Sterile neutrinos: to be or not to be?

Transcription

1 Sterile neutrinos: to be or not to be? Joachim Kopp (University of Mainz) June 9, WIN 2015, Heidelberg Joachim Kopp Sterile neutrinos: to be or not to be? 1

2 Outline 1 Sterile Neutrinos 2 Oscillation Anomalies: A Global Fit ν e Appearance ν e Disappearance ν µ Disappearance Sterile Neutrino Oscillations: The Global Picture 3 Sterile Neutrinos in Cosmology 4 Light Sterile Neutrinos and Dark Matter Searches Sterile Neutrinos and Direct Dark Matter Searches Sterile Neutrinos and Indirect Dark Matter Searches 5 Summary Joachim Kopp Sterile neutrinos: to be or not to be? 2

3 Sterile Neutrinos

4 Sterile neutrinos Definition Sterile neutrino = SM singlet fermion Very generic extension of the SM can be leftovers of extended gauge multiplets (e.g. GUT multiplets) Very useful in phenomenology: Can explain smallness of neutrino mass (seesaw mechanism, m TeV... M Pl ) Can explain baryon asymmetry of the Universe (leptogenesis, m 100 GeV) Can explain dark matter (m kev) Can explain various neutrino oscillation anomalies (m ev) Joachim Kopp Sterile neutrinos: to be or not to be? 4

5 Oscillation Anomalies: A Global Fit

6 (_ ) ν e appearance in the 3+1 scenario and beyond _ Motivated by LSND and MiniBooNE: excess of ( ) _ ν e events in ( ) ν µ beam. m MiniBooNE Ν 99 CL, 2 dof Combined MiniBooNE Ν ICARUS 2012 NOMAD E776 LBL reactors KARMEN LSND χ 2 3+1/dof χ 2 3+2/dof χ /dof LSND 11.0/11 8.6/11 7.5/11 MiniB ν 19.3/ /11 9.1/11 MiniB ν 10.7/11 9.6/ /11 E / / /24 KARMEN 9.8/9 8.6/9 9.0/9 NOMAD 0.0/1 0.0/1 0.0/1 ICARUS 2.0/1 2.3/1 1.5/1 Combined 87.9/ / /63 Global fit to all appearance data is consistent Background oscillations important in MiniBooNE and E776 Significant improvement in and JK Machado Maltoni Schwetz, see also fits by Giunti Laveder et al. Collin Conrad Ignarra Karagiorgi Shaevitz Spitz Djurcic Sorel Joachim Kopp Sterile neutrinos: to be or not to be? 6

7 (_ ) ν e appearance in the 3+1 scenario and beyond _ Motivated by LSND and MiniBooNE: excess of ( ) _ ν e events in ( ) ν µ beam. m MiniBooNE Ν 99 CL, 2 dof OPERA 2013 Combined MiniBooNE Ν Preliminary ICARUS 2014 ICARUS 2012 NOMAD E776 LBL reactors KARMEN LSND χ 2 3+1/dof χ 2 3+2/dof χ /dof LSND 11.0/11 8.6/11 7.5/11 MiniB ν 19.3/ /11 9.1/11 MiniB ν 10.7/11 9.6/ /11 E / / /24 KARMEN 9.8/9 8.6/9 9.0/9 NOMAD 0.0/1 0.0/1 0.0/1 ICARUS 2.0/1 2.3/1 1.5/1 Combined 87.9/ / /63 Global fit to all appearance data is consistent Background oscillations important in MiniBooNE and E776 Significant improvement in and JK Machado Maltoni Schwetz, see also fits by Giunti Laveder et al. Collin Conrad Ignarra Karagiorgi Shaevitz Spitz Djurcic Sorel Joachim Kopp Sterile neutrinos: to be or not to be? 6

