On the impact of the mixed $Z/ \gamma$ PDF at muon colliders

TL;DR

This paper investigates the $Z/\gamma$-interference PDF at muon colliders, revealing its significance in electroweak processes and proposing methods to accurately approximate its effects, with implications for Higgs and new physics searches.

Contribution

It provides a detailed analysis of the $Z/\gamma$ PDF's behavior, including suppression mechanisms and improved approximations, and explores its impact on various collider processes.

Findings

Suppression of the $Z/\gamma$ PDF at leading order due to cancellation.

Resummed calculations show the $Z/\gamma$ PDF is comparable to other gauge bosons.

High-energy Compton scattering can experimentally observe this electroweak effect.

Abstract

We study the role of the $Z/\gamma$-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 $Z/\gamma$ 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 $Z/\gamma$ 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 $Z/\gamma$ PDF on Higgs physics and, as a new physics example, in resonant single-production of axion-like particles (ALP).