Lepton Flavor-Violating Higgs Decays Mediated by Ultralight Gauge Boson

We present an analysis of the lepton-flavor violating decay of the Higgs boson mediated by an ultralight gauge boson, $\chi$. Our analysis matches a model generating the lepton flavor-violating interaction ${\bar{\mathrm{\ell }}}_i{\mathrm{\ell }}_j\chi$ at tree level with an effective field theory, safeguarding a physical massless $\chi$-boson limit of the observables. By utilizing the upper bounds on $H\to {\mathrm{\ell }}_i{\bar{\mathrm{\ell }}}_j$ decays from CMS and ATLAS Collaborations, we establish an indirect upper limit on the nonstandard decay $H\to {\mathrm{\ell }}_i{\bar{\mathrm{\ell }}}_j\chi$. The analysis encompasses various observables such as the lepton energy spectrum, Dalitz plot distribution, and Lepton Charge and Forward-Backward Asymmetries.