Running in the Dark Sector

Abstract

The "dark photon" ${\gamma }_d$ of a gauged $U(1{)}_d$ can become practically invisible if it primarily decays into light states from a dark sector. We point out that, in such scenarios, the running of the $U(1{)}_d$ "fine structure constant" ${\alpha }_d$, with momentum transfer $q^2$, can be significant and potentially measurable. The ${\gamma }_d$ kinetic mixing parameter ${\epsilon }^2$ is also expected to run with $q^2$, through its dependence on ${\alpha }_d$. We show how the combined running of ${\epsilon }^2{\alpha }_d$ may provide a probe of the spectrum of dark particles and, for ${\alpha }_d\gtrsim \mathrm{few}\times 0.1$, substantially modify predictions for "beam dump" or other intense source experiments. These features are demonstrated in simple models that contain light dark matter and a scalar that breaks $U(1{)}_d$. We also discuss theoretic considerations, regarding the $U(1{)}_d$ model in the ultraviolet regime, that may suggest the infrared upper bound ${\alpha }_d\lesssim 0.1$.

Comments: Revtex4, 6 pages, 4 figures. Version accepted for publication in PRD (original title kept)