8 (_ ) ν e appearance in the 3+1 scenario and beyond _ Motivated by LSND and MiniBooNE: excess of ( ) _ ν e events in ( ) ν µ beam. m MiniBooNE Ν 99 CL, 2 dof OPERA 2013 Combined MiniBooNE Ν Preliminary ICARUS 2014 ICARUS 2012 NOMAD E776 LBL reactors KARMEN LSND χ 2 3+1/dof χ 2 3+2/dof χ /dof LSND 11.0/11 8.6/11 7.5/11 MiniB ν 19.3/ /11 9.1/11 MiniB ν 10.7/11 9.6/ /11 E / / /24 KARMEN 9.8/9 8.6/9 9.0/9 NOMAD 0.0/1 0.0/1 0.0/1 ICARUS 2.0/1 2.3/1 1.5/1 Combined 87.9/ / /63 Global fit to all appearance data is consistent Background oscillations important in MiniBooNE and E776 Significant improvement in and JK Machado Maltoni Schwetz, see also fits by Giunti Laveder et al. Collin Conrad Ignarra Karagiorgi Shaevitz Spitz Djurcic Sorel Joachim Kopp Sterile neutrinos: to be or not to be? 6

9 (_ ) ν e disappearance in the 3+1 scenario observed / no osc. expected ILL m 2 = 0.44 ev 2, sin 2 2θ 14 = 0.13 m 2 = 1.75 ev 2, sin 2 2θ 14 = 0.10 m 2 = 0.9 ev 2, sin 2 2θ 14 = Bugey3,4 Rovno, SRP SRP Rovno Krasn Gosgen Bugey3 Gosgen Krasn Gosgen Krasn Bugey distance from reactor [m] ev 2 2 m CL SBL reactors All Ν e disapp U e4 2 LBL reactors Solar KamL C 12 Gallium sin 2 2θ 14 m 2 41 [ev 2 ] χ 2 min/dof (GOF) χ 2 no osc/dof (CL) SBL rates only /17 (83%) 11.4/2 (99.7%) SBL incl. Bugey3 spect /74 (91%) 9.0/2 (98.9%) SBL + Gallium /78 (87%) 14.0/2 (99.9%) global ν e disapp /427 (79%) 12.6/2 (99.8%) JK Machado Maltoni Schwetz, Joachim Kopp Sterile neutrinos: to be or not to be? 7

10 Relation between appearance and disappearance _ We find: ( _ ) ν e disappearance experiments consistent among themselves, ( ) ν e appearance experiments consistent among themselves. But: neutrinos At L 4πE/ m 2 41, but L 4πE/ m2 31 It follows P ee = 1 2 U e4 2 (1 U e4 2 ) P µµ = 1 2 U µ4 2 (1 U µ4 2 ) P eµ = 2 U e4 2 U µ4 2 2P eµ (1 P ee )(1 P µµ ) In the case, at large enough baseline, there is a one-to-one relation between the appearance and disappearance probabilities. Joachim Kopp Sterile neutrinos: to be or not to be? 8

11 Combining different oscillation channels provides the strongest, most robust constraints on sterile neutrinos

12 (_ ) ν µ disappearance in the 3+1 scenario Parameter regions favored by tentative hints are in tension with null results from (_ ) ν µ disappearance searches 10 1 LSND MB app reactors Ga ev 2 m Null results combined atm CDHS MB disapp CL U Μ4 JK Machado Maltoni Schwetz, MINOS 2011 Joachim Kopp Sterile neutrinos: to be or not to be? 10

13 (_ ) ν µ disappearance in the 3+1 scenario Parameter regions favored by tentative hints are in tension with null results from (_ ) ν µ disappearance searches ev 2 m Null results combined 99 CL JK Machado Maltoni Schwetz, SK 2014 MINOS U Μ4 2 LSND MB app reactors Ga atm CDHS MB disapp MINOS 2011 Preliminary Joachim Kopp Sterile neutrinos: to be or not to be? 10

14 IceCube and sterile neutrinos Oscillograms 101 From NuSquids, (Argüelles Delgado, et al) Neutrino Absorption (at TeV energies, neutrinos are absorbed by the earth) Energy! Vaccum Osc Wiggles Big Resonance! Hierarchy demands this be in antineutrino mode Vaccum Osc Wiggles Up (through core) Horizon Up (through core) Horizon Matter Signal antineutrino, because of the known hierarchy! Access to the antineutrino ν µ oscillation parameters! Slide courtesy of Janet Conrad Joachim Kopp Sterile neutrinos: to be or not to be? 11

