The ${^{3}\!}P_{0}$ model reloaded

TL;DR

This paper revisits the ${^{3} ext{-}P_{0}}$ model for quarkonium decay, deriving a transition rate in the heavy-quark limit and fitting it to lattice QCD results to improve understanding of quark-antiquark pair creation.

Contribution

The paper derives a transition rate in the heavy-quark limit and fits the ${^{3} ext{-}P_{0}}$ model to lattice QCD data, connecting phenomenological models with fundamental QCD calculations.

Findings

Derived a transition rate for quarkonium decay in the heavy-quark limit.

Fitted the ${^{3} ext{-}P_{0}}$ model's creation amplitude to lattice QCD string-breaking data.

Established a quantitative link between phenomenological decay models and lattice QCD results.

Abstract

We revisit the phenomenological ${^{3}\!}P_{0}$ model for the decay of quarkonium $\left( Q\bar{Q}\right) $ into two open flavor mesons ($\bar{\mathfrak{M}}\mathfrak{M}% $). We take the heavy-quark limit and derive a transition rate between $Q\bar{Q}$ and $\bar{\mathfrak{M}}\mathfrak{M}$ to be compared with the one calculated in studies of string breaking using lattice QCD. This comparison allows to fit the creation amplitude of a light quark-antiquark pair in the ${^{3}\!}P_{0}$ model to the string-breaking transition rate in QCD.