Sterile neutrinos: to be or not to be? · 0.7 0.8 0.9 1 observed / no osc. expected 1.1 Dm2 = 0.44 eV2, sin22q 14 = 0.13 Dm2 = 1.75 eV2, sin22q 14 = 0.10 Dm2 = 0.9 eV2, sin22q 14

Sterile neutrinos: to be or not to be?

Joachim Kopp (University of Mainz)

June 9, 2015 @ WIN 2015, Heidelberg

Joachim Kopp Sterile neutrinos: to be or not to be? 1

Outline

1 Sterile Neutrinos

2 Oscillation Anomalies: A Global Fitνe Appearanceνe Disappearanceνµ DisappearanceSterile Neutrino Oscillations: The Global Picture

3 Sterile Neutrinos in Cosmology

4 Light Sterile Neutrinos and Dark Matter SearchesSterile Neutrinos and Direct Dark Matter SearchesSterile Neutrinos and Indirect Dark Matter Searches

5 Summary


Sterile Neutrinos

Sterile neutrinos

Definition

Sterile neutrino = SM singlet fermion

Very generic extension of the SMI can be leftovers of extended gauge multiplets (e.g. GUT multiplets)

Very useful in phenomenology:I Can explain smallness of neutrino mass

(seesaw mechanism, m ∼ TeV . . .MPl)I Can explain baryon asymmetry of the Universe

(leptogenesis, m� 100 GeV)I Can explain dark matter

(m ∼ keV)I Can explain various neutrino oscillation anomalies

(m ∼ eV)


Oscillation Anomalies:A Global Fit

(_ )ν e appearance in the 3+1 scenario and beyondMotivated by LSND and MiniBooNE: excess of

(_ )ν e events in

(_ )ν µ beam.

10-3 10-2 10-1

10-1

100

101

sin2 2ΘΜe

Dm

41

2

ø

LSND

MiniBooNE Ν

MiniBooNE Ν

E776+LBL reactors

KARMEN

NOMADIC

AR

US

H2012

LCombined

99% CL, 2 dof

χ23+1/dof χ2

3+2/dof χ21+3+1/dof

LSND 11.0/11 8.6/11 7.5/11MiniB ν 19.3/11 10.6/11 9.1/11MiniB ν̄ 10.7/11 9.6/11 12.7/11E776 32.4/24 29.2/24 31.3/24KARMEN 9.8/9 8.6/9 9.0/9NOMAD 0.0/1 0.0/1 0.0/1ICARUS 2.0/1 2.3/1 1.5/1

Combined 87.9/66 72.7/63 74.6/63

Global fit to all appearance data is consistentBackground oscillations importantin MiniBooNE and E776Significant improvementin 3 + 2 and 1 + 3 + 1

JK Machado Maltoni Schwetz, 1303.3011see also fits by Giunti Laveder et al.

Collin Conrad Ignarra Karagiorgi Shaevitz Spitz Djurcic Sorel


3 + 1 3 + 2 1 + 3 + 1


(_ )ν e events in

(_ )ν µ beam.

10-3 10-2 10-1

10-1

100

101

sin2 2ΘΜe

Dm

41

2

ø

LSND

MiniBooNE Ν

MiniBooNE Ν

E776+LBL reactors

KARMEN

NOMADIC

AR

US

H2012

LCombined

ICA

RU

SH20

14

LO

PE

RA

H201

3L

99% CL, 2 dof

Preliminary χ23+1/dof χ2

3+2/dof χ21+3+1/dof


Combined 87.9/66 72.7/63 74.6/63





3 + 1 3 + 2 1 + 3 + 1


(_ )ν e events in

(_ )ν µ beam.

10-3 10-2 10-1

10-1

100

101

sin2 2ΘΜe

Dm

41

2

ø

LSND

MiniBooNE Ν

MiniBooNE Ν

E776+LBL reactors

KARMEN

NOMADIC

AR

US

H2012

LCombined

ICA

RU

SH20

14

LO

PE

RA

H201

3L

99% CL, 2 dof

Preliminary χ23+1/dof χ2

3+2/dof χ21+3+1/dof


Combined 87.9/66 72.7/63 74.6/63





3 + 1 3 + 2 1 + 3 + 1

(_ )ν e disappearance in the 3+1 scenario

10 100distance from reactor [m]

