Renormalization constants for 2-twist operators in twisted mass QCD

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 $\mathcal{O}(a^2)$ terms is carried out by performing the perturbative evaluation of these operators at 1-loop and up to $\mathcal{O}(a^2)$. The renormalization conditions are defined in the RI${}^{\prime }$-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 $\overline{\mathrm{MS}}$ at 2 GeV using 3-loop perturbative results for the conversion factors.

ETM Collaboration, 25 pages, 15 figures. Improvement on the continuum extrapolation and clarification on the estimate of the systematic errors. Typos corrected

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