Ricerca Indiretta di Supersimmetria nei Decadimenti dei ... · Ricerca Indiretta di Supersimmetria...

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



• 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



• 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



• 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


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


The SM Unitarity Triangle

γα

β


Remove constraints from b -> s

• 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


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)


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



• 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



• 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~



• 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)



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


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


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


• 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


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

SФK vs.Im δ for

( )LLd23δ

( )RRd23δ

( )LRd23δ

( )RLd23δ

GeV 350~~ gq mm =

CFMS

SФK vs.CФK for

( )LLd23δ

( )RRd23δ

( )LRd23δ

( )RLd23δ

GeV 350~~ gq mm =

CFMS

GeV 350~~ gq mm =SФK vs ACP(b->sγ)

( )LLd23δ ( )LRd

23δCFMS

( )LLd23δ

( )RRd23δ

∆Ms for

( ) RRLLd

=δ 23

GeV 350~~ gq mm =

Does SФK<0 imply large ∆Ms?Not really…

SФK

∆Ms

CFMS


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


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

Ricerca Indiretta di Supersimmetria nei Decadimenti dei ... · Ricerca Indiretta di Supersimmetria...

Documents

Transcript of Ricerca Indiretta di Supersimmetria nei Decadimenti dei ... · Ricerca Indiretta di Supersimmetria...