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 ^+ - pi ^0 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.
Highlights
These processes, an accuracy at the level of few per mille has been reached by both the experimental measurements of the relevant decay rates and by the lattice determinations of the corresponding hadronic parameters in the isospin symmetric limit, namely the ratio of leptonic decay constant fK / fπ and the semileptonic form factor f+K π (0) [1]
We propose a scheme of lattice twisted-mass fermion regularization which is 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 aim of the present paper is to discuss a scheme for TM regularization of lattice QCD, that we call rotated twistedmass (RTM), which is convenient for lattice calculations of IB effects, in particular within the RM123 approach discussed above
Summary
Among the various lattice regularization which are commonly employed in lattice simulations, we are concerned in this paper with the twisted-mass (TM) regularization of the fermionic action [2,3]. The main, practical advantage of this scheme is that it allows the calculation of IB effects on some mesonic observables, like e.g. the π + − π 0 mass splitting, using lattice correlation functions in which the quark and antiquark fields in the meson are regularized, in the TM setup, with opposite values of the Wilson parameter r , i.e. r = ±1. In order to illustrate the advantage of RTM scheme, we will present in this paper two numerical applications, namely the calculations of the π +−π 0 mass splitting in pure QCD, at O( m2), and in QCD + QED, at O(αem). We end this paper by presenting some final considerations in the
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