Neutrino properties: nature, mass & CP violation
I. Schienbein LPSC
prepared together with P. Serpico (LAPTH) and A. Wingerter (LPSC)
Kick-off meeting, 12/10/2012, Annecy
Friday, October 12, 12 Facts of life with neutrinos
Friday, October 12, 12 Citation: J. Beringer et al. (Particle Data Group), PR D86, 010001 (2012) (URL: http://pdg.lbl.gov)
− p η L,B < 8.9 × 10 6 CL=90% 475 D86 − p π0 ηCitation: J. Beringer et al. (ParticleL Data,B Group),< PR 2.7 , 010001 (2012)× (URL:10 5 http://pdg.lbl.gov)CL=90% 360 − − Λπ L,B < 7.2 × 10 8 CL=90% 525 −Citation: J. Beringer et al. (Particle Data Group), PR D86, 010001 (2012)× (URL:−−6 http://pdg.lbl.gov) Λpπη L,B << 81..94 ×1010 7 CL=90%CL=90% 475 525 − − 0 L B < . × −5 ep πlightη boson LF, < 22.77 ×1010− 3 CL=90%CL=95% 360– p η − L,B < 8.9 × 10 −6 CL=90% 475 Λ−π L,B < 7.2 ××10 −83 CL=90% 525 µ light0 boson LF < 5 10−5 CL=95% – p π −η L,B < 2.7 ××10 −7 CL=90% 360 Λπ− L,B < 1.4 10− CL=90% 525 Λ− L,B < 7.2 × 10 −8 CL=90% 525 e π light boson LF < 2.7 × 10 3 CL=95% – − −7 Λ−π L,B < 1.4 ××10 −3 CL=90% 525 µHeavy− light boson Charged LeptonLF Searches< 5 10− CL=95% – e light boson LF < 2.7 × 10 3 CL=95% – Neutrino properties:− × −3 LF µ light boson± < 5 10 CL=95% – HeavyL Charged–chargedlepton Lepton Searches Mass m > 100.8GeV,CL=95%[h] Decay to ν W . What we knowHeavy± Charged in 2012 Lepton Searches ±± LL± –stablechargedheavylepton–chargedlepton ± [h] L± Mass–chargedleptonMass mm >> 102100.6GeV,CL=95%8GeV,CL=95% Decay to ν W . ± L Mass–stablechargedheavyleptonm > 100.8GeV,CL=95%[h] Decay to ν W . ± • very weakly interacting, NeutrinoL± –stablechargedheavyleptonMass Propertiesm > 102.6GeV,CL=95% Mass m > 102.6GeV,CL=95% electrically neutral, spin 1/2, SeeNeutrino the note Properties on “Neutrino properties listings” in the Particle Listings. Mass m < 2eV (tritiumdecay) tiny mass Neutrino Properties See the noteMean on “Neutrino life/mass, propertiesτ/m > 300 listings” s/eV, in CL the = Partic 90%le Listings. (reactor) Mean life/mass, τ/m > 7 × 109 s/eV (solar) See the noteMass on “Neutrinom < 2eV properties (tritiumdecay) listings” in the Particle Listings. MeanMean life/mass, life/mass, τ/m > 30015.4s/eV,CL=90% s/eV, CL = 90% (reactor) (accelerator) long lived (or stable), Mass m < 2eV (tritiumdecay)− • Magnetic moment µ
TheNeutrino following Mixing values are obtained through data analyses based on theNeutrinoCitation: 3-neutrino J. Beringer Mixing mixinget al. (Particle scheme Data described Group), PR D86 in, the 010001 review (2012) (URL: “Neutr http://pdg.lbl.gov)ino Mass,The following Mixing, andvalues Oscillations” are obtained by through K. Nakamura data analyses and S.T. bas Petced onov 2 neutrinos oscillate ⟺ mν≠0 inThethe this 3-neutrino followingReviewsin . values(2 mixingθ12)=0 are scheme obtained.857 ± described0. through024 in data the review analyses “Neutr basedino on • Mass, Mixing,2 and Oscillations”± by× K.− Nakamura5 2 and S.T. Petcov the 3-neutrino∆m21 mixing=(7. scheme50 0. described20) 10 ineV the review “Neutrino Review2 [i] Mass,in this Mixing,sin .(2 andθ23 Oscillations”) > 0.95 by K. Nakamura and S.T. Petcov in this Review.2 +0.12 × −3 2[j] ∆m32 =(2.32−0.08) 10 eV 2 sin (2θ13)=0.098 ± 0.013
HTTP://PDG.LBL.GOV Page 9 Created: 6/18/2012 15:05 Heavy Neutral Leptons, Searches for Friday, October 12, 12 HTTP://PDG.LBL.GOV Page 9 Created: 6/18/2012 15:05 ForHTTP://PDG.LBL.GOV excited leptons, see Compositeness Page Limits 9 below. Created: 6/18/2012 15:05 Stable Neutral Heavy Lepton Mass Limits Mass m > 45.0GeV,CL=95% (Dirac) Mass m > 39.5GeV,CL=95% (Majorana) Neutral Heavy Lepton Mass Limits Mass m > 90.3GeV,CL=95% (Dirac νL coupling to e, µ, τ;conservativecase(τ)) Mass m > 80.5GeV,CL=95% (Majorana νL coupling to e, µ, τ;conservativecase(τ))
NOTES
[a]Thisisthebestlimitforthemodee− → νγ.Thebestlimitfor“electron disappearance” is 6.4 × 1024 yr. [b]Seethe“NoteonMuonDecayParameters”intheµ Particle Listings for definitions and details.
