Heavy meson thresholds in Born-Oppenheimer Effective field theory

TL;DR

This paper develops a nonrelativistic effective field theory framework to analyze heavy meson-antimeson pairs and their coupling to quarkonium, calculating their effects on quarkonium masses and widths using lattice data and matching techniques.

Contribution

It introduces a systematic method to derive couplings in threshold EFTs from lattice data and applies it to compute mass and width shifts in charmonium and bottomonium states.

Findings

Computed contributions of Dar{D} and Bar{B} pairs to quarkonium properties.

Extracted mixing potentials from lattice data.

Provided a matching procedure between different EFTs.

Abstract

We consider heavy meson-antimeson pairs and their coupling to quarkonium in the context of nonrelativistic EFTs incorporating the adiabatic expansion. We work out all the leading order couplings of quarkonium to heavy meson-antimeson pairs and obtain their contributions to the masses and widths of quarkonia. We match the new potentials terms to NRQCD. Using the available lattice data for the coupled system of quarkonium and the lowest laying heavy meson-antimeson pair, we extract the mixing potential and use it to compute numerically the contributions of $D\bar{D}(B\bar{B})$ and $D_s\bar{D}_s(B_s\bar{B}_s)$ to the masses and widths of the charmonium (bottomonium) states for $l=0,1,2$ and up to $n=6$ covering the states in threshold region. When a quarkonium state and a heavy meson-antimeson pair are separated by small energy gaps, their interactions can be described by a threshold EFT with contact interactions. We work out the matching between the two EFTs obtaining the couplings of the threshold EFT in terms of the mixing potential and quarkonium wave functions.