Aspetti della fisica oltre il Modello Standard all LHC (con enfasi sulla verificabilità sperimentale in gruppo I e II) Andrea Romanino SISSA e INFN TS Giornata di Seminari, INFN TS, 07.07.09
The Standard Model (at the ren level) Ψ i iγ µ D µ Ψ i 1 4 F a µνf aµν gauge few L ren SM = +λ ijψ i Ψ j H + h.c. flavor few % + D µ H 2 V (H) symmetry breaking? (indirect) An extremely successful synthesis of particle physics + neutrinos mass operator: LLHH in compact notations i = 1,2,3: family index
Many reasons to go beyond the SM Experimental problems of the SM Gravity Dark matter Baryon asymmetry Experimental hints of physics beyond the SM Neutrino masses Quantum number unification Theoretical puzzles of the SM <H> «M Pl Family replication Small Yukawa couplings, pattern of masses and mixings Gauge group, no anomaly, charge quantization, quantum numbers Theoretical problems of the SM Naturalness/unitarity problem Cosmological constant problem Strong CP problem
3 (related) highlights A solution of the supersymmetric flavour problem with specific implication on new physics effects in Kaon and B-physics: hierarchical sfermion masses A new class of supersymmetric models leading to a peculiar sfermion spectrum: tree level gauge mediation A predictive leptogenesis scenario with Calibbi, Frigerio, Giudice, Hosteins, Lavignac, Nardecchia, Ziegler
Hierarchical sfermion masses and flavour physics Giudice Nardecchia R, arxiv:0812.3610
Supersymmetry breaking and the flavour problem The supersymmetrization of the SM is straightforward and essentially unique
u c t γ ~ ~ ~ u c t ~ γ d s b g ~ ~ d s ~ b ~ g e μ τ W e μ τ ~ ~ ~ ~ W ν 1 ν 2 ν 3 Z ~ ν 1 ~ ν 2 ~ ν 3 ~ Z H 1 H 2 ~ ~ H 1 H 2
Supersymmetry breaking and the flavour problem The supersymmetrization of the SM is straightforward and essentially unique The origin of supersymmetry breaking is unknown
SUSY breaking? MSSM Hidden sector Observable sector
Supersymmetry breaking and the flavour problem The supersymmetrization of the SM is straightforward and essentially unique The origin of supersymmetry breaking is highly unknown Effective description of supersymmetry breaking (MSSM): about 100 additional physical parameters Large FCNC (and CPV) processes in most of the parameter space (SUSY flavour problem) γ γ W µ R ẽ R µ L ẽ R γ µ B e µ ν µ ν e e µ B e
A possible solution to the flavour problem Hierarchy: [Cohen Kaplan Lepeintre Nelson 97] q L m2 q L q L + d R m2 d R dr +ũ R m2 u R ũ R +... m 2 q L = ( heavy m 2 ) Expand in small off-diagonal elements of squark mass matrix M 2 = M 2 0 + M 2 1 A( F = 1) ij = f(x) ˆδ ij A( F = 2) ij = g (1) (x) ˆδ 2 ij ˆδ a3 = M2 a3 m 2 a (a =1, 2) δˆ ij : source of flavour violation, process independent f, g: loop functions (process dependent, flavour conserving)
Theoretical considerations on the hierarchical case Complementary to degeneracy The naturalness bound on m~ 1,2 is milder than the one on m~ 3 [Dimopoulos Giudice 95] 30 No FY Δ < 100 Effective supersymmetry [Cohen Kaplan Lepeintre Nelson 97] Alleviates the SUSY flavour problem: ˆδ m/ m 1,2 m 1,2 TeV 25 20 15 10 5 Related to physical quantities: squark masses, CKM angles 10 4 10 8 10 12 10 16 M susy GeV
Degeneracy vs Hierarchy Different correlation between ΔF = 1 and ΔF = 2 wrt to the complementary degenerate limit A( F = 2) [A( F = 1)] 2 = 1 degeneracy 6 g (3) g (1) ( f f (1) ) 2 A( F = 2) [A( F = 1)] 2. hierarchy E.g.: A(Δm Bs ) vs A(b sγ) LL insertion g (3) g (1) ( f f (1) ) 2 x=1 25 27
Bounds on δ s Hierarchy ˆδ LL ut ˆδ LL ct D 0 D 0 mixing < 8.0 10 3 ( ) m t δuc LL < 3.4 10 2 ( m q ) Degeneracy δ ^ sb 4 10-2 δ ^ db 0.8 10-2 Re (ˆδLL ) sb < 2.2 10 2 ( m b (ˆδLL ) Im sb < 6.7 10 2 ( m b B X s γ ) ( ) 2 10 Re ( ) δ LL < 3.8 10 2 ( m q tan β ) 2 ( 10 tan β (ˆδLL ) Re sb < 9.4 10 2 ( m b Im (ˆδLL ) sb < 7.2 10 2 ( m b sb ) Im ( δ LL sb m Bs ) < 1.1 10 1 ( m q ) ( ) Re δ LL < 4.0 10 1 ( m q sb ) Im ( δ LL sb ) < 3.1 10 1 ( m q Bd 0 B d 0 mixing Re (ˆδLL ) db < 4.3 10 3 ( ) m b Re ( ) δdb LL < 1.8 10 2 ( ) m q Im (ˆδLL ) db < 7.3 10 3 ( ) m b Im ( ) δdb LL < 3.1 10 2 ( ) m q ) 2 ( 10 tan β ) 2 ( 10 tan β ) ) ) ) ~ m = M 3 = μ A = 0 δ ^ ds 3 10-4 Re (ˆδLL db Im (ˆδLL db m K ) ˆδ LL 2 sb < 1.0 10 2 ( m b ɛ K ) ˆδ LL 2 sb < 4.4 10 4 ( m b ) Re ( δ LL ds ) Im ( δ LL ds ) 2 < 4.2 10 2 ( ) m q ) 2 < 1.8 10 3 ( ) m q
