Heavier W boson, dark matter, and gravitational waves from strings in an SO(10) axion model

Abstract

Inspired by the recent determination of the $W$-boson mass by the CDF collaboration, we revisit an $SO(10)$ axion model in which a scalar $SU(2{)}_{L}$ triplet field with zero hypercharge is known to acquire a nonzero vacuum expectation value (VEV) through its mixing with the Standard Model Higgs doublet. The triplet VEV provides a sizable contribution to the $W$ mass, which helps in significantly lowering the $7\ensuremath{\sigma}$ discrepancy between the Standard Model prediction and the higher CDF value for ${m}_{W}$. We show that the relatively light triplet mass ($\ensuremath{\sim}(1--50)\text{ }\text{ }\mathrm{TeV}$) is compatible with gauge coupling unification and observable proton decay. An unbroken ${Z}_{2}$ gauge symmetry, coupled with the presence of two fermionic 10-plets required to resolve the axion domain wall problem means that both axions and a stable intermediate mass ($\ensuremath{\sim}{10}^{9}--{10}^{10}\text{ }\text{ }\mathrm{GeV}$) fermion are plausible dark matter candidates. We also display the gravitational wave spectrum from the intermediate scale topologically stable cosmic strings predicted by the model.