  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.
