Chiral Logs in the Presence of Staggered Flavor Symmetry Breaking

TL;DR

This work derives one-loop chiral logs for the staggered-fermion pion mass in the presence of KS flavor symmetry breaking by extending the Lee-Sharpe Lagrangian to 4+4 KS flavors and then mapping to the physically relevant 2+1 case via a quark-flow analysis. The calculation shows how lattice-induced $a^2$ flavor violations modify the chiral logarithm structure, providing explicit expressions that incorporate finite-volume effects and are ready for fits to MILC data. It also treats the quenched limit and outlines how to extend the framework to other observables, highlighting that including KS flavor breaking significantly improves the agreement with lattice results. The results offer a practical, systematically improvable path to extract physical quantities from staggered simulations by accounting for taste-symmetry breaking in the chiral logs.

Abstract

Chiral logarithms in $m_π^2$ are calculated at one loop, taking into account the leading contributions to flavor symmetry breaking due to staggered fermions. I treat both the full QCD case (2+1 light dynamical flavors) and the quenched case; finite volume corrections are included. My starting point is the effective chiral Lagrangian introduced by Lee and Sharpe. It is necessary to understand the one-loop diagrams in the ``quark flow'' picture in order to adjust the calculation to correspond to the desired number of dynamical quarks.

Figures (5)

• Figure 1: Chiral perturbation theory graphs contributing to the pion propagator from kinetic energy vertex (solid square). The external lines are Goldstone pions, i.e., $\pi_5$. The dots represent the derivatives in the vertex. In (a) they act on the external lines; in (b), the internal.
• Figure 2: Same as Fig. \ref{['fig:KE_vertex']}, but from the mass vertex (solid triangle). The internal propagator in (a) is the connected propagator only (no $m_0^2$ insertions), even when it is neutral ($\pi_I$). All disconnected contributions are in (b); i.e., the cross represents one or more insertions of the $m_0^2$ vertex.
• Figure 3: Same as Fig. \ref{['fig:KE_vertex']}, but from the flavor breaking vertex ${\cal V}$ (solid circle).
• Figure 4:
• Figure 5: Quark flow diagrams corresponding to 2 into 2 meson scattering at tree level in the chiral expansion. i,j,k,n are flavor indices.