15 The global oscillation fit JK Machado Maltoni Schwetz, arxiv: Severe tension between appearance and disappearance and between exp s with and without a signal m null results combined LSND reactors Ga MB app null results disappearance CL, 2 dof sin 2 2 Θ Μe null results appearance χ 2 min/dof GOF /(689 9) 19% Joachim Kopp Sterile neutrinos: to be or not to be? 12

16 The global oscillation fit JK Machado Maltoni Schwetz, arxiv: Severe tension between appearance and disappearance and between exp s with and without a signal m null results combined LSND reactors Ga MB app null results disappearance Parameter goodness of fit (PG) test: Compares χ 2 min from global and separate fits to test compatibility of 2 data sets CL, 2 dof sin 2 2 Θ Μe null results appearance χ 2 min/dof GOF χ 2 PG/dof PG /(689 9) 19% 18.0/ Joachim Kopp Sterile neutrinos: to be or not to be? 12

17 The global oscillation fit JK Machado Maltoni Schwetz, arxiv: Severe tension between appearance and disappearance and between exp s with and without a signal Tension remains for two sterile neutrinos ev 2 m app disapp global Parameter goodness of fit (PG) test: Compares χ 2 min from global and separate fits to test compatibility of 2 data sets m 2 41 ev χ 2 min/dof GOF χ 2 PG/dof PG /(689 9) 19% 18.0/ /(689 14) 23% 25.8/ /(689 14) 30% 16.8/ Joachim Kopp Sterile neutrinos: to be or not to be? 12

18 The global oscillation fit JK Machado Maltoni Schwetz, arxiv: Severe tension between appearance and disappearance and between exp s with and without a signal Tension remains for two sterile neutrinos No significant improvement expected ev 2 m app disapp global Parameter goodness of fit (PG) test: Compares χ 2 min from global and separate fits to test compatibility of 2 data sets m 2 41 ev χ 2 min/dof GOF χ 2 PG/dof PG /(689 9) 19% 18.0/ /(689 14) 23% 25.8/ /(689 14) 30% 16.8/ Joachim Kopp Sterile neutrinos: to be or not to be? 12

19 Sterile Neutrinos in Cosmology

20 Sterile neutrinos in cosmology Models with O(eV) sterile neutrino(s) constrained by cosmology: Sum of neutrino masses # of relativistic species mν 0.23 ev N ν = 4 mildly disfavored Ade et al. (Planck), arxiv: Gonzalez-Garcia Maltoni Salvado, arxiv: Hamann Hannestad Raffelt Tamborra Wong, arxiv:1006:5276 Joachim Kopp Sterile neutrinos: to be or not to be? 14

21 Sterile neutrinos in cosmology Models with O(eV) sterile neutrino(s) constrained by cosmology: Sum of neutrino masses # of relativistic species mν 0.23 ev N ν = 4 mildly disfavored Ade et al. (Planck), arxiv: Gonzalez-Garcia Maltoni Salvado, arxiv: Hamann Hannestad Raffelt Tamborra Wong, arxiv:1006:5276 Question: What does is take to evade these constraints? Joachim Kopp Sterile neutrinos: to be or not to be? 14

22 Suppressed ν s production from thermal MSW effect ν s production in the early Universe through ν e,µ,τ ν s oscillations Dodelson Widrow 1994 Assume ν s couple to MeV gauge boson A Neutrino self energy: Leads to thermal MSW potential V T 4 At high T : mixing strongly suppressed sin 2θ sin 2θ eff = sin 2 2θ + ( ) cos 2θ 2EV 2 m 2 No ν s production through oscillations no cosmological constraints Hannestad Hansen Tram arxiv: Dasgupta JK arxiv: Joachim Kopp Sterile neutrinos: to be or not to be? 15

23 Parameter space for self-interacting sterile neutrinos Two regions: Chu Dasgupta JK arxiv: Weak coupling: No ν s production (see previous slide) Strong coupling: Lots of ν s produced, but not harmful (see next slide) Mirizzi Mangano Pisanti Saviano, arxiv: , Joachim Kopp Sterile neutrinos: to be or not to be? 16

