Three loops renormalization constants in Numerical Stochastic Perturbation Theory

Abstract

We present three loops renormalization constants for Wilson fermion bilinears (vector, scalar, axial, pseudoscalar currents). Two gluonic regularizations are considered: tree level Symanzik improved action (with N f = 2) and Iwasaki action (with N f = 4). Both cases are amenable for comparisons with non-perturbative results. We discuss the issue of taming both finite lattice spacing and finite volume artifacts. As a byproduct, we comment on two loops matching of lattice and continuum couplings.

High-loop perturbative renormalization constants for Lattice QCD (III): three-loop quark currents for Iwasaki gauge action and $$n_f=4$$ n f = 4 Wilson fermions

“…To be definite, the normalization points are in the highest ( pa) 2 region of Fig. 2, which in terms of an n-tuple reads {4, 4, 4, 4}, {4, 4, 4, 5}; the two choices have been compared and results have been proved to 3 The reader will notice a few significant corrections with respect to the preliminary results in [7]. be equivalent within errors.…”

“…The main result of the current paper is the computation of quark currents RCs in the regularization defined by the Iwasaki gauge action and four flavors of Wilson quarks (quenched computations will be reported as well, to enable a comparison). Preliminary results were quoted in [7]. For a complete discussion of our methodology the reader should refer to [4], which has been largely devoted to a discussion in some detail of the NSPT approach to the computation of renormalization constants (with a main emphasis on the control over finite lattice spacing and finite-volume effects).…”

High-loop perturbative renormalization constants for Lattice QCD (II): three-loop quark currents for tree-level Symanzik improved gauge action and n f =2 Wilson fermions

“…The simplest (and straightforward) recipe is to sum the series in the coupling β −1 . At 9 Comparing to the preliminary results in [7] the reader will recognize a typo for Z P at second loop. Table 2: One-, two-and three-loop coefficients of the renormalization constants for quark bilinears.…”

“…This is the first of two papers dealing with the three-loop computation of Lattice QCD RCs in the RI'-MOM scheme for plain Wilson fermions and improved gauge actions: in the present paper we report results for the tree-level Symanzik improved gauge action with n f = 2 and discuss the general framework of finite lattice spacing and finite size corrections; in a second one we deal with Iwasaki gauge action with n f = 4 and tackle the all the problems connected with summing PT series for Lattice QCD RCs [6]. Updates on these computations have been presented in recent years at the Lattice conferences, and in particular preliminary results were quoted in [7]. We emphasize that in both cases (n f = 2 tree-level Symanzik and n f = 4 Iwasaki) results can be compared with analogous non-perturbative computations for Twisted Mass fermions [8,9]: since the renormalization scheme is massless, RCs are the same.…”

“…enters the expression for a z (1) 3 , but since two-loop z (0) 2can be computed before we are concerned with the z (i) 3 , this is not a problem 7. This is due to the values of one-and two-loop constants z all this is of course merely a numerical accident.…”