexit sha1_base64="wpk/zjynGmYSy0lRI+eU5+ZY+O4=">AAAB8nicbZBNS8NAEIYn9avWr6pHL4tF8FQSEfRY9OKxiq2FNJTNdtMu3WTD7kQpoT/DiwdFvPprvPlv3LY5aOsLCw/vzLAzb5hKYdB1v53Syura+kZ5s7K1vbO7V90/aBuVacZbTEmlOyE1XIqEt1Cg5J1UcxqHkj+Eo+tp/eGRayNUco/jlAcxHSQiEoyitfzunRgMkWqtnnrVmlt3ZyLL4BVQg0LNXvWr21csi3mCTFJjfM9NMcipRsEkn1S6meEpZSM64L7FhMbcBPls5Qk5sU6fRErblyCZub8nchobM45D2xlTHJrF2tT8r+ZnGF0GuUjSDHnC5h9FmSSoyPR+0heaM5RjC5RpYXclbEg1ZWhTqtgQvMWTl6F9Vvcs357XGldFHGU4gmM4BQ8uoAE30IQWMFDwDK/w5qDz4rw7H/PWklPMHMIfOZ8/kR2RbQ==</latexit>

or n⌫ =1.0⇥ 10�2

cm3

✓�Ne↵

0.28

◆✓100 keV

mJ

◆s103 yr

⌧J<latexit sha1_base64="suUhoLtuHJR8wnHatzOXKWcBSxU=">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</latexit><latexit sha1_base64="suUhoLtuHJR8wnHatzOXKWcBSxU=">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</latexit><latexit sha1_base64="suUhoLtuHJR8wnHatzOXKWcBSxU=">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</latexit><latexit sha1_base64="suUhoLtuHJR8wnHatzOXKWcBSxU=">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</latexit>

Strong constraint on neutrinos from 𝐽 decays before CMB last scattering

Eav⌫ ' 1 eV

⇣ mJ

100 keV

⌘r⌧J

103 yr<latexit sha1_base64="VfESoxb0PA3RlhQI0l1FVY/Brrw=">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</latexit><latexit sha1_base64="VfESoxb0PA3RlhQI0l1FVY/Brrw=">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</latexit><latexit sha1_base64="VfESoxb0PA3RlhQI0l1FVY/Brrw=">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</latexit><latexit sha1_base64="VfESoxb0PA3RlhQI0l1FVY/Brrw=">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</latexit>

Typical energy today:

Page 11: Cosmic Neutrino Searches as Dark Matter Detectors · Cosmic Neutrino Searches as Dark Matter Detectors David McKeen KEK Theory Meeting December 6, 2018

!9

Now 𝐽 acts a decaying DM component & impacts CMB

Poulin, Lesgourgues, Serpico, arXiv: 1606.02073

2. Decays after recombination

Roughly 5% of DM allowed to decayEav

⌫ ' 1 eV⇣ mJ

10 eV

⌘✓⌧J

1010 yr

◆2/3

<latexit sha1_base64="RtBsIdbIEyGWwbpiPisuR5XfH4g=">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</latexit><latexit sha1_base64="RtBsIdbIEyGWwbpiPisuR5XfH4g=">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</latexit><latexit sha1_base64="RtBsIdbIEyGWwbpiPisuR5XfH4g=">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</latexit><latexit sha1_base64="RtBsIdbIEyGWwbpiPisuR5XfH4g=">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</latexit>

) n⌫ ⇠ 10

cm3

✓10 eV

mJ

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with

Page 12: Cosmic Neutrino Searches as Dark Matter Detectors · Cosmic Neutrino Searches as Dark Matter Detectors David McKeen KEK Theory Meeting December 6, 2018

!9

Now 𝐽 acts a decaying DM component & impacts CMB

Poulin, Lesgourgues, Serpico, arXiv: 1606.02073

2. Decays after recombination

Roughly 5% of DM allowed to decayEav

⌫ ' 1 eV⇣ mJ

10 eV

⌘✓⌧J

1010 yr

◆2/3

<latexit sha1_base64="RtBsIdbIEyGWwbpiPisuR5XfH4g=">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</latexit><latexit sha1_base64="RtBsIdbIEyGWwbpiPisuR5XfH4g=">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</latexit><latexit sha1_base64="RtBsIdbIEyGWwbpiPisuR5XfH4g=">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</latexit><latexit sha1_base64="RtBsIdbIEyGWwbpiPisuR5XfH4g=">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</latexit>

) n⌫ ⇠ 10

cm3

✓10 eV

mJ

<latexit sha1_base64="pS8Wo8conWxKCzCkHD+8v4U8Nag=">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</latexit><latexit sha1_base64="pS8Wo8conWxKCzCkHD+8v4U8Nag=">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</latexit><latexit sha1_base64="pS8Wo8conWxKCzCkHD+8v4U8Nag=">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</latexit><latexit sha1_base64="pS8Wo8conWxKCzCkHD+8v4U8Nag=">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</latexit>

Focus on this case

with

Page 13: Cosmic Neutrino Searches as Dark Matter Detectors · Cosmic Neutrino Searches as Dark Matter Detectors David McKeen KEK Theory Meeting December 6, 2018

