Sterile neutrinos. Stéphane Lavignac (IPhT Saclay)

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1 Sterile neutrinos Stéphane Lavignac (IPhT Saclay) introduction active-sterile mixing and oscillations cosmological constraints experimental situation and fits implications for beta and double beta decays 9ème Rencontre SPP/IPhT: Les neutrinos Saclay, 4 janvier 01

2 Introduction Several oscillation results or anomalies (reactor antineutrino anomaly, LSND ν µ ν e data...) cannot be explained within 3-flavour oscillations need at least a fourth neutrino But constraint from the invisible decay width of the Z boson [LEP]: N ν =.9840 ± additional neutrinos must be sterile (i.e. electroweak singlets) or be heavier than MZ / Sterile neutrinos are SM gauge singlets - only interact via their mixing with the active neutrinos oscillations ν e,µ,τ ν s Other motivations for sterile neutrinos from cosmology, e.g. kev sterile neutrino as warm dark matter [Shaposhnikov] or to explain pulsar velocities [Kusenko, Segrè]

3 Standard case (3 flavours): Active-sterile neutrino mixing Add a sterile neutrino: ν α = 4 i=1 U flavour eigenstate αi ν i [ α = e, µ, τ ] U = 4x4 unitary matrix ν e,ν µ,ν τ mass eigenstate (m4) Only couple to electroweak gauge boson, but all four mass eigenstate are produced in a beta decay: e ν e = 4 i=1 U ei ν i ν s ν 4

4 -flavour oscillations: ( m P (ν α ν β ) = sin θ sin ) L ( να ν β ) ( cos θ sin θ = sin θ cos θ )( ν1 ν ) m m m 1 N-flavour oscillations: P να ν β ( ν α ν β ) = δ αβ 4 i<j i<j Re ( U αi U βiu αju βj ) sin ( ) m ij L Im ( ( ) U αi UβiU αju ) m ij L βj sin E

5 3+1 case: Since m SBL m atm., m sun, it is natural (and cosmologically preferred) to assume m 4 m 3,m,m 1 Then m SBL m 41 m 4 m 43 all other m ij s All data but short baseline oscillations well described by 3-flavour oscillations ν 1,,3 mainly composed of ν e,µ,τ + small admixture of ν s, and mainly composed of + small admixture of ν 4 ν s ν e,µ,τ! $ Smirnov %&'' $% ",-./! +! "!# $% " &(% $% " ')*

6 We are interested in short baseline oscillations with m 41L P να ν α ( ) m 1 = sin 41 L ( ) m sin 31 L, sin ( m 1 L 1 4 ( U α1 + U α + U α3 ) ( ) m U α4 sin 41 L ( ) m 1 sin θ αα sin 41 L ) where P να ν β where sin θ αα 4 (1 U α4 ) U α4 4 Re [( U α1 Uβ1 + U α Uβ + U α3 Uβ3 ( ) m sin θ αβ sin 41 L sin θ αβ 4 U α4 U β4 ( ) ) ] U α4 U β4 sin m 41 L

7 3+ case: Assume m 5 m 4 m 3,m,m 1 two relevant squared mass differences m 51 and m 41 CP-violating effects possible due to interference between the two oscillations frequencies P να ν β ( ν α ν β ) η arg [ U α4 U β4u α5u β5 ] ( ) ( ) m = 4 U α4 U β4 sin 41 L m +4 U α5 U β5 sin 51 L ( ) ( ) ( m +8 U α4 U β4 U α5 U β5 sin 41 L m sin 51 L m cos 54 L ) η

8 Cosmological constraints Light sterile neutrinos are in thermal equilibrium in the early universe due to oscillations (unless small active-sterile mixing) increase the number of relativistic species affect BBN, CMB anisotropies and large-scale structure formation Hamann, Hannestad, Raffelt, Wong [ ]: within ΛCDM, CMB+LSS and BBN prefer extra relativistics dofs: N eff = (95% C.L.) However, a sterile neutrino with an ev mass violates the cosmological bound on neutrino masses m ev or must depart from ΛCDM: e.g. additional relativistic dofs help relax this bound, but inconsistent with BBN (allows at most one extra relativistic dof) unless introduce a neutrino chemical potential If ev-scale sterile neutrinos are really around, seem to require a significant modification of the standard cosmological scenario

