Neutrino properties: nature, mass & CP violation

Size: px

Start display at page:

Download "Neutrino properties: nature, mass & CP violation"

Amos Gordon
5 years ago
Views:

1 Neutrino properties: nature, mass & CP violation I. Schienbein LPSC prepared together with P. Serpico (LAPTH) and A. Wingerter (LPSC) Kick-off meeting, 2/0/202, Annecy

2 Facts of life with neutrinos

3 Neutrino properties: What we know in 202 very weakly interacting, electrically neutral, spin /2, tiny mass long lived (or stable), tiny or vanishing magnetic moment 3 light SM families (νe,νμ, ντ) Neutrino Properties See the note on Neutrino properties listings in the Particle Listings. Mass m < 2eV (tritiumdecay) Mean life/mass, τ/m > 300 s/ev, CL = 90% (reactor) Mean life/mass, τ/m > s/ev (solar) Mean life/mass, τ/m > 5.4 s/ev,cl=90% (accelerator) Magnetic moment µ < µ B,CL=90% (solar) Number of Neutrino Types Number N =2.984 ± (Standard Model fits to LEP data) Number N =2.92 ± 0.05 (S =.2) (Direct measurement of invisible Z width) neutrinos oscillate m ν 0 Neutrino Mixing sin 2 (2θ 2 )=0.857 ± m 2 2 =(7.50 ± 0.20) 0 5 ev 2 sin 2 (2θ 23 ) > 0.95 [i] m =( ) 0 3 ev 2[j] sin 2 (2θ 3 )=0.098 ± 0.03

4 Neutrinos oscillate!

5 Neutrino oscillations 3 neutrino states 3 masses m, m2, m3 States with definite masses (mass eigenstates) in general do not coincide with flavor states Quantum mechanics: States with same quantum numbers can mix, as it happens for the quarks The mixing matrices V are 3x3 unitary matrices CKM = Cabibbo-Kobayashi-Maskawa PMNS = Pontecorvo; Maki-Nakagawa-Sakata Flavor basis: { e i, µ i, i} Mass basis: { i, 2 i, 3 i} 0 0 d 0 s 0 A = V sa b 0 b 0 0 µ A = V 2 A 3

6 Neutrino oscillations Consider 2 flavor case: for simplicity dominant oscillations are welldescribed by 2-flavor mixing Flavor and mass eigenstates connected by a 2x2 rotation matrix µ i = cos i +sin 2 i i = sin i + cos 2 i Neutrino propagation: νμ created at t=0 with 3-momentum p Neutrino state at time t Different mass components have different energy (0)i = µ i = cos i +sin 2 i (t)i = e ie t cos i + e ie 2t sin 2 i E i = q p 2 + m 2 i ' p + m2 i 2p ' p + m2 i 2E

7 Neutrino oscillations Oscillation probability: P ( µ! ; t) = h (t)i 2 = { sin h + cos h 2 }{e iet cos i + e ie2t sin 2 i} 2 = cos 2 sin 2 e ie 2t e iet 2 = 2 cos 2 sin 2 { cos[(e 2 E )t]} apple m =sin 2 2 sin 2 2 4E t m 2 = m 2 2 m 2 As function of distance L=c*t=t: P ( µ! ; L) =sin 2 2 sin 2 apple m 2 4E L =sin 2 2 sin 2 apple.27 m 2 (ev 2 ) L(km) E(GeV) L/E determines sensitivity to Δm 2

8 3 flavor oscillations: Neutrino oscillations atmospheric solar cross mixing

9 Results in the 3 flavor mixing scheme Neutrino state cross-composition J Discovery of a non-zero angle θ3!

10 Leptonic CP violation: δcp 0? θ3 0 : necessary condition for leptonic CP violation θ3 = 0: effective 2 flavor mixing CP violation only with unitary 3x3 matrices (or larger) Dirac-neutrinos: CP violating phase Majorana-neutrinos: 2 additional CP violating phases CP violation in quark sector not sufficient to explain the baryon asymmetry of the universe (BAU) Leptonic CPV would give an additional contribution Measurement of δcp exciting challenge