u c transitions (D 0 - -D 0 ) 0.06 0.04 0.010 0.02 LL Im uc 0.00 0.02 0.005 Im LL uc 0.000 0.005 0.04 0.010 0.06 0.06 0.04 0.02 0.00 0.02 0.04 0.06 0.010 0.005 0.000 0.005 0.010 Re LL uc Re LL uc Degeneracy Hierarchy 68%, 95% C.L. ~ m = M 3 =
b d transitions (Δm Bd, sin2β eff ) 0.02 0.05 0.01 LL Im db 0.00 LL Im db 0.00 0.05 0.01 Degeneracy 0.05 0.00 0.05 Re LL db 0.02 0.02 0.01 0.00 0.01 0.02 Re LL db Hierarchy 68%, 95% C.L. ~ m = M 3 =
b s transitions (Δm Bs, b sγ, ϕ Bs ) 1.0 50 70 90 70 50 0.2 50 70 90 70 50 0.5 30 30 0.1 30 30 10 10 10 10 LL Im sb 0.0 0.5 1.0 0 0 10 30 50 70 90 70 50 10 30 1.0 0.5 0.0 0.5 1.0 Im LL sb 0.0 0.1 0.2 0 0 10 30 50 70 90 70 50 0.2 0.1 0.0 0.1 0.2 10 30 Degeneracy Re LL sb Re LL sb Hierarchy 95% C.L. m ~ = M 3 = μ =, tanβ = 10, A = 0
ϕ Bs B s H full eff B s = C Bs e 2iφ Bs Bs H SM eff B s B s H SM eff B s = A SM s e 2iβ s β s = arg( (V ts V tb)/(v cs V cb)) = 0.018 ± 0.001 [Pierini for UTfit, ICHEP08] 8 Degeneracy Hierarchy 6 4 2 0 30 20 10 0 10 20 30 Φ Bs
Tree level gauge mediation Nardecchia R Ziegler, to appear
SUSY breaking GUT heavy vectors MSSM Hidden sector Observable sector
Unification SU(3) SU(2) U(1) SO(10) L i 1 2-1/2 70 60 1 Α 1 e c i 1 1 1 50 40 Q i 3 2 1/6 16 30 20 1 Α 2 u c i d c i 3 * 1-2/3 3 * 1 1/3 10 0 1 Α 3 MSSM SM 10 3 10 6 10 99 10 10 12 10 10 15 Q GeV Y + M GUT prediction: Λ B < M GUT < M Pl
SUSY breaking GUT heavy vectors MSSM Hidden sector Observable sector Need: Heavy vectors from (at least) SO(10) (X) Hidden sector non-trivial under SO(10): 16 = F θ 2 16 =0 16 = M 16 = M
Sfermion masses Prediction: m 2 f = X(f) 2X(N) F 2 M 2 Standard embedding of SM fermions in SO(10): 16 SO(10) = (l + d c ) + (q + u c + e c ) + (N) - but note also 10 SO(10) = (l + d c ) + (l + d c ) f N q u c e c (l) 16 (d c ) 16 (l) 10 (d c ) 10 (l) 10 (d c ) 10 X 5 1 1 1-3 -3 2 2-2 -2 Positive sfermion masses with the following embedding: 16 SO(10) = (heavy) + (q + u c + e c ) + (..) 10 SO(10) = (l + d c ) + (heavy)
Sfermion masses Then m 2 q = m 2 u c = m 2 e c = m 2 10 = 1 10 m2, m 2 l = m 2 d c = m 2 5 = 1 5 m2 m 2 h u = 2 5 m2, m 2 h d = 2c2 d 3s2 d 5 m 2 In particular: all sfermion masses are positive sfermion masses are flavour universal, thus solving the supersymmetric flavour problem m 2 q,u c,e c = 1 2 m2 l,d c
Gaugino masses Are universal but the overall scale is model dependent M a = α 4π Tr(h h 1 ) F M, a =1, 2, 3, M 2 m t = 3 10 MGUT (4π) 2 λ, λ = g2 Tr(h h 1 ) 3 W = y ij 2 16 i16 j 10 + h ij 16 i 10 j 16 + h ij16 i 10 j 16 + W vev + W NR,
Against common wisdom This model shows that it is possible to communicate supersymmetry breaking to the MSSM at the tree, renormalizable level Weinberg, in The quantum theory of fields III: It would be simplest to suppose that supersymmetry is broken by effects occurring in the tree approximation of the supersymmetric standard model. This possibility may be definitely ruled out The two obstacles: The supertrace formula: in particular ( 1) 2J (2J + 1)MJ 2 =0 (but heavy fields compensate the RHS) J 2(m 2 d + m 2 s + m 2 b) = m 2 d + m 2 s + m 2 b Gaugino masses at loop level: m t... (4π) 2 M 2... 10 TeV (but... small)
Un modello predittivo di leptogenesi Frigerio Hosteins Lavignac R, arxiv:0804.0801 Calibbi Frigerio Lavignac R, to appear
The baryon asymmetry η B n B n B n γ = n B n γ Generated dynamically if = (6.15 ± 0.25) 10 10 (1 number) B is violated C and CP are violated out of equilibrium evolution Models of Baryogenesis Planck GUT Through leptogenesis Electroweak Affleck-Dine...
