An exploratory study of heavy domain wall fermions on the lattice

Abstract

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 4d overlap operator to be exponentially local, independent of the quark mass. We determine a maximum bare heavy quark mass of am h ≈ 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 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.

The decay constants fD and f D s $$ {f}_{D_s} $$ in the continuum limit of Nf = 2 + 1 domain wall lattice QCD

“…Besides the bare quark mass, DWF have two further input parameters that need to be specified in each simulation: the extent of the fifth dimension L s and the domain wall height parameter M 5 , respectively (for details see [35,37]). More specifically, M 5 is the negative mass parameter in the 4-dimensional Wilson Dirac operator which resides in the 5-dimensional DWF Dirac operator.…”

“…Given the novel nature of domain wall fermions as heavy quark discretisation we have investigated their properties in detail in two preparatory publications [34,35]. We studied the continuum limit behaviour of heavy-strange decay constants over a wide range of lattice cut-offs (2-6 GeV) within quenched QCD.…”

Form Factors for semi-leptonic $B$ decays

“…This avoids tuning the three parameters of the RHQ action and allows us to use a renormalization procedure similar to that in our B → π ν calculation. We therefore simulate charm based on the recent work featuring optimized Möbius domain-wall fermions [15,[47][48][49] i.e. we use domain-wall fermions with the Möbius kernel and choose the following parameters: without link-smearing the gauge field [49,50].…”

“…we use domain-wall fermions with the Möbius kernel and choose the following parameters: without link-smearing the gauge field [49,50]. With this set-up, discretization errors have been shown to remain small for quantities like the charmonium mass η c or D (s) meson masses and decay constants if bare input quark masses below am q 0.4 are chosen [48]. Thus on our coarse ensembles (a −1 ≈ 1.78 GeV), we cannot directly simulate charm quarks but expect a linear extrapolation to be benign [15,49].…”

Charm Physics with Domain Wall Fermions and Physical Pion Masses

“…In ref [8] we studied the Moebius domain wall parameter space with the intention of finding a region in which discretisation effects for charmed meson observables are small. We found that the choice of the domain wall height M 5 = 1.6 yields optimal results, provided the bound am bare h 0.4 is observed.…”