Unitarity Triangle Analysis: Past, Present, Future INTRODUCTION: quark masses, weak couplings and CP in the Standard Model Unitary Triangle Analysis: PAST PRESENT FUTURE Dipartimento di Fisica di Roma I Guido Martinelli HANOI August 5th-9th 2004

C, CP and CPT and their violation are related to the foundations of modern physics (Relativistic quantum mechanics, Locality, Matter-Antimatter properties, Cosmology etc.) Although in the Standard Model (SM) all ingredients are present, new sources of CP beyond the SM are necessary to explain quantitatively the BAU Almost all New Physics Theories generate new sources of CP

Quark Masses, Weak Couplings and CP Violation in the Standard Model

L quarks = L kinetic + L weak int + L yukawa In the Standard Model the quark mass matrix, from which the CKM Matrix and CP originate, is determined by the Yukawa Lagrangian which couples fermions and Higgs CP invariant CP and symmetry breaking are closely related !

QUARK MASSES ARE GENERATED BY DYNAMICAL SYMMETRY BREAKING Charge -1/3 ∑ i,k=1,N [ m u i,k (u i L u k R ) + m d i,k (d i L d k R ) + h.c. ] Charge +2/3 L yukawa  ∑ i,k=1,N [ Y i,k (q i L H C ) U k R + X i,k (q i L H ) D k R + h.c. ]

Diagonalization of the Mass Matrix Up to singular cases, the mass matrix can always be diagonalized by 2 unitary transformations u i L  U ik L u k L u i R  U ik R u k R M´= U † L M U R (M´) † = U † R (M) † U L L mass  m up (u L u R + u R u L ) + m ch (c L c R + c R c L ) + m top (t L t R + t R t L )

N(N-1)/2 angles and (N-1)(N-2) /2 phases N=3 3 angles + 1 phase KM the phase generates complex couplings i.e. CP violation; 6 masses +3 angles +1 phase = 10 parameters

CP Violation is natural with three quark generations (Kobayashi-Maskawa) With three generations all CP phenomena are related to the same unique parameter (  ) NO Flavour Changing Neutral Currents (FCNC) at Tree Level (FCNC processes are good candidates for observing NEW PHYSICS)

Quark masses & Generation Mixing Neutron Proton e e-e- down up W | V ud | | V ud | = (8) | V us | = (23) | V cd | = 0.224(16) | V cs | = 0.970(9)(70) | V cb | = (8) | V ub | = (32) | V tb | = 0.99(29) (0.999)  -decays

c ij = Cos  ij s ij = Sin  ij c ij ≥0 s ij ≥0 0    2  |s 12 | ~ Sin  c for small angles |s ij | ~ | V ij |

+ O( 4 ) The Wolfenstein Parametrization ~ 0.2 A ~ 0.8  ~ 0.2  ~ 0.3 Sin  12 = Sin  23 = A 2 Sin  13 = A 3 (  -i  )

a1a1 a2a2 a3a3 b1b1 b2b2 b3b3 d1d1 e1e1 c3c3 The Bjorken-Jarlskog Unitarity Triangle | V ij | is invariant under phase rotations a 1 = V 11 V 12 * = V ud V us * a 2 = V 21 V 22 * a 3 = V 31 V 32 * a 1 + a 2 + a 3 = 0 (b 1 + b 2 + b 3 = 0 etc.) a1a1 a2a2 a3a3    Only the orientation depends on the phase convention

From A. Stocchi ICHEP 2002

sin 2  is measured directly from B J/  K s decays at Babar & Belle  (B d 0 J/  K s, t) -  (B d 0 J/  K s, t) A J/  K s =  (B d 0 J/  K s, t) +  (B d 0 J/  K s, t) A J/  K s = sin 2  sin (  m d t)

DIFFERENT LEVELS OF THEORETICAL UNCERTAINTIES (STRONG INTERACTIONS) 1)First class quantities, with reduced or negligible uncertainties 2) Second class quantities, with theoretical errors of O(10%) or less that can be reliably estimated 3) Third class quantities, for which theoretical predictions are model dependent (BBNS, charming, etc.) In case of discrepacies we cannot tell whether is new physics or we must blame the model

Quantities used in the Standard UT Analysis

M.Bona, M.Ciuchini, E.Franco, V.Lubicz, G.Martinelli, F.Parodi, M.Pierini, P.Roudeau, C.Schiavi, L.Silvestrini, A.Stocchi Roma, Genova, Torino, Orsay THE COLLABORATION NEW 2004 ANALYSIS IN PREPARATION New quantities e.g. B -> DK will be included Upgraded experimental numbers after Bejing THE CKM

