Measurement of hybrid content of heavy quarkonia using lattice NRQCD

TL;DR

This study uses lattice NRQCD to measure the hybrid content in heavy quarkonia, specifically bottomonium, by computing off-diagonal Hamiltonian matrix elements and analyzing hybrid admixture probabilities.

Contribution

It introduces a method to quantify hybrid state admixture in heavy quarkonia using lattice NRQCD and spin-dependent interactions, providing new insights into quarkonium structure.

Findings

Ground state of $$ shows a hybrid admixture of about 0.0035(1)c_B^2.

Results are based on quenched lattice simulations with quark mass interpolation.

Hybrid admixture probability varies with $c_B^2$ in the range 1.5-3.1.

Abstract

Using lowest-order lattice NRQCD to create heavy meson propagators and applying the spin-dependent interaction, $c_B^{} \frac{-g}{2m_q}\vec\sigma\cdot\vec{B}$, at varying intermediate time slices, we compute the off-diagonal matrix element of the Hamiltonian for the quarkonium-hybrid two-state system. Thus far, we have results for one set of quenched lattices with an interpolation in quark mass to match the bottomonium spectrum. After diagonalization of the two-state Hamiltonian, we find the ground state of the $\Upsilon$ to show a $0.0035(1)c_B^2$ (with $c_B^2 \sim 1.5-3.1$) probability admixture of hybrid, $|b\bar{b}g>$.