We make the simple observation that there exists a universal unitarity triangle for all models, like the SM, the Two Higgs Doublet Models I and II and the MSSM with minimal flavour violation, that do not have any new operators beyond those present in the SM and in which all flavour changing transitions are governed by the CKM matrix with no new phases beyond the CKM phase. This universal triangle can be determined in the near future from the ratio (∆M ) d /(∆M ) s and sin 2β measured first through the CP asymmetry in B 0 d → ψK S and later in K → πνν decays. Also suitable ratios of the branching ratios for B → X d,s νν and B d,s → µ + µ − and the angle γ measured by means of CP asymmetries in B decays can be used for this determination. Comparison of this universal triangle with the nonuniversal triangles extracted in each model using ε, (∆M ) d and various branching ratios for rare decays will allow to find out in a transparent manner which of these models, if any, is singled out by experiment. A virtue of the universal triangle is that it allows to separate the determination of the CKM parameters from the determination of new parameters present in the extensions of the SM considered here.

We present analytic formulae for the QCD renormalization group factors relating the Wilson coefficients C i (µ t ) and C i (µ), with µ t = O(m t ) and µ < µ t , of the ∆F = 2 dimension six fourquark operators Q i in the Standard Model and in all of its extensions. Analogous analytic formulae for the QCD factors relating the matrix elements Q i (2 GeV) and Q i (µ K ) with µ K < 2 GeV are also presented. The formulae are given in the NDR scheme. The strongest renormalization-group effects are found for the operators with the Dirac structures (1 − γ 5 ) ⊗ (1+γ 5 ) and (1−γ 5 )⊗(1−γ 5 ). We calculate the matrix elements K 0 |Q i |K 0 in the NDR scheme using the lattice results in the LRI scheme. We give expressions for the mass differences ∆M K and ∆M B and the CP-violating parameter ǫ K in terms of the non-perturbative parameters B i and the Wilson coefficients C i (µ t ). The latter summarize the dependence on new physics contributions.

We present a new analysis of the ratio ε /ε within the Standard Model (SM) using a formalism that is manifestly independent of the values of leading (V − A) ⊗ (V − A) QCD penguin, and EW penguin hadronic matrix elements of the operators Q 4 , Q 9 , and Q 10 , and applies to the SM as well as extensions with the same operator structure. It is valid under the assumption that the SM exactly describes the data on CP-conserving K → ππ amplitudes. As a result of this and the high precision now available for CKM and quark mass parameters, to high accuracy ε /ε depends only on two non-perturbative parameters, B(1/2) 6 and B (3/2) 8, and perturbatively calculable Wilson coefficients. Within the SM, we are separately able to determine the hadronic matrix element Q 4 0 from CPconserving data, significantly more precisely than presently possible with lattice QCD. Employing B(1/2) 6 = 0.57 ± 0.19 and B (3/2) 8 = 0.76 ± 0.05, extracted from recent results by the RBC-UKQCD collaboration, we obtain ε /ε = (1.9 ± 4.5) × 10 −4 , substantially more precise than the recent RBC-UKQCD prediction and 2.9 σ below the experimental value (16.6 ± 2.3) × 10 −4 , with the error being fully dominated by that on B(1/2) 6. Even discarding lattice input completely, but employing the recently obtained bound B(1/2) 6 ≤ B (3/2) 8 ≤ 1 from the large-N approach, the SM value is found more than 2 σ below the experimental value. At B(1/2) 6 = B (3/2) 8 = 1, varying all other parameters within one sigma, we find ε /ε = (8.6 ± 3.2) × 10 −4 . We present a detailed anatomy of the various SM uncertainties, including all sub-leading hadronic matrix elements, briefly commenting on the possibility of underestimated SM contributions as well as on the impact of our results on new physics models.

We compute the 1-loop (alpha_s^2) correction to hard spectator scattering in non-leptonic B decay tree amplitudes. This forms part of the NNLO contribution to the QCD factorization formula for hadronic B decays, and introduces a new rescattering phase that corrects the leading-order result for direct CP asymmetries. Among the technical issues, we discuss the cancellation of infrared divergences, and the treatment of evanescent four-quark operators. The infrared finiteness of our result establishes factorization of spectator scattering at the 1-loop order. Depending on the values of hadronic input parameters, the new 1-loop correction may have a significant impact on tree-dominated decays such as B -> pi pi.Comment: 28 pages, 5 figures, LaTe

Tests of lepton-universality as rate ratios in b → sll transitions can be predicted very accurately in the Standard Model. The deficits with respect to expectations reported by the LHCb experiment in muon-toelectron ratios of the B → K ðÃÞ ll decay rates thus point to genuine manifestations of lepton nonuniversal new physics. In this paper, we analyze these measurements in the context of effective field theory. First, we discuss the interplay of the different operators in R K and R K à and provide predictions for R K à in the Standard Model and in new-physics scenarios that can explain R K . We also provide approximate numerical formulas for these observables in bins of interest as functions of the relevant Wilson coefficients. Secondly, we perform frequentist fits to R K and R K à . The Standard Model disagrees with these measurements at 3.7σ significance. We find excellent fits in scenarios with combinations ofwith pulls relative to the Standard Model in the region of 4σ. An important conclusion of our analysis is that a lepton-specific contribution to O 10 is important to understand the data. Under the hypothesis that new-physics couples selectively to the muons, we also present fits to other b → sμμ data with a conservative error assessment and comment on more general scenarios. Finally, we discuss new lepton universality ratios that, if new physics is the origin of the observed discrepancy, should contribute to the statistically significant discovery of new physics in the near future.

