Incontri di fisica del b, Parma, 19 th January 2006 on behalf of the Collaboration M. Bona, M. Ciuchini, E. Franco, V. Lubicz, G. Martinelli, F. Parodi, M. Pierini, P. Roudeau, C. Schiavi, L. Silvestrini, A. Stocchi, V. V. Bologna Vincenzo Vagnoni

Incontri di fisica del b, Parma, 19 th January CKM Physics: not just a triangle...

Incontri di fisica del b, Parma, 19 th January / /2 u c dsb A 3 (1- -i ) - A 2 t d, s b b V td,V ts B Oscillations A 3 ( i ) A 2 1 V tb c,u B decays b V ub,V cb Wolfenstein parametrization 4 parameters:, A, b-Physics plays a crucial role in the determination of those parameters The CKM matrix

Vincenzo Vagnoni Incontri di fisica del b, Parma, 19 th January The CKM is unitary 1 The Unitarity Triangle The non-diagonal elements of the matrix products correspond to 6 triangle equations

Incontri di fisica del b, Parma, 19 th January 2006 Bayes Theorem Standard Model + OPE/HQET/ Lattice QCD to go from quarks to hadrons }, m t } M. Bona et al. (UTfit Collaboration) JHEP07 (2005) hep-ph/ M. Bona et al. (UTfit Collaboration) hep-ph/ The UT fit method and the inputs

Vincenzo Vagnoni Incontri di fisica del b, Parma, 19 th January Standard UT fit : inputs

Vincenzo Vagnoni Incontri di fisica del b, Parma, 19 th January Standard constraints in the plane V ub /V cb K sin( ) 95% CL m d m d / m s = ± [0.289, 95% Prob. = ± [0.289, 95% Prob. = ± [0.112, 95% Prob. = ± [0.112, 95% Prob.

Incontri di fisica del b, Parma, 19 th January 2006 First crucial test of the Standard Model Determination of CP-violating parameters measuring CP-conserving observables: results fitting with sides only vs CP-violating observables sin 2 = ± experimental value from charmonium sin 2 = ± expectation from side-only results

Vincenzo Vagnoni Incontri di fisica del b, Parma, 19 th January Slight inconsistence in the fit due to an increase of V ub

Vincenzo Vagnoni Incontri di fisica del b, Parma, 19 th January Tree Processes could be used to « discover » NP comparing «direct» (which are NP free) and «indirect» (where NP contributions could show up) measurements of the same quantity. Predictions γ = (57.9 ± 7.4)° γ = 65.0 ± 18.0 γ = ± 18.0 NEW crucial TEST « Partially » DONE

Vincenzo Vagnoni Incontri di fisica del b, Parma, 19 th January Including all the constraints… = ± [0.300, 95% Prob. = ± [0.300, 95% Prob. = ± [0.141, 95% Prob. = ± [0.141, 95% Prob.

Vincenzo Vagnoni Incontri di fisica del b, Parma, 19 th January pre-B-factories analysis UT fit with angles only

Vincenzo Vagnoni Incontri di fisica del b, Parma, 19 th January m s > 14.5 ps -1 at 95% CL Sensitivity at 18.5 ps -1 SM prediction on m s from UT fits Despite the heroic efforts at LEP, SLD and CDF Run-I (now also CDF/D0 Run-II), m s is still unmeasured p.d.f. for m s in SM UT fits without using its current experimental limit m s = 22.2 ± 3.1 ps -1 Compatibility plot for an hypotetical future measurement > 31 ps 3 σ > 38 ps 5 σ

Vincenzo Vagnoni Incontri di fisica del b, Parma, 19 th January Relevance of LQCD for exploiting precise m d,s measurements in Unitarity Triangle fits m d,s enter the UT fits through the constraints m d,s enter the UT fits through the constraints where the long distance hadronic quantities are calculated in the framework of LQCD:

Vincenzo Vagnoni Incontri di fisica del b, Parma, 19 th January Fit with NP-independent constraints using Tree-level processes assumed to be NP free * the effect of the D0-D0 mixing is negligible wrt the actual error = ± 0.18 ± 0.11 = ± 0.41 ± 0.05 very important to improve: V ub /V cb from semileptonic decays from tree level processes reference starting point for NP model building

Vincenzo Vagnoni Incontri di fisica del b, Parma, 19 th January New Physics model independent parametrization in | F|=2 transitions The mixing processes being characterized by a single amplitude, they can be parametrized in a general way by means of two parameters H SM eff includes only SM box diagrams while H full eff includes New Physics contributions as well For the neutral kaon mixing case, it is convenient to introduce only one parameter m K is not considered since the long distance effects are not well controlled Four independent observables (C=1, =0 in SM) C Bd, Bd, C Bs, Bs 5 additional parameters

