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A Simple Prescription for First Order Corrections to Quark Scattering and Annihilation Processes

Michael H. Seymour

TL;DR

The paper tackles the challenge of describing first-order QCD corrections to quark scattering and annihilation in a fully exclusive, gauge-invariant way. By employing CALKUL gauge, Seymour derives exact factorisations for QCDC, Boson Gluon Fusion, and Drell-Yan processes, mapping three-parton final states to lowest-order kinematics with well-defined momentum constructs and weight-based Monte Carlo algorithms. The work provides explicit expressions for the helicity-dependent matrix elements, phase-space parameterisations, and practical procedures to generate corrected events from LO distributions, enabling direct interpretation of lepton-hadron correlations and improved integration with parton showers. These results offer a general, gauge-consistent framework for incorporating first-order matrix-element corrections into exclusive event generators across DIS and hadron-cinit processes. The approach yields tangible insights into azimuthal correlations and intrinsic transverse momentum effects, with broad applicability to high-energy EW processes.

Abstract

We formulate the first order corrections to processes involving the scattering or annihilation of quarks in a form in which the QCD and electroweak parts are exactly factorised. This allows for a straightforward physical interpretation of effects such as lepton-hadron correlations, and a simpler Monte Carlo treatment. The postscript file for this paper can also be obtained by anonymous ftp from thep.lu.se, in the file pub/Preprints/lu_tp_94_13.ps

A Simple Prescription for First Order Corrections to Quark Scattering and Annihilation Processes

TL;DR

The paper tackles the challenge of describing first-order QCD corrections to quark scattering and annihilation in a fully exclusive, gauge-invariant way. By employing CALKUL gauge, Seymour derives exact factorisations for QCDC, Boson Gluon Fusion, and Drell-Yan processes, mapping three-parton final states to lowest-order kinematics with well-defined momentum constructs and weight-based Monte Carlo algorithms. The work provides explicit expressions for the helicity-dependent matrix elements, phase-space parameterisations, and practical procedures to generate corrected events from LO distributions, enabling direct interpretation of lepton-hadron correlations and improved integration with parton showers. These results offer a general, gauge-consistent framework for incorporating first-order matrix-element corrections into exclusive event generators across DIS and hadron-cinit processes. The approach yields tangible insights into azimuthal correlations and intrinsic transverse momentum effects, with broad applicability to high-energy EW processes.

Abstract

We formulate the first order corrections to processes involving the scattering or annihilation of quarks in a form in which the QCD and electroweak parts are exactly factorised. This allows for a straightforward physical interpretation of effects such as lepton-hadron correlations, and a simpler Monte Carlo treatment. The postscript file for this paper can also be obtained by anonymous ftp from thep.lu.se, in the file pub/Preprints/lu_tp_94_13.ps

Paper Structure

This paper contains 8 sections, 60 equations, 2 figures.

Table of Contents

  1. Introduction
  2. QCD Compton Process in DIS
  3. The Matrix Element
  4. Kinematics and Phase-Space
  5. Boson Gluon Fusion
  6. Lepton-Hadron Correlations in DIS
  7. The Drell-Yan Process
  8. Summary

Figures (2)

  • Figure 1: Tree-level Feynman diagrams for $\mathrm\hbox{$\mathrm{e^+e^-}$}\to$ hadrons at $\cal O\hbox{${\cal O}$}(\alpha s\hbox{$\alpha_s$}),$ in which the lepton side is represented by an arbitrary current, $J_\mu,$ and the boson-quark coupling by $\omega^\mu$.
  • Figure 2: The average values of $\cos\phi$ and $\cos2\phi$ from the parton model (dashed) and QCD (solid), for ep collisions at $s=10^5\,\mathrm{GeV^2}$ with $Q^2=10^2\,\mathrm{GeV^2}$ (left) and $x_{{\mathrm{B}}}=0.01$ (right). We use the MRS D$-'$ distribution functions, $\Lambda_{{\mathrm{QCD}}}=230\,$MeV, with pure photon exchange, and $\left p_t\right\rangle\hbox{$\left\langle p_t\right\rangle$}=\surd\!\left p_t^2\right\rangle\hbox{$\left\langle p_t^2\right\rangle$}=500\,$MeV. The QCD curves are also broken down into the separate contributions from QCDC (dot-dashed) and BGF (dotted).