TeV Scale Resonant Leptogenesis with $L_{\mu}-L_{\tau}$ Gauge Symmetry
  in the Light of Muon $(g-2)$
  Motivated by the growing evidence for the possible lepton flavour
universality violation after the first results from Fermilab's muon $(g-2)$
measurement, we revisit one of the most widely studied anomaly free extensions
of the standard model namely, gauged $L_{\mu}-L_{\tau}$ model, to find a common
explanation for muon $(g-2)$ as well as baryon asymmetry of the universe via
leptogenesis. The minimal setup allows TeV scale resonant leptogenesis
satisfying light neutrino data while the existence of light $L_{\mu}-L_{\tau}$
gauge boson affects the scale of leptogenesis as the right handed neutrinos are
charged under it. For $L_{\mu}-L_{\tau}$ gauge boson mass at GeV scale or
above, the muon $(g-2)$ favoured parameter space is already ruled out by other
experimental data while bringing down its mass to sub-GeV regime leads to
vanishing lepton asymmetry due to highly restrictive structures of lepton mass
matrices at the scale of leptogenesis. Extending the minimal model with two
additional Higgs doublets can lead to a scenario consistent with successful
resonant leptogenesis and muon $(g-2)$ while satisfying all relevant
experimental data.
