Type II Dirac Seesaw with Observable $\Delta N_{\rm eff}$ in the light
  of W-mass Anomaly
  We propose a type II seesaw model for light Dirac neutrinos to provide an
explanation for the recently reported anomaly in W boson mass by the CDF
collaboration with $7\sigma$ statistical significance. In the minimal model,
the required enhancement in W boson mass is obtained at tree level due to the
vacuum expectation value of a real scalar triplet, which also plays a role in
generating light Dirac neutrino mass. Depending upon the couplings and masses
of newly introduced particles, we can have thermally or non-thermally generated
relativistic degrees of freedom $\Delta N_{\rm eff}$ in the form of right
handed neutrinos which can be observed at future cosmology experiments.
Extending the model to a radiative Dirac seesaw scenario can also accommodate
dark matter and lepton anomalous magnetic moment.