24 Strongly self-interacting sterile neutrinos Large coupling efficient conversion of ν e,µ,τ ν s after neutrino freeze-out (Dodelson-Widrow mechanism) conflict with neutrino mass bounds? But: self-interacting ν s don t free stream ) [(Mpc /h) 3 ] P M ( k SDSS data SM (m ν = 0 ev) SM + ν s (1 ev) SM + A + ν s (1 ev) z 0.35 Δ 2 (k) = k P F (k) / π z =5.4 z =5.0 z =4.6 z =4.2 z =4.2 =4.0 z =3.8 =3.6 SDSS data z =3.4 =3.2 MIKE data z =3.0 =2.8 HIRES data z =2.6 z =2.4 Qualitative predictions z =2.2 SM (m ν = 0 ev) SM + ν s (1 ev) SM + A + ν s (1 ev) k [h/mpc ] k [h/mpc ] Chu Dasgupta JK arxiv: Joachim Kopp Sterile neutrinos: to be or not to be? 17

25 Ε Ε Ε Hidden sector gauge forces and SBL oscillations If 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: Pospelov, arxiv: sin 2 2Θ m ev sin 2 2Θ m ev sin 2 2Θ m ev MINOS, 95 MINOS, 3Σ MiniBooNE, 95 MiniBooNE, 3Σ Solar, 3Σ Solar, dof dof dof sin 2 2Θ Ε 10. sin 2 Θ sin 2 2Θ Ε 100. sin 2 Θ 24 sin 2 Θ 24 JK, Johannes Welter, arxiv: sin 2 2Θ Ε ² 10 0 Joachim Kopp 10 0 Sterile neutrinos: to be or not to be? ² ²

26 Light Sterile Neutrinos and Dark Matter Searches

27 Neutrinos and direct dark matter detection Solar neutrinos are a well-known background to future direct DM searches: counts NA kev year pp 7 Be 13 N 15 O pep CoGeNT SM total rate Components 17 F electron recoil DAMA 8 B hep Erec kev XENON100 e Borexino counts ton kev year pp 7 Be 13 N 15 O pep hep see e.g. Gütlein et al. arxiv: Nuclear recoil Ge 8 B 17 F SM total rate Components Erec kev CoGeNT CDMS II Joachim Kopp Sterile neutrinos: to be or not to be? 20

28 Neutrinos and direct dark matter detection Solar neutrinos are a well-known background to future direct DM searches: see e.g. Gütlein et al. arxiv: SM signal will only become sizeable in multi-ton detectors But: New physics can enhance the rate Examples: Neutrino magnetic moments Sterile neutrinos + GeV scale hidden sector gauge force Joachim Kopp Sterile neutrinos: to be or not to be? 20

29 Low-energy scattering of neutrinos beyond the SM counts NA kevee year B C A CoGeNT DAMA D rec ee XENON100 e 10 5 Standard model 10 1 Line M A g eg Ν Line M Borexino A g Ng Ν sin 2 Θ A Μ Ν Μ B 10 0 A Μ Ν Μ B active 10 7 B 10 kev B 100 MeV active C 50 kev C 100 MeV D 250 kev D 10 MeV counts ton kevnr year Standard model A Nuclear recoil Ge E rec kev nr D B C CoGeNT CDMS II A: ν magnetic moment A: ν magnetic moment B, C, D: kinetically mixed A + sterile ν s B: U(1) B L boson C: kinetically mixed U(1) + sterile ν D: U(1) B + sterile ν charged under U(1) B [Pospelov , Pospelov Pradler ] Enhanced scattering at low E r for light A Negligible compared to SM scattering ( g 4 m T /MW 4 ) at energies probed in dedicated neutrino experiments [Harnik JK Machado arxiv:1202:6073] Joachim Kopp Sterile neutrinos: to be or not to be? 21