[c] Pµ is the longitudinal polarization of the muon from pion decay.In standard V −A theory, Pµ =1andρ = δ =3/4. − [d]Thisonlyincludeseventswiththeγ energy > 10 MeV. Since the e νe νµ − and e νe νµ γ modes cannot be clearly separated, we regard the latter mode as a subset of the former. [e]SeetherelevantParticleListingsfortheenergylimitsused in this mea- surement. [f ]Atestofadditivevs.multiplicativeleptonfamilynumberconservation. [g]Basismodefortheτ. [h] L± mass limit depends on decay assumptions; see the Full Listings. 2 [i]Thelimitquotedcorrespondstotheprojectionontothesin (2θ23)axis 2 − 2 of the 90% CL contour in the sin (2θ23) ∆m32 plane. 2 [j]Thesignof ∆m32 is not known at this time. The range quoted is for the absolute value.
HTTP://PDG.LBL.GOV Page 10 Created: 6/18/2012 15:05 Neutrinos oscillate!
Friday, October 12, 12 Neutrino oscillations
Flavor basis: • 3 neutrino states → 3 masses m1, m2 , m3 ⌫ , ⌫ , ⌫ {| ei | µi | ⌧ i} • States with definite masses (mass eigenstates) in general do not coincide with flavor states Mass basis:
⌫1 , ⌫2 , ⌫3 • Quantum mechanics: {| i | i | i} States with same quantum numbers can mix, as it happens for the quarks d0 d CKM s0 = V s 0 1 0 1 • The mixing matrices V are 3x3 unitary b0 b matrices @ A @ A ‣ CKM = Cabibbo-Kobayashi-Maskawa ⌫e ⌫1 ⌫ = V PMNS ⌫ ‣ PMNS = Pontecorvo; 0 µ1 0 21 Maki-Nakagawa-Sakata ⌫⌧ ⌫3 @ A @ A
Friday, October 12, 12 Neutrino oscillations
• Consider 2 flavor case: ‣ for simplicity ‣ dominant oscillations are well- described by 2-flavor mixing ⌫ = cos ✓ ⌫ +sin✓ ⌫ • Flavor and mass eigenstates connected | µi | 1i | 2i by a 2x2 rotation matrix ⌫ = sin ✓ ⌫ + cos ✓ ⌫ | ⌧ i | 1i | 2i
Neutrino propagation:
νμ created at t=0 with 3-momentum p ⌫(0) = ⌫µ = cos ✓ ⌫1 +sin✓ ⌫2 • | i | i | i | i iE t iE t Neutrino state at time t ⌫(t) = e 1 cos ✓ ⌫ + e 2 sin ✓ ⌫ • | i | 1i | 2i Different mass components have different m2 m2 • E = p2 + m2 p + i p + i ]a) energy i i ' 2p ' 2E q
Friday, October 12, 12 Neutrino oscillations
Oscillation probability:
P (⌫ ⌫ ; t)= ⌫ ⌫(t) 2 µ ! ⌧ |h ⌧ | i| iE t iE t 2 = sin ✓ ⌫ + cos ✓ ⌫ e 1 cos ✓ ⌫ + e 2 sin ✓ ⌫ |{ h 1| h 2|}{ | 1i | 2i}| 2 2 iE t iE t 2 = cos ✓ sin ✓ e 2 e 1 | | = 2 cos2 ✓ sin2 ✓ 1 cos[(E E )t] { 2 1 } 2 2 2 m 2 2 2 =sin 2✓ sin t m = m2 m1 4E As function of distance L=c*t=t:
m2 P (⌫ ⌫ ; L)=sin2 2✓ sin2 L µ ! ⌧ 4E L/E determines 2 2 2 2 L(km) =sin 2✓ sin 1.27 m (eV ) sensitivity to E(GeV) 2 Δm
Friday, October 12, 12 Neutrino oscillations 3 flavor oscillations:
atmospheric solar
cross mixing
^J)
Friday, October 12, 12 Neutrino state cross-composition
^H) The final 3 flavor mixing scheme"
Results inThe the final 33 flavor flavor mixing scheme mixing" scheme
Neutrino state cross-composition
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^H) 58)6%"7&$0$()U)53%&-)HIJH) JH`)
Discovery of a non-zero angle θ13!
