Neutrino Theory and Phenomenology. Carlo Giunti

Transcript

1 Neutrino Theory and Phenomenology PART 1 Carlo Giunti INFN, Sezione di Torino, and Dipartimento di Fisica Teorica, Università di Torino carlo.giunti@to.infn.it Neutrino Unbound: NBIA PhD School Neutrinos underground & in the heavens The Niels Bohr International Academy, Copenhagen, Denmark 3-7 June 014 C. Giunti Neutrino Theory and Phenomenology NBIA PhD School 3-7 June 014 1

2 Neutrino Theory and Phenomenology Neutrino Masses and Mixing Neutrino Oscillations in Vacuum Neutrino Oscillations in Matter C. Giunti Neutrino Theory and Phenomenology NBIA PhD School 3-7 June 014

3 Neutrino Masses and Mixing C. Giunti Neutrino Theory and Phenomenology NBIA PhD School 3-7 June 014 3

4 Fermion Mass Spectrum t m [ev] d u e c s µ ν µ b τ ν τ ν e ν 1, ν, ν C. Giunti Neutrino Theory and Phenomenology NBIA PhD School 3-7 June 014 4

5 Dirac Mass Dirac Equation: (i/ m)ν(x) = 0 (/ γ µ µ ) Dirac Lagrangian: L(x) = ν(x)(i/ m)ν(x) Chiral decomposition: ν L P L ν, ν R P R ν, ν = ν L +ν R Left and Right-handed Projectors: P L 1 γ5, P R 1+γ5 P L = P L, P R = P R, P L +P R = 1, P L P R = P R P L = 0 L = ν L i/ ν L +ν R i/ ν R m(ν L ν R +ν R ν L ) In SM only ν L by assumption = no neutrino mass Note that all the other elementary fermion fields (charged leptons and quarks) have both left and right-handed components Oscillation experiments have shown that neutrinos are massive Simplest and natural extension of the SM: consider also ν R as for all the other elementary fermion fields C. Giunti Neutrino Theory and Phenomenology NBIA PhD School 3-7 June 014 5

6 Higgs Doublet: Φ(x) = Higgs Mechanism in SM ( ) φ+ (x) φ 0 (x) Φ = Φ Φ = φ + φ + +φ 0 φ 0 Higgs Lagrangian: L Higgs = (D µ Φ) (D µ Φ) V( Φ ) Higgs Potential: V( Φ ) = µ Φ +λ Φ 4 ( µ < 0 and λ > 0 = V( Φ ) = λ v Φ v ) µ λ = ( G F ) 46GeV Vacuum: V min for Φ = v ( ) 1 = Φ = 0 v Spontaneous Symmetry Breaking: SU() L U(1) Y U(1) Q C. Giunti Neutrino Theory and Phenomenology NBIA PhD School 3-7 June 014 6

7 H φ + φ 0 ( ) Unitary Gauge: Φ(x) = 1 0 = Φ v +H(x) = v +vh + 1 H ( V = λ Φ v ) = λv H +λvh 3 + λ 4 H4 m H = λv = µ 16GeV µ (89GeV) λ = µ v 0.13 C. Giunti Neutrino Theory and Phenomenology NBIA PhD School 3-7 June 014 7

8 SM Extension: Dirac ν Masses L L ( νl l L ) l R Lepton-Higgs Yukawa Lagrangian ν R L H,L = y l L L Φl R y ν L L ΦνR +H.c. Spontaneous Symmetry Breaking Φ(x) = 1 ( ) 0 Φ = iσ v +H(x) Φ = 1 ( ) v +H(x) 0 L H,L = yl ( ) ( ) 0 νl l L l v +H(x) R yν ( ) ( ) v +H(x) νl l L ν 0 R +H.c. C. Giunti Neutrino Theory and Phenomenology NBIA PhD School 3-7 June 014 8

9 L H,L = y l v l L l R y ν v ν L ν R yl l L l R H yν ν L ν R H +H.c. m l = y l v m ν = y ν v g lh = yl = m l v g νh = yν = m ν v v = ( GF ) 1/ = 46GeV PROBLEM: y ν y e 10 6 C. Giunti Neutrino Theory and Phenomenology NBIA PhD School 3-7 June 014 9

