Dark sector radiation corrections to invisible dark photon production: beyond fixed order
In this work we study invisible dark photon production at electron-positron colliders in a dark Abelian Higgs model at NLO (next-to-leading-order), and the physical distribution of squared missing mass $M_X^2$. We show that the fixed order correction to the total cross section for the process $e^+e^-\to \gamma A'$, with $A'$ the dark photon, is infrared-safe, but the corresponding differential distribution of $M_X^2$ reveals a quasi-collinear $1/M_X^2$ divergence when the masses of dark sector particles are much smaller than the hard scale. By using the Sudakov resummation method, we obtain an integrable, normalized distribution of $M_X^2$, which is actually the ``jet mass'' of the dark photon branch. We also discuss how these dark sector corrections impact the invisible dark photon search at electron-positron colliders.