0.7

0.8

0.9

1

1.1

obse

rved

/ no

osc

. exp

ecte

d

∆m2 = 0.44 eV

2, sin

22θ

14 = 0.13

∆m2 = 1.75 eV

2, sin

22θ

14 = 0.10

∆m2 = 0.9 eV

2, sin

22θ

14 = 0.057

ILL

Bug

ey3,

4

Rov

no, S

RP SR

PR

ovno

Kra

sn

Bug

ey3

Gos

gen

Kra

snG

osge

n

Kra

snGos

gen

Bug

ey3

10- 3 10- 2 10-1

10-1

100

101

ÈUe42

Dm

412@eV

2D

ó

øç

95% CL

Gallium

SBL

reac

tors

All

Νe

dis

app

LB

Lre

acto

rs

C -12

Sola

r+

Kam

L

sin2 2θ14 ∆m241 [eV2] χ2

min/dof (GOF) ∆χ2no osc/dof (CL)

SBL rates only 0.13 0.44 11.5/17 (83%) 11.4/2 (99.7%)SBL incl. Bugey3 spect. 0.10 1.75 58.3/74 (91%) 9.0/2 (98.9%)SBL + Gallium 0.11 1.80 64.0/78 (87%) 14.0/2 (99.9%)global νe disapp. 0.09 1.78 403.3/427 (79%) 12.6/2 (99.8%)

JK Machado Maltoni Schwetz, 1303.3011Joachim Kopp Sterile neutrinos: to be or not to be? 7

Relation between appearance and disappearanceWe find:

(_ )ν e disappearance experiments consistent among themselves,

(_ )ν e appearance experiments consistent among themselves.

But:

3 + 1 neutrinosAt L� 4πE/∆m2

41, but L� 4πE/∆m231

Pee = 1− 2|Ue4|2(1− |Ue4|2)

Pµµ = 1− 2|Uµ4|2(1− |Uµ4|2)

Peµ = 2|Ue4|2|Uµ4|2

It follows

2Peµ ' (1− Pee)(1− Pµµ)

In the 3 + 1 case, at large enough baseline, there is a one-to-one relationbetween the appearance and disappearance probabilities.


Combining different oscillation channels

provides the strongest, most robust

constraints on sterile neutrinos

(_ )ν µ disappearance in the 3+1 scenario

Parameter regions favored by tentative hints are intension with null results from

(_ )ν µ disappearance searches

10-2 10-1

10-1

100

101

ÈUΜ42

Dm

41

2@eV2

D

CDHS

atm

MINOS H2011LMB disapp

LSND

MB app

reactors+Ga

Null results

combined

ø

99% CL


JK Machado Maltoni Schwetz, 1303.3011

(_ )ν µ disappearance in the 3+1 scenario

Parameter regions favored by tentative hints are intension with null results from

(_ )ν µ disappearance searches

10-2 10-1

10-1

100

101

ÈUΜ42

Dm

41

2@eV2

D

CDHS

atmS

KH20

14

LMINOS H2011L

MIN

OS

H2014

LMB disapp

LSND

MB app

reactors+Ga

Null results

combined

ø

Preliminary99% CL


JK Machado Maltoni Schwetz, 1303.3011

IceCube and sterile neutrinos

Oscillograms 101

Matter Signal antineutrino, because of the known hierarchy! Access to the antineutrino νµ oscillation parameters!

Neutrino Absorption (at TeV energies, neutrinos are absorbed by the earth)

Vaccum Osc Wiggles

Big Resonance!Hierarchy demands thisbe in antineutrino mode

Ener

gy !

Up (through core) Horizon Up (through core) Horizon

Vaccum Osc Wiggles

From NuSquids,(Argüelles Delgado, et al)

Slide courtesy of Janet Conrad


The global oscillation fit3 + 1 Severe tension between

appearance anddisappearance and betweenexp’s with and without a signal

3 + 2 Tension remains for two sterileneutrinos

3 + 3 No significant improvementexpected

10-4 10- 3 10- 2 10-110-1

100

101

sin 2 2 Θ Μe

Dm

2

LSND + reactors+ Ga + MB app

null resultsappearance

null resultsdisappearance

null resultscombined

99% CL, 2 dof


χ2min/dof GOF

χ2PG/dof PG

3+1 712/(689− 9) 19%

18.0/2 1.2× 10−4

3+2 701/(689− 14) 23% 25.8/4 3.4× 10−5

1+3+1 694/(689− 14) 30% 16.8/4 2.1× 10−3

JK Machado Maltoni Schwetz, arXiv:1303.3011





Parameter goodness of fit (PG) test:

