Validity of equivalent photon spectra and the photoproduction processes in p-p collisions

TL;DR

This paper evaluates the accuracy of the Weizs"{a}cker-Williams approximation for equivalent photon spectra in proton-proton collisions, deriving a modified photon flux and comparing it with exact calculations for photoproduction processes.

Contribution

It introduces a modified photon flux for protons and assesses its validity against exact results, improving the precision of photoproduction process calculations.

Findings

Modified photon spectrum matches exact results within 1%

Photoproduction processes contribute about 20% to dilepton and photon yields

The study clarifies the validity range of the WWA in p-p collisions

Abstract

Through a consistent analysis of the terms neglected in going from the accurate expression to the one of Weizs\"{a}cker-Williams approximation (WWA), the validity of equivalent photon spectra is studied, and a modified photon flux of proton is also derived. We take the photoproductions of photons and dileptons as examples, to provide the comparison between the exact results and the ones based on various photon fluxes. We present the results for the distributions in $Q^{2}$ (virtuality of photons), $y$ and $p_{T}$, the total cross sections are also estimated. The numerical results show that the modified equivalent photon spectrum reproduces the exact result within less than one percent. And the corrections of photoproduction processes to the dileptons and photons productions are about $20\%$.