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Mixed QCD$\otimes$QED corrections to exclusive Drell Yan production using the $q_T$-subtraction method

Leandro Cieri, Daniel de Florian, Manuel Der, Javier Mazzitelli

TL;DR

Addressing the need for high-precision predictions, the paper extends the q_T-subtraction method to mixed QCDxQED corrections for colorless final states. It derives and presents all ingredients up to $O(alpha_s alpha)$, including the master subtraction formula and the abelianised coefficient functions, and applies the framework to exclusive Z production with Z decaying to neutrinos. The phenomenological study at LHC shows mixed corrections are typically below 1% but can be larger in certain kinematic regions, and the results reveal that naive factorisation of QCD and QED corrections is a poor approximation for differential observables. The work paves the way for fully exclusive mixed corrections and potential extensions to other massive colorless final states and resummation contexts.

Abstract

In this work we extend the $q_T$-subtraction formalism, originally developed for QCD corrections, to the case of mixed QCD$\otimes$QED corrections, and apply it to the fully exclusive calculation of the ${\cal{O}}(α_sα)$ contribution to the production of an off-shell $Z$ boson in hadronic collisions. We present explicit results for the subtraction term and the hard factor, therefore providing all the ingredients needed for the application of the formalism up to ${\cal{O}}(α_sα)$. To study the phenomenological impact we consider the decay of the off-shell $Z$ boson into a pair of neutrinos, and present kinematical distributions for the final-state leptons at LHC energies.

Mixed QCD$\otimes$QED corrections to exclusive Drell Yan production using the $q_T$-subtraction method

TL;DR

Addressing the need for high-precision predictions, the paper extends the q_T-subtraction method to mixed QCDxQED corrections for colorless final states. It derives and presents all ingredients up to , including the master subtraction formula and the abelianised coefficient functions, and applies the framework to exclusive Z production with Z decaying to neutrinos. The phenomenological study at LHC shows mixed corrections are typically below 1% but can be larger in certain kinematic regions, and the results reveal that naive factorisation of QCD and QED corrections is a poor approximation for differential observables. The work paves the way for fully exclusive mixed corrections and potential extensions to other massive colorless final states and resummation contexts.

Abstract

In this work we extend the -subtraction formalism, originally developed for QCD corrections, to the case of mixed QCDQED corrections, and apply it to the fully exclusive calculation of the contribution to the production of an off-shell boson in hadronic collisions. We present explicit results for the subtraction term and the hard factor, therefore providing all the ingredients needed for the application of the formalism up to . To study the phenomenological impact we consider the decay of the off-shell boson into a pair of neutrinos, and present kinematical distributions for the final-state leptons at LHC energies.

Paper Structure

This paper contains 4 sections, 34 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Mixed order corrections with $q_T$-subtraction formalism
  3. Phenomenological results
  4. Summary

Figures (5)

  • Figure 1: Transverse momentum distributions for the hardest (left) and softer (right) lepton. The upper panel shows the NLO QCD prediction, while the lower panel shows the NNLO QCD (blue), NLO QED (green) and mixed (red) corrections, normalized to the NLO result.
  • Figure 2: Rapidity distributions for the hardest (left) and softer (right) lepton. The upper panel shows the NLO QCD prediction, while the lower panel shows the NNLO QCD (blue), NLO QED (green) and mixed (red) corrections, normalized to the NLO result.
  • Figure 3: Lepton-pair transverse momentum (left) and rapidity (right) distributions. The upper panel shows the NLO QCD prediction, while the lower panel shows the NNLO QCD (blue), NLO QED (green) and mixed (red) corrections, normalized to the NLO result.
  • Figure 4: The $\phi^*$ distribution. The upper panel shows the NLO QCD prediction, while the lower panel shows the NNLO QCD (blue), NLO QED (green) and mixed (red) corrections, normalized to the NLO result.
  • Figure 5: Comparison between the mixed QCD$\otimes$QED corrections (red) and the naive factorisation approximation (purple), for the transverse momentum of the hardest (left) and softer (center) lepton, and the rapidity of the pair (right).