Abstract
We present an exploratory lattice study for the two-photon decay of $\eta_c$ using $N_f=2$ twisted mass lattice QCD gauge configurations generated by the European Twisted Mass Collaboration. Two different lattice spacings of $a=0.067$fm and $a=0.085$fm are used in the study, both of which are of physical size of 2$fm$. The decay widths are found to be $1.025(5)$KeV for the coarser lattice and $1.062(5)$KeV for the finer lattice respectively where the errors are purely statistical. A naive extrapolation towards the continuum limit yields $\Gamma\simeq 1.122(14)$KeV which is smaller than the previous quenched result and most of the current experimental results. Possible reasons are discussed.
Highlights
Charmonium systems play a major role in the understanding of the foundation of quantum chromodynamics (QCD), the fundamental theory for the strong interaction
The gauge configurations utilized in this study are generated by the European Twisted Mass Collaboration (ETMC) [18,19,20,21,22,23,24,25,26,27,28,29], where the twisted mass fermion parameters are set at the maximal twist
If using the two-step fitting procedure using Eq (20) and using Eq (21), with the values of mηc obtained from each ensemble substituted in, we obtain for the decay width = 1.019(3) KeV for the coarser and = 1.043(3) KeV for the finer lattice ensembles
Summary
Charmonium systems play a major role in the understanding of the foundation of quantum chromodynamics (QCD), the fundamental theory for the strong interaction. Since photons are not QCD eigenstates, one has to rely on perturbative methods to “replace” the photon states by the corresponding electromagnetic currents that they couple to The details of this idea was illustrated in Refs. The gauge configurations utilized in this study are generated by the European Twisted Mass Collaboration (ETMC) [18,19,20,21,22,23,24,25,26,27,28,29], where the twisted mass fermion parameters are set at the maximal twist This ensures the so-called automatic O(a) improvement for on-shell observables where a is the lattice spacing [30].
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