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Register a new userOn the perturbative renormalisation of four-quark operators for new physics
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We discuss the renormalisation properties of the full set of $Delta F=2$ operators involved in BSM processes, including the definition of R
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We perform a non-perturbative study of the scale-dependent renormalisation factors of a complete set of dimension-six four-fermion operators. The renormalisation-group (RG) running is determined in the continuum limit for a specific Schrdinger Functional (SF) renormalisation scheme in the framework of lattice QCD with two dynamical flavours ( $N_f = 2$ ). The theory is regularised on a lattice with a plaquette Wilson action and $mathcal{O}(a)$-improved Wilson fermions. For one of these operators, the computation had been performed in ref. [1]; 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 $Delta F = 2$ 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 ref. [2] 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 (matrix-SSFs), 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 $mathcal{O}(Lambda_{rm QCD})$ to $mathcal{O}(M_W)$.
We compute the renormalisation factors (Z-matrices) of the $Delta F=2$ four-quark operators needed for Beyond the Standard Model (BSM) kaon mixing. We work with nf=2+1 flavours of Domain-Wall fermions whose chiral-flavour properties are essential to maintain a continuum-like mixing pattern. We introduce new RI-SMOM renormalisation schemes, which we argue are better behaved compared to the commonly-used corresponding RI-MOM one. We find that, once converted to MS, the Z-factors computed through these RI-SMOM schemes are in good agreement but differ significantly from the ones computed through the RI-MOM scheme. The RI-SMOM Z-factors presented here have been used to compute the BSM neutral kaon mixing matrix elements in the companion paper [1]. We argue that the renormalisation procedure is responsible for the discrepancies observed by different collaborations, we will investigate and elucidate the origin of these differences throughout this work.
High luminosity accelerators have greatly increased the interest in semi-exclusive and exclusive reactions involving nucleons. The relevant theoretical information is contained in the nucleon wavefunction and can be parametrized by moments of the nucleon distribution amplitudes, which in turn are linked to matrix elements of local three-quark operators. These can be calculated from first principles in lattice QCD. Defining an RI-MOM renormalization scheme, we renormalize three-quark operators corresponding to low moments non-perturbatively and take special care of the operator mixing. After performing a scheme matching and a conversion of the renormalization scale we quote our final results in the MSbar scheme at mu=2 GeV.
We investigate the renormalization of a class of gauge-invariant nonlocal quark bilinear operators, including a finite-length Wilson-line (called Wilson-line operators). The matrix elements of these operators are involved in the recent quasi-distribution approach for computing light-cone distributions of Hadronic Physics on the lattice. We consider two classes of Wilson-line operators: straight-line and staple-shaped operators, which are related to the parton distribution functions (PDFs) and transverse momentum-dependent distributions (TMDs), respectively. We present our one-loop results for the conversion factors of straight-line operators between the RI (appropriate for nonperturbative renormalization on the lattice) and MSbar (typically used in phenomenology) renormalization schemes in the presence of nonzero quark masses. In addition, we present the first results of our preliminary work for the renormalization of staple-shaped operators both in continuum (Dimensional Regularization) and lattice (Wilson/clover fermions and Symanzik improved gluons) regularizations. We identify the observed mixing pairs among these operators, which must be disentangled in the nonperturbative investigations of heavy-quark quasi-PDFs and of light-quark quasi-TMDs.
We calculate one-loop renormalization factors of generic DeltaS=2 four-quark operators for domain-wall QCD with the plaquette gauge action and the Iwasaki gauge action. The renormalization factors are presented in the modified minimal subtraction (MS-bar) scheme with the naive dimensional regularization. As an important application we show how to construct the renormalization factors for the operators contributing to K^0-K^0bar mixing in the supersymmetric models with the use of our results.
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