Abstract

We perform a dedicated study of the qoverline{q} -initiated two-loop electroweak-QCD Drell-Yan scattering amplitude in dimensional regularization schemes for vanishing light quark and lepton masses. For the relative order α and αs one-loop Standard Model corrections, details of our comparison to the original literature are given. The infrared pole terms of the mixed two-loop amplitude are governed by a known generalization of the dipole formula and we show explicitly that exactly the same two-loop polarized hard scattering functions are obtained in both the standard ’t Hooft-Veltman-Breitenlohner-Maison γ5 scheme and Kreimer’s anticommuting γ5 scheme.

Highlights

  • A precise theoretical understanding of the neutral- and charged-current Drell-Yan processes [1] in Standard Model perturbation theory is essential to the success of the Large Hadron Collider physics program

  • Due to the size of the next-to-leading order electroweak corrections, it has long been of interest to calculate the mixed EW-Quantum Chromodynamics (QCD) corrections of relative order ααs as well

  • We present an explicit application of Kreimer’s γ5 scheme to a non-trivial calculation of two-loop box-type diagrams involving chiral couplings and show that it does yield physically sensible results

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Summary

Introduction

A precise theoretical understanding of the neutral- and charged-current Drell-Yan processes [1] in Standard Model perturbation theory is essential to the success of the Large Hadron Collider physics program. As has been known since the earliest higher-order studies of the Drell-Yan process, it is important to have a solid understanding of the γ5 problem of dimensional regularization [32,33,34,35,36] if one wishes to calculate all Feynman diagrams at a given order, including those where a W or Z connect the initial- and final-state fermion lines.

Universal features of dimensional regularization
HVBM’s prescription for γ5 in dimensional regularization
Kreimer’s prescription for γ5 in dimensional regularization
MS renormalization of α and αs
On-shell electroweak gauge boson wavefunction and mass renormalization
On-shell wavefunction renormalization for massless fermion fields
Chiral symmetry restoration in HVBM’s γ5 scheme and Larin’s principle
Calculational details
Form factor decomposition
Calculations in Kreimer’s γ5 scheme
Infrared dipole singularity structure and subtraction functions
One-loop scattering amplitudes
One-loop integral definitions
Assembly of one-loop results
Two-loop scattering amplitudes
Two-loop integral definitions
Assembly of two-loop results
Helicity amplitudes
Final results
Summary and outlook
A Decoupling of irrelevant Lorentz structures
Relative order αs results
Relative order α results
Full Text
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