30 Sterile neutrinos and DM annihilation in the Sun Neutrino telescope limits on neutrinos from dark matter annihilation in the Sun depend crucially on oscillation physics. If sterile neutrinos exist, new MSW resonances can lead to strong conversion of active neutrinos into sterile neutrinos in the Sun. Esmaili Peres, arxiv: Argüelles JK, arxiv: Joachim Kopp Sterile neutrinos: to be or not to be? 22

31 Oscillation probabilities for a 3+3 toy scenario P(ν e ν X ) P(ν µ ν X ) P(ν τ ν X ) P( ν e ν X ) P( ν µ ν X ) P( ν τ ν X ) Thick red lines = active sterile oscillations plots from Argüelles JK, arxiv: see also Esmaili Peres, arxiv: Joachim Kopp Sterile neutrinos: to be or not to be? 23

32 Summary

33

34 Four independent anomalies Consistent with each other Tension in global fit Are the anomalies real? Are the null results real? Cosmological limits: Avoided elegantly by self-interacting sterile ν s With and without new interactions: rich phenomenology in dark matter detectors

35 Thank you!

36 Data sets included in our fit _ ( ) ν e disappearance SBL reactor experiments LBL reactor experiments KamLAND Radioactive source (Ga) experiments Solar neutrinos Atmospheric neutrinos ν e 12 C scattering in KARMEN, LSND _ ( ) ν e appearance LSND MiniBooNE KARMEN NOMAD ICARUS E776 _ ( ) 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) CDHS Joachim Kopp Sterile neutrinos: to be or not to be? 28

37 Relation between appearance and disappearance neutrinos At L 4πE/ m41 2, but L 4πE/ m2 31 P ee = 1 2 [ U e4 2 (1 U e4 2 ) + U e5 2 (1 U e5 2 ) U e4 2 U e5 2] P µµ = 1 2 [ U µ4 2 (1 U µ4 2 ) + U µ5 2 (1 U µ5 2 ) U µ4 2 U µ5 2] [ ] P eµ = 2 U e4 2 U µ4 2 + U e5 2 U µ5 2 + Re(Ue4U µ4 U e5 Uµ5) Joachim Kopp Sterile neutrinos: to be or not to be? 29

38 Relation between appearance and disappearance neutrinos At L 4πE/ m41 2, but L 4πE/ m2 31 P ee = 1 2 [ U e4 2 (1 U e4 2 ) + U e5 2 (1 U e5 2 ) U e4 2 U e5 2] P µµ = 1 2 [ U µ4 2 (1 U µ4 2 ) + U µ5 2 (1 U µ5 2 ) U µ4 2 U µ5 2] [ ] P eµ = 2 U e4 2 U µ4 2 + U e5 2 U µ5 2 + Re(Ue4U µ4 U e5 Uµ5) It follows 2P eµ (1 P ee )(1 P µµ ) + 4 [Re(Ue4U µ4 U e5 Uµ5) + 4 U e4 2 U µ U e5 2 U µ4 2] = (1 P ee )(1 P µµ ) 2 [ U e4 2 U µ5 2 + U e5 2 U µ4 2] 2 Ue4 U µ5 U e5 U µ4 2 Joachim Kopp Sterile neutrinos: to be or not to be? 29

39 Relation between appearance and disappearance neutrinos At L 4πE/ m41 2, but L 4πE/ m2 31 P ee = 1 2 [ U e4 2 (1 U e4 2 ) + U e5 2 (1 U e5 2 ) U e4 2 U e5 2] P µµ = 1 2 [ U µ4 2 (1 U µ4 2 ) + U µ5 2 (1 U µ5 2 ) U µ4 2 U µ5 2] [ ] P eµ = 2 U e4 2 U µ4 2 + U e5 2 U µ5 2 + Re(Ue4U µ4 U e5 Uµ5) It follows 2P eµ (1 P ee )(1 P µµ ) Unlike in the case, for models, there is NO one-to-one relation between the appearance and disappearance probabilities. However, there is an inequality, which can be used to set meaningful constraints. Joachim Kopp Sterile neutrinos: to be or not to be? 29

