Renormalization functions for Nf=2 and Nf=4 Twisted Mass fermions

TL;DR

This paper computes non-perturbative renormalization functions for quark fields and fermion bilinears in twisted mass lattice QCD with Nf=2 and Nf=4, using RI' scheme and perturbative corrections, to facilitate continuum physics studies.

Contribution

It provides a detailed calculation of renormalization functions for twisted mass fermions with Nf=2 and Nf=4, including lattice artifact subtraction and conversion to MSbar scheme.

Findings

Renormalization functions are obtained for multiple pion masses and lattice spacings.

Lattice artifacts are subtracted to improve continuum extrapolation.

Results are converted to the MSbar scheme at 2 GeV.

Abstract

We present results on the renormalization functions of the quark field and fermion bilinears with up to one covariant derivative. For the fermion part of the action we employ the twisted mass formulation with $N_f{=}2$ and $N_f{=}4$ degenerate dynamical quarks, while in the gluon sector we use the Iwasaki improved action. The simulations for $N_f{=}4$ have been performed for pion masses in the range of 390MeV - 760MeV and at three values of the lattice spacing, $a$, corresponding to $\beta{=}1.90,\,1.95,\,2.10$. The $N_f{=}2$ action includes a clover term with $c_{\rm sw}{=}1.57551$ at $\beta{=}2.10$, and three ensembles at different values of $m_\pi$. The evaluation of the renormalization functions is carried out in the RI$'$ scheme using a momentum source. The non-perturbartive evaluation is complemented with a perturbative computation, which is carried out at one-loop level and to all orders in the lattice spacing, $a$. For each renormalization function computed non-perturbatively we subtract the corresponding lattice artifacts to all orders in $a$, so that a large part of the cut-off effects is eliminated. The renormalization functions are converted to the ${\overline{\rm MS}}$ scheme at a reference energy scale of $\mu{=}2$ GeV after taking the chiral limit.