Lattice QCD study of the ${\chi }_{c1}\to J\mathrm{/}\psi \gamma$ decay

We present the results of our lattice QCD computation of the electric ($E_1$) and magnetic $(M_2)$ form factors relevant to the ${\chi }_{c1}\to J\mathrm{/}\psi \gamma$ 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 $m_{\pi }\simeq 175\mathrm{M}\mathrm{e}\mathrm{V}$). In the continuum limit, we obtain $\mathrm{\Gamma }({\chi }_{c1}\to J\mathrm{/}\psi \gamma )=0.3265(79)\mathrm{M}\mathrm{e}\mathrm{V}$, which agrees to $(1÷2)\sigma$ with the experimental results and disagrees with a previous (unquenched) lattice QCD calculation. Our result for the magnetic quadrupole fractional transition amplitude, $a_2=M_2\mathrm{/}\sqrt{E_1^2+M_2^2}=-0.0666(22)$, 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.