Compares χ2min from global and separate

fits to test compatibility of 2 data sets

10-4 10- 3 10- 2 10-110-1

100

101

sin 2 2 Θ Μe

Dm

2

LSND + reactors+ Ga + MB app

null resultsappearance

null resultsdisappearance

null resultscombined

99% CL, 2 dof


χ2min/dof GOF χ2

PG/dof PG

3+1 712/(689− 9) 19% 18.0/2 1.2× 10−4

3+2 701/(689− 14) 23% 25.8/4 3.4× 10−5

1+3+1 694/(689− 14) 30% 16.8/4 2.1× 10−3









10-1 100 10110-1

100

101

Dm412 @eV 2 D

Dm

512@e

V2

D

3+2

1+3+1

�

è

ø

� èø

95 % 99 %

è app

� disapp

ø ø global


χ2min/dof GOF χ2

PG/dof PG

3+1 712/(689− 9) 19% 18.0/2 1.2× 10−4

3+2 701/(689− 14) 23% 25.8/4 3.4× 10−5

1+3+1 694/(689− 14) 30% 16.8/4 2.1× 10−3









10-1 100 10110-1

100

101

Dm412 @eV 2 D

Dm

512@e

V2

D

3+2

1+3+1

�

è

ø

� èø

95 % 99 %

è app

� disapp

ø ø global


χ2min/dof GOF χ2

PG/dof PG

3+1 712/(689− 9) 19% 18.0/2 1.2× 10−4

3+2 701/(689− 14) 23% 25.8/4 3.4× 10−5

1+3+1 694/(689− 14) 30% 16.8/4 2.1× 10−3


Sterile Neutrinos in Cosmology

Sterile neutrinos in cosmologyModels with O(eV) sterile neutrino(s) constrained by cosmology:

Sum of neutrino masses

∑mν . 0.23 eV

# of relativistic species

Nν = 4 mildly disfavored

Ade et al. (Planck), arXiv:1303.5076Gonzalez-Garcia Maltoni Salvado, arXiv:1006.3795

Hamann Hannestad Raffelt Tamborra Wong, arXiv:1006:5276


Sterile neutrinos in cosmologyModels with O(eV) sterile neutrino(s) constrained by cosmology:

Sum of neutrino masses

∑mν . 0.23 eV

# of relativistic species

Nν = 4 mildly disfavored

Ade et al. (Planck), arXiv:1303.5076Gonzalez-Garcia Maltoni Salvado, arXiv:1006.3795

Hamann Hannestad Raffelt Tamborra Wong, arXiv:1006:5276

Question:

What does is take to evade these constraints?


Suppressed νs production from thermal MSW effectνs production in the early Universe through νe,µ,τ → νs oscillations

Dodelson Widrow 1994Assume νs couple to & MeV gauge boson A′

Neutrino self energy:

Leads to thermal MSW potential V ∝ T 4

At high T : mixing strongly suppressed

sin 2θeff =sin 2θ√

sin2 2θ +(cos 2θ − 2EV

∆m2

)2

No νs production through oscillations→ no cosmological constraints Hannestad Hansen Tram arXiv:1310.5926

Dasgupta JK arXiv:1310.6337


Parameter space for self-interacting sterile neutrinos

Chu Dasgupta JK arXiv:1505.02795Two regions:

Weak coupling: No νs production (see previous slide)Strong coupling: Lots of νs produced, but not harmful (see next slide)

Mirizzi Mangano Pisanti Saviano, arXiv:1410.1385, 1409.1680


Strongly self-interacting sterile neutrinosLarge coupling→ efficient conversion of νe,µ,τ → νs

after neutrino freeze-out (Dodelson-Widrow mechanism)I conflict with neutrino mass bounds?

But: self-interacting νs don’t free stream

10-2 10-1

104

105

|k→

| [h /Mpc ]

PM(|

k→

|)[(

Mpc

/h)3 ]

z ≃ 0.35

SDSS dataSM (m ν = 0 eV)

SM +νs (1 eV)

SM +A′ +νs (1 eV)

◇

◇ ◇ ◇◇ ◇

◇◇

◇

◇◇

◇

◇

◇◇

◇◇ ◇

◇

◇

◇

◇

◇◇

◇ ◇

◇◇

◇◇

▲▲ ▲

▲▲ ▲ ▲

▲▲

▲▲

▲

▲▲

▲

▲ ▲ ▲▲

▲

▲▲

▲ ▲

▲▲ ▲ ▲

▲

▲▲

▲▲

▲

▲ ▲▲ ▲

▲▲

10-1 100 101

10-2

10-1

100

k [h /Mpc ]

Δ2 (

k)=

kP

F(k)/π

z = 2.2z = 2.4z = 2.6z = 2.8z = 3.0z = 3.2z = 3.4z = 3.6z = 3.8z = 4.0z = 4.2

z = 4.2

z = 4.6

z = 5.0

z = 5.4

SDSS data◇◇ MIKE data▲▲ HIRES data

Qualitative predictionsSM (m ν = 0 eV)SM +νs (1 eV)SM +A′ +νs (1 eV)

Chu Dasgupta JK arXiv:1505.02795


Hidden sector gauge forces and SBL oscillationsIf sterile neutrinos have new interactions with SM fermions(e.g. in models with “baryonic sterile neutrinos”),new MSW potentials will influence oscillations.