!9

Now 𝐽 acts a decaying DM component & impacts CMB

Poulin, Lesgourgues, Serpico, arXiv: 1606.02073

2. Decays after recombination

Roughly 5% of DM allowed to decayEav

⌫ ' 1 eV⇣ mJ

10 eV

⌘✓⌧J

1010 yr

◆2/3

<latexit sha1_base64="RtBsIdbIEyGWwbpiPisuR5XfH4g=">AAACXHicbVFdSxwxFM2Mtl3X2m4VfPEldCnYFztjhfZRFEF8UuiuwmZ3yGTv7AaTzJjcEZZh/JG++eJf0eyHxa8DFw7nnEuSk7RQ0mEU3QXh0vKHj58aK83Vz2tfvra+rXddXloBHZGr3F6k3IGSBjooUcFFYYHrVMF5enk49c+vwTqZm384KaCv+cjITAqOXkpa7ihhphxUzGrKr2vmpIYrGt/MBOjWTEGG2yyzXFQ6OamrOPrv1czK0Rh/Ps8w5OU8NvBT30yjE/uUHFS7v37XSasd7UQz0LckXpA2WeA0ad2yYS5KDQaF4s714qjAfsUtSqGgbrLSQcHFJR9Bz1PDNbh+NSunpj+8MqRZbv0YpDP1+UbFtXMTnfqk5jh2r72p+J7XKzH726+kKUoEI+YHZaWimNNp03QoLQhUE0+4sNLflYox9yWh/4+mLyF+/eS3pLu7E3t+ttfeP1jU0SBb5DvZJjH5Q/bJMTklHSLIHXkIGsFKcB8uh6vh2jwaBoudDfIC4eYj/KS2fg==</latexit><latexit sha1_base64="RtBsIdbIEyGWwbpiPisuR5XfH4g=">AAACXHicbVFdSxwxFM2Mtl3X2m4VfPEldCnYFztjhfZRFEF8UuiuwmZ3yGTv7AaTzJjcEZZh/JG++eJf0eyHxa8DFw7nnEuSk7RQ0mEU3QXh0vKHj58aK83Vz2tfvra+rXddXloBHZGr3F6k3IGSBjooUcFFYYHrVMF5enk49c+vwTqZm384KaCv+cjITAqOXkpa7ihhphxUzGrKr2vmpIYrGt/MBOjWTEGG2yyzXFQ6OamrOPrv1czK0Rh/Ps8w5OU8NvBT30yjE/uUHFS7v37XSasd7UQz0LckXpA2WeA0ad2yYS5KDQaF4s714qjAfsUtSqGgbrLSQcHFJR9Bz1PDNbh+NSunpj+8MqRZbv0YpDP1+UbFtXMTnfqk5jh2r72p+J7XKzH726+kKUoEI+YHZaWimNNp03QoLQhUE0+4sNLflYox9yWh/4+mLyF+/eS3pLu7E3t+ttfeP1jU0SBb5DvZJjH5Q/bJMTklHSLIHXkIGsFKcB8uh6vh2jwaBoudDfIC4eYj/KS2fg==</latexit><latexit sha1_base64="RtBsIdbIEyGWwbpiPisuR5XfH4g=">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</latexit><latexit sha1_base64="RtBsIdbIEyGWwbpiPisuR5XfH4g=">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</latexit>

) n⌫ ⇠ 10

cm3

✓10 eV

mJ

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Focus on this case

withNote: invoked as explanation of 𝛔8 and 𝑯0 tensions (Berezhiani et al.; Enqvist et al.)

Page 14: Cosmic Neutrino Searches as Dark Matter Detectors · Cosmic Neutrino Searches as Dark Matter Detectors David McKeen KEK Theory Meeting December 6, 2018

!10

Back to the plot

�⌫ =d(a3n⌫)

dE⌫

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=2⌦J

E⌫

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mJ

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Flux is given by

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Width determined by range of redshifts for decay

Page 15: Cosmic Neutrino Searches as Dark Matter Detectors · Cosmic Neutrino Searches as Dark Matter Detectors David McKeen KEK Theory Meeting December 6, 2018

!11

About the C𝜈BThermal relics that decoupled when 𝑇=3-4 MeV

G2F

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n⌫i =3

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◆=

112

cm3<latexit sha1_base64="knCJ2s9s9tDxWZ8p3cBh6SL06+s=">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</latexit><latexit sha1_base64="knCJ2s9s9tDxWZ8p3cBh6SL06+s=">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</latexit><latexit sha1_base64="knCJ2s9s9tDxWZ8p3cBh6SL06+s=">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</latexit><latexit sha1_base64="knCJ2s9s9tDxWZ8p3cBh6SL06+s=">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</latexit>

Number density per flavor

(fermions)

Slightly colder than CMB sincephotons heated by 𝑒+ 𝑒- annihilation

T⌫ =

✓4

11

◆1/3

T� = 1.9 K = 1.7⇥ 10�4 eV<latexit sha1_base64="+R+twOhpXBb2EtbM1j9JhIEjQ0w=">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</latexit><latexit sha1_base64="+R+twOhpXBb2EtbM1j9JhIEjQ0w=">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</latexit><latexit sha1_base64="+R+twOhpXBb2EtbM1j9JhIEjQ0w=">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</latexit><latexit sha1_base64="+R+twOhpXBb2EtbM1j9JhIEjQ0w=">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</latexit>

Huge number density but extremely low energy and challenging to detect

See talk by Martin Spinrath yesterday

Page 16: Cosmic Neutrino Searches as Dark Matter Detectors · Cosmic Neutrino Searches as Dark Matter Detectors David McKeen KEK Theory Meeting December 6, 2018

