Mixed Meson Masses with Domain-Wall Valence and Staggered Sea Fermions

TL;DR

This paper calculates the leading and next-to-leading order additive mass shifts of mixed mesons in lattice QCD with domain-wall valence and staggered sea fermions, providing essential corrections for accurate low-energy hadronic physics simulations.

Contribution

It provides the first detailed determination of the mixed meson mass shift for this specific lattice action combination, including chiral logarithms and effective field theory parameters.

Findings

The additive mass shift is approximately 291 MeV squared in physical units.

The shift depends on the pion mass and lattice spacing, with a specific parameterization.

Next-to-leading order effects are consistent with the leading order within the calculation's precision.

Abstract

Mixed action lattice calculations allow for an additive lattice spacing dependent mass renormalization of mesons composed of one sea and one valence quark, regardless of the type of fermion discretization methods used in the valence and sea sectors. The value of the mass renormalization depends upon the lattice actions used. This mixed meson mass shift is an important lattice artifact to determine for mixed action calculations; because it modifies the pion mass, it plays a central role in the low energy dynamics of all hadronic correlation functions. We determine the leading order, $\mathcal{O}(a^2)$, and next to leading order, $\mathcal{O}(a^2 m_\pi^2)$, additive mass shift of \textit{valence-sea} mesons for a mixed lattice action with domain-wall valence fermions and rooted staggered sea fermions, relevant to the majority of current large scale mixed action lattice efforts. We find that on the asqtad improved coarse MILC lattices, this additive mass shift is well parameterized in lattice units by $\Delta(am)^2 = 0.034(2) -0.06(2) (a m_\pi)^2$, which in physical units, using $a=0.125$ fm, corresponds to $\Delta(m)^2 = (291\pm 8 \textrm{MeV})^2 -0.06(2) m_\pi^2$. In terms of the mixed action effective field theory parameters, the corresponding mass shift is given by $a^2 \Delta_\mathrm{Mix} = (316 \pm 4 \textrm{MeV})^2$ at leading order plus next-to-leading order corrections including the necessary chiral logarithms for this mixed action calculation, determined in this work. Within the precision of our calculation, one can not distinguish between the full next-to-leading order effective field theory analysis of this additive mixed meson mass shift and the parameterization given above.