The role of the double pole in lattice QCD with mixed actions

TL;DR

Problem: Mixed-action lattice QCD introduces unphysical scaling violations at finite lattice spacing due to different valence and sea discretizations. Approach: The authors use an effective-field-theory framework (Symanzik action plus chiral perturbation theory) to derive the neutral Goldstone meson propagator and its double pole residue, and examine its impact on observables. Key findings: The double pole persists at finite lattice spacing with a residue equal to $R=(M_{ss}^2-M_{vv}^2)/N+a^2( abla_{vv}+ abla_{ss}-2 abla_{vs})$, combining PQ-like and $O(a^2)$ contributions; some observables show enhanced finite-volume or time-dependent scaling violations, but these effects are typically small, especially for GW/domain-wall fermions. Significance: The work quantifies unphysical mixed-action effects, clarifies tuning possibilities, and guides practical lattice-QCD simulations.

Abstract

We investigate effects resulting from the use of different discretizations for the valence and the sea quarks in lattice QCD, considering Wilson and/or Ginsparg-Wilson fermions. We assume that such effects appear through scaling violations that can be studied using effective lagrangian techniques. We show that a double pole is present in flavor-neutral Goldstone meson propagators,even if the charged Goldstone mesons made out of valence quarks and those made out of sea quarks have equal masses. We then consider some observables known to be anomalously sensitive to the presence of a double pole. For these observables, we find that the double-pole enhanced scaling violations may turn out to be rather small in practice.