!12

Detecting the C𝜈B

A very old idea

Neutrino capture on neutron (nucleus), no threshold

Ee� = Eend +m⌫ + E⌫ ' Eend + 2m⌫<latexit sha1_base64="f6zwzJTGepO3ZfEu+X0+t6mCvE4=">AAACIXicbVDLSgMxFM3Ud31VXboJFkEolpki2I0giuBSwT6gU4dMetuGJpkxyQhl6K+48VfcuFCkO/FnTB+L2noguYdz7iW5J4w508Z1v53M0vLK6tr6RnZza3tnN7e3X9VRoihUaMQjVQ+JBs4kVAwzHOqxAiJCDrWwdz3ya8+gNIvkg+nH0BSkI1mbUWKsFOTKN0EKj6eDC1t9JTDI1qAgAl8mhZvR7Wsm4AnPuqWxHeTybtEdAy8Sb0ryaIq7IDf0WxFNBEhDOdG64bmxaaZEGUY5DLJ+oiEmtEc60LBUEgG6mY43HOBjq7RwO1L2SIPH6uxESoTWfRHaTkFMV897I/E/r5GYdrmZMhknBiSdPNROODYRHsWFW0wBNbxvCaGK2b9i2iWKUGNDzdoQvPmVF0m1VPQsvz/LX15N41hHh+gInSAPnaNLdIvuUAVR9ILe0Af6dF6dd+fLGU5aM8505gD9gfPzC8nho0c=</latexit><latexit sha1_base64="f6zwzJTGepO3ZfEu+X0+t6mCvE4=">AAACIXicbVDLSgMxFM3Ud31VXboJFkEolpki2I0giuBSwT6gU4dMetuGJpkxyQhl6K+48VfcuFCkO/FnTB+L2noguYdz7iW5J4w508Z1v53M0vLK6tr6RnZza3tnN7e3X9VRoihUaMQjVQ+JBs4kVAwzHOqxAiJCDrWwdz3ya8+gNIvkg+nH0BSkI1mbUWKsFOTKN0EKj6eDC1t9JTDI1qAgAl8mhZvR7Wsm4AnPuqWxHeTybtEdAy8Sb0ryaIq7IDf0WxFNBEhDOdG64bmxaaZEGUY5DLJ+oiEmtEc60LBUEgG6mY43HOBjq7RwO1L2SIPH6uxESoTWfRHaTkFMV897I/E/r5GYdrmZMhknBiSdPNROODYRHsWFW0wBNbxvCaGK2b9i2iWKUGNDzdoQvPmVF0m1VPQsvz/LX15N41hHh+gInSAPnaNLdIvuUAVR9ILe0Af6dF6dd+fLGU5aM8505gD9gfPzC8nho0c=</latexit><latexit sha1_base64="f6zwzJTGepO3ZfEu+X0+t6mCvE4=">AAACIXicbVDLSgMxFM3Ud31VXboJFkEolpki2I0giuBSwT6gU4dMetuGJpkxyQhl6K+48VfcuFCkO/FnTB+L2noguYdz7iW5J4w508Z1v53M0vLK6tr6RnZza3tnN7e3X9VRoihUaMQjVQ+JBs4kVAwzHOqxAiJCDrWwdz3ya8+gNIvkg+nH0BSkI1mbUWKsFOTKN0EKj6eDC1t9JTDI1qAgAl8mhZvR7Wsm4AnPuqWxHeTybtEdAy8Sb0ryaIq7IDf0WxFNBEhDOdG64bmxaaZEGUY5DLJ+oiEmtEc60LBUEgG6mY43HOBjq7RwO1L2SIPH6uxESoTWfRHaTkFMV897I/E/r5GYdrmZMhknBiSdPNROODYRHsWFW0wBNbxvCaGK2b9i2iWKUGNDzdoQvPmVF0m1VPQsvz/LX15N41hHh+gInSAPnaNLdIvuUAVR9ILe0Af6dF6dd+fLGU5aM8505gD9gfPzC8nho0c=</latexit><latexit sha1_base64="f6zwzJTGepO3ZfEu+X0+t6mCvE4=">AAACIXicbVDLSgMxFM3Ud31VXboJFkEolpki2I0giuBSwT6gU4dMetuGJpkxyQhl6K+48VfcuFCkO/FnTB+L2noguYdz7iW5J4w508Z1v53M0vLK6tr6RnZza3tnN7e3X9VRoihUaMQjVQ+JBs4kVAwzHOqxAiJCDrWwdz3ya8+gNIvkg+nH0BSkI1mbUWKsFOTKN0EKj6eDC1t9JTDI1qAgAl8mhZvR7Wsm4AnPuqWxHeTybtEdAy8Sb0ryaIq7IDf0WxFNBEhDOdG64bmxaaZEGUY5DLJ+oiEmtEc60LBUEgG6mY43HOBjq7RwO1L2SIPH6uxESoTWfRHaTkFMV897I/E/r5GYdrmZMhknBiSdPNROODYRHsWFW0wBNbxvCaGK2b9i2iWKUGNDzdoQvPmVF0m1VPQsvz/LX15N41hHh+gInSAPnaNLdIvuUAVR9ILe0Af6dF6dd+fLGU5aM8505gD9gfPzC8nho0c=</latexit> n <latexit sha1_base64="GdBVemXiv/TOlUwPzt56MWAmveg=">AAAB7XicbZDLSgMxFIbPeK31VnXpJlgEV2VGBF2WunFZwV6gM5RMmmljcxmSjFCGvoMbF4q49X3c+Tam7Sy09YfAx3/OIef8ccqZsb7/7a2tb2xubZd2yrt7+weHlaPjtlGZJrRFFFe6G2NDOZO0ZZnltJtqikXMaSce387qnSeqDVPywU5SGgk8lCxhBFtntcMGG4Z5v1L1a/5caBWCAqpQqNmvfIUDRTJBpSUcG9ML/NRGOdaWEU6n5TAzNMVkjIe051BiQU2Uz7edonPnDFCitHvSorn7eyLHwpiJiF2nwHZklmsz879aL7PJTZQzmWaWSrL4KMk4sgrNTkcDpimxfOIAE83croiMsMbEuoDKLoRg+eRVaF/WAsf3V9V6o4ijBKdwBhcQwDXU4Q6a0AICj/AMr/DmKe/Fe/c+Fq1rXjFzAn/kff4AXuyO+w==</latexit><latexit sha1_base64="GdBVemXiv/TOlUwPzt56MWAmveg=">AAAB7XicbZDLSgMxFIbPeK31VnXpJlgEV2VGBF2WunFZwV6gM5RMmmljcxmSjFCGvoMbF4q49X3c+Tam7Sy09YfAx3/OIef8ccqZsb7/7a2tb2xubZd2yrt7+weHlaPjtlGZJrRFFFe6G2NDOZO0ZZnltJtqikXMaSce387qnSeqDVPywU5SGgk8lCxhBFtntcMGG4Z5v1L1a/5caBWCAqpQqNmvfIUDRTJBpSUcG9ML/NRGOdaWEU6n5TAzNMVkjIe051BiQU2Uz7edonPnDFCitHvSorn7eyLHwpiJiF2nwHZklmsz879aL7PJTZQzmWaWSrL4KMk4sgrNTkcDpimxfOIAE83croiMsMbEuoDKLoRg+eRVaF/WAsf3V9V6o4ijBKdwBhcQwDXU4Q6a0AICj/AMr/DmKe/Fe/c+Fq1rXjFzAn/kff4AXuyO+w==</latexit><latexit sha1_base64="GdBVemXiv/TOlUwPzt56MWAmveg=">AAAB7XicbZDLSgMxFIbPeK31VnXpJlgEV2VGBF2WunFZwV6gM5RMmmljcxmSjFCGvoMbF4q49X3c+Tam7Sy09YfAx3/OIef8ccqZsb7/7a2tb2xubZd2yrt7+weHlaPjtlGZJrRFFFe6G2NDOZO0ZZnltJtqikXMaSce387qnSeqDVPywU5SGgk8lCxhBFtntcMGG4Z5v1L1a/5caBWCAqpQqNmvfIUDRTJBpSUcG9ML/NRGOdaWEU6n5TAzNMVkjIe051BiQU2Uz7edonPnDFCitHvSorn7eyLHwpiJiF2nwHZklmsz879aL7PJTZQzmWaWSrL4KMk4sgrNTkcDpimxfOIAE83croiMsMbEuoDKLoRg+eRVaF/WAsf3V9V6o4ijBKdwBhcQwDXU4Q6a0AICj/AMr/DmKe/Fe/c+Fq1rXjFzAn/kff4AXuyO+w==</latexit><latexit sha1_base64="GdBVemXiv/TOlUwPzt56MWAmveg=">AAAB7XicbZDLSgMxFIbPeK31VnXpJlgEV2VGBF2WunFZwV6gM5RMmmljcxmSjFCGvoMbF4q49X3c+Tam7Sy09YfAx3/OIef8ccqZsb7/7a2tb2xubZd2yrt7+weHlaPjtlGZJrRFFFe6G2NDOZO0ZZnltJtqikXMaSce387qnSeqDVPywU5SGgk8lCxhBFtntcMGG4Z5v1L1a/5caBWCAqpQqNmvfIUDRTJBpSUcG9ML/NRGOdaWEU6n5TAzNMVkjIe051BiQU2Uz7edonPnDFCitHvSorn7eyLHwpiJiF2nwHZklmsz879aL7PJTZQzmWaWSrL4KMk4sgrNTkcDpimxfOIAE83croiMsMbEuoDKLoRg+eRVaF/WAsf3V9V6o4ijBKdwBhcQwDXU4Q6a0AICj/AMr/DmKe/Fe/c+Fq1rXjFzAn/kff4AXuyO+w==</latexit>

