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−(μ+μ−) collisions, at the TeV c.m. energies with a moderate acceptance cut, that governs the overall event shape up to about {p}_T^j ∼ 60 GeV. To complete the picture, we also provide an estimation of the total cross section for the photon-induced hadronic production at low partonic energies, which can reach the level of one hundred or a few tens of nb in high-energy electron or muon collisions.
Highlights
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 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
Since the simulations for photon-induced high-pT jet events from perturbative QCD calculations do not exist in the current event-generator packages, our formalism should be adopted by the event generators to simulate SM processes and the leading QCD backgrounds at lepton colliders
Summary
Different from a proton beam, the parton contents inside of a lepton can be calculated perturbatively. The leading order QCD and QED splitting functions are known for decades and can be found in textbooks [36, 37] They are extended to include mixed term O(ααs) in ref. The QCD and QED evolutions run simultaneously until μEW, where the complete SM sector begins to evolve according to the unbroken SM gauge group. In such a way, we need two matchings, at μQCD and μEW, respectively.. As the QED and QCD gauge groups conserve the charge and parity symmetry, the PDFs below μEW can be treated with no polarization, as long as the initial lepton beams are unpolarized. The photon and gluon become polarized due to the fermion chiral interactions
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