10 Three-Generations Dirac Neutrino Masses L el ν el l el e L L µl ν µl l µl µ L L τl ν τl l τl τ L l er e R l µr µ R l τr τ R ν er ν µr ν τr Lepton-Higgs Yukawa Lagrangian L D = [ Y αβ l L αl Φl βr +Y ν αβ L Φν ] αl βr +H.c. α,β=e,µ,τ Spontaneous Symmetry Breaking Φ(x) = 1 0 Φ = iσ Φ = 1 v v 0 C. Giunti Neutrino Theory and Phenomenology NBIA PhD School 3-7 June

11 L D = α,β=e,µ,τ [ v Y l αβ l αl l βr + v ] Y αβ ν ν αl ν βr [ ] L D = l L M l l R +ν L M ν ν R +H.c. +H.c. e L l L µ L τ L e l R R µ R τ R ν ν L el ν µl ν τl ν ν R er ν µr ν τr M l = v Y l M ν = v Y ν M l M ee l M eµ l M eτ l M µe l M µµ l M µτ l M l τe M l τµ M l ττ M ν M ee ν M eµ ν M eτ ν M µe ν M µµ ν M µτ ν M ν τe M ν τµ M ν ττ C. Giunti Neutrino Theory and Phenomenology NBIA PhD School 3-7 June

12 L D = l L M l l R ν L M ν ν R +H.c. Diagonalization of M l and M ν with unitary V l L, Vl R, Vν L, Vν R l L = Vl L l L l R = Vl R l R ν L = Vν L n L ν R = Vν R n R Important general remark: unitary transformations are allowed because they leave invariant the kinetic terms in the Lagrangian L kin = l L i/ l L +l R i/ l R +ν L i/ ν L +ν R i/ ν R = l L V l L i/ Vl L l L +... = l L i/ l L +l R i/ l R +ν L i/ ν L +ν R i/ ν R C. Giunti Neutrino Theory and Phenomenology NBIA PhD School 3-7 June 014 1

13 L D = l L M l l R ν L M ν ν R +H.c. l L = Vl L l L l R = Vl R l R ν L = Vν L n L ν R = Vν R n R L D = l L V l L M l V l R l R ν L V ν L M ν V ν R ν R +H.c. V l L M l V l R = Ml M l αβ = ml α δ αβ (α,β = e,µ,τ) V ν L M ν V ν R = Mν M ν kj = mν k δ kj (k,j = 1,,3) Real and Positive m l α, mν k C. Giunti Neutrino Theory and Phenomenology NBIA PhD School 3-7 June

14 Massive Chiral Lepton Fields l L = V l L l L n L = V ν L ν L e L µ L τ L ν 1L ν L ν 3L l R = V l R l R n R = V ν R ν R e R µ R τ R ν 1R ν R ν 3R L D = l L M l l R n L M ν n R +H.c. = 3 mα l l αll αr mk ν ν klν kr +H.c. α=e,µ,τ k=1 C. Giunti Neutrino Theory and Phenomenology NBIA PhD School 3-7 June

15 Mixing Charged-Current Weak Interaction Lagrangian L (CC) I Weak Charged Current: = g jρ W W ρ +H.c. j ρ W = jρ W,L +jρ W,Q Leptonic Weak Charged Current j ρ W,L = l αl γρ ν αl = l L γρ ν L α=e,µ,τ l L = Vl L l L ν L = Vν L n L j ρ W,L = l LV l L γρ V ν L n L = l L γ ρ V l L Vν L n L = l L γ ρ Un L Mixing Matrix U = V l L Vν L C. Giunti Neutrino Theory and Phenomenology NBIA PhD School 3-7 June

16 Definition: Left-Handed Flavor Neutrino Fields ν L = Un L = V l L Vν L n L = V l L ν L = ν el ν µl ν τl They allow us to write the Leptonic Weak Charged Current as in the SM: j ρ W,L = l Lγ ρ ν L = l αl γ ρ ν αl α=e,µ,τ Each left-handed flavor neutrino field is associated with the corresponding charged lepton field which describes a massive charged lepton: j ρ W,L = (e Lγ ρ ν el +µ L γ ρ ν µl +τ L γ ρ ν τl ) In practice left-handed flavor neutrino fields are useful for calculations in the SM approximation of massless neutrinos (interactions). If neutrino masses must be taken into account, it is necessary to use j ρ W,L = l Lγ ρ Un L = 3 l αl γ ρ U αk ν kl α=e,µ,τ k=1 C. Giunti Neutrino Theory and Phenomenology NBIA PhD School 3-7 June