We investigate rare semileptonicB →K * + − decays, providing a comprehensive treatment of theoretical uncertainties in the low-q 2 region as needed for interpreting current and future LHCb and B-factory data in terms of the new physics search. We go beyond the usual focus on formfactor uncertainties, paying proper attention to non-factorizable terms.A central point is the systematic exploitation of the V − A structure of SM weak interactions, which leads to the suppression of two helicity amplitudes and some of the angular coefficients. We review how this works at the level of (helicity) form factors, and show that the hierarchies extend to non-factorizable terms. For virtual charm effects, we give an argument for it in terms of light-cone QCD sum rules that continues to hold at the level of "long-distance" Λ 2 QCD /m 2 c power corrections, reducing an important source of theoretical uncertainty in anyB,B s → V + − (orB → V γ) decay. The contributions of the remaining hadronic weak Hamiltonian respect a similar hierarchy. We employ a resonance model to preclude (in theB →K * case) large long-distance corrections to this.A phenomenological part pays particular attention to the region of lowest dilepton mass, 4m 2 ≤ q 2 ≤ 2 GeV 2 . Two observables remain theoretically clean, implying a (theoretical) sensitivity to the real (imaginary) part of the "right-handed" Wilson coefficient C 7 to 10% (1%) of C SM 7 , both in the muonic and the electronic mode. We also show that there are two near-exact relations between angular coefficients, even in the presence of new physics and when lepton masses are not neglected.

In the past decade, one of the major challenges of particle physics has been to gain an in-depth understanding of the role of quark flavor. In this time frame, measurements and the theoretical interpretation of their results have advanced tremendously. A much broader understanding of flavor particles has been achieved; apart from their masses and quantum numbers, there now exist detailed measurements of the characteristics of their interactions allowing stringent tests of Standard Model predictions. Among the most interesting phenomena of flavor physics is the violation of the CP symmetry that has been subtle and difficult to explore. In the past, observations of CP violation were confined to neutral K mesons, but since the early 1990s, a large number of CP-violating processes have been studied in detail in neutral B mesons. In parallel, measurements of the couplings of the heavy quarks and the dynamics for their decays in large samples of K, D, and B mesons have been greatly improved in accuracy and the results are being used as probes in the search for deviations from the Standard Model. In the near future, there will be a transition from the current to a new generation of experiments; thus a review of the status of quark flavor physics is timely. This report is the result of the work of physicists attending the 5th CKM workshop, hosted by the University of Rome "La Sapienza", September 9-13, 2008. It summarizes the results of the current generation of experiments that are about to be completed and it confronts these results with the theoretical understanding of the field which has greatly improved in the past decade. (C) 2010 Elsevier B.V. All rights reserved

We critically examine the potential to disentangle Standard Model (SM) and New Physics (NP) in B → K * µ + µ − and B → K * e + e − decays, focusing on (i) the LHCb anomaly, (ii) the search for righthanded currents, and (iii) lepton-universality violation. Restricting ourselves to the large-recoil region, we advocate a parameterisation of the hadronic matrix elements that separates model-independent information about nonperturbative QCD from the results of model calculations. We clarify how to estimate corrections to the heavy-quark limit that would generate a right-handed (virtual) photon in the b → sγ contribution to the decay. We then apply this approach to the discussion of various sets of observables of increasing theoretical cleanness. First, we show that angular observables in the optimized P ( ) i basis are, in general, still not robust against the long-distance QCD effects, both numerically and by examining analytically the dependence on corrections to the (model-independent) heavy-quark limit. As a result, while a fit to data favours a NP contribution to the semileptonic operators of the type δC 9 −1.5, this comes at a relatively small statistical significance of 2σ, once such power corrections are properly accounted for. Second, two of these observables, P 1 and P CP 3 are particularly clean at very low q 2 and sensitive probes of right-handed quark currents. We discuss their potential to set stringent bounds on the Wilson coefficient C 7 , especially using data of the electronic mode, and we update the bounds with current angular data in the muonic channel. Finally, in light of the recent hint of lepton-universality violation in B + → K + , we introduce and investigate new lepton-universality observables involving angular observables of the muonic and electronic modes and their zero crossings, and show that, if the effect is of the size suggested by experiment, these can clearly distinguish between different NP explanations in terms of underlying semileptonic operators.