On the Run from the Dark Side of the Muon

TL;DR

The paper introduces a PDF-based strategy to search for beyond-Standard-Model physics at a future high-energy muon collider by exploiting modifications to muon parton distribution functions from new muon-specific gauge bosons. Using LePDF and a $L_{\mu}-L_{\tau}$ $Z'$ as a case study, it shows that back-reaction on PDFs can imprint observable, shape-level deviations in SM-dominated processes, enabling indirect sensitivity to couplings that direct production might miss. A shape-focused analysis of the observable $\partial_\tau\sigma$ across multiple final states, combined via an extended likelihood with luminosity systematics, yields strong projected constraints in the $M_{Z'}\sim 50$--$100$ GeV range, outperforming existing bounds. The work demonstrates a powerful, complementary approach to probing muon-philic new physics at a muon collider and motivates further theoretical refinements and detector studies.

Abstract

We present an analysis strategy for probing physics beyond the Standard Model via modifications to the parton distribution functions (PDFs) in a muon beam, which measurably alter the kinematics of all hard processes at a future muon collider. High-energy muon colliders represent an opportunity to probe new physics using precision measurements and novel search strategies. At sufficiently high energies, light particles act as ``constituents'' of the muon described by PDFs. As a concrete case study, we apply this framework to an $L_μ - L_τ$ gauge boson and demonstrate that, for masses in the range of approximately 50--100 GeV, this indirect PDF-based approach outperforms traditional searches relying on direct gauge boson production. These results highlight muon PDF probes as a powerful and promising avenue for beyond the Standard Model physics searches at a future muon collider.

Figures (7)

• Figure 1: Upper: PDFs for the muon, photon, and $Z^\prime$ (summed over chiral/transverse polarizations) with a particular choice of $Z^\prime$ parameters and factorization scale $Q$. Lower: percent deviation of the muon and photon PDFs from the SM. The subscript $T$ ($L$) denotes the transverse (longitudinal) polarization. Our calculations also include PDFs for the rest of the SM.
• Figure 2: Blue: SM differential cross section $\partial_\tau \sigma$ for the $\mu^+\mu^-$ final state. Orange: percent deviation of $\partial_\tau \sigma$ from the SM for $M_{Z^\prime}=50\,\text{GeV}$ and $g^\prime=0.02$. The solid (dashed) are for $|\eta|<2.5$$(2.0)$.
• Figure 3: Sensitivity to an $L_\mu-L_\tau$ gauge boson. Projected reach obtained using the PDF-based analysis for $|\eta|<2.0$ ( red dashed) and $|\eta|<2.5$ ( red solid). Existing constraints ( gray shaded) include ATLAS ATLAS:2023vxg and CMS CMS:2018yxg searches for $pp\to\mu^+\mu^-\mu^+\mu^-$, where $Z^\prime\to\mu^+\mu^-$ is radiated from a final-state muon in Drell–Yan production, as well as bounds from neutrino trident production Altmannshofer:2014cfaAltmannshofer:2014pba. Also shown are projected sensitivities from direct searches at a 10 TeV muon collider in the $\nu\bar{\nu}\gamma$ ( black) and $\tau^+\tau^-\gamma$ ( blue) channels.
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