Ricerca Indiretta diSupersimmetria nei
Decadimenti dei Mesoni BL. Silvestrini – INFN, Roma
•Introduction to CP Violation in the SM•Introduction to CP Violation in the MSSM
•A model-independent analysis of SUSY effects in b->s transitions
•Conclusions & Outlook
Roma, 6/5/2003 L. Silvestrini, INFN - Roma 2
Flavour & CP violation in the SM
• The SM gauge sector is invariant under CP & U(3)5 flavour symmetry: indep. transf. of QL, dR, uR, LL, eR.
• Flavour & CP broken by Yukawacouplings: for quarks U(3)3→U(1)B.
• Due to Higgs mechanism, gauge group SU(2)L⊗U(1)Y →U(1)emYukawa couplings → fermion masses
Roma, 6/5/2003 L. Silvestrini, INFN - Roma 3
Flavour & CP violation in the SM
• Fermion mass matrices in general not flavour diagonal and complex
⇒ flavour & CP violation• Turn to mass eigenstate basis for
quarks: needcancel in neutral currents (GIM):
RLRL DDUU UUUU , , ,AQU
( ) AQQ
AAA qUUqqq AA µ+µ γ→γ
Roma, 6/5/2003 L. Silvestrini, INFN - Roma 4
Flavour & CP violation in the SM
• do not cancel in charged weak currents:
described by 3 angles & 1 phase• SM flavour physics entirely determined
by these 4 parameters ⇒ strong correlations in FCNC & CPV
AQU
( ) LCKMLLDU
LLL dVudUUudu LL µµ+µ γ≡γ→γ
CKMV
Roma, 6/5/2003 L. Silvestrini, INFN - Roma 5
Flavour & CP violation in the SM
• CP violation needs 3 families: – need 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 6
Parameters in the CKM matrix
1. λ ∼ 0.2 Cabibbo angle: 1st-2nd generation mixing (u↔s, c↔d)
2. Αλ2 ∼ 0.04 2nd-3rd generation mixing (c↔b, t↔s)
3. Αλ3σ ∼ 0.003 1st-3rd generation mixing (u↔b, t↔d)
UT fit: constrain ρ and η from exp.η+ρ⇔σ δ iei
• Phase of mixing ΦM=2β• Two decay amplitudes
ΦD=0
dd BB −
tmta SKJCP sin2sin)(/ ∆β=Ψ
CP Violation in B decays: B->J/ΨKS
• Phase of mixing ΦM=2β• Only penguin amplitude ⇒ ΦD=0
strong sensitivity to new physics
dd BB −
tmta SKCP sin2sin)( ∆β=Φ
s
s
s
sΦ
s
s
CP Violation in B decays: B->ΦKS
Roma, 6/5/2003 L. Silvestrini, INFN - Roma 11
Why NP (SUSY) in b->s ?• NP in s -> d or b -> d transitions is
– Strongly constrained by the UT fit – “Unnecessary”, given the great success and
consistency of the fit• NP in b -> s transitions is
– Much less (un-) constrained by the UT fit– Natural in many flavour models, given the strong
breaking of family SU(3)– Hinted at by ν’s in SUSY-GUTs (Moroi; Chang, Masiero &
Murayama; Hisano & Shimizu)
Roma, 6/5/2003 L. Silvestrini, INFN - Roma 12
Flavour & CP violation in the MSSM
• SUSY introduced to make the SM a consistent low-energy effective theory (MW,Z << Λ)
• SUSY requires fermion ↔ boson:– Quarks ↔ squarks– Gauge bosons ↔ gauginos– Higgs ↔ Higgsinowith superpartner masses MSUSY ∼ MW,Z
Roma, 6/5/2003 L. Silvestrini, INFN - Roma 13
Flavour & CP violation in the MSSM
• Super-CKM basis: – Quark masses diagonal– Gauge interactions governed by CKM
• Squark mass matrices in general non diagonal in Super-CKM basis: new source of flavour & CP violation!
• To compute SUSY corrections to SM processes, treat off-diagonal squarkmass terms as interactions
Roma, 6/5/2003 L. Silvestrini, INFN - Roma 14
Flavour & CP violation in the MSSM
• In each squark propagator, consider off-diagonal mass insertions:
four insertions AB=LL, LR, RL, RR• Expand to lowest order in dimensionless
Ab~
Bs~( )ABd
23∆
( ) ( )ABd
ABd 23
23∆
≡δqm~
Roma, 6/5/2003 L. Silvestrini, INFN - Roma 15
Flavour & CP violation in the MSSM
• For generic δ’s, gluino-exchange dominant contribution (αs vs. αw)
• Model-independent analysis: switch on one single δ and study phenomenology
• Available data: suppression in d↔s, d↔b squark mixings needed (UT fit)
Roma, 6/5/2003 L. Silvestrini, INFN - Roma 16
Flavour & CP violation in the MSSM
From ∆MK & εK, @ 500 GeV: (Ciuchini et al.)
