Lattice QCD study of the $\chi_{c1}\to J/\psi \, \gamma$ decay

TL;DR

This lattice QCD study computes decay form factors and decay width for $ ext{chi}_{c1} o J/ ext{psi} \, ext{gamma}$, providing results consistent with experiments and improving previous lattice calculations.

Contribution

First unquenched lattice QCD calculation of $ ext{chi}_{c1} o J/ ext{psi} \, ext{gamma}$ decay form factors and width with multiple lattice spacings and physical quark masses.

Findings

Decay width $ o 0.3265(79)$ MeV, consistent with experiments.

Magnetic quadrupole amplitude $a_2 = -0.0666(22)$, in agreement with experiment.

Significant improvement over previous quenched lattice results.

Abstract

We present the results of our lattice QCD computation of the electric ($E_{1}$) and magnetic $(M_{2})$ form factors relevant to the $\chi_{c1}\to J/\psi\,\gamma$ decay by using the gauge field configurations produced by the Extended Twisted Mass Collaboration with $N_{f}=2+1+1$ dynamical Wilson-Clover twisted mass fermions at four different lattice spacings with physical dynamical $u$ , $d$, $s$ and $c$ quark masses (except for the coarsest lattice for which the lightest sea quark corresponds to a pion with $m_{\pi}\simeq 175~\mathrm{MeV}$). In the continuum limit, we obtain $\Gamma( \chi_{c1}\to J/\psi\ \gamma ) = 0.3265(79)~\mathrm{MeV}$, which agrees to $(1\div 2) \sigma$ with the experimental results and disagrees with a previous (unquenched) lattice QCD calculation. Our result for the magnetic quadrupole fractional transition amplitude, $a_{2} =M_{2}/\sqrt{E_{1}^{2}+M_{2}^{2}} = -0.0666(22)$, is in agreement with the experiment and represents an improvement by a factor of about $30$ with respect to the only existing (quenched) lattice QCD result.