[Paper Review] Hadron spectra from overlap fermions on HISQ gauge configurations

Subhasish Basak, Saumen Datta+4 more|arXiv (Cornell University)|Dec 11, 2013

Particle physics theoretical and experimental studies1 references3 citations

TL;DR

This study computes charmed and charmed-strange hadron spectra and decay constants using overlap fermions on 2+1+1 flavor HISQ gauge configurations, employing a mixed-action approach to reduce discretization errors. The key result is a consistent hyperfine splitting of 144–145 MeV for 1S charmonia, with decay constants $f_{D_s}$ and $f_{D_s^*}/f_{D_s}$ in agreement with PDG values, validating the method for heavy quark spectroscopy.

ABSTRACT

Adopting a mixed action approach, we report here results on hadron spectra containing one or more charm quarks. We use overlap valence quarks on a background of 2+1+1 flavor HISQ gauge configurations generated by the MILC collaboration. We also study the ratio of leptonic decay constants, f_Ds*/f_Ds. Results are obtained at two lattice spacings.

Motivation & Objective

• To compute hadron masses and decay constants for charmed and charmed-strange states using a mixed-action lattice QCD approach.
• To reduce discretization errors in heavy quark spectroscopy by tuning the charm quark mass using the kinetic mass instead of the pole mass, as suggested by the Fermilab formulation.
• To evaluate the performance and reliability of overlap valence fermions on HISQ dynamical gauge configurations for heavy-light hadron physics.
• To provide precise predictions for $f_{D_s}$ and $f_{D_s^*}/f_{D_s}$, essential for extracting CKM matrix elements.
• To lay the groundwork for future continuum and chiral extrapolations using mixed-action partially quenched chiral perturbation theory.

Proposed method

• Adopt a mixed-action approach: use overlap fermions for valence quarks on dynamical 2+1+1 flavor HISQ gauge configurations generated by the MILC collaboration.
• Tune the charm quark mass by matching the spin-averaged 1S charmonium state mass $(m_{ar{c}c}^{1S})$ to its physical value, using the kinetic mass $M_2$ as the physical observable.
• Compute energy-momentum dispersion relations for pseudoscalar mesons to estimate residual $O((ma)^2)$ discretization effects, fitting to $E(p)^2 = M_1^2 + M_1/M_2 extbf{p}^2 + O( extbf{p}^4)$.
• Use Coulomb gauge fixing and HYP smearing to improve signal-to-noise ratios in correlation functions.
• Compute two-point correlation functions using point, wall, and wall-point sources, with lattice currents $A_ u$, $V_ u$, and $P$ to extract matrix elements.
• Estimate decay constants via $M_{D_s}^2 f_{D_s} = (m_c + m_s) raket{0|P|D_s}$, with $Z_A/Z_V \approx 1$ assumed for the ratio $f_{D_s^*}/f_{D_s}$.

Experimental results

Research questions

• RQ1 Can the overlap fermion action on HISQ gauge configurations yield reliable hadron spectra for charmed hadrons with $ma \lesssim 1$?
• RQ2 Does tuning the charm quark mass via the kinetic mass $M_2$ reduce $O((ma)^2)$ discretization errors compared to pole mass tuning?
• RQ3 How accurately can the hyperfine splitting in 1S charmonia be reproduced using this mixed-action setup?
• RQ4 Are the computed decay constants $f_{D_s}$ and $f_{D_s^*}/f_{D_s}$ consistent with experimental and PDG values?
• RQ5 What is the impact of mixed-action effects on decay constant ratios, and can they be minimized through operator choice and renormalization?

Key findings

• The hyperfine splitting in 1S charmonia is found to be $145(10)$ MeV on the coarser lattice and $144(10)$ MeV on the finer lattice, consistent across both ensembles.
• The velocity of light $c$ extracted from the energy-momentum dispersion relation is $0.96(2)$ on the finer lattice and $0.92(3)$ on the coarser lattice, indicating reduced $O((ma)^2)$ errors when using kinetic mass tuning.
• The pseudoscalar decay constant $f_{D_s}$ shows minimal dependence on $m_c$ and $m_s$ across the studied range and is consistent with the PDG value of $259.7(5)$ MeV.
• The ratio $f_{D_s^*}/f_{D_s}$ is computed under the assumption $Z_A = Z_V$, yielding results that are consistent with expectations and expected to be robust against mixed-action effects.
• The $D_s$ decay constant is extracted from the matrix element $M_{D_s}^2 f_{D_s} = (m_c + m_s) raket{0|P|D_s}$, with uncertainties estimated via jackknife resampling.
• The study confirms the viability of using overlap valence fermions on HISQ ensembles for precision calculations in heavy quark spectroscopy, with promising results for future continuum and chiral extrapolations.