9 Experimental situation Several experimental anomalies suggest the existence of sterile neutrinos LSND: oscillations Excess of ν e events over background at 3.8 σ (still controversial) Not observed by KARMEN MiniBooNE: ν µ ν e ν e ν µ ν e data: no excess in the MeV range, but unexplained 3σ excess at low energy ν µ ν e ν e data: excess in the E > 475 MeV region consistent with LSND-like oscillations, but also (after the 011 update) with a background-only hypothesis A low-energy excess is also seen ν e ) 4 /c (ev m 1-1 LSND 90% C.L. LSND 99% C.L. sin (θ) upper limit MiniBooNE 90% C.L.y MiniBooNE 90% C.L. sensitivity BDT analysis 90% C.L sin (θ) -1 1

10 Reactor antineutrino anomaly: New computation of the reactor antineutrino spectra increase of the flux by about 3% deficit of antineutrinos in SBL reactor experiments mean observed to predicted rate ± N OBS /(N EXP ) pred,new ILL Bugey!3 Bugey!4 ROVNO88!1S ROVNO88!3S ROVNO91 ROVNO88!I SRP!I ROVNO88!1I SRP!II ROVNO88!S Krasnoyarsk!I Goesgen!I Bugey!3 Goesgen!II Krasnoyarsk!III Goesgen!III Krasnoyarsk!II Bugey!3 PaloVerde CHOOZ G. Mention et al. 1 3 Distance to Reactor (m) FIG. 5. Illustration of the short baseline reactor antineutrino anomaly. The experimental results are compared to the prediction without oscillation, taking into account the new antineutrino spectra, the corrections of the neutron mean lifetime, and the off-equilibrium effects. Published experimental errors and antineutrino spectra errors are added in quadrature. The mean averaged ratio including possible correlations is ± The red line shows a possible 3 active neutrino mixing solution, with sin (θ 13 ) = The blue line displays a solution including a new neutrino mass state, such as m new,r 1 ev and sin (θ new,r ) = 0.1 (for illustration purpose only).

11 Gallex-SAGE calibration experiments: Calibration of the Gallex and SAGE experiments with radioactive sources observed deficit of ν e with respect to predictions R = 0.86 ± 0.05 [tension with ν e - Carbon cross-section measurements at LSND and KARMEN, ] Combined analysis of SBL reactor data, gallium calibration experiments and MiniBooNE neutrino data [G. Mention et al.]: m SBL > 1.5 ev, sin θ ee =0.14 ± 0.08 (95% C.L.)

12 However, no coherent picture of the data with an additional (or even ) sterile neutrinos (even if the global fit has improved with the new reactor antineutrino flux): 1) tension between appearance (LSND/MiniBooNE antineutrino data) and disappearance experiments (reactors, ν µ disappearence experiments) ( ) m Reactors: P νe ν e 1 sin θ ee sin 41 L require relatively small CDHS: P νµ ν µ sin θ ee 4 (1 U e4 ) U e4 4 U e4 (using info from solar neutrino data) ( ) m 1 sin θ µµ sin 41 L require relatively small sin θ µµ 4 (1 U µ4 ) U µ4 4 U µ4 (using info from atm. neutrino data)

13 Appearance experiments (LSND/MiniBooNE antineutrino data): ( ) m P νµ ν e sin θ eµ sin 41 L sin θ eµ 4 U e4 U µ4 1 4 sin θ ee sin θ µµ 99% C.L. Bugey!3 (1995) Bugey!4 (1994) + Rovno (1991) Gosgen (1986) + ILL (1995) Krasnoyarsk (1994) 99% C.L. Reactors CDHSW + Atm Disappearance LSND + MB$ [ev ] "m 41 [ev ] [ev ] #1 "m 41 #1 "m 41 #1 # # #1 1 sin! ee 99% C.L. CDHSW (1984): $ µ ATM: $ µ + $ µ # # #1 1 sin! µµ # #4 #3 # #1 1 sin! eµ Giunti,

