On the impact of the mixed Z/γ PDF at muon colliders

We study the role of the Z/γ-interference parton distribution function (PDF) in high-energy muon colliders. We review how this PDF emerges when electroweak interactions are applied to the collinear splitting process and show that the leading-order approximation is significantly suppressed due to an accidental cancellation. However, this suppression does not appear in the leading-logarithm resummed numerical result, where the Z/γ PDF is instead comparable to those of other electroweak gauge bosons. By extending the analytical approximation to next-to-leading order, we show the mechanism by which the suppression is lifted and provide a more accurate approximation to the numerical result. Furthermore, we explore the impact of the Z/γ PDF in several processes at future muon colliders. High-energy Compton scattering is identified as a promising process for observing experimentally this peculiar electroweak effect with high precision. We also quantify the impact of the Z/γ PDF on Higgs physics and, as a new physics example, in resonant single-production of axion-like particles (ALP).