Friday, October 12, 12 Leptonic CP violation: δCP ≠ 0?
• θ13 ≠ 0 : necessary condition for leptonic CP violation
‣ θ13 = 0: effective 2 flavor mixing ‣ CP violation only with unitary 3x3 matrices (or larger) • Dirac-neutrinos: 1 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
Friday, October 12, 12 Neutrinos and the Standard Model
Friday, October 12, 12 Neutrinos and the Standard Model
• Neutrino oscillations: The Standard Model ‣ at least two massive neutrino states
‣ why should neutrinos be massless anyway? Particles Spin SU(3)C SU(2)L U(1)Y
(no symmetry) uL 1 1 Q = 2 323 dL 3c 4 1 4 In the original SM, neutrinos are massless uR 2 31 3 • c 1 ≠2 ⇒ oscillation results = physics beyond the SM dR 2 313 ‹L 1 L = 2 12-1 However, massive neutrinos possible by a eL • 3c 4 1 ‹R 2 1 1 0 minimal extension of the SM: c 1 eR 2 112 + H = 0 1 2 1 ‣ right-handed neutrino 0 3– 4 Gµ 1 810 ‣ gauge singlet (“sterile neutrino”) a Wµ 1 130 11 ‣ can be a Dirac fermion like the electron Bµ 1 0
★ mass term via Yukawa interaction with
Higgs boson (Higgs mechanism) 3/20
★ neutrino masses of order meV: tiny(!) Yukawa couplings
Friday, October 12, 12 Neutrinos and the Standard Model • Neutrino oscillations: ‣ at least two massive neutrino statesThe Standard Model
‣ why should neutrinos be massless anyway? (no symmetry) Particles Spin SU(3)C SU(2)L U(1)Y uL 1 1 Q = 2 323 In the original SM, neutrinos are massless dL • 3c 4 1 4 ⇒ oscillation results = physics beyond the SM uR 2 31 3 c 1 ≠2 dR 2 313 Conversely, neutrino only fermion in the SM ‹L 1 • L = 2 12-1 without electric charge: eL 3c 4 1 ‹R 2 1 1 0 0 0 c 1 ‣ can be its own anti-particle (like γ, Z ,π ,η) eR 2 112 + H = 0 1 2 1 M 0 ‣ it’s called Majorana-Neutrino (ν ) if it is its 3 4 M M c – own anti-particle: ν =(ν ) Gµ 1 810 a Wµ 1 130 ‣ non-minimal extension of the SM: Bµ 1 110
★ mass term in � can be a gauge singlet ⇒ heavy mass term possible 3/20 [not related to the Higgs mechanism]
★ seesaw mechanism can explain tiny masses
Friday, October 12, 12 Neutrinos and the Standard Model
Why the neutrino mass is so small ?"
Why the Whyneutrino the neutrino mass is mass so small is so ?small" ?"
& m() 3 ) # & 1 # $ ! ( $ 12 ! $ & m(&) 3!) m()#) & # 1& #1 # % m(top$ quark$ ) " % 3!3'(10 ! " $ $ ! $ ! ( $ 12 ! 12 ! m(top%quarkm(top )quark% )3"'10% 3'"10 " o#0%M,) % "
0'7) o#0%M,) o#0%M,) 2)
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-"3$(',) 2) 0'7) d&'M(Q,M.=)x0'0A&70=))))))))))))))))))))))))))) H 2) -"3$(',) H -"3$(',) \""U,0Q)+"/40'&,+) O"--U+0''=)E0+('7=)\-0',M.)d&'M(Q,M.=)x0'0A&70=))))))))))))))))))))))))))) \""U,0Q)+"/40'&,+)d&'M(Q,M.=)x0'0A&70=)))))))))))))))))))))))))))O"--U+0''=)E0+('7=)\-0',M.) \""U,0Q)+"/40'&,+) O"--U+0''=)E0+('7=)\-0',M.)