11 Neutrinos and the Standard Model

12 Neutrinos and the Standard Model Neutrino oscillations: at least two massive neutrino states why should neutrinos be massless anyway? (no symmetry) In the original SM, neutrinos are massless oscillation results = physics beyond the SM However, massive neutrinos possible by a minimal extension of the SM: right-handed neutrino gauge singlet ( sterile neutrino ) can be a Dirac fermion like the electron Particles Spin SU(3) C SU(2) L U() 3 4 Y ul Q = d L L = H = ur c d 3 R c L e L 4 R c e 3 R c G µ 8 0 W a µ 3 0 B µ 0 mass term via Yukawa interaction with Higgs boson (Higgs mechanism) neutrino masses of order mev: tiny(!) Yukawa couplings

13 Neutrinos and the Standard Model Neutrino oscillations: at least two massive neutrino states why should neutrinos be massless anyway? (no symmetry) In the original SM, neutrinos are massless oscillation results = physics beyond the SM Conversely, neutrino only fermion in the SM without electric charge: can be its own anti-particle (like γ, Z 0,π 0,η) it s called Majorana-Neutrino (ν M ) if it is its own anti-particle: ν M =(ν M ) c non-minimal extension of the SM: Particles Spin SU(3) C SU(2) L U() 3 4 Y ul Q = d L L = H = ur c d 3 R c L e L 4 R c e 3 R c G µ 8 0 W a µ 3 0 B µ 0 mass term in L can be a gauge singlet heavy mass term possible [not related to the Higgs mechanism] seesaw mechanism can explain tiny masses

14 d0,,)*"wp/ H 2) Neutrinos and the Standard Model Why the neutrino mass is so small?" o#0%m,) 0'7) -"3$(',) \""U,0Q)+"/40'&,+) & m () # 3) $! ( % m( top quark) " & $ % 3' 0 2 #! " d&'m(q,m.=)x0'0a&70=))))))))))))))))))))))))))) O"--U+0''=)E0+('7=)\-0',M.) m "! m m 2 q N Z:)Q")&'3#$)+!] )0'7)+ Y) *+ $(3 )&,)#,"72=) Q")A"$)+! j)ji J_) O"w)! 2! 3 A"'"%0(') F4&,),#AA",$,)$40$)34.,&/,)(:)'"#$%&'()+0,,)/(#-7)?") %"-0$"7)$()34.,&/,)(:)O%0'7)B'&m/0('h)))

15 The SM with massive neutrinos (i) Too many free parameters Gauge sector: 3 couplings g 0, g, g 3 3 Quark sector: 6 masses, 3 mixing angles, CP phase 0 Lepton sector: 6 masses, 3 mixing angles and -3 phases 0 Higgs sector: Quartic coupling and vev v 2 parameter of QCD 26 (ii) Structure of gauge symmetry SU(3) c SU(2) L U() Y? SU(5)? SO(0)? E6? E8 Why 3 di erent coupling constants g 0, g, g 3? Particles Spin SU(3) C SU(2) L U() 3 4 Y ul Q = d L L = H = ur c d 3 R c L e L 4 R c e 3 R c G µ 8 0 W a µ 3 0 B µ 0 (iii) Structure of family multiplets (3,2) /3 + (3,) -4/3 + (,) -2 + (3,) 2/3 + (,2) - + (,) 0? = 6 Q ū ē d L Fits nicely into the 6-plet of SO(0)

16 Majorana or Dirac? That is here the question

17 Nature of neutrinos: Majorana or Dirac? Lepton number: L= for neutrinos L = - for anti-neutrinos L not conserved for Majorana-Neutrinos e + n! e + p L =+0=+0 Lepton number conserved; Reaction has been observed The second reaction should be possible if Not observed! Naive conclusion: electron-neutrino is not Majorana! Conclusion valid only for mν 0! Otherwise: neutrino (h=-) anti-neutrino (h=+) e = e e = e e + n! e + p L = +06= +0 Lepton number not conserved; Reaction has not been observed and vertex with h=+ might be forbidden

18 Neutrinoless double-beta decay p Vertex I : n p + e + e n I Vertex II : νe + n p + e ν e Together : 2 n 2p +2e ν p L = n II e Necessary condition: neutrinos are Majorana fermions e = e If observed neutrinos are Majorana fermions Even for Majorana neutrinos: forbidden if neutrinos massless and interaction vertices with fixed helicity the smaller masses, the smaller 0νββ m=0: distinction between Majorana and Dirac neutrinos not possible