17 Flavor Lepton Numbers Flavor Neutrino Fields are useful for defining Flavor Lepton Numbers as in the SM L e L µ L τ (ν e, e ) (ν µ, µ ) (ν τ, τ ) L e L µ L τ (ν c e, e+ ) ( ν c µ, µ +) (ν c τ, τ + ) L = L e +L µ +L τ Standard Model: Lepton numbers are conserved C. Giunti Neutrino Theory and Phenomenology NBIA PhD School 3-7 June

18 L e, L µ, L τ are conserved in the Standard Model with massless neutrinos Mass term: L D = ( ) mee D meµ D m D eτ ν er ν el ν µl ν τl m µe D mµµ D mµτ D ν µr +H.c. mτe D mτµ D mττ D ν τr L e, L µ, L τ are not conserved L is conserved: L(ν αr ) = L(ν βl ) = L = 0 C. Giunti Neutrino Theory and Phenomenology NBIA PhD School 3-7 June

19 Mixing Matrix U e1 U e U e3 U = V l L Vν L = U µ1 U µ U µ3 U τ1 U τ U τ3 Unitary N N matrix depends on N independent real parameters N = 3 = Not all phases are physical observables N(N 1) = 3 Mixing Angles N(N +1) = 6 Phases Only physical effect of mixing matrix occurs through its presence in the Leptonic Weak Charged Current C. Giunti Neutrino Theory and Phenomenology NBIA PhD School 3-7 June

20 Weak Charged Current: j ρ W,L = α=e,µ,τ k=1 3 l αl γ ρ U αk ν kl Apart from the Weak Charged Current, the Lagrangian is invariant under the global phase transformations (6 arbitrary phases) l α e iϕα l α (α = e,µ,τ), ν k e iϕ k ν k (k = 1,,3) Performing this transformation, the Charged Current becomes j ρ W,L = 3 l αl e iϕα γ ρ U αk e iϕ k ν kl j ρ W,L = e i(ϕe ϕ 1) }{{} 1 α=e,µ,τ k=1 3 α=e,µ,τ k=1 l αl e i(ϕα ϕe) }{{} γ ρ U αk e i(ϕ k ϕ 1 ) }{{} ν kl There are 5 independent combinations of the phases of the fields that can be chosen to eliminate 5 of the 6 phases of the mixing matrix It is convenient to express the 3 3 unitary mixing matrix only in terms of the four physical parameters: 3 Mixing Angles and 1 Phase C. Giunti Neutrino Theory and Phenomenology NBIA PhD School 3-7 June 014 0

21 Standard Parameterization of Mixing Matrix ν el U e1 U e U e3 ν 1L ν µl = U µ1 U µ U µ3 ν L ν τl U τ1 U τ U τ3 ν 3L c 13 0 s 13 e iδ 13 c 1 s 1 0 U = 0 c 3 s s 1 c s 3 c 3 s 13 e iδ 13 0 c = c 1 c 13 s 1 c 13 s 13 e iδ 13 s 1 c 3 c 1 s 3 s 13 e iδ 13 c 1 c 3 s 1 s 3 s 13 e iδ 13 s 3 c 13 s 1 s 3 c 1 c 3 s 13 e iδ 13 c 1 s 3 s 1 c 3 s 13 e iδ 13 c 3 c 13 c ab cosϑ ab s ab sinϑ ab 0 ϑ ab π 0 δ 13 < π 3 Mixing Angles ϑ 1, ϑ 3, ϑ 13 and 1 Phase δ 13 C. Giunti Neutrino Theory and Phenomenology NBIA PhD School 3-7 June 014 1

22 Standard Parameterization c 13 0 s 13 e iδ 13 c 1 s 1 0 U = 0 c 3 s s 1 c s 3 c 3 s 13 e iδ 13 0 c Example of Different Phase Convention c 13 0 s 13 c 1 s 1 0 U = 0 c 3 s 3 e iδ s 1 c s 3 e iδ 3 c 3 s 13 0 c U = Example of Different Parameterization c 1 s 1 e iδ s 1 eiδ 1 c c 3 s 3 0 s 3 c 3 c 13 0 s s 13 0 c 13 C. Giunti Neutrino Theory and Phenomenology NBIA PhD School 3-7 June 014

