7 KIT, 6-10 February ’12 Beyond the Standard Model Neutrino Masses & Mixings 2012 Guido Altarelli Universita’ di Roma Tre CERN
In the last 2 decades data on ν oscillations have added some (badly needed) fresh experimental input to particle physics Schwetz ν masses are not all vanishing but they are very small This suggests that ν ' s are Majorana particles and that the lepton number L is not conserved ν mixing angles follow a different pattern from quark mixings This also is probably related to the Majorana nature of ν ’s
ν Oscillations Imply Different ν Masses ν e : same weak isospin doublet as e - flavour mass ν e ν e ν 1 e - = U + ν µ ν 2 W - ν τ ν 3 U = U PMNS U: mixing matrix Pontecorvo ν e = cos θ ν 1 + sin θ ν 2 Maki, Nakagawa, Sakata e.g 2 flav. Stationary source: ν µ = -sin θ ν 1 + cos θ ν 2 Stodolsky ν 1, 2 : different mass, different x-dep: ν a (x)=e ip a x ν a 2 =E 2 -m a 2 p a P( ν e <-> ν µ ) = |< ν µ (L)| ν e >| 2 =sin 2 (2 θ ) . sin 2 ( Δ m 2 L/4E) At a distance L, ν µ from µ - decay can produce e - via charged weak interact's
Evidence for solar and atmosph. ν oscillations confirmed on earth by K2K, KamLAND, MINOS, T2K... Δ m 2 values: Δ m 2 atm ~ 2.5 10 -3 eV 2 , Δ m 2 sol ~ 8 10 -5 eV 2 and mixing angles measur’d: θ 12 (solar) large θ 23 (atm) large~ maximal θ 13 (T2K, MINOS, DOUBLE CHOOZ) small A 3rd frequency? A persisting confusion: LSND+MiniBooNE Sterile (no weak int’s) neutrinos?
Are sterile ν ’s coming back? A number of “hints” (they do not make an evidence but pose an experimental problem that needs clarification) • LSND and MiniBoone • Reactor flux & anomaly • Gallium ν e disappearance vs ν ebar reactor limits If all true (unlikely) then need at least 2 sterile ν ’s Important information also from • Neutrino counting from cosmology
MiniBooNE Unidentified excess at low energy
The reactor anomaly Lasserre new old Systematic errors not shown in this figure (estimated in paper)! Certainly of the same order of the shift. They could well be larger than estimated
Depends on assumed cross section! Do not really large angle small angle agree!
This is the compromise realized in the fit
Cosmology could accept one sterile neutrino The bound from nucleosynthesis is the most stringent (assuming thermal properties at decoupling) BBN: N s < 1.54 (95% CL) [ M. Pettini, et al, arXiv:0805.0594]
From other than nucleosynthesis: WMAP+BAO+H 0 N s =1.34±0.87 Komatsu et al WMAP only
In any case only a small leakage from active to sterile neutrinos is allowed by present data Most common EW scale BSM do not contain sterile neutrinos. A sterile neutrino would probably be a remnant of some hidden sector or of gravity. So would be a great discovery.
ν e Still the main framework: 3- ν Models ν e ν 1 e - W - = U + ν µ ν 2 U = U PMNS ν τ ν 3 Pontecorvo flavour mass Maki, Nakagawa, Sakata δ : CP violation In basis where e - , µ - , τ - are diagonal: c 13 0 s 13 e -i δ 1 0 0 c 12 s 12 0 U = ~ 0 c 23 s 23 -s 12 c 12 0 0 1 0 -s 13 e i δ 0 c 13 0 - s 23 c 23 0 0 1 s = solar: large CHOOZ: |s 13 | small c 13 c 12 c 13 s 12 s 13 e -i δ ~ ... ... c 13 s 23 ... ... c 13 c 23 atm.: ~ max (some signs are conventional) In general: U = U +e U ν
Recent Fits (2011)
Recent results on θ 13 (T2K, MINOS, DOOBLE CHOOZ) Normal Hierarchy Inverse Hierarchy Cabibbo CHOOZ T2K: 6 ν µ -> ν e events seen 1.5 ± 0.3 expected for θ 13 = 0 0.03 < sin 2 2 θ 13 < 0.28 for NH, 90%cl MINOS: 62 ν µ -> ν e events seen 49.6 ± 7.5 expected 0 < sin 2 2 θ 13 < 0.12 for NH, 90%cl DOUBLE CHOOZ: sin 2 2 θ 13 = 0.085±0.051
Fogli et al ‘11 solid: old fluxes dashed: new fluxes
The near future of θ 13 Fogli Schwetz
ν oscillations measure Δ m 2 . What is m 2 ? Δ m 2 atm ~ 2.5 10 -3 eV 2 =(0.05 eV) 2 ; Δ m 2 sun ~ 8 10 -5 eV 2 =(0.009 eV) 2 End-point tritium • Direct limits β decay (Mainz, Troitsk) m " ν e" < 2.2 eV Future: Katrin, MARE m " ν µ " < 170 KeV 0.2 eV sensitivity m " ντ " < 18.2 MeV (Karsruhe) • 0 νββ m ee < 0.2 - 0.7 - ? eV (nucl. matrix elmnts) Evidence of signal? Klapdor-Kleingrothaus Ω ν h 2 ~ Σ i m i /94eV • Cosmology (h 2 ~1/2) Σ i m i < 0.2-0.7 eV (dep. on data&priors) WMAP, SDSS, 2dFGRS, Ly- α Any ν mass < 0.06 - 0.23 - 2.2 eV
By itself CMB (eg WMAP) is only mildly sensitive to Σ i m i Only with Large Scale Structure the limit becomes stronger. Melchiorri best estimate Σ m ν < 0.58 eV (95% CL) WMAP +BAO+ Hubble constant Komatsu et al, 2009
