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We discuss the renormalization properties of the full set of $$\Delta F=2$$ operators involved in BSM processes, including the definition of RGI versions of operators that exhibit mixing under RG transformations. As a first step for a fully non-perturbative determination of the scale-dependent renormalization factors and their runnings, we introduce a family of appropriate Schrödinger Functional schemes, and study them in perturbation theory. This allows, in particular, to determine the NLO anomalous dimensions of all $$\Delta F=1,2$$ operators in these schemes. Finally, we discuss the systematic uncertainties related to the use of NLO perturbation theory for the RG running of four-quark operators to scales in the GeV range, in both our SF schemes and standard $${\overline{\mathrm{MS}}}$$ and RI-MOM schemes. Large truncation effects are found for some of the operators considered. [ABSTRACT FROM AUTHOR]

We present the first unquenched, continuum limit, lattice QCD results for the matrix elements of the operators describing neutral kaon oscillations in extensions of the Standard Model. Owing to the accuracy of our calculation on ∆ S = 2 weak Hamiltonian matrix elements, we are able to provide a refined Unitarity Triangle analysis improving the bounds coming from model independent constraints on New Physics. In our nonperturbative computation we use a combination of Nf = 2 maximally twisted sea quarks and Osterwalder-Seiler valence quarks in order to achieve both O( a)-improvement and continuum-like renormalization properties for the relevant four-fermion operators. The calculation of the renormalization constants has been performed non-perturbatively in the RI-MOM scheme. Based on simulations at four values of the lattice spacing and a number of quark masses we have extrapolated/interpolated our results to the continuum limit and physical light/strange quark masses.[Figure not available: see fulltext.] [ABSTRACT FROM AUTHOR]

We present a quenched lattice study of the vector form factors at zero-momentum transfer,f V(0), relevant for the determination of |V us| from semileptonicK?pl?(Kl3) andS- ?nl?decays. Using suitable double ratios of three-point correlation functions we show that in case of both kaon and hyperon decays it is possible to calculate the form factorf V(0) at the percent precision, which is the one required for a significant determination of |V us|. In case ofKl3 decay the leading quenched chiral logarithms are corrected for by using analytic calculations in quenched chiral perturbation theory. Our final result,f V(K0 p-) = 0.960 ± 0.005stat ± 0.007syst, where the systematic error does not include the residual quenched effects, is in good agreement with the estimate made by Leutwyler and Roos. The impact of our result on the extraction of |V us| is briefly illustrated.PACS:12.15.Hh Determination of CKM matrix elements - 13.20.Eb Semileptonic decays of K mesons - 13.30.Ce Semileptonic decays of baryons - 12.38.Gc Lattice QCD calculations [ABSTRACT FROM AUTHOR]

We report our results for the bag parameterBK obtained from the quenched simulations on the lattice with Wilson fermions for three values of the lattice spacing. We implemented the method by which no subtraction of the mixing with other four-fermionoperators is needed. Our final result, in terms of the renormalization group invariant bag parameter, is. [ABSTRACT FROM AUTHOR]

We perform a non-perturbative study of the scale-dependent renormalisation factors of a complete set of dimension-six four-fermion operators without power subtractions. The renormalisation-group (RG) running is determined in the continuum limit for a specific Schrödinger Functional (SF) renormalisation scheme in the framework of lattice QCD with two dynamical flavours (Nf=2). The theory is regularised on a lattice with a plaquette Wilson action and O(a)-improved Wilson fermions. For one of these operators, the computation had been performed in Dimopoulos et al. (JHEP 0805, 065 (2008). arXiv:0712.2429); the present work completes the study for the rest of the operator basis, on the same simulations (configuration ensembles). The related weak matrix elements arise in several operator product expansions; in ΔF=2 transitions they contain the QCD long-distance effects, including contributions from beyond-Standard Model (BSM) processes. Some of these operators mix under renormalisation and their RG-running is governed by anomalous dimension matrices. In Papinutto et al. (Eur Phys J C 77(6), 376 (2017). arXiv:1612.06461) the RG formalism for the operator basis has been worked out in full generality and the anomalous dimension matrix has been calculated in NLO perturbation theory. Here the discussion is extended to the matrix step-scaling functions, which are used in finite-size recursive techniques. We rely on these matrix-SSFs to obtain non-perturbative estimates of the operator anomalous dimensions for scales ranging from O(ΛQCD) to O(MW). [ABSTRACT FROM AUTHOR]