How does this affect the tension in the SBL data?

Karagiorgi Shaevitz Conrad, arXiv:1202.1024Pospelov, arXiv:1103.3261

Min

iBo

oN

E,9

5%

Min

iBo

oN

E,3

ΣSola

r,3

Σ

Sola

r,95

%

MIN

OS,3

Σ

MIN

OS,95

%

10-4

10-3

10-2

10-1

100

100

101

102

103

104

sin2

Θ24

Ε

sin2H2Θ14L = 0.12

Dm41

2= 0.2 eV

2

2 dof

10-4

10-3

10-2

10-1

100

100

101

102

103

104

sin2

Θ24

Ε

sin2H2Θ14L = 0.12

Dm41

2= 0.4 eV

2

2 dof

10-4

10-3

10-2

10-1

100

100

101

102

103

104

sin2

Θ24

Ε

sin2H2Θ14L = 0.12

Dm41

2= 0.6 eV

2

2 dof

10-4

10-3

10-2

10-1

100

10-2

10-1

100

101

sin2

Θ24

Dm

41

2@e

V²D

sin2H2Θ14L = 0.12

Ε = 10.

2 dof

10-4

10-3

10-2

10-1

100

10-2

10-1

100

101

sin2

Θ24

Dm

41

2@e

V²D

sin2H2Θ14L = 0.12

Ε = 100.

2 dof

10-4

10-3

10-2

10-1

100

10-2

10-1

100

101

sin2

Θ24

Dm

41

2@e

V²D

sin2H2Θ14L = 0.12

Ε = 10 000.

2 dof

JK, Johannes Welter, arXiv:1408.0289


Light Sterile Neutrinos andDark Matter Searches

Neutrinos and direct dark matter detectionSolar neutrinos are a well-known background to future direct DM searches:

see e.g. Gütlein et al. arXiv:1003.5530

ææ

æ

ææææææææææææææææææææææææææææææææææ

10-1 100 101 102 103 10410-1410-1310-1210-1110-1010-910-810-710-610-510-410-310-210-1100101102

Erec HkeVL

coun

ts�N

A�k

eV�y

ear

electron recoil

DAMA

Borexino

XENON100 e-

CoGeNT

pp7Be

13N 15Opep

8B17F

hepSM total rateComponents

10-4 10-3 10-2 10-1 100 10110-2

10-1

100

101

102

103

104

105

106

107

108

Erec HkeVL

coun

ts�to

n�ke

V�y

ear

Nuclear recoil - Ge

pp7Be

13N 15Opep

8B

17F

hep

CoGeNT

CDMS-II

SM total rateComponents


Neutrinos and direct dark matter detectionSolar neutrinos are a well-known background to future direct DM searches:

see e.g. Gütlein et al. arXiv:1003.5530

SM signal will only become sizeable in multi-ton detectors

But: New physics can enhance the rate

Examples:Neutrino magnetic momentsSterile neutrinos + . GeV scale hidden sector gauge force


Low-energy scattering of neutrinos beyond the SM

æ

æ

æ

æ æææææææææææææææææææææææææææææææææ

10-1 100 101 102 10310-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

Erec HkeVeeL

coun

ts�N

A�k

eVee

�yea

r

electron recoil

DAMA

Borexino

XENON100 e-

CoGeNT

Standard model

B

C

DA

Line MA¢ gegΝ

A ΜΝ = 0.32 ´ 10-10ΜB

B 10 keV 4 ´ 10-12

C 50 keV 4 ´ 10-12

D 250 keV 6 ´ 10-12

10-4 10-3 10-2 10-1 100 10110-2

10-1

100

101

102

103

104

105

106

107

108

Erec HkeVnrLco

unts

�ton�

keV

nr�y

ear

Nuclear recoil –Ge

CoGeNT

CDMS-II

D

C

B

A

Standard model

Line MA¢ gNgΝ sin2Θ24

A ΜΝ = 0.32 ´ 10-10ΜB activeB 100 MeV 9 ´ 10-8 activeC 100 MeV 8 ´ 10-7 0.02D 10 MeV 10-6 0.02

A: ν magnetic moment A: ν magnetic momentB, C, D: kinetically mixed A′ + sterile νs B: U(1)B−L boson

C: kinetically mixed U(1)′ + sterile νD: U(1)B + sterile ν charged under U(1)B[Pospelov 1103.3261, Pospelov Pradler 1203.0545]Enhanced scattering at low Er for light A′

Negligible compared to SM scattering (∼ g4mT /M4W ) at energies probed in dedicated

neutrino experiments [Harnik JK Machado arXiv:1202:6073]


Sterile neutrinos and DM annihilation in the SunNeutrino telescope limits on neutrinos from dark matter annihilationin the Sun depend crucially on oscillation physics.If sterile neutrinos exist, new MSW resonances can lead to strongconversion of active neutrinos into sterile neutrinos in the Sun.