See-saw induced neutrino masses L eff E Λ = L ren SM + a ij 2Λ (hl i)(hl j ) +... N (1,1,0) l i h h M X l j N h N k See-saw type I h h See-saw type II Δ h Δ (1,3,1) l i l j T (1,3,0) l i h h M X l j T h T k See-saw type III (Any number of N h, T h, Δ h ) (SU(3) c,su(2) L,Y)
Model dependence in see-saw type-i Relevant interactions: λ E ije c il j h d + λ N ij N i l j h u + M ij 2 N in j [ m ν = v 2 u λ T N ] 1 M λ N Overall size of neutrino Yukawa couplings λ N k λ N M k 2 M m ν m ν BR(e i e j γ) k 4 log k BR(e i e j γ) Unknown flavour structure v d λ E, v u λ N, M m e m µ m τ, m ν1 m ν2 m ν3, U e.g. v u λ N = v u λ diag N V N or M diag, R = 1/ M diag v u λ N U / M diag 21 physical parameters 12 known or measurable parameters 9 unknowns = 3 masses + 3 angles + 3 phases Type-II: LFV more predictive [Rossi 02], leptogenesis as well in SO(10)
Type-II see-saw in SO(10) Standard embedding of SM fermions in SO(10): 16 SO(10) = (l + d c ) + (q + u c + e c ) + (N) Note also: 10 SO(10) = (l + d c ) + (l + d c ) Simplest embedding of type-ii see-saw in SO(10) implies: 16 SO(10) = (heavy) + (q + u c + e c ) + (..) 10 SO(10) = (l + d c ) + (heavy)
CP asymmetry l j Type II L l f lj l j h Type I l j λ N kj h f ij l i L k ( ) fij 2 10 i10 j 54 f kl S, T f ki 24 SU(5) l i N 1 λ N 1i l i N 1 λ N 1j h λ N ki N k l i f ij, M L ij from m ν, m E (up to overall factors, W NR ) L 1 lighter than M Δ /2? M L1 < M Δ < M L2, M 24 : (in the diagonal m E basis) M L1 ɛ 1 10π h 1 V 16 0.5 1011 GeV cos β M M 24 λ 4 l λ 2 l + λ2 h λ 2 l ij ( Im[m 11(mm m) 11 ] ( i m2 i )2 ) V 16 2 10 16 GeV f ij 2, λ 2 h σ 2 ɛ 2 Γ( l l ) Γ( ll) Γ + Γ
Maximal CP asymmetry Need: ηɛ 10 8 ε max /λ 2 L Normal Hierarchy 2 10 4 Inverted Hierarchy 10 4 10 4 10 2 5 10 5 sin 2 Θ 13 10 2 5 10 5 sin 2 Θ 13 10 5 10 5 10 3 10 2 10 1 m lightest ev 10 3 10 3 10 2 10 1 m lightest ev
O(1) efficiency region m 1 «m 2 «m 3, M Δ /M 24 = 0.1, sin2σ = 1, sin 2 θ 13 = 0.05, tanβ = 10 0.30 K L 1 0.25 Ε 10 10 Ε 10 8 Ε 10 7 0.20 Λ H 0.15 M 10 13 GeV 0.10 0.05 M 10 12 GeV K L1 c 1 K H 1 0.00 0.00 0.05 0.10 0.15 0.20 0.25 0.30 (K = Γ/H) Λ L
By implementing type-ii see-saw in SO(10) we improve on dependence on unknown parameters dependence on initial conditions perturbativity D=5 proton decay Baryogenesis closer to be testable