for nonrel. neutrinos

Need incredible energy resolution…

Page 17: Cosmic Neutrino Searches as Dark Matter Detectors · Cosmic Neutrino Searches as Dark Matter Detectors David McKeen KEK Theory Meeting December 6, 2018

!13

C𝜈B capture on Tritium

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𝛽-decays with long lifetime

Tritiated graphene to reduce molecular smearing

Electrons below endpoint filtered out

PTOLEMY Experiment:

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Page 18: Cosmic Neutrino Searches as Dark Matter Detectors · Cosmic Neutrino Searches as Dark Matter Detectors David McKeen KEK Theory Meeting December 6, 2018

!14

C𝜈B capture on Tritium

t1/2 ' 12 yr<latexit sha1_base64="IQUV+rznh4pXjDAeMp3kNDKuC+4=">AAACAnicbZDLSsNAFIYn9VbrLepK3AwWwVVNiqDLohuXFewFmhAm00k7dGYSZyZCCdGNr+LGhSJufQp3vo3TNgtt/WHg4z/ncOb8YcKo0o7zbZWWlldW18rrlY3Nre0de3evreJUYtLCMYtlN0SKMCpIS1PNSDeRBPGQkU44uprUO/dEKhqLWz1OiM/RQNCIYqSNFdgHOsjc03ruKcrJHXTrD5knORzLPLCrTs2ZCi6CW0AVFGoG9pfXj3HKidCYIaV6rpNoP0NSU8xIXvFSRRKER2hAegYF4kT52fSEHB4bpw+jWJonNJy6vycyxJUa89B0cqSHar42Mf+r9VIdXfgZFUmqicCzRVHKoI7hJA/Yp5JgzcYGEJbU/BXiIZIIa5NaxYTgzp+8CO16zTV8c1ZtXBZxlMEhOAInwAXnoAGuQRO0AAaP4Bm8gjfryXqx3q2PWWvJKmb2wR9Znz9S7Za8</latexit><latexit sha1_base64="IQUV+rznh4pXjDAeMp3kNDKuC+4=">AAACAnicbZDLSsNAFIYn9VbrLepK3AwWwVVNiqDLohuXFewFmhAm00k7dGYSZyZCCdGNr+LGhSJufQp3vo3TNgtt/WHg4z/ncOb8YcKo0o7zbZWWlldW18rrlY3Nre0de3evreJUYtLCMYtlN0SKMCpIS1PNSDeRBPGQkU44uprUO/dEKhqLWz1OiM/RQNCIYqSNFdgHOsjc03ruKcrJHXTrD5knORzLPLCrTs2ZCi6CW0AVFGoG9pfXj3HKidCYIaV6rpNoP0NSU8xIXvFSRRKER2hAegYF4kT52fSEHB4bpw+jWJonNJy6vycyxJUa89B0cqSHar42Mf+r9VIdXfgZFUmqicCzRVHKoI7hJA/Yp5JgzcYGEJbU/BXiIZIIa5NaxYTgzp+8CO16zTV8c1ZtXBZxlMEhOAInwAXnoAGuQRO0AAaP4Bm8gjfryXqx3q2PWWvJKmb2wR9Znz9S7Za8</latexit><latexit sha1_base64="IQUV+rznh4pXjDAeMp3kNDKuC+4=">AAACAnicbZDLSsNAFIYn9VbrLepK3AwWwVVNiqDLohuXFewFmhAm00k7dGYSZyZCCdGNr+LGhSJufQp3vo3TNgtt/WHg4z/ncOb8YcKo0o7zbZWWlldW18rrlY3Nre0de3evreJUYtLCMYtlN0SKMCpIS1PNSDeRBPGQkU44uprUO/dEKhqLWz1OiM/RQNCIYqSNFdgHOsjc03ruKcrJHXTrD5knORzLPLCrTs2ZCi6CW0AVFGoG9pfXj3HKidCYIaV6rpNoP0NSU8xIXvFSRRKER2hAegYF4kT52fSEHB4bpw+jWJonNJy6vycyxJUa89B0cqSHar42Mf+r9VIdXfgZFUmqicCzRVHKoI7hJA/Yp5JgzcYGEJbU/BXiIZIIa5NaxYTgzp+8CO16zTV8c1ZtXBZxlMEhOAInwAXnoAGuQRO0AAaP4Bm8gjfryXqx3q2PWWvJKmb2wR9Znz9S7Za8</latexit><latexit sha1_base64="IQUV+rznh4pXjDAeMp3kNDKuC+4=">AAACAnicbZDLSsNAFIYn9VbrLepK3AwWwVVNiqDLohuXFewFmhAm00k7dGYSZyZCCdGNr+LGhSJufQp3vo3TNgtt/WHg4z/ncOb8YcKo0o7zbZWWlldW18rrlY3Nre0de3evreJUYtLCMYtlN0SKMCpIS1PNSDeRBPGQkU44uprUO/dEKhqLWz1OiM/RQNCIYqSNFdgHOsjc03ruKcrJHXTrD5knORzLPLCrTs2ZCi6CW0AVFGoG9pfXj3HKidCYIaV6rpNoP0NSU8xIXvFSRRKER2hAegYF4kT52fSEHB4bpw+jWJonNJy6vycyxJUa89B0cqSHar42Mf+r9VIdXfgZFUmqicCzRVHKoI7hJA/Yp5JgzcYGEJbU/BXiIZIIa5NaxYTgzp+8CO16zTV8c1ZtXBZxlMEhOAInwAXnoAGuQRO0AAaP4Bm8gjfryXqx3q2PWWvJKmb2wR9Znz9S7Za8</latexit>