From ∆Md & SJ/ΨK, @ 500 GeV: (Becirevic et al.)
( ) 2212 106.4 Re −⋅<δ LLd ( ) 32
12 101.6 Im −⋅<δ LLd
( ) 3212 108.2 Re −⋅<δ LRd ( ) 42
12 107.3 Im −⋅<δ LRd
( ) 113 104.1 Re −⋅<δ LLd ( ) 1
13 100.3 Im −⋅<δ LLd
( ) 213 103.3 Re −⋅<δ LRd ( ) 2
13 104.7 Im −⋅<δ LRd
Roma, 6/5/2003 L. Silvestrini, INFN - Roma 17
Effects of δ23 in B physics
• Single mass insertion: ∆B=1– b -> s γ, b -> s l+ l- clean rare decays– CPV in B -> Φ KS clean only in SM– CPV in B -> K π, η’ KS not clean
• Double mass insertion: ∆B=2– ∆Ms relatively clean (lattice m.e.) – CPV in BS -> J/ΨΦ clean
Roma, 6/5/2003 L. Silvestrini, INFN - Roma 18
Experimental information• Large BR’s of b->s charmless modes:
B->K(*)π, B->η’ K, B->Ф K, ...• Time-dependent CP asymmetries:
BaBar Belle SMSKФ -0.18±0.51±0.07 -0.73±0.64±0.22 ∼0.7CKФ -0.80±0.38±0.12 0.56±0.41±0.16 ∼0.0Sη’K 0.02±0.34±0.03 0.71±0.37±0.06 ∼0.7Cη’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 19
• We compute @ NLO (except for SUSY matching): – b -> s γ (BR and ACP) – b -> s l+ l-– ∆Ms (with lattice QCD matrix el. from Becirevic et al.)– B -> Φ KS (BR and time-dependent asymmetry
coefficients SФK, CФK) – BS -> J/ΨΦ (time-dep asymmetry SJ/Ψ Ф)– B -> K π (BR’s and direct CP asymmetryes)
Related 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…
Ciuchini, Franco, Masiero & L.S.
Our analysis: ingredients
Roma, 6/5/2003 L. Silvestrini, INFN - Roma 20
Our analysis: ingredients (cont’d)
• Constraints on b-> s transitions:
perform a MonteCarlo analysis, studying clustering in Re δ, Im δ plane. Keep in mind that hadronic uncertainties in nonleptonic decays are not fully under control!
)( ps 4.14
10)3.14.11.6()(
)04.002.0()(10)34.029.3()(
1
6
4
π→>∆
×±±=→
±−=γ→×±=γ→
−
−−+
−
KBBRMllXBBR
XBAXBBR
S
S
SCP
S
Im δ vs.Re δ for
( )LLd23δ
( )RRd23δ
( )LRd23δ
( )RLd23δ
GeV 350~~ gq mm =
Blue: ∆Ms<20 ps-1 Blue: ∆Ms<20 ps-1
Blue: SФK<0 Blue: SФK<0
CFMS
( )LLd23δ
( )RRd23δ
∆Ms for
( ) RRLLd
=δ 23
GeV 350~~ gq mm =
Does SФK<0 imply large ∆Ms?Not really…
SФK
∆Ms
CFMS
Roma, 6/5/2003 L. Silvestrini, INFN - Roma 26
Conclusions• Many independent th and exp
motivations for SUSY in b->s transitions:– Consistency of SM UT fit– Possible deviations from SM in SФK, CФK– Flavour Symmetries– SUSY GUTs + neutrino oscillations
• In the presence of NP, SФK, CФK suffer from sizable hadronic uncertainties
Roma, 6/5/2003 L. Silvestrini, INFN - Roma 27
Conclusions (cont’d)• At present, SUSY models with
orand 350 GeV squark/gluinos can reproduce all exp data including deviations from SM in SФK, CФK
• Future data on rare B decays and ∆Ms will allow us to test the SM and SUSY
• Interesting correlations with other observables in B physics and LFV
( ) )10( 1or 23
−≈δ ORRLLd ( ) )10( 3
or 23−≈δ ORLLR
d