Hybrid configuration content of heavy S-wave mesons

TL;DR

This paper uses lattice NRQCD to quantify the hybrid configuration admixture in the ground states of heavy S-wave mesons, extending previous work with improved methods and multiple lattice spacings.

Contribution

It introduces a lattice NRQCD approach to measure hybrid content in heavy mesons, including multiple lattice spacings and both pseudoscalar and vector channels.

Findings

Quantifies hybrid admixture in bottomonium and charmonium ground states.

Provides results across different lattice spacings for bottomonium.

Shows hybrid content is small but measurable in heavy S-wave mesons.

Abstract

We use the non-relativistic expansion of QCD (NRQCD) on the lattice to study the lowest hybrid configuration contribution to the ground state of heavy S-wave mesons. Using lowest-order lattice NRQCD to create the heavy-quark propagators, we form a basis of ``unperturbed'' S-wave and hybrid states. We then apply the lowest-order coupling of the quark spin and chromomagnetic field at an intermediate time slice to create ``mixed'' correlators between the S-wave and hybrid states. From the resulting amplitudes, we extract the off-diagonal element of our two-state Hamiltonian. Diagonalizing this Hamiltonian gives us the admixture of hybrid configuration within the meson ground state. The present effort represents a continuation of previous work: the analysis has been extended to include lattices of varying spacings, source operators having better overlap with the ground states, and the pseudoscalar (along with the vector) channel. Results are presented for bottomonium ($\Upsilon$, $\eta_b^{}$) using three different sets of quenched lattices. We also show results for charmonium ($J/\psi$, $\eta_c^{}$) from one lattice set, although we note that the non-relativistic approximation is not expected to be very good in this case.