Determination of the renormalized heavy-quark mass in Lattice QCD

Abstract

We study on the lattice the correlator of heavy-quark currents in the vicinity of vanishing momentum. The renormalized charmed quark mass, the renormalized strong coupling constant and gluon condensate can be defined in terms of the derivatives of that correlator at zero momentum. We analyze quenched Monte-Carlo data on a small lattice $8^3\ast 16$ for $\beta =6$. We generalize dispersion relations to the lattice theory in a simple way and use them successfully to fit the correlator at both small and large distances. We fit the short-distance part of the correlator with the relevant expressions of perturbative QCD on the lattice and obtain the value of the renormalized quark mass $m_c^{\overline{MS}}(m_c)=1.20(4)GeV$.

20 pages Latex + 18 figures with captions. Thoroughly revised version with new results on the renormalised charmed quark mass

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• FLAG Review 2019
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• Twenty-first Century Lattice Gauge Theory: Results from the QCD Lagrangian
• FLAG Review 2024
• Challenges in Semileptonic B Decays
• A Vademecum on Quark-Hadron Duality
• A precise determination of the charm quark's mass in quenched QCD
• Charm quark mass from QCD sum rules for the charmonium system
• Charm Quark Mass
• Phenomenology from lattice QCD
• QCD moment sum rules for Coulomb systems: the charm and bottom quark masses
• Application of the Maximum Entropy Method to the (2+1)d Four-Fermion Model
• QCD sum rule analysis of the charmonium system: The charm quark mass