Improved staggered quark actions with reduced flavor symmetry violations for lattice QCD

Abstract

We introduce a new class of actions for staggered quarks in lattice QCD which significantly reduce flavour symmetry violations in the pion mass spectrum.An action introduced by the MILC collaboration for the same purpose is seen to be a special case. We discus how such actions arise from a systematic attempt to reduce flavour symmetry violations in the weak coupling limit. It is shown that for quenched lattice QCD at 6/g 2 = 5.7, representative actions of this class give a considerable reduction in flavour symmetry violation over the standard staggered action, and a significant reduction over what is achieved by the MILC action.

One-loop matching coefficients for improved staggered bilinears

“…Lepage [2,8] and Lagae and Sinclair [6] have argued that flavor symmetry breaking can be substantially reduced by suppressing the coupling of high momentum gluons which connect "physical" quarks residing at different corners of the Brillouin zone. Such suppression is also expected to reduce the size of one-loop contributions to perturbative matching factors, since, as noted by Golterman [15], their size is largely due to tadpole-type diagrams which involve these flavor-changing vertices.…”

“…Improved staggered fermions are an attractive choice for numerical simulations of unquenched QCD [1][2][3][4][5][6][7][8][9][10][11]. They maintain the positive features of unimproved staggered fermions-smaller CPU requirements than other fermion discretizations, a remnant chiral symmetry, and O(a 2 ) discretization errors-while potentially avoiding its drawbackslarge flavor symmetry breaking and large perturbative matching factors.…”

Lattice results with three quark flavours

“…An improved gauge action was applied in 1995 [4]. Soon thereafter calculations were done with the Naik term and an improved gauge action [5] and the importance of "fattening" the action to reduce taste symmetry breaking was tested and understood [6][7][8][9][10]. About the same time, the P4 action was introduced because of it's improved rotational symmetry [11,12] All of these improvement schemes are analagous to higher order methods in numerical analysis, but with the twist of applying to QFT.…”

Matching coefficients for improved staggered bilinears

“…This is one part of the Symanzik improvement program applied at tree level [3]. Smeared links are expected to substantially reduce the non-perturbative taste-symmetry breaking, and this is observed in the pion spectrum [2,4,5]. It turns out that the largest reduction is for multiple APE smearing or HYP links [6].…”

“…The key ingredient is the use of "smeared" links, which reduce the tastebreaking couplings of high momentum gluons to quarks [1][2][3]. This is one part of the Symanzik improvement program applied at tree level [3].…”