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.