𝛽-decays with long lifetime

� = 3.8⇥ 10�45 cm2<latexit sha1_base64="Uw9ecMGgOgLKL7qoSoaC1grZ7ZQ=">AAACDHicbVDLSgMxFM34rPVVdekmWAQ3lplasRuh6MZlBfuAzrRk0kwbmmSGJCOUYdy78VfcuFDErR/gzr8xbWehrQcCh3PO5eYeP2JUadv+tpaWV1bX1nMb+c2t7Z3dwt5+U4WxxKSBQxbKto8UYVSQhqaakXYkCeI+Iy1/dD3xW/dEKhqKOz2OiMfRQNCAYqSN1CsUXUUHHF2elaquppwox+4mp5Xz9CFxJYeYd8upSdklewq4SJyMFEGGeq/w5fZDHHMiNGZIqY5jR9pLkNQUM5Lm3ViRCOERGpCOoQKZvV4yPSaFx0bpwyCU5gkNp+rviQRxpcbcN0mO9FDNexPxP68T66DqJVREsSYCzxYFMYM6hJNmYJ9KgjUbG4KwpOavEA+RRFib/vKmBGf+5EXSLJccw28rxdpVVkcOHIIjcAIccAFq4AbUQQNg8AiewSt4s56sF+vd+phFl6xs5gD8gfX5A/Tqmkg=</latexit><latexit sha1_base64="Uw9ecMGgOgLKL7qoSoaC1grZ7ZQ=">AAACDHicbVDLSgMxFM34rPVVdekmWAQ3lplasRuh6MZlBfuAzrRk0kwbmmSGJCOUYdy78VfcuFDErR/gzr8xbWehrQcCh3PO5eYeP2JUadv+tpaWV1bX1nMb+c2t7Z3dwt5+U4WxxKSBQxbKto8UYVSQhqaakXYkCeI+Iy1/dD3xW/dEKhqKOz2OiMfRQNCAYqSN1CsUXUUHHF2elaquppwox+4mp5Xz9CFxJYeYd8upSdklewq4SJyMFEGGeq/w5fZDHHMiNGZIqY5jR9pLkNQUM5Lm3ViRCOERGpCOoQKZvV4yPSaFx0bpwyCU5gkNp+rviQRxpcbcN0mO9FDNexPxP68T66DqJVREsSYCzxYFMYM6hJNmYJ9KgjUbG4KwpOavEA+RRFib/vKmBGf+5EXSLJccw28rxdpVVkcOHIIjcAIccAFq4AbUQQNg8AiewSt4s56sF+vd+phFl6xs5gD8gfX5A/Tqmkg=</latexit><latexit sha1_base64="Uw9ecMGgOgLKL7qoSoaC1grZ7ZQ=">AAACDHicbVDLSgMxFM34rPVVdekmWAQ3lplasRuh6MZlBfuAzrRk0kwbmmSGJCOUYdy78VfcuFDErR/gzr8xbWehrQcCh3PO5eYeP2JUadv+tpaWV1bX1nMb+c2t7Z3dwt5+U4WxxKSBQxbKto8UYVSQhqaakXYkCeI+Iy1/dD3xW/dEKhqKOz2OiMfRQNCAYqSN1CsUXUUHHF2elaquppwox+4mp5Xz9CFxJYeYd8upSdklewq4SJyMFEGGeq/w5fZDHHMiNGZIqY5jR9pLkNQUM5Lm3ViRCOERGpCOoQKZvV4yPSaFx0bpwyCU5gkNp+rviQRxpcbcN0mO9FDNexPxP68T66DqJVREsSYCzxYFMYM6hJNmYJ9KgjUbG4KwpOavEA+RRFib/vKmBGf+5EXSLJccw28rxdpVVkcOHIIjcAIccAFq4AbUQQNg8AiewSt4s56sF+vd+phFl6xs5gD8gfX5A/Tqmkg=</latexit><latexit sha1_base64="Uw9ecMGgOgLKL7qoSoaC1grZ7ZQ=">AAACDHicbVDLSgMxFM34rPVVdekmWAQ3lplasRuh6MZlBfuAzrRk0kwbmmSGJCOUYdy78VfcuFDErR/gzr8xbWehrQcCh3PO5eYeP2JUadv+tpaWV1bX1nMb+c2t7Z3dwt5+U4WxxKSBQxbKto8UYVSQhqaakXYkCeI+Iy1/dD3xW/dEKhqKOz2OiMfRQNCAYqSN1CsUXUUHHF2elaquppwox+4mp5Xz9CFxJYeYd8upSdklewq4SJyMFEGGeq/w5fZDHHMiNGZIqY5jR9pLkNQUM5Lm3ViRCOERGpCOoQKZvV4yPSaFx0bpwyCU5gkNp+rviQRxpcbcN0mO9FDNexPxP68T66DqJVREsSYCzxYFMYM6hJNmYJ9KgjUbG4KwpOavEA+RRFib/vKmBGf+5EXSLJccw28rxdpVVkcOHIIjcAIccAFq4AbUQQNg8AiewSt4s56sF+vd+phFl6xs5gD8gfX5A/Tqmkg=</latexit>

Long, Lunardini, Sabancilar

Tiny rates but a crucial target

�Dir. =1

2�Maj. =

4

yr

✓MT

100 g

◆⇣ n⌫

56 cm�3

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Page 19: Cosmic Neutrino Searches as Dark Matter Detectors · Cosmic Neutrino Searches as Dark Matter Detectors David McKeen KEK Theory Meeting December 6, 2018

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2

adecayatoday

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The electron energy gap can be larger in this case

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n⌫ ⇠ 10

cm3

✓10 eV

mJ

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R =2.42

yr

✓MT

100 g

◆✓f⌫e

1/3

◆✓n⌫

100 cm3

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Page 20: Cosmic Neutrino Searches as Dark Matter Detectors · Cosmic Neutrino Searches as Dark Matter Detectors David McKeen KEK Theory Meeting December 6, 2018

!16

A Lesson from History?

Page 21: Cosmic Neutrino Searches as Dark Matter Detectors · Cosmic Neutrino Searches as Dark Matter Detectors David McKeen KEK Theory Meeting December 6, 2018

!16

A Lesson from History?

Page 22: Cosmic Neutrino Searches as Dark Matter Detectors · Cosmic Neutrino Searches as Dark Matter Detectors David McKeen KEK Theory Meeting December 6, 2018

Wrap upCosmic neutrino background is an extremely

important target to probe cosmology

PTOLEMY experiment hopes to explore this area

Interestingly, could also be sensitive to decaying dark matter, what else?

