Baryons with Ginsparg-Wilson quarks in a staggered sea

TL;DR

This work develops a mixed-action PQχPT framework for Ginsparg-Wilson valence quarks on a staggered sea to study octet baryon properties. It derives the Symanzik effective theory, constructs the meson and baryon sectors, and computes baryon magnetic moments to ${\mathcal{O}}({\varepsilon})$ and masses to ${\mathcal{O}}({\varepsilon}^3)$, showing that taste-symmetry breaking does not enter at these orders. The analysis identifies three lattice-spacing parameters ${C_0}$, ${C_{\text{mix}}}$, and ${C_3+C_4}$ that govern baryon masses and a single new LEC ${C_{\text{mix}}}$ that governs magnetic moments, with finite-volume corrections discussed in the Appendix. The results provide practical, systematically improvable formulas to extrapolate mixed-action lattice QCD data for baryon observables and to quantify lattice artifacts in simulations using GW valence quarks on a staggered sea.

Abstract

We determine the masses and magnetic moments of the octet baryons in chiral perturbation theory formulated for a mixed lattice action of Ginsparg-Wilson valence quarks and staggered sea quarks. Taste-symmetry breaking does not occur at next-to-leading order in the combined lattice-spacing and chiral expansion. Expressions derived for masses and magnetic moments are required for addressing lattice artifacts in mixed-action simulations of these observables.

Figures (2)

• Figure 1: Loop diagrams contributing to the octet baryon magnetic moments at ${\mathcal{O}}({\varepsilon})$. The photon is pictured as a wiggly line, mesons are denoted by a dashed line, and a thin solid line denotes a $\bm{1938}$ baryon, while the double line denotes a $\bm{1086}$ baryon.
• Figure 2: Loop diagrams contributing to the octet baryon masses at ${\mathcal{O}}({\varepsilon}^3)$. Mesons are denoted by a dashed line, flavor neutrals (hairpins) by a crossed dashed line, and a thin solid line denotes a $\bm{1938}$ baryon, while the double line denotes a $\bm{1086}$ baryon.