Partial Flavor Symmetry Restoration for Chiral Staggered Fermions

TL;DR

The paper addresses flavor symmetry breaking in staggered fermions by constructing a continuum effective action with $O(a^2)$ corrections, showing that the leading discretization effects preserve an $SO(4)$ flavor subgroup in the chiral limit. The authors derive the corresponding chiral Lagrangian, map the $a^2$ operators into the pion sector, and predict three degeneracies among the seven lattice pion irreps, all consistent with observed data. They show that this partial symmetry restoration does not extend to non-Goldstone hadrons and can be spoiled by $O(a^4)$ effects, though current actions do not exhibit such breaking; they also discuss a staggered analog of the Aoki phase, which would require special conditions and is not realized in studied actions. The results have practical implications for improving staggered fermion actions, suggesting that targeted tuning of a subset of operators might reduce pion-splitting while full $O(a^2)$ improvement would still require addressing multiple independent coefficients.

Abstract

We study the leading discretization errors for staggered fermions by first constructing the continuum effective Lagrangian including terms of O(a^2), and then constructing the corresponding effective chiral Lagrangian. The terms of O(a^2) in the continuum effective Lagrangian completely break the SU(4) flavor symmetry down to the discrete subgroup respected by the lattice theory. We find, however, that the O(a^2) terms in the potential of the chiral Lagrangian maintain an SO(4) subgroup of SU(4). It follows that the leading discretization errors in the pion masses are SO(4) symmetric, implying three degeneracies within the seven lattice irreducible representations. These predictions hold also for perturbatively improved versions of the action. These degeneracies are observed, to a surprising degree of accuracy, in existing data. We argue that the SO(4) symmetry does not extend to the masses and interactions of other hadrons (vector mesons, baryons, etc), nor to higher order in a^2. We show how it is possible that, for physical quark masses of O(a^2), the new SO(4) symmetry can be spontaneously broken, leading to a staggered analogue of the Aoki-phase of Wilson fermions. This does not, however, appear to happen for presently studied versions of the staggered action.

Figures (2)

• Figure 1: Splittings between non-Goldstone and Goldstone pions at $\beta=6$ in the quenched approximation ishizuka. Results are in lattice units. The solid horizontal lines show the average value for the three pairs which are predicted to become degenerate in the chiral limit. Errors are approximate, as they have been obtained ignoring the error in the Goldstone pion mass, and the correlation between the masses of pions in different representations.
• Figure 2: Splittings between non-Goldstone and Goldstone pions in dynamical simulations orginos. Notation is as in Fig. \ref{['fig:ishizuka']}. The upper two sets of points come from simulations with unimproved gauge and fermion actions, while the lower two use improved gauge and fermion actions (the latter being the "fat+Naik" action). For clarity, some points have been offset horizontally.