Non-Perturbative Renormalisation of the Lattice $\Delta s=2$ Four-Fermion Operator

Abstract

We compute the renormalised four-fermion operator $O^{\Delta S=2}$ using a non-perturbative method recently introduced for determining the renormalisation constants of generic lattice composite operators. Because of the presence of the Wilson term, $O^{\Delta S=2}$ mixes with operators of different chiralities. A projection method to determine the mixing coefficients is implemented. The numerical results for the renormalisation constants have been obtained from a simulation performed using the SW-Clover quark action, on a $16^3\times 32$ lattice, at $\beta =6.0$. We show that the use of the constants determined non-perturbatively improves the chiral behaviour of the lattice kaon matrix element $\<\bar K^0| O^{ΔS=2} | K^0\>_{\latt}$.

LaTeX, 16 pages, 2 postscript figures

References in corpus (5)

• On the Viability of Lattice Perturbation Theory
• A General Method for Non-Perturbative Renormalization of Lattice Operators
• The $\Delta S=1$ Effective Hamiltonian Including Next-to-Leading Order QCD and QED Corrections
• Gribov Noise on the Lattice Axial Current Renormalisation Constant
• The Kaon $B$-parameter with Wilson Fermions

Cited by in corpus (29)

• Next-to-Leading Order QCD Corrections to $\Delta F=2$ effective Hamiltonians
• The QCD Chiral Condensate from the Lattice
• Continuum Limit of $B_K$ from 2+1 Flavor Domain Wall QCD
• New lattice approaches to the $\Delta I=1/2$ rule
• Kaon B parameter from quenched domain-wall QCD
• B-parameters for DeltaS = 2 Supersymmetric Operators
• Non-perturbative Renormalization of Quark bilinears
• Lattice B-parameters for $\Delta S=2$ and $\Delta I=3/2$ Operators
• Matching factors for Delta S=1 four-quark operators in RI/SMOM schemes
• K0-K0bar Mixing with Wilson Fermions without Subtractions
• Hadronic Weak Interactions of Light Quarks
• Combined analysis of the unitarity triangle and CP violation in the Standard Model
• Leptonic Decays of Heavy Quarks on the Lattice
• Four quark operators for kaon bag parameter with gradient flow
• The Kaon B-parameter with the Wilson Quark Action using Chiral Ward Identities
• Mixing of B mesons and Decay Constants with the Non-Perturbatively Improved Action
• Non-perturbative Renormalization in Lattice Field Theory
• Non-perturbative renormalization of QCD
• A calculation of the $B_B$ parameter in the static limit
• Matrix elements relevant for Delta I=1/2 rule and epsilon-prime from Lattice QCD with staggered fermions
• Lattice QCD Calculation of the Kaon B-parameter with the Wilson Quark Action
• B-parameters for $\Delta S=2$ SUSY Operators
• Non-perturbative renormalization in kaon decays
• Non-Perturbative Renormalisation and Running of BSM Four-Quark Operators in $N_f=2$ QCD
• B_K with the Wilson Quark Action: A Non-Perturbative Resolution of Operator Mixing using Chiral Ward Identities
• The Kaon B-parameter with the Wilson Quark Action using Chiral Ward Identities
• Non-perturbative calculation of $Z_V$ and $Z_A$ in domain-wall QCD on a finite box
• Status and Perspective of Non-perturbative Renormalization in Weak Decays
• Non-perturbative renormalization in lattice QCD