2 2
2 d0,,)*"wp/ d0,,)*"wp/ mq mq Z:)Q")&'3#$)+ )0'7)+Z:)Q")&'3#$)+*+ !])0'7)+)&,)#,"72=)Y)*+$(3)&,)#,"72=) d0,,)*"wp/ mmq ! !] Y) $(3 m" ! " Z:)Q")&'3#$)+!])0'7)+J_)Y)*+$(3)&,)#,"72=) m" ! Q")A"$)+m j)JIJ_)Q")A"$)+O"w) !j)JI O"w) mN Q")A"$)+!N j)JIJ_)O"w) mN ! ! 3 ! ! 2 ! 3 ! 3 2 ! 2
F4&,),#AA",$,)$40$)34.,&/,)(:)'"#$%&'()+0,,)/(#-7)?") F4&,),#AA",$,)$40$)34.,&/,)(:)'"#$%&'()+0,,)/(#-7)?")F4&,),#AA",$,)$40$)34.,&/,)(:)'"#$%&'()+0,,)/(#-7)?")%"-0$"7)$()34.,&/,)(:)O%0'7)B'&m/01('h))) %"-0$"7)$()34.,&/,)(:)O%0'7)B'&m/01('h)))A"'"%01(')%"-0$"7)$()34.,&/,)(:)O%0'7)B'&m/01('h))) 58)6%"7&$0$()U)53%&-)HIJH) J]^) A"'"%01(')A"'"%01(') 58)6%"7&$0$()U)53%&-)HIJH)58)6%"7&$0$()U)53%&-)HIJH) J]^) J]^)
Friday, October 12, 12 Motivation Specific Example All Models Small Groups Why Are We Not HappyThe With SM the Standard with Model? massive neutrinos
(i) Too many free parameters The Standard Model
Gauge sector: 3 couplings g 0, g, g3 3 Quark sector: 6 masses, 3 mixing angles, 1 CP phase 10 Particles Spin SU(3)C SU(2)L U(1)Y
Lepton sector: 6 masses, 3 mixing angles and 1-3 phases 10 uL 1 1 Q = 2 323 dL Higgs sector: Quartic coupling and vev v 2 3c 4 1 4 uR 2 31 3 ✓ parameter of QCD 1 c 1 ≠2 dR 2 313 Motivation Specific Example All Models Small Groups 26 ‹L 1 L = 2 12-1 Why Are We Not Happy With the Standard Model? eL 3c 4 1 ‹R 2 1 1 0 c 1 eR 2 112 (ii) StructureAkın of Wingerter, gauge symmetry LPSC Grenoble Tribimaximal Mixing From Small Groups + H = 0 1 2 1 0 ? ? ? ? 3 4 SU(3)c SU(2)L U(1)Y SU(5) SO(10) E6 E8 – ⇥ ⇥ ⇢ ⇢ ⇢ ⇢ Gµ 1 810 a Why 3 di↵erent coupling constants g 0, g, g3? Wµ 1 130 Bµ 1 110
(iii) Structure of family multiplets
? (3,2)1/3 +(3,1)-4/3 +(1,1)-2 +(3,1)2/3 +(1,2)-1 +(1,1)0 = 16 Q u¯ e¯ dL¯ ⌫¯ Fits nicely into the 3/20 16-plet of SO(10)
Akın Wingerter, LPSC Grenoble Tribimaximal Mixing From Small Groups
Friday, October 12, 12 Majorana or Dirac? That is here the question
Friday, October 12, 12 Nature of neutrinos: Majorana or Dirac?
• Lepton number: ⌫e + n e + p ‣ L=1 for neutrinos ! L =1+0=1+0
‣ L = -1 for anti-neutrinos Lepton number conserved; Reaction has been observed ‣ L not conserved for Majorana-Neutrinos
⌫e =¯⌫e • The second reaction should be possible if ⌫e =¯⌫e ‣ Not observed! Naive conclusion: ⌫¯ + n e + p electron-neutrino is not Majorana! e ! L = 1+0=1+0 6 ‣ Conclusion valid only for mν≠0! Lepton number not conserved; Otherwise: Reaction has not been observed
‣ neutrino (h=-1)
‣ anti-neutrino (h=+1)
‣ and vertex with h=+1 might be forbidden
Friday, October 12, 12 Neutrinoless double-beta decay
p
I n Vertex I : n → p + e +¯⌫e ν¯ e− Vertex II : νe + n → p + e
p Together : 2 n → 2p +2e ν
n L = 0 ≠ 0 + 2 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
Friday, October 12, 12 Enigmatic neutrino masses
Friday, October 12, 12 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! (14 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
Friday, October 12, 12 Neutrino masses Why the neutrino mass is so small ?" Oscillations: 2 2 2 3 2 & m() ) # & 1 # m32 = m3 m2 =2.3 10 eV $ 3 ! ⇥ $ ! ( $ 12 ! 2 2 2 5 2 m(top quark) % 3'10 " m = m m =7.5 10 eV % " 21 2 1 ⇥ o#0%M,)
Oscillations in matter: m2 >m1 0'7) 2) H -"3$(',) d&'M(Q,M.=)x0'0A&70=))))))))))))))))))))))))))) 2 \""U,0Q)+"/40'&,+) O"--U+0''=)E0+('7=)\-0',M.) Sign of m32 unknown: normal or inverted hierarchy 2
d0,,)*"wp/ m q Z:)Q")&'3#$)+ )0'7)+ *+ )&,)#,"72=) m3 m2 m ! !] Y) $(3 " J_) m1 Q")A"$)+ j)JI O"w) mN !
m2 ! 3 ! 2 m1 m3
Mass m of heaviest neutrino: F4&,),#AA",$,)$40$)34.,&/,)(:)'"#$%&'()+0,,)/(#-7)?") m2 m2, m 50 meV 32 ' ' %"-0$"7)$()34.,&/,)(:)O%0'7)B'&m/01('h))) A"'"%01(') ENIGMASS: Fermion masses over 14 orders of magnitude 58)6%"7&$0$()U)53%&-)HIJH) J]^)
Friday, October 12, 12 Flavor symmetries: Fun for theorists?
