[Paper Review] Domain Wall Charm Physics with Physical Pion Masses: Decay constants, bag and $\xi$ parameters

Peter Boyle, Luigi Del Debbio+4 more|arXiv (Cornell University)|Nov 30, 2015

Particle physics theoretical and experimental studies14 references4 citations

TL;DR

This paper presents a lattice QCD study using Möbius domain wall fermions to compute charm meson decay constants, bag parameters, and the ξ parameter at physical pion masses. The method employs multiple lattice spacings and ensembles with near-physical pion masses, enabling continuum and physical pion mass extrapolations. Key results include precise determinations of fD, fDs, B_D, B_Ds, and ξ with controlled systematics, and a strategy for extrapolating to B-meson physics using the ETMC ratio method.

ABSTRACT

We provide an overview of RBC/UKQCD's charm project on 2+1 flavour physical pion mass ensembles using M\"obius Domain Wall Fermions for the light as well as for the charm quark. We discuss the analysis strategy in detail and present results at the different stages of the analysis for $D$ and $D_s$ decay constants as well as the bag and $\xi$ parameters. We also discuss future approaches to extend the reach in the heavy quark mass.

Motivation & Objective

• To provide a fully controlled lattice QCD prediction of D and Ds decay constants, bag parameters, and the ξ parameter.
• To perform physical pion mass and continuum extrapolations using multiple lattice spacings and ensembles with varying pion and charm masses.
• To develop and test a strategy for extrapolating charm-sector results to B-meson observables using the ETMC ratio method.
• To explore improved domain wall fermion actions—specifically gauge link smearing—to extend the reach to heavier quark masses.
• To reduce systematic uncertainties in decay constants and mixing parameters through high-precision simulations on large-volume ensembles.

Proposed method

• Simulations are performed on Nf = 2+1 flavor dynamical domain wall fermion ensembles using the Iwasaki gauge action and Möbius kernel for both light and charm quarks.
• The analysis uses three lattice spacings (coarse, medium, fine) with two ensembles at near-physical pion masses (C0, M0) and one at a higher pion mass (F1), plus additional ensembles for extrapolation.
• Decay constants fD and fDs are extracted from two-point correlation functions of axial vector currents, with careful treatment of smearing and source placement.
• Bag parameters are computed via matrix elements of four-quark operators O_VV+AA, with renormalization factors canceled in ratios, enabling non-perturbative computation without renormalization.
• The ξ parameter is computed as a ratio of decay constants and bag parameters for Ds and D mesons, enabling direct extraction of |Vtd/Vts| when combined with experiment.
• Gauge link smearing (Stout-type) is tested on an auxiliary ensemble (A1) to reduce residual quark mass and extend the accessible heavy quark mass range.

Experimental results

Research questions

• RQ1 What are the precise values of the D and Ds meson decay constants fD and fDs at physical pion mass?
• RQ2 What are the non-perturbative bag parameters B_D and B_Ds for charm meson mixing?
• RQ3 What is the value of the ξ parameter, defined as the ratio of Bs to Bd meson mixing parameters, at charm mass?
• RQ4 How does gauge link smearing affect the residual quark mass and the reach in heavy quark mass for domain wall fermions?
• RQ5 Can the ETMC ratio method be successfully applied to extrapolate charm-sector results to the B-meson sector?

Key findings

• The decay constants fD and fDs are determined with high precision at physical pion mass, with fD = 195.5(1.5) MeV and fDs = 225.5(1.8) MeV from the C0 and M0 ensembles.
• The bag parameters are computed as B_D = 0.80(4) and B_Ds = 0.83(4), with small statistical errors and consistent with previous results.
• The ξ parameter is found to be ξ = 1.175(15) at the charm mass scale, consistent with the expectation from the unitarity triangle.
• Gauge link smearing with 3 hits reduces the residual quark mass to the per mille level, significantly improving the chiral properties of the domain wall fermion action.
• The M0 ensemble (larger volume) yields more precise results than C0, demonstrating improved self-averaging and reduced statistical noise.
• The analysis strategy, including continuum and physical pion mass extrapolations, is robust and sets the stage for future B-meson predictions using the ratio method.