Ricerca Iniretta i Supersimmetria nei Decaimenti ei Mesoni B L. Silvestrini INFN, Roma Introuction to CP Violation in the SM Introuction to CP Violation in the MSSM A moel-inepenent analysis of SUSY effects in b->s transitions Conclusions & Outlook
Flavour & CP violation in the SM The SM gauge sector is invariant uner CP & U(3) 5 flavour symmetry: inep. transf. of Q L, R, u R, L L, e R. Flavour & CP broken by Yukawa couplings: for quarks U(3) 3 U(1) B. Due to Higgs mechanism, gauge group SU(2) L U(1) Y U(1) em Yukawa couplings fermion masses Roma, 6/5/2003 L. Silvestrini, INFN - Roma 2
Flavour & CP violation in the SM Fermion mass matrices in general not flavour iagonal an complex flavour & CP violation Turn to mass eigenstate basis for quarks: nee U U Q A U L, U cancel in neutral currents (GIM): q A γ µ q A q A Roma, 6/5/2003 L. Silvestrini, INFN - Roma 3 U R, U D L, U ( ) U Q + A γ µ U QAqA D R
Flavour & CP violation in the SM U Q A o not cancel in charge weak currents: u L γ µ V CKM L u L ( U ) + L µ DL µ U γ U L ulvckm γ L escribe by 3 angles & 1 phase SM flavour physics entirely etermine by these 4 parameters strong correlations in FCNC & CPV Roma, 6/5/2003 L. Silvestrini, INFN - Roma 4
Flavour & CP violation in the SM CP violation nees 3 families: nee top contribution sensitivity to top mass sensitive to new heavy particles running in the loops strong probe of new physics up to scales of 100 TeV Roma, 6/5/2003 L. Silvestrini, INFN - Roma 5
Parameters in the CKM matrix 1. λ 0.2 Cabibbo angle: 1st-2n generation mixing (u s, c ) 2. Αλ 2 0.04 2n-3r generation mixing (c b, t s) 3. Αλ 3 σ 0.003 1st-3r generation mixing (u b, t ) σe iδ ρ + iη UT fit: constrain ρ an η from exp. Roma, 6/5/2003 L. Silvestrini, INFN - Roma 6
The SM Unitarity Triangle α γ β Roma, 6/5/2003 L. Silvestrini, INFN - Roma 7
Remove constraints from b -> s Roma, 6/5/2003 L. Silvestrini, INFN - Roma 8
CP Violation in B ecays: B->J/ΨK S Phase of B mixing Φ M =2β B Two ecay amplitues Φ D =0 a J CP / ΨK S ( t) = sin 2β sin m t
CP Violation in B ecays: s s B->ΦK S Φ s s Phase of B mixing Φ M =2β B Only penguin amplitue Φ D =0 s s a ΦK CP S ( t) = sin 2β sin m t strong sensitivity to new physics
Why NP (SUSY) in b->s? NP in s -> or b -> transitions is Strongly constraine by the UT fit Unnecessary, given the great success an consistency of the fit NP in b -> s transitions is Much less (un-) constraine by the UT fit Natural in many flavour moels, given the strong breaking of family SU(3) Hinte at by ν s in SUSY-GUTs (Moroi; Chang, Masiero & Murayama; Hisano & Shimizu) Roma, 6/5/2003 L. Silvestrini, INFN - Roma 11
Flavour & CP violation in the MSSM SUSY introuce to make the SM a consistent low-energy effective theory (M W,Z << Λ) SUSY requires fermion boson: Quarks squarks Gauge bosons gauginos Higgs Higgsino with superpartner masses M SUSY M W,Z Roma, 6/5/2003 L. Silvestrini, INFN - Roma 12
Flavour & CP violation in the MSSM Super-CKM basis: Quark masses iagonal Gauge interactions governe by CKM Squark mass matrices in general non iagonal in Super-CKM basis: new source of flavour & CP violation! To compute SUSY corrections to SM processes, treat off-iagonal squark mass terms as interactions Roma, 6/5/2003 L. Silvestrini, INFN - Roma 13
Flavour & CP violation in the MSSM In each squark propagator, consier off-iagonal mass insertions: b ~ A ( ) 23 AB four insertions AB=LL, LR, RL, RR Expan to lowest orer in imensionless 23 δ 23 ( ) ( ) AB AB m~ q Roma, 6/5/2003 L. Silvestrini, INFN - Roma 14 s~ B
