Opening the Rome-Southampton window for operator mixing matrices

Abstract

We show that the running of operators which mix under renormalization can be computed fully non-perturbatively as a product of continuum step scaling matrices. These step scaling matrices are obtained by taking the "ratio" of Z matrices computed at different energies in an RI-MOM type scheme for which twisted boundary conditions are an essential ingredient. Our method allows us to relax the bounds of the Rome-Southampton window. We also explain why such a method is important in view of the light quark physics program of the RBC-UKQCD collaborations. To illustrate our method, using n_f=2+1 domain-wall fermions, we compute the non-perturbative running matrix of four-quark operators needed in K->pipi decay and neutral kaon mixing. Our results are then compared to perturbation theory.

8 pages, 7 figures. v2: PRD version, minor changes and few references added

References in corpus (13)

• Continuum Limit Physics from 2+1 Flavor Domain Wall QCD
• Lattice QCD at the physical point: Simulation and analysis details
• Precision computation of the kaon bag parameter
• Non-perturbative renormalization of quark bilinear operators and B_K using domain wall fermions
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• Two-loop matching factors for light quark masses and three-loop mass anomalous dimensions in the RI/SMOM schemes
• Step Scaling with off-shell renormalisation
• Gap Domain Wall Fermions
• $K$ to $\pi \pi$ Decay amplitudes from Lattice QCD
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• Matching factors for Delta S=1 four-quark operators in RI/SMOM schemes
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Cited by in corpus (15)

• Domain wall QCD with physical quark masses
• $K\to \pi \pi$ $\Delta I=3/2$ decay amplitude in the continuum limit
• Domain Wall QCD with Near-Physical Pions
• The $K\to (\pi \pi {)}_{I=2}$ Decay Amplitude from Lattice QCD
• Lattice determination of the $K\to (\pi \pi {)}_{I=2}$ Decay Amplitude $A_2$
• Neutral Kaon Mixing Beyond the Standard Model with $n_f=2+1$ Chiral Fermions Part 1: Bare Matrix Elements and Physical Results
• Heavy physics contributions to neutrinoless double beta decay from QCD
• The Low Energy Constants of $SU(2)$ Partially Quenched Chiral Perturbation Theory from $N_f=2+1$ Domain Wall QCD
• Direct CP violation and the $\Delta I=1/2$ rule in $K\to \pi \pi$ decay from the Standard Model
• Neutral kaon mixing beyond the standard model with nf=2+1 chiral fermions
• Lattice QCD Inputs for Nuclear Double Beta Decay
• Neutrinoless Double Beta Decay from Lattice QCD: The Short-Distance ${\pi }^{-}\to {\pi }^{+}{e}^{-}{e}^{-}$ Amplitude
• Bilinear quark operator renormalization at generalized symmetric point
• Calculating the two-pion decay and mixing of neutral K mesons
• On the perturbative renormalisation of four-quark operators for new physics