Twisted mass QCD and lattice approaches to the $\Delta I=1/2$ rule

Abstract

Twisted mass lattice QCD (tmQCD), generalised to four Wilson quark flavours, can be used for the computation of some weak matrix elements related to $\Delta I=1/2$ transitions. Besides eliminating unphysical zero modes, tmQCD may alleviate long-standing renormalisation problems of the four-quark operators which contribute to CP-conserving $K\to \pi$ transitions. With an active charm quark, the renormalisation of the $K\to \pi$ matrix elements requires at most the subtraction of a linearly divergent counterterm. Furthermore, in the (partially) quenched approximation the twist angles can be chosen so that only a finite counterterm needs to be subtracted.

35 pages;final version with references added

References in corpus (3)

• Chirally improving Wilson fermions II. Four-quark operators
• Twisted-mass lattice QCD with mass non-degenerate quarks
• A strategy to study the role of the charm quark in explaining the Delta{I}=1/2 rule

Cited by in corpus (32)

• Chirally improving Wilson fermions II. Four-quark operators
• Dynamical Twisted Mass Fermions with Light Quarks
• Light Hadron Masses from Lattice QCD
• Twisted mass lattice QCD
• Twisted mass chiral perturbation theory at next-to-leading order
• Computing K and D meson masses with N_f = 2+1+1 twisted mass lattice QCD
• BK-parameter from Nf = 2 twisted mass lattice QCD
• Numerical simulation of QCD with u, d, s and c quarks in the twisted-mass Wilson formulation
• Strange quarks in quenched twisted mass lattice QCD
• A precise determination of $B_K$ in quenched QCD
• A strategy to study the role of the charm quark in explaining the Delta{I}=1/2 rule
• Nucleon and Delta masses in twisted mass chiral perturbation theory
• Flavour symmetry restoration and kaon weak matrix elements in quenched twisted mass QCD
• Past, present, and future of precision determinations of the QCD coupling from lattice QCD
• A perturbative study of two four-quark operators in finite volume renormalization schemes
• Non-perturbative renormalisation of left-left four-fermion operators with Neuberger fermions
• Quenched $B_K$-parameter from Osterwalder-Seiler tmQCD quarks and mass-splitting discretization effects
• A strategy for implementing non-perturbative renormalisation of heavy-light four-quark operators in the static approximation
• Probing the chiral weak Hamiltonian at finite volumes
• A quenched study of the Schroedinger functional with chirally rotated boundary conditions: applications
• A quenched study of the Schroedinger functional with chirally rotated boundary conditions: non-perturbative tuning
• Non-Perturbative Renormalisation and Running of BSM Four-Quark Operators in $N_f=2$ QCD
• Lattice QCD with a twisted mass term and a strange quark
• A tmQCD mixed-action approach to flavour physics
• Exploring the role of the charm quark in the $\Delta I=1/2$ rule
• Topics in Effective Field Theory for Lattice QCD
• Nf=2 Lattice QCD and Chiral Perturbation Theory
• Twisted mass QCD for weak matrix elements
• K* vector and tensor couplings from Nf = 2 tmQCD
• The Spectrum of tmLQCD with Quark and Link Smearing
• Lattice QCD at maximal twist
• $f_K/f_{\pi }$ in iso-symmetric QCD and the CKM matrix unitarity