Friday, October 12, 12 Introduction T7 Model NLO Which Group? Conclusions
Neutrino Mixing MatrixNeutrino mixing
„ Neutrinos have mass and the di↵erent flavors can mix Super-Kamiokande Collaboration, Y. Fukuda et al.,“Evidenceforoscillationofatmosphericneutrinos,” Phys. Rev. Lett. 81 (1998) 1562–1567, hep-ex/9807003 SNO Collaboration, Q. R. Ahmad et al.,“Directevidenceforneutrinoflavortransformationfrom neutral-current interactions in the Sudbury Neutrino Observatory,” Phys. Rev. Lett. 89 (2002) 011301, nucl-ex/0204008
„ Charged lepton and neutrino mass matrices cannot be simultaneously diagonalized ˆ ˆ M`+ = DLM`+ DR† , M⌫ = ULM⌫UR†
„ Pontecorvo-Maki-Nakagawa-Sakata matrix B. Pontecorvo, “Mesonium and antimesonium,” Sov. Phys. JETP 6 (1957) 429 Z. Maki, M. Nakagawa, and S. Sakata, “Remarks on the unified model of elementary particles,” Prog. Theor. Phys. 28 (1962) 870–880
⌫e ⌫1 ⌫ = D U† ⌫ 0 µ1 L L 0 21 ⌫⌧ ⌫3 UPMNS @ A @ A Friday, October 12, 12 Akın Wingerter, LPSC Grenoble| {z A} Minimal Model of Neutrino Flavor Neutrino mixing
mismatch between flavour and mass basis expressed via mixing matrix U
slk ≡ Sin θlk , clk≡ Cos θlk
2 2 2 m m32 m31 21 i c12 s12 0 10 0 c13 0 e s13 s12 c12 0 0 c23 s23 010 0 10 i 10 1 0 s c e s13 0 c13 001 23 23 @ A@ A@ A 2-3 sector: atmospheric 3-flavour effects (& CP) 1-2 sector: “solar ν problem” anomaly → consistent with suppressed by the smallness → LMA & MSW in the Sun maximal mixing (SK, LBL dis.) of θ13 and Δm212<< Δm312 Radiochemical, SNO, Reactor (dis)+LBL (app.) Borexino, SK, KamLAND
dominant oscillations are well described by effective two-flavour mixing
Friday, October 12, 12 Introduction T7 Model NLO Which Group? Conclusions Tribimaximal Mixing 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) 167, hep-ph/0202074
2/31/p30 U =? U = -1/p61/p3 -1/p2 PMNS HPS 0p 1 -1/p61/p31/p2 @ A , ✓ = 35.26 , ✓ = 45 , ✓ =0 ! 12 23 13
„ Agreement still quite good for ✓12, ✓23,but✓13 =0 excluded @5
Forero et al, 1205.4018, DAYA-BAY Collaboration, 1203.1669, RENO Collaboration, 1204.0626 Parameter Tribimaximal Global fit 1 Daya Bay Reno
✓ 35.26 33.40 35.37 - - 3 12 ✓ 45.00 41.55 49.02 - - 3 23 ✓ 0.00 8.53 9.80 8.8 9.8 7 13
Akın Wingerter, LPSC Grenoble A Minimal Model of Neutrino Flavor Friday, October 12, 12 Introduction T7 Model NLO Which Group? Conclusions Post-Daya Bay ConfusionFun for theorists
• „RegularRegular pattern patter ofU PMNSPMNS -matrix:is suggestive of a family symmetry
Introduction T7 Model NLO Which Group?2/31Conclusions/p30 210 U =? U = -1/p61/p3 -1/p2 111 PMNS HPS 0p 1 ⇠ 0 1 Discrete Flavor Symmetries-1/p61/p31/p2 111 @ A @ A „ Daya„ bayIntroduce and Reno relations rule out tribimaximal between families Mixing of quarks and leptons • Suggestive of a discrete family symmetry. „IntroduceWhat„ are relationBut our which options? between discrete families group of quarks do we and take leptons: for the family symmetry? Give up family symmetries? Some remarks towards the end . . .
Look for groups that give ✓13 =0 R. d. A. Toorop, F. Feruglio, and C. Hagedorn,6 “Discrete Flavour Symmetries in Light of T2K,” Phys.Lett. B703 (2011) 447–451, 1107.3486 Keep TBM and calculate higher corrections This talk! !
Akın Wingerter, LPSC Grenoble A Minimal Model of Neutrino Flavor
Friday, October 12, 12 Akın Wingerter, LPSC Grenoble A Minimal Model of Neutrino Flavor Motivation Specific Example All Models Small Groups Motivation Specific Example All Models Small Groups Why Are We Not Happy With the Standard Model? Why Are We Not Happy With the Standard Model?