19 Enigmatic neutrino masses

20 Neutrino masses Why knowledge of neutrino masses interesting? Fundamental parameters of the SM Neutrinos with O(meV) masses make the fermion mass spectrum of the SM even more bizarre! (4 orders of magnitude!) Need masses to compute contribution of the neutrinos to the matter density of the universe Matter density important for the evolution of the universe Contribute a part to the non-baryonic dark matter (hot DM) How to determine neutrino masses? direct determination via kinematics of weak decays (tritium β decay) neutrino oscillations neutrinoless double-beta-decay

d0,,)*"wp/ H 2) Neutrino masses Oscillations: m 2 32 = m 2 3 m 2 2 =2.3 0 3 ev 2 m 2 2 = m 2 2 m 2 =7.

21 d0,,)*"wp/ H 2) Neutrino masses Oscillations: m 2 32 = m 2 3 m 2 2 = ev 2 m 2 2 = m 2 2 m 2 = ev 2 Oscillations in matter: m 2 >m Sign of m 2 32 unknown: normal or inverted hierarchy o#0%m,) 0'7) -"3$(',) m3 m2 m m2 m m3! 2! 3 Mass m of heaviest neutrino: m 2 32 ' m 2, m ' 50 mev ENIGMASS: Fermion masses over 4 orders of magnitude A"'"%0(')

22 Flavor symmetries: Fun for theorists?

23 Neutrino mixing Neutrinos have mass and the di erent flavors can mix Super-Kamiokande Collaboration, Y. Fukuda et al., Evidence for oscillation of atmospheric neutrinos, Phys. Rev. Lett. 8 (998) , hep-ex/ SNO Collaboration, Q. R. Ahmad et al., Direct evidence for neutrino flavor transformation from neutral-current interactions in the Sudbury Neutrino Observatory, Phys. Rev. Lett. 89 (2002) 030, nucl-ex/ Charged lepton and neutrino mass matrices cannot be simultaneously diagonalized ˆM`+ = D L M`+D R, ˆM = U L M U R Pontecorvo-Maki-Nakagawa-Sakata matrix B. Pontecorvo, Mesonium and antimesonium, Sov. Phys. JETP 6 (957) 429 Z. Maki, M. Nakagawa, and S. Sakata, Remarks on the unified model of elementary particles, Prog. Theor. Phys. 28 (962) µ A = D L U L {z } U PMNS 2 A 3

Neutrino mixing mismatch between flavour and mass basis expressed via mixing matrix U s lk Sin θ lk, c lk Cos θ lk 0 m 2 32 @ 0 0 0 c 23 s 23 0 s 23 c 23 A 0 @ m 2 3 c 3 0 e i s 3 0 0 e i s 3 0 c 3 A

24 Neutrino mixing mismatch between flavour and mass basis expressed via mixing matrix U s lk Sin θ lk, c lk Cos θ lk 0 m c 23 s 23 0 s 23 c 23 A m 2 3 c 3 0 e i s e i s 3 0 c 3 A 0 m 2 s 2 c 2 0 c 2 s A 2-3 sector: atmospheric anomaly consistent with maximal mixing (SK, LBL dis.) 3-flavour effects (& CP) suppressed by the smallness of θ3 and Δm2 2 << Δm3 2 Reactor (dis)+lbl (app.) -2 sector: solar ν problem LMA & MSW in the Sun Radiochemical, SNO, Borexino, SK, KamLAND dominant oscillations are well described by effective two-flavour mixing

25 Tribimaximal mixing Until recently, our best guess was tribimaximal mixing (TBM) P. F. Harrison, D. H. Perkins, and W. G. Scott, Tri-bimaximal mixing and the neutrino oscillation data, Phys. Lett. B530 (2002) 67, hep-ph/ p p 2/3 / 3 0 U PMNS? = UHPS -/ p 6 / p 3 -/ p 2 -/ p 6 / p 3 / p 2 A,! 2 = 35.26, 23 = 45, 3 =0 Agreement still quite good for 2, 23,but 3 =0 Forero et al, , DAYA-BAY Collaboration, , RENO Collaboration, Parameter Tribimaximal Global fit Daya Bay Reno