PAST and PRESENT (the Standard Model)

With the constraint from  m s  =   =  [ ] [ ] at 95% C.L. sin 2  =  0.25 sin 2  =  [ ] [ ] Results for  and  & related quantities 68% and 95% C.L.

sin 2  measured =  Comparison of sin 2  from direct measurements (Aleph, Opal, Babar, Belle and CDF) and UTA analysis sin 2  UTA = ± Very good agreement no much room for physics beyond the SM !! sin 2  UTA = ± prediction from Ciuchini et al. (2000)

Theoretical predictions of Sin 2  in the years predictions exist since '95 experiments

Crucial Test of the Standard Model Triangle Sides (Non CP) compared to sin 2  and  K From the sides only sin 2  =0.715  0.050

PRESENT: sin 2  from B ->  &   and (2  +  ) from B -> DK & B -> D(D*)  FROM UTA

 m s Probability Density Without the constraint from  m s  m s = (20.6 ± 3.5 ) ps -1 [ ] ps -1 at 95% C.L. With the constraint from  m s  m s = (18.3 ) ps -1 [ ] ps -1 at 95% C.L

Hadronic parameters f Bd √B Bd = 223  33  12 MeV f Bd √B Bd = 217  12 MeV UTA B K = 0.86  0.06  0.14 lattice B K = 0.69 (+0.13) (-0.08) UTA lattice f Bs √B Bs = 276  38 MeV 14% f Bs √B Bs = 279  21 MeV 8% lattice UTA 6% 4%

Limits on Hadronic Parameters f Bs √B Bs

PRESENT (the Standard Model) NEW MEASUREMENTS

 B  BB     sin 2  from B -> 

 could be extracted by measuring

sin 2  from B -> 

PRESENT & NEAR FUTURE I cannot resist to show the next 3 trasparencies

MAIN TOPICS Factorization (see M. Neubert talk) What really means to test Factorization B  and B  K  decays and the determination of the CP parameter  Results including non-factorizable contributions Asymmetries Conclusions & Outlook From g.m. martinafranca

CHARMING PENGUINS GENERATE LARGE ASYMMETRIES BR(B) - BR(B) BR(B) + BR(B) A = BR( K +  0 ) BR( K +  - ) BR(  +  - ) Large uncertainties  typical A ≈0.2 (factorized 0.03) From g.m. martinafranca

Tree level diagrams, not influenced by new physics

FUTURE: FCNC & CP Violation beyond the Standard Model

CP beyond the SM (Supersymmetry) Spin 1/2 Quarks q L, u R, d R Leptons l L, e R Spin 0 SQuarks Q L, U R, D R SLeptons L L, E R Spin 1 Gauge bosons W, Z, , g Spin 1/2 Gauginos w, z, , g Spin 0 Higgs bosons H 1, H 2 Spin 1/2 Higgsinos H 1, H 2

In general the mixing mass matrix of the SQuarks (SMM) is not diagonal in flavour space analogously to the quark case We may either Diagonalize the SMM z, , g QjLQjL qjLqjL FCNC or Rotate by the same matrices the SUSY partners of the u- and d- like quarks (Q j L ) ´ = U ij L Q j L UjLUjL UiLUiL dkLdkL g

In the latter case the Squark Mass Matrix is not diagonal (m 2 Q ) ij = m 2 average 1 ij +  m ij 2  ij =  m ij 2 / m 2 average

Deviations from the SM ? Model independent analysis: Example B 0 -B 0 mixing (M.Ciuchini et al. hep-ph/ )

SM solution Second solution also suggested by BNNS analysis of B ->K ,   decays

TYPICAL BOUNDS FROM  M K AND  K x = m 2 g / m 2 q x = 1 m q = 500 GeV | Re (  12 2 ) LL | < 3.9  | Re (  12 2 ) LR | < 2.5  | Re (  12 ) LL (  12 ) RR | < 8.7  from  M K

from  K x = 1 m q = 500 GeV | Im (  12 2 ) LL | < 5.8  | Im (  12 2 ) LR | < 3.7  | Im (  12 ) LL (  12 ) RR | < 1.3  10 -4

 M B and A (B J/  K s )  M B d = 2 Abs |  B d | H | B d  | eff  B=2 A (B J/  K s ) = sin 2  sin  M B d t 2  = Arg |  B d | H | B d  | eff  B=2 sin 2  =  from exps BaBar & Belle & others