Questions(vi) Light neutrinos and texture of Yukawa couplings (v) Mass Hierarchies and Yukawa Textures 3 Why are neutrinos so light? up-quark mass 2 10 GeV top-quark mass 172.3 GeV ⇠ ⇥ $ ⇠ Yukawa couplingWhy of is top mixing1, but in why the are quark the other sector quarks so so different light? from mixing m2 in 10the2 lepton10 5 eV,sector?m < 2 eV • ⇠ ⌫ ⇠ ⌫ P Minimal mixing in quark sector Maximal mixing in lepton sector Minimal mixing in the quark sector: Maximal/Large mixing in lepton sector:
Vud Vus Vub 0.97 0.22 0.00 Ue1 Ue2 Ue3 0.80.50.0 V = V V V 0.22 0.97 0.04 UPMNS = Uµ1 Uµ2 Uµ3 -0.40.60.7 CKM 0 cd cs cb 1 ' 0 1 0 1 ' 0 1 Vtd Vts Vtb 0.00 0.04 0.99 U⌧1 U⌧2 U⌧3 0.4 -0.60.7 @ A @ A @ A @ A θ13 = 9.3°:
0.80.55 0.16z⇤ U Akın= Wingerter,0.4 LPSC0. Grenoble1z 0.6 Tribimaximal0.06z Mixing0 From.7 Small,z Groups= ei PMNS 0 1 Akın Wingerter, LPSC Grenoble Tribimaximal Mixing From Small Groups 0.4 0.1z 0.6 0.06z 0.7 @ A
• Which discrete group to take? [S3,A4, S 4, T 7,Δ(96),...] ‣ Many discrete groups can give tribimaximal mixing (ruled out now) K. M. Parattu, A. Wingerter, “Tribimaximal Mixing From Small Groups”,PRD84(2011)013011
‣ Look for groups that give θ13 ≠ 0? (Still many possibilities!) C. Luhn, K. M. Parattu, A. Wingerter, “A Minimal Model of Neutrino Flavor”,1210.1197
‣ Keep tribimaximal mixing at leading order and include higher dimensional ops.? • Need guiding principle; More fundamental theory which “predicts” flavor symmetry
Friday, October 12, 12 Who does not believe in sterile neutrinos?
Friday, October 12, 12 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 58)6%"7&$0$()U)53%&-)HIJH) JHc) • Mass scale of (some) these states? ‣ Order eV: modifies neutrino oscillations (more freedom to explain certain puzzles) ‣ Order 1015 GeV: seesaw, GUTs (theoretically more appealing?)
Friday, October 12, 12 58)6%"7&$0$()U)53%&-)HIJH) JHc) Sum puzzles
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 1112.0907 ?!)
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 anti-νe flux predictions from reactors require to convert measured e-spectra from 235U, 239Pu, 241Pu into ν-spectra: recent calculation yield 3% higher fluxes (Mueller et al., 1101.2663, P. Huber, 1106.0687) 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, 1106.3244)
Friday, October 12, 12 Fine, but maybe the “simple” three flavor mixing scheme is too simple?"
Sterile neutrinos??) LSND
requires a 3rd Δm2
58)6%"7&$0$()U)53%&-)HIJH) JHa)
Friday, October 12, 12 MiniBooNE νe results
Affaire à suivre….) 58)6%"7&$0$()U)53%&-)HIJH) J]I)
Friday, October 12, 12 Sterile neutrinos and cosmology
Friday, October 12, 12 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+1 (3+2) models
• Big Bang Nucleosynthesis (BBN)
‣ excludes Neff = 5, barely consistent with Neff = 4
‣ small preference for Neff ≥ 3 (1 σ) G. Mangano, P. Serpico, PLB701(2011)296
• CMB data have a small preference for Neff ≥ 3
Friday, October 12, 12 Early universe would produce sterile neutrinos
• Are sterile ν’s fitting the lab. anomalies the cause of Neff>3? Most likely not!
‣ In 3+1 models (fully thermalized) m4<0.48 eV (95% CL) (vs. about 1 eV expected from Lab)
‣ In 3+2 models (fully thermalized) m4 + m5<0.9 eV (95% CL) (vs. about 1.5 eV expected from Lab)
• What if Lab confirms eV-scale sterile neutrinos? ‣ One would need to go to much more contrived cosmologies!
Friday, October 12, 12 Concluding wishlist
Friday, October 12, 12 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 > m1 from MSW effect] • mixing matrix (PMNS-matrix): ‣ more precise measurement of mixing angles ‣ is the PMNS matrix unitary? ‣ is there leptonic CP violation?
Friday, October 12, 12 Merci!