26 Fun for theorists Regular pattern of PMNS-matrix: 0p p U PMNS =? 2/3 / 3 0 UHPS p 6 / p 3 -/ p 2 -/ p 6 / p 3 / p A A Suggestive of a discrete family symmetry. Introduce relation between families of quarks and leptons:

27 Questions Why is mixing in the quark sector so different from mixing in the lepton sector? P Minimal mixing in the quark sector: V CKM = V ud V us V ub V cd V cs V cb V td V ts V tb A ' A Maximal/Large mixing in lepton sector: U PMNS = U e U e2 U e3 U µ U µ2 U µ3 U U 2 U 3 A ' A θ3 = 9.3 : U PMNS = z z z 0.7 A,z= e i z z 0.7 Which discrete group to take? [S3,A4, S4, T7,Δ(96),...] Many discrete groups can give tribimaximal mixing (ruled out now) K. M. Parattu, A. Wingerter, Tribimaximal Mixing From Small Groups,PRD84(20)030 Look for groups that give θ3 0? (Still many possibilities!) C. Luhn, K. M. Parattu, A. Wingerter, A Minimal Model of Neutrino Flavor,20.97 Keep tribimaximal mixing at leading order and include higher dimensional ops.? Need guiding principle; More fundamental theory which predicts flavor symmetry

28 Who does not believe in sterile neutrinos?

29 Sterile neutrinos Sterile neutrinos: SM gauge group singlets (do not interact via weak force) Mixed with active neutrinos Simplest models to give mass to neutrinos include such fields Mass scale of (some) these states? Order ev: modifies neutrino oscillations (more freedom to explain certain puzzles) Order 0 5 GeV: seesaw, GUTs (theoretically more appealing?)

30 LSND anti-νμ anti-νe 87.9 ± 22.4 ± 6.0 excess events, 3.8 σ away from zero (< 2.3 σ according to background analysis in ?!) KARMEN anti-νμ anti-νe tight constraints on LSND (slightly smaller L/E) MiniBoone (ν) νμ νe E > 475 MeV (a priori search region): no excess, E < 475 MeV: ~3 σ excess (after unblinding, background understood?) MiniBoone (anti-ν) anti-νμ anti-νe inconclusive, consistent with both ν-run results and LSND Reactor Anomaly Sum puzzles anti-νe flux predictions from reactors require to convert measured e-spectra from 235 U, 239 Pu, 24 Pu into ν-spectra: recent calculation yield 3% higher fluxes (Mueller et al., , P. Huber, ) Hints of short baseline disappearance? Gallium Anomaly deficit of νe measured in the GALLEX and SAGE solar ν-detectors (~3 σ? See e.g. Giunti & Laveder, )

31 LSND requires a 3rd Δm 2 58)6%"7&$0$()U)53%&-)HIJH)

32 MiniBooNE νe results Affaire à suivre.)

33 Sterile neutrinos and cosmology

34 Early universe would produce sterile neutrinos For parameters suggested by laboratory anomalies: active neutrinos oscillate into sterile neutrinos before decoupling there is time to replenish the active neutrinos via ordinary weak interactions with electrons hence the additional species can be brought into equilibrium Signatures: Neff ~ 4 (5) in 3+ (3+2) models Big Bang Nucleosynthesis (BBN) excludes Neff = 5, barely consistent with Neff = 4 small preference for Neff 3 ( σ) G. Mangano, P. Serpico, PLB70(20)296 CMB data have a small preference for Neff 3

35 Early universe would produce sterile neutrinos Are sterile ν s fitting the lab. anomalies the cause of Neff>3? Most likely not! In 3+ models (fully thermalized) m4<0.48 ev (95% CL) (vs. about ev expected from Lab) In 3+2 models (fully thermalized) m4 + m5<0.9 ev (95% CL) (vs. about.5 ev expected from Lab) What if Lab confirms ev-scale sterile neutrinos? One would need to go to much more contrived cosmologies!

36 Concluding wishlist

37 Neutrino properties: What we want to know nature of neutrinos: Majorana or Dirac fermions? are there sterile neutrinos? neutrino masses: what are the absolute neutrino masses? normal (m2 m3) or inverted (m2 m3) mass hierarchy? [we know m2 > m from MSW effect] mixing matrix (PMNS-matrix): more precise measurement of mixing angles is the PMNS matrix unitary? is there leptonic CP violation?