Esmaili Peres, arXiv:1202.2869Argüelles JK, arXiv:1202.3431


Oscillation probabilities for a 3+3 toy scenarioP(νe → νX ) P(νµ → νX ) P(ντ → νX )

P(ν̄e → ν̄X ) P(ν̄µ → ν̄X ) P(ν̄τ → ν̄X )

Thick red lines = active–sterile oscillations plots from Argüelles JK, arXiv:1202.3431see also Esmaili Peres, arXiv:1202.2869


Summary

Four independent anomaliesI Consistent with each other

Tension in global fitI Are the anomalies real?I Are the null results real?

Cosmological limits: Avoided elegantly byself-interacting sterile νs

With and without new interactions: richphenomenology in dark matter detectors

Thank you!

Data sets included in our fit

(_ )ν e disappearance

SBL reactor experimentsLBL reactor experimentsKamLANDRadioactive source (Ga) experimentsSolar neutrinosAtmospheric neutrinosνe–12C scattering in KARMEN, LSND

(_ )ν e appearance

LSNDMiniBooNEKARMENNOMADICARUSE776

(_ )ν µ disappearance

Atmospheric neutrinos (includes either(_ )ν e disapp. or full matter effects)

MiniBooNE (includes oscillations of backgrounds)

MINOS CC+NC (full n-flavour oscillations in matter)

CDHSJoachim Kopp Sterile neutrinos: to be or not to be? 28

Relation between appearance and disappearance3 + 2 neutrinosAt L� 4πE/∆m2

41, but L� 4πE/∆m231

Pee = 1− 2[|Ue4|2(1− |Ue4|2) + |Ue5|2(1− |Ue5|2)− |Ue4|2|Ue5|2

]Pµµ = 1− 2

[|Uµ4|2(1− |Uµ4|2) + |Uµ5|2(1− |Uµ5|2)− |Uµ4|2|Uµ5|2

]Peµ = 2

[|Ue4|2|Uµ4|2 + |Ue5|2|Uµ5|2 + Re(U∗e4Uµ4Ue5U∗µ5)

]



41, but L� 4πE/∆m231


]Pµµ = 1− 2

[|Uµ4|2(1− |Uµ4|2) + |Uµ5|2(1− |Uµ5|2)− |Uµ4|2|Uµ5|2

]Peµ = 2


]It follows

2Peµ ' (1− Pee)(1− Pµµ)

+ 4[Re(U∗e4Uµ4Ue5U∗µ5) + 4|Ue4|2|Uµ5|2 + 4|Ue5|2|Uµ4|2

]= (1− Pee)(1− Pµµ)− 2

[|Ue4|2|Uµ5|2 + |Ue5|2|Uµ4|2

]− 2∣∣Ue4Uµ5 − Ue5Uµ4

∣∣2Joachim Kopp Sterile neutrinos: to be or not to be? 29


41, but L� 4πE/∆m231


]Pµµ = 1− 2

[|Uµ4|2(1− |Uµ4|2) + |Uµ5|2(1− |Uµ5|2)− |Uµ4|2|Uµ5|2

]Peµ = 2


]It follows

2Peµ ≤ (1− Pee)(1− Pµµ)

Unlike in the 3 + 1 case, for 3 + 2 models, there is NO one-to-one relationbetween the appearance and disappearance probabilities.

However, there is an inequality, which can be used to set meaningfulconstraints.


Impact of θ13

10- 3 10- 2 10-10.

0.05

0.1

0.15

0.2

0.25

0.3

ÈUe42

Sin

22

Θ13

95% CL

Dm412

= 10 eV 2Gallium

SBL

reac

tors

LBL reactorsC

-12

Solar +KamL

çã

10- 3 10- 2 10-10.

0.05

0.1

0.15

0.2

0.25

0.3

ÈUe42

Sin

22

Θ13

95% CL

Dm412

= 1.78 eV 2Gallium

SBL

reac

tors

LBL reactors

C-

12

Solar +KamL

çã

Sterile neutrinos do not impact θ13 measurementθ13 6= 0 does not impact sterile neutrino search



(_ )ν µ disappaearance in the 3+1 scenario

Parameter regions favored by tentative hints are intension with null resultsConstraints on |Uτ4| ∼ sin θ34 possible due to NC events and mattereffects

Complex phases important

10- 2 10-1 1000.

0.2

0.4

0.6

0.8

1.

ÈU Μ42

ÈU Τ4

2

Unitarity

bound90%, 99%

atm

MINOS

solar

all ΝH — L

Μ disapp.

Dm412

= 0.1 eV 2

10- 2 10-1 1000.

0.2

0.4

0.6

0.8

1.

