Heavy quarkonium potential from Bethe-Salpeter wave function on the lattice

Abstract

We propose a novel method for the determination of the interquark potential together with quark "kinetic mass'' $m_Q$ from the equal-time $Q\bar{Q}$ Bethe-Salpeter (BS) amplitude in lattice QCD. Our approach allows us to calculate spin-dependent $Q\bar{Q}$ potentials, e.g. the spin-spin potential, as well. In order to investigate several systematic uncertainties on such $Q\bar{Q}$ potentials, we carry out lattice QCD simulations using quenched gauge configurations generated with the single plaquette gauge action with three different lattice spacings, $a\approx$ 0.093, 0.068 and 0.047 fm, and two different physical volumes, $L\approx$ 2.2 and 3.0 fm. For heavy quarks, we employ the relativistic heavy quark (RHQ) action which can control large discretization errors introduced by large quark mass $m_Q$. The spin-independent central $Q\bar{Q}$ potential for the charmonium system yields the "Coulomb plus linear'' behavior with good scaling and small volume dependence. We explore the quark mass dependence over the wide mass range from the charm to beyond the bottom region, and then demonstrate that the spin-independent central $Q\bar{Q}$ potential in the $m_Q\to \infty$ limit is fairly consistent with the static $Q\bar{Q}$ potential obtained from Wilson loops. The spin-spin potential at finite quark mass provides a repulsive interaction with a finite range, which becomes narrower as the quark mass increases. We also discuss the applicability of the $1/m_Q$ expansion approach for the spin-spin potential.

20 pages, 18 figures

References in corpus (8)

• Nuclear Force from Lattice QCD
• The Exotic XYZ Charmonium-like Mesons
• Spin-dependent potentials from lattice QCD
• Hyperon-nucleon force from lattice QCD
• Relativistic Heavy Quark Effective Action
• Non-perturbatively Determined Relativistic Heavy Quark Action
• Charmonium-nucleon potential from lattice QCD
• Nonperturbative tuning of an improved relativistic heavy-quark action with application to bottom spectroscopy

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