Rotated twisted-mass: a convenient regularization scheme for isospin breaking QCD and QED lattice calculations

TL;DR

The paper introduces a rotated twisted-mass lattice regularization scheme that simplifies isospin breaking calculations in QCD and QED by reducing statistical fluctuations in mesonic observables.

Contribution

It presents a novel rotated twisted-mass regularization method that improves the calculation of isospin breaking effects in lattice QCD and QED, especially for mesonic observables.

Findings

Reduced statistical fluctuations in correlation functions

Effective calculation of pi+ - pi0 mass splitting

Validated scheme through numerical applications in QCD and QCD+QED

Abstract

We propose a scheme of lattice twisted-mass fermion regularization which is particularly convenient for application to isospin breaking (IB) QCD and QED calculations, based in particular on the so called RM123 approach, in which the IB terms of the action are treated as a perturbation. The main, practical advantage of this scheme is that it allows the calculation of IB effects on some mesonic observables, like e.g. the pi+ - pi0 mass splitting, using lattice correlation functions in which the quark and antiquark fields in the meson are regularized with opposite values of the Wilson parameter r. These correlation functions are found to be affected by much smaller statistical fluctuations, with respect to the analogous functions in which quark and antiquark fields are regularized with the same value of r. Two numerical application of this scheme, that we call "rotated twisted-mass", within pure QCD and QCD+QED respectively, are also provided for illustration.