Incontri di fisica del b, Parma, 19 th January 2006 not yet available 6 available constraints Allowing for NP in | F|=2 transitions the additional parameters are left free in the fit

Vincenzo Vagnoni Incontri di fisica del b, Parma, 19 th January |V ub /V cb | m d K A CP (J/ K 0 ) (DK) |V ub /V cb | m d K A CP (J/ K 0 ) (DK) + cos2 A SL cos2 A SL Using the NP model independent approach in the fit SM-like solution The inclusion of A SL has an impact for suppressing the satellite NP solution (very suppressed) « NP » solution

Vincenzo Vagnoni Incontri di fisica del b, Parma, 19 th January C Bd = 1.27 ± 0.44 Bd = -4.7 ± 2.3 C K = 0.95 ± 0.18 Still 50% room for New Physics in m d amplitude But the New Physics mixing phase is already very constrained, must be close to zero! Using the NP model independent approach in the fit (II)

Vincenzo Vagnoni Incontri di fisica del b, Parma, 19 th January New Physics in the b d sector starts to be quite constrained and most probably will not come as an alternative to the CKM picture, but rather as a «correction» What to say/hope then? Basically two scenarios Minimal Flavour Violation: the only source of flavour violation is in the SM Yukawa couplings (implies =0) New Physics couplings between third and second families (b s sector) are stronger with respect to the b d ones Physics case for SuperB and LHCb Flavour physics needs to improve existing measurements in the B d sector and perform precise measurement in the B s sector: Physics case for SuperB and LHCb

Vincenzo Vagnoni Incontri di fisica del b, Parma, 19 th January Universal Unitarity Triangle: generalized SM analysis and MFV MFV = no additional flavour mixing only mixing processes are sensitive to NP For UUT we do not use K and m d in the fit = ± from UUT fit = ± from UUT fit = ± from UUT fit = ± from UUT fit Buras et al. hep-ph/

Vincenzo Vagnoni Incontri di fisica del b, Parma, 19 th January NP bounds in MFV scenario with small tan NP enters as additional contribution to the top box diagram (D'Ambrosio et al. hep-ph/ ) 0 = 2.4 TeV 0 is the equivalent SM scale > % for S 0 (x t ) > 0 > % for S 0 (x t ) < 0 S 0 = ± 0.54 [-0.90, Prob. S 0 = ± 0.54 [-0.90, Prob. a = 1 (as a reference)

Vincenzo Vagnoni Incontri di fisica del b, Parma, 19 th January S 0 B S 0 K > % for S 0 (x t ) > 0 > % for S 0 (x t ) < 0 > % for S 0 (x t ) > 0 > % for S 0 (x t ) < 0 S 0 B S 0 K NP bounds in MFV scenario with large tan

Vincenzo Vagnoni Incontri di fisica del b, Parma, 19 th January : where will we stand? Observable Sensitivity in 2010 sin2 sin o5o5o5o 5o5o5o5o |V cb | 1% |V ub | 4% BKBKBKBK5% 5% 3% m s m s 0.3 ps -1 (syst.) sin2 sin Assumptions B Factories will collect L=2 ab -1 two good years of data taking at LHCb (L=4 fb -1 ) improvements in LQCD quantities

Vincenzo Vagnoni Incontri di fisica del b, Parma, 19 th January sensitivity to New Physics observables in | F|=2 transitions from UT fits (assuming Standard Model validity) 0.1 (now ~0.2) K 0 sector 1.3 ° (now ~3°) B d sector 0.14 (now ~0.5) 1.3 o B s sector 0.12 Only using the measurements from a few key LHCb B s channels (in particular m s and sin2 ), the precision on NP observables for b s FCNC transitions in 2010 will be at the same level as the b d transitions!

Vincenzo Vagnoni Incontri di fisica del b, Parma, 19 th January Concluding remarks A large set of new bounds from B-factories allows over-constraining the Unitarity Triangle Standard Model is sadly showing an impressive consistency in the CKM sector If NP will show up, it will appear as a correction to the SM rather than as a revolution The only tension in the fit comes from a slight disagreement between sin2 and V ub By using only the constraints from |V ub |/|V cb | and, we have a (NP free) tree level determination of and This is a starting reference point for NP model building, since all the NP models have to agree with it Adopting a NP model independent parametrization, we fit SM ( and ) and NP (corrections to SM in mixing amplitudes and phases) together Constributions of NP to the B d mixing phase are already very constrained same phase of SM MFV scenarios seem preferred by data UUT fits are then the starting point of a MFV analysis We can translate the measurement of MFV NP sensitive quantities (mixing) into bounds on the tested scale More data are needed for NP hunting at low energies!