Effects of an H-mu-tau coupling in quarkonium lepton flavor violation decays

In this work we study the consistency of a possible non-vanishing coupling $H\mu \tau $ of the order of $3.6\times 10^{-3}$ as pointed recently by the CMS and ATLAS collaborations, with measured lepton flavor violation processes involving quarkonium. We show that the most promising channel to confirm this excess is to look for the lepton flavor tau decay into a $f_0$ and $\mu$ where the experimental limit could strongly improved with the new B factories as Belle II.