Abstract
We report on an exploratory study of domain wall fermions (DWF) as a lattice regularisation for heavy quarks. Within the framework of quenched QCD with the tree-level improved Symanzik gauge action we identify the DWF parameters which minimise discretisation effects. We find the corresponding effective 4$d$ overlap operator to be exponentially local, independent of the quark mass. We determine a maximum bare heavy quark mass of $am_h\approx 0.4$, below which the approximate chiral symmetry and O(a)-improvement of DWF are sustained. This threshold appears to be largely independent of the lattice spacing. Based on these findings, we carried out a detailed scaling study for the heavy-strange meson dispersion relation and decay constant on four ensembles with lattice spacings in the range $2.0-5.7\,\mathrm{GeV}$. We observe very mild $a^2$ scaling towards the continuum limit. Our findings establish a sound basis for heavy DWF in dynamical simulations of lattice QCD with relevance to Standard Model phenomenology.
Highlights
Simulations of full lattice QCD where both the physical light quarks (u, d and s) and the charm or heavier quarks are represented by the same discretisation are still rather scarce
We report on an exploratory study of domain wall fermions (DWF) as a lattice regularisation for heavy quarks
A further quantity that we wish to monitor during our simulations is the residual quark mass amres [44], which provides an estimate of residual chiral symmetry breaking in the Mobius DWF (MDWF) formalism
Summary
To some extent the problem of critical slowing down [25,26,27] can be circumvented by brute force This enables us to probe finer lattice spacings than those affordable in dynamical simulations and check the scaling of the theory towards the continuum limit in more detail. The restoration of chiral symmetry in the massless limit is crucial to the simulation of QCD on the lattice, and is responsible for automatic O(a)-improvement, which is especially important when studying heavy quark physics. M5 is the negative mass parameter in the 4-dimensional Wilson Dirac operator that resides in the 5-dimensional MDWF Dirac operator Since both Ls and M5 are parameters of the discretisation rather than of QCD we have some freedom in varying them.
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