[Paper Review] Matching the Bare and MSbar Charm Quark Masses Using Weak Coupling Simulations

I. F. Allison, Kit Yan Wong+9 more|arXiv (Cornell University)|Oct 2, 2008

Particle physics theoretical and experimental studies8 references3 citations

TL;DR

This paper presents a new determination of the charm quark mass in the $¯{MS}$ scheme using the Highly Improved Staggered Quark (HISQ) action and weak coupling lattice simulations. By combining high-β Monte Carlo simulations with second-order lattice perturbation theory, the authors extract perturbative matching coefficients and find $m_{c}^{\overline{MS}}(3\,\text{GeV}) = 0.983(23)\,\text{GeV}$, providing a precise, independent cross-check with existing results.

ABSTRACT

We provide a new determination of the charm quark mass using the Highly Improved Staggered Quark (HISQ) action, finding m_c(3 GeV) = 0.983(23) GeV. Our determination makes extensive use of second order lattice perturbation theory in matching the bare lattice mass to the MSbar scheme. This matching utilises both traditional diagrammatic perturbation theory and weak coupling simulations. The second of these techniques allows us to extract perturbative coefficients from Monte-Carlo simulations and the process of doing this is laid out in some detail here.

Motivation & Objective

• To provide a precise, independent determination of the charm quark mass in the $\overline{MS}$ scheme using dynamical lattice QCD with the HISQ action.
• To overcome the computational cost of higher-order diagrammatic perturbation theory by using weak coupling simulations to extract second-order matching coefficients.
• To validate the method by comparing results with a prior independent determination using similar actions and techniques.
• To quantify uncertainties from missing higher-order perturbative terms and scale setting via $r_1$.

Proposed method

• Employing the HISQ quark action to reduce taste-symmetry-breaking errors and improve precision in charm physics simulations.
• Using high-β lattice simulations with twisted boundary conditions to access the perturbative regime and extract $c_1$, $c_{2,g}$, and $c_{2,q}$ coefficients via Monte Carlo fitting.
• Applying second-order lattice perturbation theory to match the bare lattice mass to the $\overline{MS}$ scheme, with constraints from diagrammatic results for $c_1$.
• Performing infinite-volume extrapolations of $c_{2,g}$ using a functional form informed by finite-size scaling and known $X_{c_1,1}$ values.
• Combining results across multiple lattice spacings and fitting to a common continuum limit while accounting for discretization and perturbative errors.
• Estimating higher-order perturbative uncertainties by varying the third-order coefficient $A_{30}$ over a wide prior and assessing impact on the final mass value.

Experimental results

Research questions

• RQ1 What is the value of the charm quark mass in the $\overline{MS}$ scheme at $\mu = 3\,\text{GeV}$, determined using the HISQ action and high-β lattice simulations?
• RQ2 How accurately can second-order perturbative matching coefficients for the HISQ action be extracted using weak coupling simulations instead of diagrammatic field theory?
• RQ3 To what extent do finite-volume effects influence the extraction of the $c_{2,g}$ coefficient, and how can they be corrected?
• RQ4 How do uncertainties from missing higher-order perturbative terms and scale setting ($r_1$) affect the final charm quark mass determination?

Key findings

• The final result for the charm quark mass in the $\overline{MS}$ scheme at $\mu = 3\,\text{GeV}$ is $m_{c}^{\overline{MS}}(3\,\text{GeV}) = 0.9830(64)(49)(213)\,\text{GeV}$, with statistical, scale, and higher-order perturbative errors.
• The high-β simulation method successfully extracted the gluonic part of the $c_2$ coefficient for HISQ, $c_{2,g} = 0.327(34)$ at $am = 0.30$, with results consistent across multiple masses.
• The infinite-volume extrapolation of $c_{2,g}$ shows good agreement with diagrammatic perturbation theory at larger masses, though the $am = 0.30$ point may be affected by finite-volume effects.
• The estimated uncertainty from missing third-order perturbative terms is conservative, as shown by varying $A_{30}$ over a wide prior and observing small shifts in the final mass value.
• The result is in excellent agreement with a prior independent determination ($m_c^{\overline{MS}}(3\,\text{GeV}) = 0.986(10)\,\text{GeV}$), validating the method and the HISQ action's precision.
• The study demonstrates the viability of weak coupling simulations for extracting high-order matching coefficients, reducing reliance on costly diagrammatic calculations.