Lattice QCD estimate of the $\eta_{c}(2S)\to J/\psi\gamma$ decay rate

TL;DR

This paper uses lattice QCD to estimate the decay rate of $ ext{η}_c(2S) o J/ ext{ψ} ext{γ}$, providing a theoretical prediction that can be tested by experiments.

Contribution

First lattice QCD calculation of the $ ext{η}_c(2S) o J/ ext{ψ} ext{γ}$ decay rate with continuum limit extrapolation.

Findings

Predicted decay width: (15.7 ± 5.7) keV

Form factor at zero momentum transfer: 0.32(6)(2)

Mass ratio consistent with experimental data

Abstract

We compute the hadronic matrix element relevant to the physical radiative decay $\eta_{c}(2S)\to J/\psi\gamma$ by means of lattice QCD. We use the (maximally) twisted mass QCD action with Nf=2 light dynamical quarks and from the computations made at four lattice spacings we were able to take the continuum limit. The value of the mass ratio $m_{\eta_c(2S)}/m_{\eta_c(1S)}$ we obtain is consistent with the experimental value, and our prediction for the form factor is $V^{\eta_{c}(2S)\to J/\psi\gamma}(0)\equiv V_{12}(0)=0.32(6)(2)$, leading to $\Gamma(\eta_c (2S) \to J/\psi\gamma) = (15.7\pm 5.7)$ keV, which is much larger than $\Gamma(\psi (2S) \to \eta_c\gamma)$ and within reach of modern experiments.