23 Jarlskog Rephasing Invariant Simplest rephasing invariants: U αk = U αk U αk, U αku αj U βk U βj Im [ U αk UαjU βk U βj] = ±J J = Im [ U e Ue3 U µ U ] µ3 = Im In standard parameterization: J = c 1 s 1 c 3 s 3 c 13 s 13sinδ 13 = 1 8 sinϑ 1 sinϑ 3 cosϑ 13 sinϑ 13 sinδ 13 Jarlskog invariant is useful for quantifying CP violation due to U U in a parameterization-independent way. All measurable CP-violation effects depend on J. C. Giunti Neutrino Theory and Phenomenology NBIA PhD School 3-7 June 014 3

24 U U = CP Violation CP Violation General conditions for CP violation (14 conditions): 1. No two charged leptons or two neutrinos are degenerate in mass (6 conditions). No mixing angle is equal to 0 or π/ (6 conditions) 3. The physical phase is different from 0 or π ( conditions) These 14 conditions are combined into the single condition detc 0 C = i [M ν M ν, M l M l ] detc = J ( mν mν )( 1 m ν3 mν )( 1 m ν3 mν ) ( m µ me )( m τ me )( m τ mµ) [C. Jarlskog, Phys. Rev. Lett. 55 (1985) 1039, Z. Phys. C 9 (1985) 491] [O. W. Greenberg, Phys. Rev. D 3 (1985) 1841] [I. Dunietz, O. W. Greenberg, Dan-di Wu, Phys. Rev. Lett. 55 (1985) 935] C. Giunti Neutrino Theory and Phenomenology NBIA PhD School 3-7 June 014 4

25 Maximal CP Violation Maximal CP violation is defined as the case in which J has its maximum possible value J max = In the standard parameterization it is obtained for ϑ 1 = ϑ 3 = π/4, s 13 = 1/ 3, sinδ 13 = ±1 This case is called Trimaximal Mixing. All the absolute values of the elements of the mixing matrix are equal to 1/ 3: i 3 U = 1 i 1 3 i = i e ±iπ/6 e iπ/6 1 1 i 1 3 i 1 3 e iπ/6 e ±iπ/ C. Giunti Neutrino Theory and Phenomenology NBIA PhD School 3-7 June 014 5

26 GIM Mechanism [S.L. Glashow, J. Iliopoulos, L. Maiani, Phys. Rev. D (1970) 185] The unitarity of VL l, Vl R and Vν L implies that the expression of the neutral weak current in terms of the lepton fields with definite masses is the same as that in terms of the primed lepton fields: j ρ Z,L =gν L ν L γρ ν L +gl L l L γρ l L +gl R l R γρ l R =g ν L n LV ν L γρ V ν L n L +g l L l LV l L γρ V l L l L +g l R l R V l R γρ V l R l R =g ν L n Lγ ρ n L +g l L l Lγ ρ l L +g l R l R γ ρ l R The unitarity of U implies the same expression for the neutral weak current in terms of the flavor neutrino fields ν L = Un L : j ρ Z,L = gν L ν LUγ ρ U ν L +g l L l Lγ ρ l L +g l R l R γ ρ l R = g ν L ν Lγ ρ ν L +g l L l Lγ ρ l L +g l R l R γ ρ l R C. Giunti Neutrino Theory and Phenomenology NBIA PhD School 3-7 June 014 6

27 Lepton Numbers Violating Processes Dirac mass term allows L e, L µ, L τ violating processes Example: µ ± e ± +γ, µ ± e ± +e + +e µ e +γ Uµk U ek = 0 = only part of ν k propagator m k contributes k Γ = G Fmµ 5 3α 19π 3 Uµk 3π U m k ek m k W }{{} BR Suppression factor: (BR) the m k m W U µk W γ W µ ν k e U ek for m k 1eV (BR) exp C. Giunti Neutrino Theory and Phenomenology NBIA PhD School 3-7 June 014 7