Non-Perturbative Renormalisation and Running of BSM Four-Quark Operators in $N_f=2$ QCD

Abstract

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 $\mathcal{O}({\Lambda }_{\mathrm{QCD}})$ to $\mathcal{O}(M_W)$.

arXiv comment45 pages, 17 figures

References in corpus (12)

• Chiral symmetry and O(a) improvement in lattice QCD
• The Schrödinger Functional - a Renormalizable Probe for Non-Abelian Gauge Theories
• Two-Loop QCD Anomalous Dimensions of Flavour-Changing Four-Quark Operators Within and Beyond the Standard Model
• Chirally improving Wilson fermions II. Four-quark operators
• Next-to-Leading Order QCD Corrections to $\Delta F=2$ effective Hamiltonians
• Computation of the Running Coupling in the SU(2) Yang-Mills Theory
• Precision computation of the kaon bag parameter
• Non-Perturbative Renormalization of Lattice Four-Fermion Operators without Power Subtractions
• Twisted mass QCD and lattice approaches to the $\Delta I=1/2$ rule
• Non-Perturbative Renormalisation of the Lattice $\Delta s=2$ Four-Fermion Operator
• Non-perturbative renormalization of left-left four-fermion operators in quenched lattice QCD
• Non-perturbative renormalisation of left-left four-fermion operators with Neuberger fermions

Cited by in corpus (4)

• FLAG Review 2019
• FLAG Review 2021
• FLAG Review 2024
• Gauge-invariant Renormalization Scheme in QCD: Application to fermion bilinears and the energy-momentum tensor