TYPICAL BOUNDS ON THE  -COUPLINGS  B 0 | H eff  B=2 | B 0  = Re A SM + Im A SM + A SUSY Re(  13 d ) AB 2 + i A SUSY Im(  13 d ) AB 2 A, B =LL, LR, RL, RR 1,3 = generation index A SM = A SM (  SM )

TYPICAL BOUNDS ON THE  -COUPLINGS  B 0 | H eff  B=2 | B 0  = Re A SM + Im A SM + A SUSY Re(  13 d ) AB 2 + i A SUSY Im(  13 d ) AB 2 Typical bounds: Re,Im(  13 d ) AB  1  5  Note: in this game  SM is not determined by the UTA From Kaon mixing: Re,Im(  12 d ) AB  1  SERIOUS CONSTRAINTS ON SUSY MODELS

CP Violation beyond the Standard Model Strongly constrained for b  d transitions, Much less for b  s : BR(B  X s  ) = (3.29 ± 0.34)  A CP (B  X s  ) = ± 0.04 BR(B  X s l + l - ) = (6.1 ± 1.4 ± 1.3)  The lower bound on B 0 s mixing  m s > 14 ps - 1

b b s s s g W b s s s t SM Penguins

SUSY Penguins b b s s s g W b s s s t Recent analyses by G. Kane et al., Murayama et al.and Ciuchini et al. Also Higgs (h,H,A) contributions

A  Ks = - C  Ks cos(  m B t) + S  Ks sin(  m B t ) A CP (B d ->  K s ) (2002 results) Observable BaBar Belle Average SM prediction BR (in )   ~ 5 S  Ks   0.64    C  Ks _ 0.56  0.41   One may a also consider B s ->  (for which there is an upper bound from Tevatron, CDF BR < ) [A CP (B d ->  K ) do not give significant constraints ]

A  Ks = - C  Ks cos(  m B t) + S  Ks sin(  m B t ) A CP (B d ->  K s ) (2003 results) Observable BaBar Belle Average SM prediction S  Ks    0.07 see M. Ciuchini et al. Presented at Moriond 2004 by L. Silvestrini

WHY RARE DECAYS ? Rare decays are a manifestation of broken (accidental) symmetries e.g. of physics beyond the Standard Model Proton decay baryon and lepton number conservation  -> e +  lepton flavor number i -> k

RARE DECAYS WHICH ARE ALLOWED IN THE STANDARD MODEL FCNC: q i -> q k + q i -> q k + l + l - q i -> q k +  these decays occur only via loops because of GIM and are suppressed by CKM THUS THEY ARE SENSITIVE TO NEW PHYSICS

Why we like K   ? For the same reason as A J/  K s : 1) Dominated by short distance dynamics (hard GIM suppression, calculable in pert. theory ) 2) Negligible hadronic uncertainties (matrix element known) O (G 2 F ) Z and W penguin/box s  d diagrams SM Diagrams

H eff =G 2 F  / (2√2  s 2 W )[ V td V ts * X t + V cd V cs * X c ]  ( s   (1 -  5 ) d) (   (1 -  5 ) ) NLO QCD corrections to X t,c and O (G 3 F m 4 t ) contributions known the hadronic matrix element ‹  | s   (1 -  5 ) d | K› is known with very high accuracy from Kl3 decays sensitive to V td V ts * and expected large CP

A(s  d ) O ( 5 m 2 t ) + i O ( 5 m 2 t ) CKM suppressed O ( m 2 c ) + i O ( 5 m 2 c ) O (  2 QCD ) GIM CP conserving: error of O (10%) due to NNLO corrections in the charm contribution and CKM uncertainties BR(K + ) SM = (7.2  2.0)  BR(K + ) EXP = ( )  events observed by E787 - central value about 2 the value of the SM - E events in 2 years

K + ->  +

CP Violating K L   0 O ( 5 m 2 t ) + i O ( m 2 t ) O ( m 2 c ) + i O ( 5 m 2 c ) O (  2 QCD ) BR(K + ) SM = 4.30  (m t (m t )/170GeV) 2.3  (Im(V ts * V td )/ 5 ) 2 = (2.8  1.0)  dominated by the top quark contribution -> short distances (or new physics) theoretical error ˜ 2 % Using  (K L   0 ) <  (K +   + ) One gets BR(K L   0 ) < 1.8  (90% C.L.) 2 order of magnitude larger than the SM expectations