Hadronic decay of vector charmonium from the lattice

TL;DR

This paper introduces a ratio method for extracting decay parameters from lattice QCD simulations, applied to the $ ext{J/} ext{ψ}(3770)$ decay, providing results compatible with physical expectations without requiring multiple volumes.

Contribution

The study demonstrates a novel ratio method to determine decay widths and energy shifts directly from lattice correlation functions, simplifying the analysis of hadronic decays.

Findings

Decay width $ ext{Γ}$ agrees with experimental values

Method allows precise on-shell kinematic tuning

Spectrum shifts inform about dynamical effects

Abstract

Estimating decay parameters in lattice simulations is a computationally demanding problem, requiring several volumes and momenta. We explore an alternative approach, where the transition amplitude can be extracted from the spectral decomposition of particular ratios built from correlation functions. This so-called ratio method has the advantage of not needing various irreducible representations or volumes, and it allows us to predict the decay width $\Gamma$ and the energy shift $\epsilon$ of the spectrum directly. In this work, we apply this method to study the hadronic decay $\psi(3770)\to \bar{D}D$ on two CLS $N_\text{f}=2$ ensembles. This approach requires close to on-shell kinematics to work, and we employ twisted boundary conditions to precisely tune the on-shell point. Although our study is yet to approach the continuum limit, we find a value of $\Gamma$ fully compatible to the physical result, and $\epsilon$ informs us by how much our spectrum would shift in a fully dynamical simulation. Besides lattice calculations, many analytical tools have been proposed to understand decay processes. A relatively simple, early example is the ${}^3P_0$ quark model, which provides a physical insight of the decay process.