Lattice QCD study of the $\ddot{I}{‡}_{c1}\to J/\ddot{I}ˆ{\hat{I}}^3$ decay

Abstract

We present the results of our lattice QCD computation of the electric ($E_1$) and magnetic $(M_2)$ form factors relevant to the $\ddot{I}{‡}_{c1}\to J/\ddot{I}ˆ{\hat{I}}^3$ 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 $m_{\ddot{I}}€\simeq 175\mathrm{MeV}$). In the continuum limit, we obtain $\hat{I}“(\ddot{I}{‡}_{c1}\to J/\ddot{I}ˆ{\hat{I}}^3)=0.3265(79)\mathrm{MeV}$, which agrees to $(1\tilde{A}\cdot 2)\ddot{I}ƒ$ 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.

10 pages, 7 figures, 2 tables. arXiv admin note: text overlap with arXiv:2504.16807