Friday, October 12, 12 58)6%"7&$0$()U)53%&-)HIJH) ]H) Friday, October 12, 12 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
•)7&r"%"'$)3($"'10-):(%)7&r"%"'$)k0C(%,)*$4"%")0%")'()+#(',)(%)$0#)&')(%7&'0%.)+0S"%2) •)$4")"r"/1C")3($"'10-)0r"/$,)$4")k0C(%)3%(30A01(')&')+0S"%) •)+0S"%)"r"/1C")3($"'10-,)40C")(33(,&$"),&A',):(%)'"#$%&'(,)0'7)0'1'"#$%&'(,) 58)6%"7&$0$()U)53%&-)HIJH) ^`)
Friday, October 12, 12 Expected NuSOnG Event Rates (5 yr Run)
x100 NuTeV
x20 CHARM II x40 CHARM II Expected NuSOnG Event Rates (5 yr Run)
Leptonic Precision Observables x100 NuTeV x20 CHARM II Neutrino interactions A unique opportunity for px4re0c CisHiAoRnM m IIeasurements in NC ES: y-spectra and total x-secs these channels! - NuSOnG will measure: νµ νµ νµ µ
Z W leptonic: ● NC ES A unique opportunity for pre- cision measu-remen- ts in very clean eGoal: e e νe 6 SM physics, these channels! n_µ-ES/IMD at but lower - νµ νµ ν0µ .7% precision! µ statistics ● CC QE (IMD) Z W
- - - ν ● NC DIS e e e e 6
● CC DIS 7 5
Friday, October 12, 12 Long Baseline experiments
Long Baseline Experiment • Long Baseline experiments
ν L = O(A few 100 km)
Near detector: NearbyDet. FarawayDet.Far detector: neutrinomeasurements: flux – observation observation of charged of and charged and neutrino– beamneutrino energy flux spectrum neutralneutral current reactionscurrent reactions cross sections– neutrino before energy oscillation spectrum – cross sections for the various reactions
LBL BeamLBL beam Place place L [km]
K2K 12 GeV protonK2K 12 GeVKEK → SKKEK SK250 250 km 1.4 1.4 GeV H2OWater 1999-2004running νμ → proton νμ, νe ; θ13, δ 2 T2K 50 GeV MINOSproton NUMIJParc → SKFermilab 295 732 km ~0.6 3, 7, H2OIron 20052010- Δm23 , θ23 → Sudan 15 GeV νA x-secs. ICARUS CNGS CERN SPS 732 km 17 GeV Argon 2005 NC/CC ratio MINOS NuMI FNAL → Soudan →735 3, 7, 15 Fe 2005-2014 νμ ν ; θ ν /OPERA Gransasso Lab. Iron , e 13; S OPERA CNGS CERN → GS 732 17 Pb 2008-2012 ντ
Note: νμ, νe ; θ13, δ NOvA NuMI FNAL → Ash River 810 ~2 liquid scint. 2013- mass hierarchy K2K: νµ disappearance • νA x-secs. MINOS: • Friday, October 12, 12 – measurements of NC/CC ratio
– ντ , νe appearance and νµ disappearance
OPERA/ICARUS: ντ , νe appearance • Neutrino cross sections
Flux ⊗ Cross section ⊗ Nuclear effects
current precision: ca. 30%
need to improve this for precision measurements of the MNS mixing matrix!
Friday, October 12, 12 Neutrino nucleon interactions: Overview
Resonance production (RES) • ν(¯ν) l−(l+) Charged Current (CC): − + ±,0 ± ν(¯ν)+N l (l )+N +π q π ,0 → Neutral Current (NC): R ν(¯ν)+N ν(¯ν)+N + π±,0 N N " → Deep inelastic scattering (DIS) • ν(¯ν) l−(l+)
CC: ν(¯ν)+N l−(l+)+X q → NC: ν(¯ν)+N ν(¯ν)+X X → N Neutrino nucleon interactions Quasi-elastic scattering (QE) • ν(¯ν) l−(l+)
CC: ν(¯ν)+N l−(l+)+N " q → NC: ν(¯ν)+N ν(¯ν)+N " → N N "
Need these cross sections on free nucleons and nuclear targets •
Friday, October 12, 12 Neutrino nucleon interactions: Overview
Resonance production (RES) • ν(¯ν) l−(l+) Charged Current (CC): − + ±,0 ± ν(¯ν)+N l (l )+N +π q π ,0 → Neutral Current (NC): R ν(¯ν)+N ν(¯ν)+N + π±,0 N N " → Deep inelastic scattering (DIS) • ν(¯ν) l−(l+)
CC: ν(¯ν)+N l−(l+)+X q → NC: ν(¯ν)+N ν(¯ν)+X X → N Neutrino nucleon interactions Quasi-elastic scattering (QE) • ν(¯ν) l−(l+)