Important to be open minded about possible signs of new physics so that we don’t miss

anything—only nature gets a vote

Page 23: Cosmic Neutrino Searches as Dark Matter Detectors · Cosmic Neutrino Searches as Dark Matter Detectors David McKeen KEK Theory Meeting December 6, 2018

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Page 24: Cosmic Neutrino Searches as Dark Matter Detectors · Cosmic Neutrino Searches as Dark Matter Detectors David McKeen KEK Theory Meeting December 6, 2018

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Page 25: Cosmic Neutrino Searches as Dark Matter Detectors · Cosmic Neutrino Searches as Dark Matter Detectors David McKeen KEK Theory Meeting December 6, 2018

!19

Back upIf 𝐽 is “the” majoron

Model building exercise to get right mass/abundance

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Lint =im⌫

fJ⌫⌫ + h.c.

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⌧J ⇠ 109 yr , f ⇠ 100 TeV<latexit sha1_base64="d69vr1oGxvPUdkeF8t44Vd7HKIY=">AAACJHicbVC7SgNBFJ31GeMramkzGASrsCuCik3QRsRCwUQhG8Ps5G4yZGZ3mbmrhCX+i42/YmPhAwsbv8VJsoWvAwOHc87lzj1BIoVB1/1wJianpmdmC3PF+YXFpeXSymrdxKnmUOOxjPVVwAxIEUENBUq4SjQwFUi4DHpHQ//yBrQRcXSB/QSainUiEQrO0Eqt0oGPLG2d+EYo6rnX+3eZrxXt64F/CiFq0eki0zq+pWEecceJC6gPWqWyW3FHoH+Jl5MyyXHWKr367ZinCiLkkhnT8NwEmxnTKLiEQdFPDSSM91gHGpZGTIFpZqMjB3TTKm0axtq+COlI/T6RMWVMXwU2qRh2zW9vKP7nNVIM95qZiJIUIeLjRWEqKcZ02BhtCw0cZd8SxrWwf6W8yzTjaHst2hK83yf/JfXtimf5+U65epjXUSDrZINsEY/skio5JmekRji5J4/kmbw4D86T8+a8j6MTTj6zRn7A+fwCdsukrQ==</latexit><latexit sha1_base64="d69vr1oGxvPUdkeF8t44Vd7HKIY=">AAACJHicbVC7SgNBFJ31GeMramkzGASrsCuCik3QRsRCwUQhG8Ps5G4yZGZ3mbmrhCX+i42/YmPhAwsbv8VJsoWvAwOHc87lzj1BIoVB1/1wJianpmdmC3PF+YXFpeXSymrdxKnmUOOxjPVVwAxIEUENBUq4SjQwFUi4DHpHQ//yBrQRcXSB/QSainUiEQrO0Eqt0oGPLG2d+EYo6rnX+3eZrxXt64F/CiFq0eki0zq+pWEecceJC6gPWqWyW3FHoH+Jl5MyyXHWKr367ZinCiLkkhnT8NwEmxnTKLiEQdFPDSSM91gHGpZGTIFpZqMjB3TTKm0axtq+COlI/T6RMWVMXwU2qRh2zW9vKP7nNVIM95qZiJIUIeLjRWEqKcZ02BhtCw0cZd8SxrWwf6W8yzTjaHst2hK83yf/JfXtimf5+U65epjXUSDrZINsEY/skio5JmekRji5J4/kmbw4D86T8+a8j6MTTj6zRn7A+fwCdsukrQ==</latexit><latexit sha1_base64="d69vr1oGxvPUdkeF8t44Vd7HKIY=">AAACJHicbVC7SgNBFJ31GeMramkzGASrsCuCik3QRsRCwUQhG8Ps5G4yZGZ3mbmrhCX+i42/YmPhAwsbv8VJsoWvAwOHc87lzj1BIoVB1/1wJianpmdmC3PF+YXFpeXSymrdxKnmUOOxjPVVwAxIEUENBUq4SjQwFUi4DHpHQ//yBrQRcXSB/QSainUiEQrO0Eqt0oGPLG2d+EYo6rnX+3eZrxXt64F/CiFq0eki0zq+pWEecceJC6gPWqWyW3FHoH+Jl5MyyXHWKr367ZinCiLkkhnT8NwEmxnTKLiEQdFPDSSM91gHGpZGTIFpZqMjB3TTKm0axtq+COlI/T6RMWVMXwU2qRh2zW9vKP7nNVIM95qZiJIUIeLjRWEqKcZ02BhtCw0cZd8SxrWwf6W8yzTjaHst2hK83yf/JfXtimf5+U65epjXUSDrZINsEY/skio5JmekRji5J4/kmbw4D86T8+a8j6MTTj6zRn7A+fwCdsukrQ==</latexit><latexit sha1_base64="d69vr1oGxvPUdkeF8t44Vd7HKIY=">AAACJHicbVC7SgNBFJ31GeMramkzGASrsCuCik3QRsRCwUQhG8Ps5G4yZGZ3mbmrhCX+i42/YmPhAwsbv8VJsoWvAwOHc87lzj1BIoVB1/1wJianpmdmC3PF+YXFpeXSymrdxKnmUOOxjPVVwAxIEUENBUq4SjQwFUi4DHpHQ//yBrQRcXSB/QSainUiEQrO0Eqt0oGPLG2d+EYo6rnX+3eZrxXt64F/CiFq0eki0zq+pWEecceJC6gPWqWyW3FHoH+Jl5MyyXHWKr367ZinCiLkkhnT8NwEmxnTKLiEQdFPDSSM91gHGpZGTIFpZqMjB3TTKm0axtq+COlI/T6RMWVMXwU2qRh2zW9vKP7nNVIM95qZiJIUIeLjRWEqKcZ02BhtCw0cZd8SxrWwf6W8yzTjaHst2hK83yf/JfXtimf5+U65epjXUSDrZINsEY/skio5JmekRji5J4/kmbw4D86T8+a8j6MTTj6zRn7A+fwCdsukrQ==</latexit>

