Simulations with different lattice Dirac operators for valence and sea quarks

TL;DR

We address discretization and chiral extrapolation in lattice QCD by employing a mixed-action setup with Wilson sea quarks and Ginsparg-Wilson valence quarks. The authors derive the local Symanzik action to $O(a)$ and build the corresponding chiral Lagrangian, yielding an $NLO$ meson-mass formula that explicitly involves the Gasser-Leutwyler coefficients $L_i$ and the additional $W_i$ terms. This framework preserves a PQ-like symmetry and connects lattice data to continuum QCD, enabling more reliable extraction of $L_i$ by exploring lighter valence quark masses. The approach promises a practical path to improved chiral extrapolations and invites future work on $O(a^2)$ effects and other mixed-action combinations.

Abstract

We discuss simulations with different lattice Dirac operators for sea and valence quarks. A goal of such a "mixed" action approach is to probe deeper the chiral regime of QCD by enabling simulations with light valence quarks. This is achieved by using chiral fermions as valence quarks while computationally inexpensive fermions are used in the sea sector. Specifically, we consider Wilson sea quarks and Ginsparg-Wilson valence quarks. The local Symanzik action for this mixed theory is derived to O(a), and the appropriate low energy chiral effective Lagrangian is constructed, including the leading O(a) contributions. Using this Lagrangian one can calculate expressions for physical observables and determine the Gasser-Leutwyler coefficients by fitting them to the lattice data.

Figures (1)

• Figure 1: Qualitative representation of the space of quark masses. The "chiral regime", where PQ $\chi$ PT can be applied, is the quarter-circular region. The upper right rectangle, limited by the dashed line, describes the part of the space covered by present simulations. As current data suggest, there is very little or no overlap between that rectangle and the chiral regime. It is expected that improvement in algorithms and computer power will allow reducing the sea and valence quark masses in PQ simulations, as is represented by the enlargement of the previous rectangle. It is possible that the chiral region will be penetrated by such simulations, as shown by the small section of overlap between the enlarged rectangle and the chiral region. Finally, using chiral valence fermions in a mixed action simulation would make it possible to extend the reach of simulations significantly in the direction of lighter valence quarks.