40 Impact of θ m ev 2 Gallium 0.3 m ev 2 Gallium 0.25 Solar KamL 0.25 Solar KamL Sin 2 2 Θ SBL reactors 0.1 LBL reactors 0.05 C CL Sin 2 2 Θ SBL reactors C 12 LBL reactors 95 CL U e4 2 U e4 2 Sterile neutrinos do not impact θ 13 measurement θ 13 0 does not impact sterile neutrino search JK Machado Maltoni Schwetz, arxiv: Joachim Kopp Sterile neutrinos: to be or not to be? 30

41 (_ ) ν µ disappaearance in the 3+1 scenario Parameter regions favored by tentative hints are in tension with null results Constraints on U τ4 sin θ 34 possible due to NC events and matter effects 1. m ev 2 1. m ev 2 UΤ solar MINOS Unitarity bound UΤ CDHS MB disapp LBL reactors solar MINOS Unitarity bound 0.2 all Ν Μ disapp. 0.2 all Ν Μ disapp. atm , 99 atm , 99 JK Machado Maltoni Schwetz, arxiv: Joachim Kopp Sterile neutrinos: to be or not to be? 31

42 (_ ) ν µ disappaearance in the 3+1 scenario Parameter regions favored by tentative hints are in tension with null results Constraints on U τ4 sin θ 34 possible due to NC events and matter effects Complex phases important ev 2 m MINOS atm MB disapp CDHS worst phases MINOS best phases 10 1 worst phases best phases JK Machado Maltoni Schwetz, arxiv: Joachim Kopp Sterile neutrinos: to be or not to be? 31

43 The MIT/Columbia fit _ ( ) ν µ (_ ) ν e appearance data: LSND MiniBooNE KARMEN NOMAD (_ ) ν µ disappearance data: MiniBooNE Minos CC νµ CDHS CCFR Atmospheric neutrinos _ ( ) ν e disappearance data: Short baseline reactor experiments Gallium experiments νe 12 C CC scattering in KARMEN, LSND Conrad Ignarra Karagiorgi Shaevitz Spitz, arxiv: Poster by Gabriel Collin χ 2 /dof and PG test results in qualitative agreement with ours tension confirmed Joachim Kopp Sterile neutrinos: to be or not to be? 32

44 The GL 4 fit _ ( ) ν µ (_ ) ν e appearance data: LSND MiniBooNE E776 KARMEN NOMAD ICARUS _ OPERA ( ) ν µ disappearance data: MiniBooNE/SciBooNE Minos NC+CC νµ CDHS CCFR Atmospheric neutrinos _ ( ) ν e disappearance data: Reactor experiments Gallium experiments Solar neutrinos νe 12 C scattering in KARMEN, LSND [ev 2 ] 2 m GLO 68.27% CL 90.00% CL 95.45% CL 99.00% CL 99.73% CL sin 2 2ϑ eµ 3+1 3σ ν e DIS ν µ DIS DIS APP Giunti Laveder Li Long arxiv: Giunti Laveder Li Liu Long arxiv: Giunti Laveder arxiv: Conclusion NO tension found Joachim Kopp Sterile neutrinos: to be or not to be? 33

45 Differences between our fit and Giunti et al. MiniBooNE fit we use MB analysis based on official MC events, include BG oscillation MINOS fit we fit CC+NC data, including ND and FD, detector response matrices based on official MINOS MC Reactor fit minor differences in the data set, possibly different treatment of correlations among systematic uncertainties LSND fit Note that LSND spectral data is more constraining than the total count rate. We use this information; our fit is consistent with the numbers reported in hep-ex/ (Church, Eitel, Mills, Steidl, combined LSND+KARMEN analysis) Atmospheric neutrinos Full fit vs. tabulated χ 2 Joachim Kopp Sterile neutrinos: to be or not to be? 34