CC: ν(¯ν)+N l−(l+)+N " q → Neutrino nucleon interactions: Overview NC: ν(¯ν)+N ν(¯ν)+N " → N N " Resonance production (RES) • ν(¯ν) l−(l+) Charged Current (CC): Need these cross sections on free nucleons and− nuclear+ targets±,0 • ± ν(¯ν)+N l (l )+N +π q π ,0 → Neutral Current (NC): R ν(¯ν)+N ν(¯ν)+N + π±,0 N N " → Deep inelastic scattering (DIS) • ν(¯ν) l−(l+)
CC: ν(¯ν)+N l−(l+)+X q → NC: ν(¯ν)+N ν(¯ν)+X X → N Friday, October 12, 12 Quasi-elastic scattering (QE) • ν(¯ν) l−(l+)
CC: ν(¯ν)+N l−(l+)+N " q → NC: ν(¯ν)+N ν(¯ν)+N " → N N "
Need these cross sections on free nucleons and nuclear targets • Neutrino nucleon interactions: Overview
Resonance production (RES) • ν(¯ν) l−(l+) Charged Current (CC): − + ±,0 ± ν(¯ν)+N l (l )+N +π q π ,0 → Neutral Current (NC): R ν(¯ν)+N ν(¯ν)+N + π±,0 N N " → Deep inelastic scattering (DIS) • ν(¯ν) l−(l+)
CC: ν(¯ν)+N l−(l+)+X q → NC: ν(¯ν)+N ν(¯ν)+X X → N Neutrino nucleon interactions Quasi-elastic scattering (QE) • ν(¯ν) l−(l+)
CC: ν(¯ν)+N l−(l+)+N " q → Neutrino nucleon interactions: Overview Overview NC: ν(¯ν)+N ν(¯ν)+N " → N N " Resonance production (RES) • ν(¯ν) l−(l+) Charged Current Current (CC): (CC): Need these cross sections on free nucleons and−− nuclear++ targets±±,,00 • ± 0 ν(¯ν)+)+NN ll ((ll )+)+NN++ππ q π ,0 →→ Neutral Current Current (NC): (NC): R ν(¯ν)+)+NN νν(¯(¯νν)+)+NN ++ ππ±±,,00 N N " →→ Deep inelastic scattering (DIS) • ν(¯ν) l−(l+)
CC: νν(¯(¯νν)+)+NN ll−−((ll++)+)+XX q →→ NC: νν(¯(¯νν)+)+NN νν(¯(¯νν)+)+XX X →→ N Friday, October 12, 12 Quasi-elastic scattering (QE) • − ν(¯ν) l−(l+)
CC: νν(¯(¯νν)+)+NN ll−−((ll++)+)+NN"" q →→ NC: νν(¯(¯νν)+)+NN νν(¯(¯νν)+)+NN"" →→ " N N "
Need these cross sections on free nucleons andand nuclearnuclear targets targets • Neutrino nucleon interactions: Overview
Resonance production (RES) • ν(¯ν) l−(l+) Charged Current (CC): − + ±,0 ± ν(¯ν)+N l (l )+N +π q π ,0 → Neutral Current (NC): R ν(¯ν)+N ν(¯ν)+N + π±,0 N N " → Deep inelastic scattering (DIS) • ν(¯ν) l−(l+)
CC: ν(¯ν)+N l−(l+)+X q → NC: ν(¯ν)+N ν(¯ν)+X X → N Neutrino nucleon interactions Quasi-elastic scattering (QE) • ν(¯ν) l−(l+)
CC: ν(¯ν)+N l−(l+)+N " q → Neutrino nucleon interactions: Overview Overview NC: ν(¯ν)+N ν(¯ν)+N " → N N " Resonance production (RES) • ν(¯ν) l−(l+) Need these cross sections on freeCharged nucleons Current Currentand (CC): (CC):nuclear targets −− ++ ±±,,00 Need these cross sections on • ±,0 ν(¯ν)+)+NN ll ((ll )+)+NN++ππ q π →→ free nucleons and nuclear targets Neutral Current Current (NC): (NC): R ν(¯ν)+)+NN νν(¯(¯νν)+)+NN ++ ππ±±,,00 N N " →→ Deep inelastic scattering (DIS) • ν(¯ν) l−(l+)
CC: νν(¯(¯νν)+)+NN ll−−((ll++)+)+XX q →→ NC: νν(¯(¯νν)+)+NN νν(¯(¯νν)+)+XX X →→ N Friday, October 12, 12 Quasi-elastic scattering (QE) • − ν(¯ν) l−(l+)
CC: νν(¯(¯νν)+)+NN ll−−((ll++)+)+NN"" q →→ NC: νν(¯(¯νν)+)+NN νν(¯(¯νν)+)+NN"" →→ " N N "
Need these cross sections on free nucleons andand nuclearnuclear targets targets • NeNeuutrtriinnoo crcroossss sseectctiioonnss aatt aatmtmoosspphheerriicc nn eenneerrggiieess
Paschos,JYY,PRD65(2002)033002
P. Lipari, hep-ph/0207172
Friday, October 12, 12 What if Lab confirms eV-scale steriles?
One would need to go to contrived (hence exciting?!) cosmologies
Introduce chemical potentials of O(0.1) 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., 1108.4136
Fortunately, progress is forthcoming...
Friday, October 12, 12