Abstract
The quark potential models with an energy-independent central potential have been successful for understanding the conventional charmonium states especially below the open charm threshold. As one might consider, however, the interquark potential is in general energy-dependent, and its tendency gets stronger in higher lying states. Confirmation of whether the interquark potential is energy-independent is also important to verify the validity of the quark potential models. In this talk, we examine the energy dependence of the charmonium potential, which can be determined from the Bethe-Salpeter (BS) amplitudes of cc̅ mesons in lattice QCD.We first calculate the BS amplitudes of radially excited charmonium states, the ηc(2S) and ψ(2S) states, using the variational method and then determine both the quark kinetic mass and the charmonium potential within the HAL QCD method. Through a direct comparison of charmonium potentials determined from both the 1S and 2S states, we confirm that neither the central nor spin-spin potential shows visible energy dependence at least up to 2S state.
Highlights
The constituent quark description has been successful in qualitatively understanding properties of the charmonium and bottomonium states, especially below the thresholds for decays to mesons with open heavy flavor [1,2,3]
For the heavy quarkonium system, the Cornell potential, which consists of the Coulomb and linear terms, is often adopted
The Cornell potential was not directly derived from QCD, the functional form has been qualitatively justified by the static heavy quark potential obtained from Wilson loops in lattice QCD [4]
Summary
The constituent quark description has been successful in qualitatively understanding properties of the charmonium and bottomonium states, especially below the thresholds for decays to mesons with open heavy flavor [1,2,3]. Ikeda and Iida applied the same idea to the quarkonium system in order to compute the interquark potential without the adiabatic approximation [7, 8]. These preceding studies led us to propose a novel approach, where both the quark kinetic mass and the interquark potential are self-consistently determined within the BS amplitude method, in order to obtain proper interquark potential at finite quark mass using lattice QCD [9]. We naturally have the question whether a universal interquark potential and a unique quark mass can be simultaneously defined in a series of the BS amplitudes from the ground state to excited states. Comparing the interquark potential of the ground state with the one of the radially excited state, we will answer the above question later
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