Renormalization constants for 2-twist operators in twisted mass QCD

TL;DR

This paper presents both perturbative and non-perturbative calculations of renormalization constants for twist-2 operators in twisted mass QCD, using lattice simulations with dynamical quarks and improved gluon actions.

Contribution

It provides the first comprehensive non-perturbative evaluation of renormalization constants for twist-2 operators in twisted mass QCD with dynamical quarks.

Findings

Renormalization constants are computed at multiple lattice spacings and pion masses.

Results are evolved to a common scale and converted to MS-bar scheme at 2 GeV.

Perturbative subtraction of lattice artifacts improves accuracy.

Abstract

Perturbative and non-perturbative results on the renormalization constants of the fermion field and the twist-2 fermion bilinears are presented with emphasis on the non-perturbative evaluation of the one-derivative twist-2 vector and axial vector operators. Non-perturbative results are obtained using the twisted mass Wilson fermion formulation employing two degenerate dynamical quarks and the tree-level Symanzik improved gluon action. The simulations have been performed for pion masses in the range of about 450-260 MeV and at three values of the lattice spacing $a$ corresponding to $\beta=3.9, 4.05, 4.20$. Subtraction of ${\cal O}(a^2)$ terms is carried out by performing the perturbative evaluation of these operators at 1-loop and up to ${\cal O}(a^2)$. The renormalization conditions are defined in the RI$'$-MOM scheme, for both perturbative and non-perturbative results. The renormalization factors, obtained for different values of the renormalization scale, are evolved perturbatively to a reference scale set by the inverse of the lattice spacing. In addition, they are translated to ${\bar{\rm MS}}$ at 2 GeV using 3-loop perturbative results for the conversion factors.