[Paper Review] Charm physics with Moebius Domain Wall Fermions

Andreas Jüttner, Francesco Sanfilippo+6 more|arXiv (Cornell University)|Jan 4, 2015

Particle physics theoretical and experimental studies10 references3 citations

TL;DR

This paper demonstrates that Möbius Domain Wall Fermions provide a viable discretization for simulating charm quarks in lattice QCD, with controlled discretization effects across the continuum limit. Using a quenched setup and four ensembles with $a^{-1}$ from 2 to 5.6 GeV, it shows $O(a^2)$ scaling of decay constants and stable residual mass, validating the method for upcoming dynamical $2+1f$ charm simulations.

ABSTRACT

We present results showing that Domain Wall fermions are a suitable discretisation for the simulation of heavy quarks. This is done by a continuum scaling study of charm quarks in a Möbius Domain Wall formalism using a quenched set-up. We find that discretisation effects remain well controlled by the choice of Domain Wall parameters preparing the ground work for the ongoing dynamical $2+1f$ charm program of RBC/UKQCD.

Motivation & Objective

• To assess the feasibility of using Möbius Domain Wall Fermions for simulating heavy quarks, particularly charm quarks, in lattice QCD.
• To investigate discretization effects and residual mass behavior in the continuum limit using a quenched approximation.
• To lay the groundwork for the RBC/UKQCD $2+1f$ dynamical charm program by validating the formalism on fine lattices.
• To test whether chiral symmetry and $O(a)$ improvement are preserved in the heavy quark regime using Möbius Domain Wall Fermions.
• To enable future precision calculations of $D_s$ and $η_c$ decay constants by establishing a controlled scaling framework.

Proposed method

• Simulated four tree-level improved Symanzik gauge ensembles with fixed physical volume ($L \approx 1.6~\mathrm{fm}$) and inverse lattice spacings from 2 to 5.6 GeV.
• Used Möbius Domain Wall Fermions with $L_s^{\text{M"{o}bius}} = 12$ (equivalent to $L_s^{\text{Shamir}} = 24$) to maintain chiral symmetry and $O(a)$ improvement.
• Employed the Wilson flow with $w_0$ scale and cross-checked with $r_0$ and $t_0$ for accurate scale setting.
• Measured pseudo-scalar masses and matrix elements for $\eta_s$-, $D_s$-, and $\eta_c$-like states using valence quarks with $am_q \leq 0.4$.
• Computed decay constants normalized at $m_{\mathrm{PS}}^{\mathrm{norm}} = 1.0~\mathrm{GeV}$ and used ratios to cancel renormalization constants.
• Performed continuum extrapolation using $O(a^2)$ fits to decay constant ratios, with data from three finer ensembles for the heaviest reference masses.

Experimental results

Research questions

• RQ1 Can Möbius Domain Wall Fermions maintain controlled discretization effects in the heavy quark regime, particularly for charm quarks?
• RQ2 How does the residual mass behave as a function of bare quark mass and lattice spacing in Möbius Domain Wall Fermion simulations?
• RQ3 To what extent does the scaling of decay constants follow $O(a^2)$ behavior, indicating $O(a)$ improvement?
• RQ4 Is the quenched approximation sufficient to validate the formalism for future dynamical $2+1f$ charm simulations?
• RQ5 Can the method be extended to $B$-physics via the ratio method and static limit matching?

Key findings

• Discretization effects in decay constants of $D_s$ and $\eta_c$ mesons are well-controlled, with scaling behavior consistent with $O(a^2)$, indicating successful $O(a)$ improvement.
• The residual mass remains stable and under control for $am_q \leq 0.4$, with no significant unphysical behavior observed.
• The continuum limit of decay constant ratios shows a flat approach, with no significant deviations across the $a^{-1} = 2$ to $5.6~\mathrm{GeV}$ range.
• Scale setting using the $w_0$ parameter and cross-checks with $r_0$ and $t_0$ confirm consistency and minimal finite-size effects for volumes $>1.2~\mathrm{fm}$.
• The quenched data set provides a validated framework for future dynamical $2+1f$ charm simulations, with the method expected to remain robust beyond quenching.
• The results support the use of Möbius Domain Wall Fermions for precision $B$-physics studies via the ratio method and static limit extrapolation.