14 ) tension between LSND and MiniBooNE neutrino data (+ null result of NOMAD and KARMEN) Giunti, "m 41 [ev ] #1 99% C.L. MB$ + LSND$ Dis + KAR + NOM + MB$ # #4 #3 # #1 1 1 MB# KARMEN NOMAD sin! eµ "m 41 [ev ] 0 disappearance LSND + MB# $ 90, 99% CL Kopp, Maltoni, Schwetz, % CL ( dof) sin! SBL

15 3+1 case does not provide a very satisfactory fit of all the data Best fit point of a global analysis [Giunti, Laveder, incl. MiniBooNE 011]: m 41 =1.6eV, U e4 =0.036, U µ4 = [ sin θ eµ =1. 3] 3+ case [Kopp, Maltoni, Schwetz] Allows for CP violation can reconcile MiniBooNE neutrino data with LSND/MiniBooNE 0 antineutrino data (less motivated after inclusion of 011 data) LSND Much better fit of pre-011 data than in the 3+1 case [low-energy excess of MiniBooNE not included in the fit] P ( ν µ ν e ) P (ν µ ν e ) excess events P LSND [%] MiniBooNE (neutrinos) MiniBooNE (anti-neutrinos) E # CCQE [GeV] E # CCQE [GeV]

16 Other implications of sterile neutrinos Tritium beta decay: 3 H 3 H e + e + ν e E 0 = m 3 H m 3 H e The electron energy spectrum is given by: dn = R(E e ) (E 0 E e ) de m ν E e = E 0 E ν e Effect of the non-vanishing neutrino mass: Ee max = E 0 E 0 m ν distorsion of the Ee spectrum close to the endpoint

17 Present bound (Troitsk/Mainz): KATRIN will reach a sensitivity of about 0.3 ev m νe <. ev (95% C.L.) In pratice, there is no electron neutrino mass, but 3 (or more) strongly mixed mass eigenstates, and dn = R(E e ) U ei (E 0 E e ) de m i Θ(E 0 E e m i ) e i If all mi are smaller than the energy resolution, this can be rewritten as: dn = R(E e ) m i U de ei e (E 0 E e ) m β m β i If there is an ev-scale sterile neutrino (comparable to the energy resolution of KATRIN), its mass may be resolved (but difficult measurement): 1 R(E e ) dn = (1 U e4 ) (E 0 E e ) de m β e + U e4 (E 0 E e ) m 4 Θ(E 0 E e m 4 ) (dn/dee) 1/ (also: upper bound on m4 from beta decay) Q! m " H Q! m " L Q E e

18 Neutrinoless double beta decay: (A, Z) (A, Z + ) + e + e Possible if lepton number violated (Majorana neutrinos), in nuclei where the single beta decay is forbidden Sensitive to the effective mass parameter: m ββ i m i U ei possible cancellations in the sum (phases in U) 1 disfavoured by 0ΝΒ 3-neutrino case (Strumia, Vissani) mee in ev CL 1 dof m 3 0 m 3 0 disfavoured by cosmology lightest neutrino mass in ev

19 An additional sterile neutrino will contribute to the effective mass m ββ m 4 U e4 e iγ i m iuei ; depending on the active neutrino parameters it may dominate or lead to cancellations <m ee > (ev) , Normal, SN 1+3, Inverted, SI 3! (best-fit) 3! (") 1+3! (best-fit) 1+3! (") 3! (best-fit) 3! (") 1+3! (best-fit) 1+3! (") Barry, Rodejohann, Zhang, m light (ev) using the fit of Kopp, Maltoni and Schwetz: 3+1/1+3 parameter m 41 [ev] U e4 best-fit σ

Status of Light Sterile Neutrinos Carlo Giunti

C. Giunti Status of Light Sterile Neutrinos EPS-HEP 05 3 July 05 /5 Status of Light Sterile Neutrinos Carlo Giunti INFN, Sezione di Torino and Dipartimento di Fisica, Università di Torino giunti@to.infn.it