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Register a new userNeutral kaon mixing beyond the Standard Model with nf=2+1 chiral fermions part II: Non Perturbative Renormalisation of the $Delta F=2$ four-quark operators
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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.
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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 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 Delta 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 non-perturbative 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.
We discuss the renormalisation properties of the full set of $Delta F=2$ operators involved in BSM processes, including the definition of R
We present the ETMC results for the bag parameters describing the neutral kaon mixing in the Standard Model and beyond and preliminary results for the bag parameters controlling the short distance contributions in the D^0-bar{D}^0 oscillations. We also present preliminary results for the B_{Bd}, B_{Bs}, B_{Bs}/B_{Bd} and xi -parameter controlling B^0_-bar{B}^0 oscillations in the Standard Model employing the so-called ratio method. Using Nf=2 maximally twisted sea quarks and Osterwalder-Seiler valence quarks we achieve both O(a)-improvement and continuum like renormalization pattern. Simulations are performed at three-values of the lattice spacing and several values of quark masses in the light, strange, charm region and above charm up to ~2.5m_c. Our results are extrapolated to the continuum limit and extrapolated/interpolated to the physical quark masses.
We present preliminary results of a non-perturbative study of the scale-dependent renormalization constants of a complete basis of Delta F=2 parity-odd four-fermion operators that enter the computation of hadronic B-parameters within the Standard Model (SM) and beyond. We consider non-perturbatively O(a) improved Wilson fermions and our gauge configurations contain two flavors of massless sea quarks. The mixing pattern of these operators is the same as for a regularization that preserves chiral symmetry, in particular there is a physical mixing between some of the operators. The renormalization group running matrix is computed in the continuum limit for a family of Schrodinger Functional (SF) schemes through finite volume recursive techniques. We compute non-perturbatively the relation between the renormalization group invariant operators and their counterparts renormalized in the SF at a low energy scale, together with the non-perturbative matching matrix between the lattice regularized theory and the various SF schemes.
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