for mJ ⇠ eV<latexit sha1_base64="yzwTsi5mI51PmBpHeryt4IzArN4=">AAAB+HicbZDLSgMxFIbP1Futl1ZdugkWwVWZEUGXRTfiqoK9QGcYMmmmDU0yQ5IR6tAnceNCEbc+ijvfxrSdhbb+EPj4zzmckz9KOdPGdb+d0tr6xuZWebuys7u3X60dHHZ0kilC2yThiepFWFPOJG0bZjjtpYpiEXHajcY3s3r3kSrNEvlgJikNBB5KFjOCjbXCWlWEd75mIveVQLQzDWt1t+HOhVbBK6AOhVph7csfJCQTVBrCsdZ9z01NkGNlGOF0WvEzTVNMxnhI+xYlFlQH+fzwKTq1zgDFibJPGjR3f0/kWGg9EZHtFNiM9HJtZv5X62cmvgpyJtPMUEkWi+KMI5OgWQpowBQlhk8sYKKYvRWREVaYGJtVxYbgLX95FTrnDc/y/UW9eV3EUYZjOIEz8OASmnALLWgDgQye4RXenCfnxXl3PhatJaeYOYI/cj5/AJtGkwo=</latexit><latexit sha1_base64="yzwTsi5mI51PmBpHeryt4IzArN4=">AAAB+HicbZDLSgMxFIbP1Futl1ZdugkWwVWZEUGXRTfiqoK9QGcYMmmmDU0yQ5IR6tAnceNCEbc+ijvfxrSdhbb+EPj4zzmckz9KOdPGdb+d0tr6xuZWebuys7u3X60dHHZ0kilC2yThiepFWFPOJG0bZjjtpYpiEXHajcY3s3r3kSrNEvlgJikNBB5KFjOCjbXCWlWEd75mIveVQLQzDWt1t+HOhVbBK6AOhVph7csfJCQTVBrCsdZ9z01NkGNlGOF0WvEzTVNMxnhI+xYlFlQH+fzwKTq1zgDFibJPGjR3f0/kWGg9EZHtFNiM9HJtZv5X62cmvgpyJtPMUEkWi+KMI5OgWQpowBQlhk8sYKKYvRWREVaYGJtVxYbgLX95FTrnDc/y/UW9eV3EUYZjOIEz8OASmnALLWgDgQye4RXenCfnxXl3PhatJaeYOYI/cj5/AJtGkwo=</latexit><latexit sha1_base64="yzwTsi5mI51PmBpHeryt4IzArN4=">AAAB+HicbZDLSgMxFIbP1Futl1ZdugkWwVWZEUGXRTfiqoK9QGcYMmmmDU0yQ5IR6tAnceNCEbc+ijvfxrSdhbb+EPj4zzmckz9KOdPGdb+d0tr6xuZWebuys7u3X60dHHZ0kilC2yThiepFWFPOJG0bZjjtpYpiEXHajcY3s3r3kSrNEvlgJikNBB5KFjOCjbXCWlWEd75mIveVQLQzDWt1t+HOhVbBK6AOhVph7csfJCQTVBrCsdZ9z01NkGNlGOF0WvEzTVNMxnhI+xYlFlQH+fzwKTq1zgDFibJPGjR3f0/kWGg9EZHtFNiM9HJtZv5X62cmvgpyJtPMUEkWi+KMI5OgWQpowBQlhk8sYKKYvRWREVaYGJtVxYbgLX95FTrnDc/y/UW9eV3EUYZjOIEz8OASmnALLWgDgQye4RXenCfnxXl3PhatJaeYOYI/cj5/AJtGkwo=</latexit><latexit sha1_base64="yzwTsi5mI51PmBpHeryt4IzArN4=">AAAB+HicbZDLSgMxFIbP1Futl1ZdugkWwVWZEUGXRTfiqoK9QGcYMmmmDU0yQ5IR6tAnceNCEbc+ijvfxrSdhbb+EPj4zzmckz9KOdPGdb+d0tr6xuZWebuys7u3X60dHHZ0kilC2yThiepFWFPOJG0bZjjtpYpiEXHajcY3s3r3kSrNEvlgJikNBB5KFjOCjbXCWlWEd75mIveVQLQzDWt1t+HOhVbBK6AOhVph7csfJCQTVBrCsdZ9z01NkGNlGOF0WvEzTVNMxnhI+xYlFlQH+fzwKTq1zgDFibJPGjR3f0/kWGg9EZHtFNiM9HJtZv5X62cmvgpyJtPMUEkWi+KMI5OgWQpowBQlhk8sYKKYvRWREVaYGJtVxYbgLX95FTrnDc/y/UW9eV3EUYZjOIEz8OASmnALLWgDgQye4RXenCfnxXl3PhatJaeYOYI/cj5/AJtGkwo=</latexit>

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