Astrophysical Consequences of an Electroweak $\eta_{\rm w}$ Pseudo-Scalar

Recently, it has been suggested that the spectrum of physical states in the Standard Model may include an ultralight pseudo-scalar, denoted by $\eta_{\rm w}$, in analogy with the $\eta'$ state arising from the strong interactions. We find that typical expectations for the properties of $\eta_{\rm w}$ get challenged by astrophysical constraints on the couplings of ultralight bosons. Our strongest limit sets a lower bound of $\mathcal{O}({\rm 100~TeV})$ on the decay constant of the hypothesized pseudo-scalar. We also briefly discuss whether $\eta_{\rm w}$ could be a dark matter candidate, or the origin of dark energy, but conclude that those identifications appear unlikely. Given the important implications of a potentially overlooked $\eta_{\rm w}$ state for a more complete understanding of the electroweak interactions and a fundamental description of Nature, further theoretical and phenomenological investigations of this possibility and its associated physics are warranted.