ÈU Μ42

ÈU Τ4

2

Unitarity

bound

90%, 99%

atm

MINOS

CD

HS

+M

Bd

isap

p+

LB

Lre

acto

rs

solar

all ΝH — L

Μ disapp.

Dm412

= 1. eV 2



(_ )ν µ disappaearance in the 3+1 scenario

Parameter regions favored by tentative hints are intension with null resultsConstraints on |Uτ4| ∼ sin θ34 possible due to NC events and mattereffectsComplex phases important

0. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

10-1

100

101

ÈUΤ42

Dm

412@eV

2D

99%

MINOS

MIN

OS

+at

m+

MB

dis

app

+C

DH

S

best

ph

ases

wor

stp

has

es

best

ph

ases

wor

stp

has

es



The MIT/Columbia fit(_ )ν µ →

(_ )ν e appearance data:

I LSNDI MiniBooNEI KARMENI NOMAD

(_ )ν µ disappearance data:

I MiniBooNEI Minos CC νµI CDHSI CCFRI Atmospheric neutrinos

(_ )ν e disappearance data:

I Short baseline reactor experimentsI Gallium experimentsI νe–12C CC scattering in KARMEN, LSND

Conrad Ignarra Karagiorgi Shaevitz Spitz, arXiv:1207.4765Poster by Gabriel Collin

χ2/dof and PG test results in qualitativeagreement with ours→ tension confirmed


The GL4 fit(_ )ν µ →

(_ )ν e appearance data:

I LSNDI MiniBooNEI E776I KARMENI NOMADI ICARUSI OPERA

(_ )ν µ disappearance data:

I MiniBooNE/SciBooNEI Minos NC+CC νµI CDHSI CCFRI Atmospheric neutrinos

(_ )ν e disappearance data:

I Reactor experimentsI Gallium experimentsI Solar neutrinosI νe–12C scattering in KARMEN, LSND

sin22ϑeµ

∆m412

[e

V2 ]

10−4 10−3 10−2 10−1 110−1

1

10

+

10−4 10−3 10−2 10−1 110−1

1

10

+

3+1 − GLO

68.27% CL90.00% CL95.45% CL99.00% CL99.73% CL

3+1 − 3σνe DISνµ DISDISAPP

Giunti Laveder Li Long arXiv:1308.5288Giunti Laveder Li Liu Long arXiv:1210.5715

Giunti Laveder arXiv:1111.1069

ConclusionNO tension found


Differences between our fit and Giunti et al.MiniBooNE fitwe use MB analysis based on official MC events, include BG oscillation

MINOS fitwe fit CC+NC data, including ND and FD, detector response matrices based onofficial MINOS MC

Reactor fitminor differences in the data set, possibly different treatment of correlationsamong systematic uncertainties

LSND fitNote that LSND spectral data is more constraining than the total count rate. Weuse this information; our fit is consistent with the numbers reported inhep-ex/0203023 (Church, Eitel, Mills, Steidl, combined LSND+KARMEN analysis)

Atmospheric neutrinosFull fit vs. tabulated χ2


Are light sterile neutrinos ruled out by cosmology?νs production in the early Universe through νe,µ,τ → νs oscillations at T & MeV

Dodelson Widrow 1994

Making sterile neutrinos fully consistent with cosmology> 1 new relativistic degrees of freedom + w < −1 + µν 6= 0

Hamann Hannestad Raffelt Wong, arXiv:1108.4136

Entropy production after neutrino decoupling (e.g. due to late decay of heavysterile neutrinos or other particles)→ neutrinos diluted

Fuller Kishimoto Kusenko 1110.6479, Ho Scherrer 1212.1689

Very low reheating temperatureGelmini Palomares-Ruiz Pascoli, astro-ph/0403323

Large lepton asymmetry (& 0.01)→ νs production MSW-suppressedFoot Volkas hep-ph/9508275, Chu Cirelli astro-ph/0608206, Saviano et al. arXiv:1302.1200

Couplings to a Majoron field→ suppressed productionBento Berezhiani, hep-ph/0108064

New gauge interaction in the νs sector→ νs production suppressed by thermal potential

Hannestad et al. 1310.5926Dasgupta JK 1310.6337


Two further remarks

If sterile and visible sectors have ever been in thermal equilbrium, νs willhave been produced thermally very early on.But temperatures of the two sectors are very different:

Tvisible > Tsterile

after the SM phase transitions.→ νs abundance� active neutrino abundance

Mixing of U(1)s-charged νs with active neutrinos:

L ⊃ −L̄YνH̃νR − ν̄sYsHsνR −12

(νR)cMRνR + h.c. ,

(H̃ = SM Higgs, Hs = sterile sector Higgs)

see e.g. Harnik JK Machado arXiv:1202.6073


Two further remarks

If sterile and visible sectors have ever been in thermal equilbrium, νs willhave been produced thermally very early on.But temperatures of the two sectors are very different:

Tvisible > Tsterile

after the SM phase transitions.→ νs abundance� active neutrino abundance

Mixing of U(1)s-charged νs with active neutrinos:

L ⊃ −L̄YνH̃νR − ν̄sYsHsνR −12

(νR)cMRνR + h.c. ,

(H̃ = SM Higgs, Hs = sterile sector Higgs)

see e.g. Harnik JK Machado arXiv:1202.6073


Suppression of νs production by thermal MSW effect

M=

103 M

eV

M=

10M

eV

M=

0.1

MeV

Dm 2� H2 EL

M=

0.1M

eV

M=

103 M

eV

M=

10M

eV

BBN

Neu

trin

ode

coup

ling

QC

Dph

ase

tran

sitio

n

103 104 105 106 107 108 10910-10

10-8

10-6

10-4

10-2

100

102

104

TΓ @eVD

Neu

trin

opo

tent

ialÈ

Vef

fÈ@e

VD

For α′ ∼ 10−3 and MA′ . 10 MeV:

effective potential Veff � oscillation frequency ∆m2/(2E)

until neutrino decoupling.⇒ sterile neutrino production suppressed, no cosmological constraints

Hannestad Hansen Tram arXiv:1310.5926Dasgupta JK arXiv:1310.6337


Hidden sector gauge forces and dark matterInteresting connection to dark matter physics:

The same gauge force that suppressed sterile neutrino productioncan also solve small scale structure problems:

Too big to fail problemCusp vs. core problemMissing satellites problem

Νsov

erpr

oduc

tion

IDm

2=

1eV

2 M

Cluster bound violated

Missing

satellites solved

Α Χ = 10-3

Mcut

=10 9

MSun

Mcut

=10 10

MSun

XΣT \ � mΧ = 0.1 cm 2� g

XΣT \ � mΧ = 1 cm2� g

XΣT \ �mΧ > 1 cm2�gfor vrel ~ 103 km �s

for vrel ~ 10 km �s

Cusp vs. core&

Too big to failsolved

sin2

2Θ

m>

10-

3

10-3 10-2 10-1 100 101 102 103100

101

102

103

104

105

106

Dark photon mass M @MeVD

Dar

km

atte

rm

ass

mΧ

@GeV

D

Dasgupta JK arXiv:1310.6337Joachim Kopp Sterile neutrinos: to be or not to be? 38

Example 1: Neutrino magnetic momentsAssume neutrinos carry an enhanced magnetic moment

Lµν⊃ µν ν̄σαβ∂βAαν , µν � µν,SM = 3.2× 10−19µB

Cross section large at low energies due to photon propagator ∝ q−2

dσµ(νe→ νe)

dEr= µ2

να

(1Er− 1

Eν

),

10 1 100 101 102 10310 -8

10 -7

10 -6

10 -5

10 -4

10 -3

10 -2

10 -1

100

101

102

Erec keVee

coun

tsNA

keV

eeye

ar

electron recoil

DAMA

Borexino

XENON100 e

CoGeNT

Standard model

A

A ΜΝ = 0.32 x 10-10ΜB

10 -4 10 -3 10 -2 10 -1 100 10110 -2

10 -1

100

101

102

103

104

105

106

107

108

E /rec keVnr

coun

ts/t

on/k

eV

/nr

year

Nuclear recoil – Ge

CoGeNT

CDMS II

A

Standard model

A ΜΝ = 0.32 x 10 -10 ΜB


Example: A not-so-sterile 4th neutrinoIntroduce a new U(1)′ gauge boson A′ (hidden photon) and alight sterile neutrino νs

Related model with gauged U(1)B first discussed in Pospelov 1103.3261detailed studies in Harnik JK Machado 1202:6073 and Pospelov Pradler 1203.0545

νs charged under U(1)′ → direct coupling to A′

SM particles couple to A′ only through kinetic mixing

L ⊃ −14

F ′µνF ′µν − 14

FµνFµν − 12εF ′µνFµν + ν̄s i /∂νs + g′ν̄sγ

µνsA′µ

− (νL)cmνLνL − (νs)cmνsνs − (νL)cmmixνs

A small fraction of solar neutrinos can oscillate into νs

νs scattering cross section in the detector given by

dσA′(νse→ νse)

dEr=

ε2e2g′2me

4πp2ν(M2

A′ + 2Er me)2

[2E2

ν + E2r − 2Er Eν − Er me −m2

ν

]Joachim Kopp Sterile neutrinos: to be or not to be? 40

Temporal modulation of neutrino signalsSignals of new light force mediators and/or sterile neutrinos can showseasonal modulation:

The Earth–Sun distance: Solar neutrino flux peaks in winter.