46 Are light sterile neutrinos ruled out by cosmology? ν s production in the early Universe through ν e,µ,τ ν s oscillations at T MeV Making sterile neutrinos fully consistent with cosmology Dodelson Widrow 1994 > 1 new relativistic degrees of freedom + w < 1 + µ ν 0 Hamann Hannestad Raffelt Wong, arxiv: Entropy production after neutrino decoupling (e.g. due to late decay of heavy sterile neutrinos or other particles) neutrinos diluted Very low reheating temperature Fuller Kishimoto Kusenko , Ho Scherrer Gelmini Palomares-Ruiz Pascoli, astro-ph/ Large lepton asymmetry ( 0.01) ν s production MSW-suppressed Foot Volkas hep-ph/ , Chu Cirelli astro-ph/ , Saviano et al. arxiv: Couplings to a Majoron field suppressed production New gauge interaction in the ν s sector ν s production suppressed by thermal potential Bento Berezhiani, hep-ph/ Hannestad et al Dasgupta JK Joachim Kopp Sterile neutrinos: to be or not to be? 35

47 Two further remarks If sterile and visible sectors have ever been in thermal equilbrium, ν s will have been produced thermally very early on. But temperatures of the two sectors are very different: T visible > T sterile after the SM phase transitions. ν s abundance active neutrino abundance Joachim Kopp Sterile neutrinos: to be or not to be? 36

48 Two further remarks If sterile and visible sectors have ever been in thermal equilbrium, ν s will have been produced thermally very early on. But temperatures of the two sectors are very different: T visible > T sterile after the SM phase transitions. ν s abundance active neutrino abundance Mixing of U(1) s -charged ν s with active neutrinos: L LY ν HνR ν s Y s H s ν R 1 2 (ν R) c M R ν R + h.c., ( H = SM Higgs, H s = sterile sector Higgs) see e.g. Harnik JK Machado arxiv: Joachim Kopp Sterile neutrinos: to be or not to be? 36

49 Neutrino decoupling QCD phase transition Suppression of ν s production by thermal MSW effect 10 4 BBN Neutrino potential Veff ev M 0.1 MeV m 2 2 E M 10 MeV M 10 3 MeV M 0.1 MeV M 10 MeV M 10 3 MeV For α 10 3 and M A 10 MeV: T Γ ev effective potential V eff oscillation frequency m 2 /(2E) until neutrino decoupling. sterile neutrino production suppressed, no cosmological constraints Hannestad Hansen Tram arxiv: Dasgupta JK arxiv: Joachim Kopp Sterile neutrinos: to be or not to be? 37

50 sin 2 2 Θm 10 3 m 2 1 ev 2 Hidden sector gauge forces and dark matter Interesting connection to dark matter physics: The same gauge force that suppressed sterile neutrino production can also solve small scale structure problems: Too big to fail problem Cusp vs. core problem Missing satellites problem 10 6 Α Χ 10 3 Dark matter mass mχ GeV ΣT mχ 0.1 cm 2 g for v rel 10 km s ΣT mχ 1 cm 2 g Missing satellites solved Mcut MSun Cluster bound violated ΣT mχ 1 cm 2 g for v rel 10 3 km s Mcut 10 9 MSun Cusp vs. core & Too big to fail solved Νs overproduction Dark photon mass M MeV Dasgupta JK arxiv: Joachim Kopp Sterile neutrinos: to be or not to be? 38

51 Example 1: Neutrino magnetic moments Assume neutrinos carry an enhanced magnetic moment L µν µ ν νσ αβ β A α ν, µ ν µ ν,sm = µ B Cross section large at low energies due to photon propagator q 2 ( dσ µ (νe νe) 1 = µ 2 de να 1 ), r E r E ν counts NA kevee year electron recoil 10 2 CoGeNT DAMA 10-1 XENON100 e A Standard model Borexino A 10-8 ΜΝ = 0.32 x ΜB Erec kevee counts/ton/kev nr / year Standard model A A Nuclear recoil Ge ΜΝ = 0.32 x ΜB E rec / kevnr CoGeNT CDMS II Joachim Kopp Sterile neutrinos: to be or not to be? 39

