An exploratory study of heavy domain wall fermions on the lattice

Boyle, Peter; Marinkovic, Marina Krstic; Tsang, Justus Tobias; Juttner, Andreas; Sanfilippo, Francesco; Spraggs, Matthew

doi:10.1007/JHEP04(2016)037

Article
Report number	arXiv:1602.04118
Title	An exploratory study of heavy domain wall fermions on the lattice
Author(s)	Boyle, Peter (Edinburgh U.) ; Juttner, Andreas (Southampton U.) ; Marinkovic, Marina Krstic (Southampton U. ; CERN) ; Sanfilippo, Francesco (Southampton U.) ; Spraggs, Matthew (Southampton U.) ; Tsang, Justus Tobias (Southampton U.)
Publication	2016-04-06
Imprint	12 Feb 2016
Number of pages	22
Note	Comments: 23 pages, 8 figures 23 pages, 8 figures
In:	JHEP 04 (2016) 037
DOI	10.1007/JHEP04(2016)037
Subject category	Particle Physics - Lattice ; Particle Physics - Lattice
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.
Copyright/License	arXiv nonexclusive-distrib. 1.0 publication: © 2016-2025 The Author(s) (License: CC-BY-4.0), sponsored by SCOAP³

$\uline{Left}: decay constant $f_{hh}$ for heavy-heavy pseudoscalar mesons as a function of the inverse pseudoscalar mass $m_{hh}$, for different values of $M_{5}$ on the coarsest ensemble. The data is normalised at $m_{hh}^{\mathrm{norm}}=1.5\mathrm{\,GeV}$ to remove the multiplicative renormalisation constant. The vertical lines correspond to $m_{\eta_{c}}$ and to $m_{hh}^{norm}$. \uline{Right}: overlay of the results obtained at two different lattice spacings for three values of $M_{5}$.$ $\uline{Left}: decay constant $f_{hh}$ for heavy-heavy pseudoscalar mesons as a function of the inverse pseudoscalar mass $m_{hh}$, for different values of $M_{5}$ on the coarsest ensemble. The data is normalised at $m_{hh}^{\mathrm{norm}}=1.5\mathrm{\,GeV}$ to remove the multiplicative renormalisation constant. The vertical lines correspond to $m_{\eta_{c}}$ and to $m_{hh}^{norm}$. \uline{Right}: overlay of the results obtained at two different lattice spacings for three values of $M_{5}$.$ $\uline{Left}: behaviour of the \emph{effective} residual mass $am_{\mathrm{res}}^{\mathrm{eff}}$ as a function of time on our coarsest ensemble, for $M_{5}=1.6$. \uline{Right}: residual mass determined at $t=T/2$ as a function of the bare quark mass for several values of $M_{5}$.$ Show more plots

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