Most of the Universe is not made up of Dark Matter atoms: Ω tot ~1, Ω b ~0.045, Ω m ~0.27 WMAP, BAO…. Most is Dark Matter and Dark Energy Most Dark Matter is Cold (non relativistic at freeze out) Significant Hot Dark matter is disfavoured Hot Dark Matter does not “stick” enough at short distances (Galaxy haloes...) Neutrinos are not much cosmo-relevant: Ω ν < 0.015
Neutrino masses t Log 10 m/eV are really special! 10 b τ c m t /( Δ m 2 atm ) 1/2 ~10 12 s 8 µ d u Massless ν ’s? 6 e • no ν R 4 • L conserved Small ν masses? 2 • ν R very heavy WMAP 0 Upper limit on m ν • L not conserved ( Δ m 2 atm ) 1/2 ( Δ m 2 sol ) 1/2 -2 Very likely: KamLAND ν ’s are special as they are Majorana fermions
Are neutrinos Dirac or Majorana fermions? Under charge conjugation C: particle <--> antiparticle For bosons there are many cases of particles that coincide (up to a phase) with their antiparticle: π 0 , ρ 0 , ω , γ , Ζ 0 ..... A fermion that coincides with its antiparticle is called a Majorana fermion Are there Majorana fermions? Neutrinos are probably Majorana fermions
The fundamental fermions of the Standard Model: ccc ν µ ttt ν τ uuu ν e ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ bbb τ sss µ ⎣ ⎦ ddde ⎣ ⎦ ⎣ ⎦ •� Of all fundamental fermions only ν ’s are neutral If lepton number L conservation is violated then no conserved charge distinguishes neutrinos from antineutrinos Majorana ν ’s : neutrinos and antineutrinos coincide neutrinos are their own antiparticles •� ν ’s have very small masses The two facts are probably related
The field of an electron (massive, charged) has 4 components In fact there are 4 dof: e - , e + , h = +, − (h is the helicity: component of spin along momentum) Lorentz boost |e -- , h = − > |e -- , h = + > TCP TCP Lorentz boost |e + , h = − > |e + , h = + >
A 2-component description is possible in two cases: • for a massless neutrino | ν L > = | ν , h= --1 > and | ν R > = | ν , h= +1 > can be enough because massless particles go at the speed of light (no boost can flip h) But now we know that (at least two) neutrinos have non vanishing masses, although very small • for a completely neutral neutrino there is the possibility that neutrino and antineutrino coincide (Majorana neutrino) Each neutrino mass eigenstate of definite helicity coincides with its own antiparticle
ν 's have no electric charge. Their only charge is lepton number L. IF L is not conserved (not a good quantum number) ν and ν are not really different TCP, "Lorentz" | ν , h= -1/2 > | ν , h= +1/2> For a massive Majorana neutrino only two states are enough A Majorana neutrino is identical with its charge conjugated C | ν > = | ν > = | ν > Each neutrino mass eigenstate of definite helicity coincides with its own antiparticle
recall: ν R : ann | ν R > creates | ν L > ν masses: ν L : ann | ν R > creates | ν L > For massive fermions L,R refer to chirality, not helicity ν R ν L Dirac mass: ν L ν R + ν R ν L (needs ν R ) Lepton number (L)-conserving Don’t confuse left-chirality and lepton n. ν c ν− > ν Τ R C ν R or ν Τ L C ν L Majorana mass: ψ c = C ψ Τ C=i γ 2 γ 0 Violates L, B-L by | Δ L| = 2 ν R ν L ν T R ν R or ν T L ν L short-hand:
Weak isospin I ν L => I = 1/2, I 3 = 1/2 ν R => I = 0, I 3 = 0 For Dirac ν ’s Dirac Mass: ν L ν R + ν R ν L | Δ I|=1/2 no explanation of small masses Can be obtained from Higgs doublets: ν L ν R H Majorana Mass: • ν T L ν L | Δ I|=1 Non ren., dim. 5 operator: ν T L ν L HH Directly • ν T R ν R | Δ I|=0 compatible with SU(2)xU(1)!
See-Saw Mechanism Minkowski; Glashow; Yanagida; Gell-Mann, Ramond , Slansky; Mohapatra, Senjanovic….. M ν T R ν R allowed by SU(2)xU(1) Large Majorana mass M (as large as the cut-off) m D ν L ν R Dirac mass m D from Higgs doublet(s) ν L ν R ν L 0 m D M >> m D ν R m D M Eigenvalues | ν light | = , ν heavy = M m D 2 M
A very natural and appealing explanation: ν 's are nearly massless because they are Majorana particles and get masses through L non conserving interactions suppressed by a large scale M ~ M GUT m 2 m: ≤ m t ~ v ~ 200 GeV m ν ~ M M: scale of L non cons. Note: m ν ∼ ( Δ m 2atm ) 1/2 ~ 0.05 eV m ~ v ~ 200 GeV M ~ 10 14 - 10 15 GeV Neutrino masses are a probe of physics at M GUT !
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