52 Example: A not-so-sterile 4th neutrino Introduce a new U(1) gauge boson A (hidden photon) and a light sterile neutrino ν s Related model with gauged U(1) B first discussed in Pospelov detailed studies in Harnik JK Machado 1202:6073 and Pospelov Pradler ν s charged under U(1) direct coupling to A SM particles couple to A only through kinetic mixing L 1 4 F µνf µν 1 4 F µνf µν 1 2 ɛf µνf µν + ν s i / ν s + g ν s γ µ ν s A µ (ν L ) c m νl ν L (ν s ) c m νs ν s (ν L ) c m mix ν s A small fraction of solar neutrinos can oscillate into ν s ν s scattering cross section in the detector given by dσ A (ν s e ν s e) ɛ 2 e 2 g 2 m e [ = 2E 2 de r 4πpν(M 2 A 2 + 2E r m e ) 2 ν + Er 2 2E r E ν E r m e mν 2 ] Joachim Kopp Sterile neutrinos: to be or not to be? 40

53 Temporal modulation of neutrino signals Signals of new light force mediators and/or sterile neutrinos can show seasonal modulation: The Earth Sun distance: Solar neutrino flux peaks in winter. Joachim Kopp Sterile neutrinos: to be or not to be? 41

54 Temporal modulation of neutrino signals Signals of new light force mediators and/or sterile neutrinos can show seasonal modulation: The Earth Sun distance: Solar neutrino flux peaks in winter. Active sterile neutrino oscillations: For oscillation lengths 1 AU, sterile neutrino appearance depends on the time of year. Harnik JK Machado, arxiv: Joachim Kopp Sterile neutrinos: to be or not to be? 41

55 Temporal modulation of neutrino signals Signals of new light force mediators and/or sterile neutrinos can show seasonal modulation: The Earth Sun distance: Solar neutrino flux peaks in winter. Active sterile neutrino oscillations: For oscillation lengths 1 AU, sterile neutrino appearance depends on the time of year. Sterile neutrino absorption: For strong ν s A couplings and not-too-weak A SM couplings, sterile neutrino cannot traverse the Earth. lower flux at night. And nights are longer in winter. Joachim Kopp Sterile neutrinos: to be or not to be? 41

56 Temporal modulation of neutrino signals Signals of new light force mediators and/or sterile neutrinos can show seasonal modulation: The Earth Sun distance: Solar neutrino flux peaks in winter. Active sterile neutrino oscillations: For oscillation lengths 1 AU, sterile neutrino appearance depends on the time of year. Sterile neutrino absorption: For strong ν s A couplings and not-too-weak A 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 flux of certain neutrino flavors at night. And nights are longer in winter. Joachim Kopp Sterile neutrinos: to be or not to be? 41

57 Hidden photons L 1 4 F µνf µν 1 4 F µνf µν 1 2 ɛf µνf µν + ν s i / ν s + g ν s γ µ ν s A µ Kinetic mixing Ε g 2 Μ Atomic Physics Atomic Physics g Ν 2 sin 2 2Θ g Ν 2 sin 2 2Θ 10 4 CMB Kinetically Mixed Gauge Boson CMB LSW Fixed target Dark Photon Mass M A' GeV CAST Borexino in models with U 1 ' charged sterile Ν Sun Globular Clusters, energy loss via Ν s in models with 10 kev sterile neutrinos A' capture in Sun partly allowed Globular Clusters g 2 e SN1987A Constraints from Jaeckel Ringwald , Redondo , Bjorken Essig Schuster Toro , Dent Ferrer Krauss , Harnik JK Machado Joachim Kopp Sterile neutrinos: to be or not to be? 42 Sun

58 3+3 flavor toy model Consider toy model with 3 sterile neutrinos, each of them mixing with only one of the active flavors: Hamiltonian: U = R 14 (θ) R 25 (θ) R 36 (θ) U PMNS, R ij = rotation in ij-plane. H E + 1 2E U D U + V MSW, D = diag(0, m 2 21, m 2 31, m 2 41, m 2 51, m 2 61) Mikheyev-Smirnov-Wolfenstein (MSW) potential: V MSW = 2G F diag(n e n n /2, n n /2, n n /2, 0, 0, 0), n e (n n) = electron (neutron) number density Oscillation probability: P(ν α ν β ) = ν β e iht ν α 2 Joachim Kopp Sterile neutrinos: to be or not to be? 43

59 Impact on IceCube limits plot from Carlos Argüelles JK, arxiv: see also Esmaili Peres, arxiv: Joachim Kopp Sterile neutrinos: to be or not to be? 44