Quark and Gluon Contents of a Lepton at High Energies

TL;DR

This paper develops a formalism to compute quark and gluon parton distribution functions inside leptons at high energies, incorporating electroweak and QCD effects, and evaluates their impact on jet production at TeV scales.

Contribution

It extends the Standard Model formalism to include QCD sector in lepton PDFs and evaluates their significance at high-energy colliders.

Findings

Quark and gluon PDFs inside leptons are significant at high energies.

Jet production cross sections can reach several tens of picobarns at TeV scales.

Massive gauge bosons contribute substantially to PDFs at high scales.

Abstract

In high-energy leptonic collisions, such as at a multi-TeV muon collider, the collinear splittings of the electroweak (EW) gauge bosons and leptons are the dominant phenomena, and the scattering processes should thus be formulated in terms of the EW parton distribution functions (EW PDFs). We complete this formalism in the Standard Model to include the QCD sector and evaluate the quark and gluon PDFs inside a lepton at the double-log accuracy. The splittings of the photon and subsequently the quarks and gluons control the quark/gluon PDFs below the EW scale. The massive gauge bosons lead to substantial contributions at high scales. The jet production cross section can reach the order of a few nb (50 pb) in $e^+e^-$ ($\mu^+\mu^-$) collisions, at the TeV c.m. energies with a moderate acceptance cut, that governs the overall event shape up to about $p_T^j \sim 60$ GeV.