Active–sterile neutrino oscillations: For oscillation lengths . 1 AU, sterileneutrino appearance depends on the time of year.Sterile neutrino absorption: For strong νs–A′ couplings and not-too-weakA′–SM couplings, sterile neutrino cannot traverse the Earth.→ lower flux at night. And nights are longer in winter.Earth matter effects: An MSW-type resonance can lead to modified fluxof certain neutrino flavors at night. And nights are longer in winter.



The Earth–Sun distance: Solar neutrino flux peaks in winter.Active–sterile neutrino oscillations: For oscillation lengths . 1 AU, sterileneutrino appearance depends on the time of year.

Harnik JK Machado, arXiv:1202.6073

Sterile neutrino absorption: For strong νs–A′ couplings and not-too-weakA′–SM couplings, sterile neutrino cannot traverse the Earth.→ lower flux at night. And nights are longer in winter.Earth matter effects: An MSW-type resonance can lead to modified fluxof certain neutrino flavors at night. And nights are longer in winter.



The Earth–Sun distance: Solar neutrino flux peaks in winter.Active–sterile neutrino oscillations: For oscillation lengths . 1 AU, sterileneutrino appearance depends on the time of year.Sterile neutrino absorption: For strong νs–A′ couplings and not-too-weakA′–SM couplings, sterile neutrino cannot traverse the Earth.→ lower flux at night. And nights are longer in winter.

Earth matter effects: An MSW-type resonance can lead to modified fluxof certain neutrino flavors at night. And nights are longer in winter.



The Earth–Sun distance: Solar neutrino flux peaks in winter.Active–sterile neutrino oscillations: For oscillation lengths . 1 AU, sterileneutrino appearance depends on the time of year.Sterile neutrino absorption: For strong νs–A′ couplings and not-too-weakA′–SM couplings, sterile neutrino cannot traverse the Earth.→ lower flux at night. And nights are longer in winter.Earth matter effects: An MSW-type resonance can lead to modified fluxof certain neutrino flavors at night. And nights are longer in winter.


Hidden photons

L ⊃ −14

F ′µνF ′µν − 14

FµνFµν − 12εF ′µνFµν + ν̄s i /∂νs + g′ν̄sγ

µνsA′µ

10-24 10-21 10-18 10-15 10-12 10-9 10-6 10-3 110-16

10-14

10-12

10-10

10-8

10-6

10-4

10-210-24 10-21 10-18 10-15 10-12 10-9 10-6 10-3 1

10-16

10-14

10-12

10-10

10-8

10-6

10-4

10-2

Dark Photon Mass MA'HGeVL

Kin

etic

mix

ing

Ε

Fixedtarget

Kinetically Mixed Gauge Boson

Hg-2LΜ

Hg-2Le

U

SN1987A

Atomic PhysicsAtomic Physics

CMB

Glo

bula

rC

lust

ers

Sun�Globular Clusters, energy loss via Νs

Hin models with d 10 keV sterile neutrinosL

Sun

A' capture in SunHpartly allowedL

CASTCMB

LSW

gΝ2 sin22Θ=10-4

gΝ2 sin22Θ=10-12

Borexino Hin models with UH1L'-charged sterile ΝL

Constraints from Jaeckel Ringwald 1002.0329, Redondo 0801.1527,Bjorken Essig Schuster Toro 0906.0580, Dent Ferrer Krauss 1201.2683, Harnik JK Machado

1202.6073Joachim Kopp Sterile neutrinos: to be or not to be? 42

3+3 flavor toy modelConsider toy model with 3 sterile neutrinos, each of them mixing with only oneof the active flavors:

U = R14(θ) R25(θ) R36(θ) UPMNS , Rij = rotation in ij-plane .

Hamiltonian:

H ' E +1

2EU DU† + VMSW , D = diag(0,∆m2

21,∆m231,∆m2

41,∆m251,∆m2

61)

Mikheyev-Smirnov-Wolfenstein (MSW) potential:

VMSW =√

2GF diag(ne − nn/2,−nn/2,−nn/2,0,0,0) ,

ne (nn) = electron (neutron) number density

Oscillation probability:

P(να → νβ) =∣∣∣〈νβ |e−iHt |να〉

∣∣∣2


Impact on IceCube limits

plot from Carlos Argüelles JK, arXiv:1202.3431see also Esmaili Peres, arXiv:1202.2869


Documents

Sterile neutrinos: to be or not to be? · 0.7 0.8 0.9 1 observed / no osc. expected 1.1 Dm2 = 0.44 eV2, sin22q 14 = 0.13 Dm2 = 1.75 eV2, sin22q 14 = 0.10 Dm2 = 0.9 eV2, sin22q 14