On-shell-improved lattice QCD with staggered fermions

Abstract

By using Symanzik's improvement program, we study on-shell improved lattice QCD with staggered fermions. We find that there are as many as 15 independent lattice operators of dimension of six (including both gauge and fermion operators) which must be added to the unimproved action to form an O(a 2 ) improved action. Among them, the total number of dimension-6 gauge operators and fermion bilinears is 5. The other 10 terms are four-fermion operators. At the tree-level and tadpole-improved tree-level, all the 10 four fermion operators are absent.

Flavor-symmetry restoration and Symanzik improvement for staggered quarks

“…It was also observed that this interaction is a short-distance lattice artifact of relative order a 2 which can be removed by tree-level modifications of the lattice action. A more recent study, however, contradicts this conclusion by arguing that the one-gluon mechanism is redundant in O(a 2 ), and therefore that flavor-changing interactions are higher order in a or α s [3]. In this paper we resolve this contradiction by showing that one-gluon exchange is indeed responsible for the dominant flavor-changing interaction, as originally argued; the flavor-changing effects are not redundant in O(a 2 ).…”

“…Thus the effects of these exchanges can be canceled by adding four-quark interactions to the quark action [1]. The contact terms required at tree-level were explicitly constructed in [3]; these could be added to the staggered-quark action and the leading flavor-changing interactions removed. There is, however, a simpler modification of the action that accomplishes the same goal.…”

“…This means that the errors introduced by these interactions are O(a 2 ) at tree-level in the original theory [1,2]. In [3] the relevant contact interactions were converted into quark bilinears by transforming the gluon field in the path integral. The bilinears that resulted were of the form…”

“…There are only two sources of O(a 2 ) error at tree-level. One is the flavor-changing interaction due to one-gluon exchange; the other is a kinetic term common to all standard quark discretizations [5,3]. In this paper, we show how to correct for both of these.…”

Next-to-Leading-Order Staggered Chiral Perturbation Theory

“…In practice it is easiest to first determine all allowed lattice operators of dimension ≤ 6, as in Refs. [15,6], and then map these onto continuum quark-level operators [6]. Next one maps the continuum quark-level operators onto chiral operators describing the PGB sector.…”