38 Merci!

40 Neutrino oscillations in matter (MSW effect) Mikheyev-Smirnov-Wolfenstein (MSW) effect: Matter along the path of a neutrino: equivalent to the presence of an effective potential different potentials for different flavors the effective potential affects the flavor propagation in matter matter effective potentials have opposite signs for neutrinos and anti-neutrinos

41 Neutrino interactions ν µ ν µ NC ES Z e - e - CC QE (IMD) ν µ W µ - NC DIS e - ν e CC DIS

42 Long Baseline experiments ν L = O(A few 00 km) Near detector: neutrino flux neutrino beam energy spectrum cross sections before oscillation Far detector: observation of charged and neutral current reactions LBL Beam Place L [km] <Eν> [GeV] Target Year Goals K2K 2 GeV proton KEK SK H2O νμ T2K 50 GeV proton JParc SK 295 ~0.6 H2O 200- MINOS NuMI FNAL Soudan 735 3, 7, 5 Fe νμ, νe ; θ3, δ Δm23 2, θ23 νa x-secs. NC/CC ratio νμ, νe; θ3; νs OPERA CNGS CERN GS Pb ντ NOvA NuMI FNAL Ash River 80 ~2 liquid scint νμ, νe ; θ3, δ mass hierarchy νa x-secs.

43 Neutrino cross sections Flux Cross section Nuclear effects current precision: ca. 30% need to improve this for precision measurements of the MNS mixing matrix!

44 Quasi-elastic scattering (QE) ν( ν) l (l + ) Neutrino nucleon interactions q CC: ν( ν) +N l (l + )+N NC: ν( ν) +N ν( ν) +N N N

45 Quasi-elastic scattering (QE) ν( ν) l (l + ) Neutrino nucleon interactions q CC: ν( ν) +N l (l + )+N NC: ν( ν) +N ν( ν) +N N Resonance production (RES) ν( ν) q R N N l (l + ) π ±,0 N Charged Current (CC): ν( ν)+n l (l + )+N +π ±,0 Neutral Current (NC): ν( ν) +N ν( ν) +N + π ±,0

46 Quasi-elastic scattering (QE) ν( ν) l (l + ) Neutrino nucleon interactions q CC: ν( ν) +N l (l + )+N NC: ν( ν) +N ν( ν) +N N Resonance production (RES) ν( ν) q R N N l (l + ) π ±,0 N Deep inelastic scattering (DIS) ν( ν) l (l + ) q Charged Current (CC): ν( ν)+n l (l + )+N +π ±,0 Neutral Current (NC): ν( ν) +N ν( ν) +N + π ±,0 CC: ν( ν) +N l (l + )+X N X NC: ν( ν) +N ν( ν) +X

47 Quasi-elastic scattering (QE) ν( ν) l (l + ) Neutrino nucleon interactions q CC: ν( ν) +N l (l + )+N N Resonance production (RES) ν( ν) q R N N l (l + ) π ±,0 N Deep inelastic scattering (DIS) ν( ν) l (l + ) q NC: ν( ν) +N ν( ν) +N Charged Current (CC): ν( ν)+n l (l + )+N +π ±,0 Neutral Current (NC): ν( ν) +N ν( ν) +N + π ±,0 CC: ν( ν) +N l (l + )+X Need these cross sections on free nucleons and nuclear targets N X NC: ν( ν) +N ν( ν) +X

48 Neutrino cross sections at atmospheric n energies Paschos,JYY,PRD65(2002) P. Lipari, hep-ph/020772

49 What if Lab confirms ev-scale steriles? One would need to go to contrived (hence exciting?!) cosmologies Introduce chemical potentials of O(0.) to get around BBN (how to generate them?) modify dark energy sector (eg. wcdm) plus add additional non-massive radiation Explain why cluster determination of DM does not seem to fit (any idea?) see e.g. Hamann et al., Fortunately, progress is forthcoming...

Status and prospects of neutrino oscillations

Status and prospects of neutrino oscillations S. Bilenky JINR(Dubna)TRIUMF June 10, 2017 The award of the 2015 Nobel Prize to T. Kajita and A. McDonald for the discovery of neutrino oscillations, which