Radial Excited States for Heavy Quark Systems in NRQCD

TL;DR

This study uses NRQCD and gauge invariant smearing on a lattice to measure excitation energies of heavy quark-antiquark systems, finding results consistent with experimental data and indicating limited rotational invariance breaking.

Contribution

It introduces a gauge invariant smearing method combined with factorization to measure heavy quark excitation energies in NRQCD on a lattice, with results aligning with experimental spectra.

Findings

Mass splittings are insensitive to quark mass variations.

Results agree with experimental spin-averaged energy gaps of the $$ system.

Degeneracy between $DE$ and $DT$ D-wave states suggests limited rotational invariance breaking.

Abstract

Following the Non-Relativistic QCD approach we use a gauge invariant smearing method with factorization to measure the excitation energies for a heavy $Q\bar{Q}$ system on a $24^3\times 48$ lattice at $\beta=6.2$. The results come from averaging over an ensemble of 60 QCD configurations. In order to enhance the signal from each configuration we use wall sources for quark propagators. The quark Hamiltonian contains only the simplest non-relativistic kinetic energy term. The results are listed for a range of bare quark masses. The mass splittings are insensitive to this variable though there are a slight trends with increasing quark mass. For an appropriate choice of UV cut-off ($a^{-1}=3.2$Gev) the mass spectrum compares reasonably well with the experimental values for the spin-averaged energy gaps of the $\Upsilon$ system. We also present results for the $DE$ and $DT$ waves for the lowest bare quark mass. The results are consistent with degeneracy between the two types of $D$ wave. This encourages the idea that even with our simple quark Hamiltonian the departure from rotational invariance is not great.