Singlet extensions and W boson mass in the light of the CDF II result
  Recently, the CDF collaboration has reported the precise measurement of the W
boson mass, $M_W = 80433.5\pm 9.4 \,$MeV, based on $8.8$ fb$^{-1}$ of
$\sqrt{s}=1.96$ TeV $p\bar{p}$ collision data from the CDF II detector at the
Fermilab Tevatron. This is about $7\sigma$ away from the Standard Model
prediction, $M_{W}^{\rm SM}=80357 \pm 6 \,$MeV. Such a large discrepancy may be
partially due to exotic particles that radiatively alter the relation between
the W and Z boson masses. In this Letter, we study singlet extensions of the
Standard Model focusing on the shift of the W boson mass. In the minimal
extension with a real singlet field, using the bounds from the electroweak
oblique parameters, B meson decays, LEP, and LHC, we find that the W boson mass
shift is at most a few MeV, and therefore it does not alleviate the tension
between the CDF II result and the SM prediction. We then examine how much
various bounds are relaxed when the singlet is allowed to decay invisibly and
find that the increase of the W boson mass does not exceed $5$ MeV due to the
bound from the Higgs signal strength. We also discuss phenomenological and
cosmological implications of the singlet extensions such as the muon $g-2$
anomaly, axion/hidden photon dark matter, and self-interacting dark radiation
as a possible alleviation of the Hubble tension.