Flavour & CP violation in the MSSM For generic δ s, gluino-exchange ominant contribution (α s vs. α w ) Moel-inepenent analysis: switch on one single δ an stuy phenomenology Available ata: suppression in s, b squark mixings neee (UT fit) Roma, 6/5/2003 L. Silvestrini, INFN - Roma 15
Flavour & CP violation in the MSSM From M K & ε K, @ 500 GeV: (Ciuchini et al.) Re Re ( ) 2 2 δ 12 < 4.6 10 ( ) 2 3 Im δ 12 < 6.1 10 LL ( ) 2 3 δ 12 < 2.8 10 ( ) 2 4 Im δ 12 < 3.7 10 LR LL LR From M & S J/ΨK, @ 500 GeV: (Becirevic et al.) Re Re ( ) 1 δ 13 < 1.4 10 ( ) 1 LL Im δ 13 LL < 3.0 10 ( ) 2 δ 13 < 3.3 10 ( ) 2 Im δ 13 < 7.4 10 LR LR Roma, 6/5/2003 L. Silvestrini, INFN - Roma 16
Effects of δ 23 in B physics Single mass insertion: B=1 b-> s γ, b -> s l + l - clean rare ecays CPV in B -> Φ K S clean only in SM CPV in B -> K π, η K S not clean Double mass insertion: B=2 M s relatively clean (lattice m.e.) CPV in B S -> J/ΨΦ clean Roma, 6/5/2003 L. Silvestrini, INFN - Roma 17
Experimental information Large BR s of b->s charmless moes: B->K (*) π, B->η K, B->Ф K,... Time-epenent CP asymmetries: BaBar Belle SM S KФ -0.18±0.51±0.07-0.73±0.64±0.22 0.7 C KФ -0.80±0.38±0.12 0.56±0.41±0.16 0.0 S η K 0.02±0.34±0.03 0.71±0.37±0.06 0.7 C η K 0.10±0.22±0.03-0.26±0.22±0.04 0.0 Plus rate CP asymmetries in B -> K π channels Roma, 6/5/2003 L. Silvestrini, INFN - Roma 18
Our analysis: ingreients Ciuchini, Franco, Masiero & L.S. We compute @ NLO (except for SUSY matching): b -> s γ (BR an A CP ) b -> s l + l - M s (with lattice QCD matrix el. from Becirevic et al.) B -> Φ K S (BR an time-epenent asymmetry coefficients S ФK, C ФK ) B S -> J/ΨΦ (time-ep asymmetry S J/Ψ Ф ) B -> K π (BR s an irect CP asymmetryes) Relate work: Bertolini, Borzumati & Masiero; Ciuchini et al.; Barbieri & Strumia; Abel, Cottingham & Wittingham; Kagan; Borzumati et al.; Besmer, Greub & Hurth; Lunghi & Wyler; Causse; Hiller; Khalil & Kou; Kane et al.; Harnik et al.; Baek; Hisano & Shimizu; +RPV Roma, 6/5/2003 L. Silvestrini, INFN - Roma 19
Our analysis: ingreients (cont ) Constraints on b-> s transitions: BR( B A CP BR( B M ( B S X X X S S γ) S l γ) + > 14.4 ps l = (3.29 ± 0.34) 10 = ( 0.02 ± 0.04) 1 ) BR( B perform a MonteCarlo analysis, stuying clustering in Re δ, Im δ plane. Keep in min that haronic uncertainties in nonleptonic ecays are not fully uner control! Roma, 6/5/2003 L. Silvestrini, INFN - Roma 20 4 = (6.1± 1.4 ± 1.3) 10 Kπ) 6
Blue: M s <20 ps -1 Im δ vs. Blue: M s <20 ps -1 Re δ for ( δ ) 23 LL ( δ ) 23 RR Blue: S ФK <0 Blue: S ФK <0 ( δ ) 23 LR ( δ ) 23 RL m = m q~ g~ 350 GeV CFMS
S ФK vs. Im δ for ( δ ) 23 LL ( δ ) 23 RR ( δ ) 23 LR ( δ ) 23 RL m = m q~ g~ 350 GeV CFMS
S ФK vs. C ФK for ( δ ) 23 LL ( δ ) 23 RR ( δ ) 23 LR ( δ ) 23 RL m = m q~ g~ 350 GeV CFMS
S ФK vs A CP (b->sγ) m = m q~ g~ 350 GeV ( δ ) ( ) 23 CFMS LL δ 23 LR
M s for ( δ ) 23 LL ( δ ) 23 RR ( δ ) 23 LL= RR M s Does S ФK <0 imply large M s? Not really m = m q~ g~ 350 GeV CFMS S ФK
Conclusions Many inepenent th an exp motivations for SUSY in b->s transitions: Consistency of SM UT fit Possible eviations from SM in S ФK, C ФK Flavour Symmetries SUSY GUTs + neutrino oscillations In the presence of NP, S ФK, C ФK suffer from sizable haronic uncertainties Roma, 6/5/2003 L. Silvestrini, INFN - Roma 26
Conclusions (cont ) At present, SUSY moels with ( ) 1 3 δ 23 or LL or RR O(10 ) δ 23 LR or RL O(10 an 350 GeV squark/gluinos can reprouce all exp ata incluing eviations from SM in S ФK, C ФK Future ata on rare B ecays an M s will allow us to test the SM an SUSY Interesting correlations with other observables in B physics an LFV ( ) ) Roma, 6/5/2003 L. Silvestrini, INFN - Roma 27