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Transversity K Factors for Drell-Yan

Philip G. Ratcliffe

TL;DR

This work addresses how higher-order QCD corrections (K-factors) affect transversely polarized Drell–Yan processes, where DIS cannot provide a straightforward reference point for transversity. By introducing a DIS-like process with a Higgs-like scalar vertex to induce spin-flip, the authors define process-dependent Wilson coefficients and compute NLO corrections in both DIS and DY, using the MMS scheme to manage γ5. They reveal that transversity carries distinct K-factor structures, including a unique term -6 z ln^2 z/(1−z), and that corrections can be notably enhanced at small z, potentially shifting observed transverse-spin asymmetries by about 10–15% in certain kinematics. The approach offers a consistency framework for interpreting transversity in models anchored to DIS inputs and highlights the need for careful consideration of kinematic regions when extracting transversity from DY measurements.

Abstract

The question of the K factor in transversely polarised Drell-Yan (DY) processes is examined. The transverse-spin case is peculiar for the absence of a reference point in deeply inelastic scattering (DIS). Therefore, in order to study more fully the possible effects of higher-order corrections on DY asymmetries, a DIS definition for transversity is devised using a hypothetical scalar (Higgs-like) vertex. The results show that some care may be required in interpreting experimentally extracted partonic transversity, in particular when comparing with model calculations or predictions.

Transversity K Factors for Drell-Yan

TL;DR

This work addresses how higher-order QCD corrections (K-factors) affect transversely polarized Drell–Yan processes, where DIS cannot provide a straightforward reference point for transversity. By introducing a DIS-like process with a Higgs-like scalar vertex to induce spin-flip, the authors define process-dependent Wilson coefficients and compute NLO corrections in both DIS and DY, using the MMS scheme to manage γ5. They reveal that transversity carries distinct K-factor structures, including a unique term -6 z ln^2 z/(1−z), and that corrections can be notably enhanced at small z, potentially shifting observed transverse-spin asymmetries by about 10–15% in certain kinematics. The approach offers a consistency framework for interpreting transversity in models anchored to DIS inputs and highlights the need for careful consideration of kinematic regions when extracting transversity from DY measurements.

Abstract

The question of the K factor in transversely polarised Drell-Yan (DY) processes is examined. The transverse-spin case is peculiar for the absence of a reference point in deeply inelastic scattering (DIS). Therefore, in order to study more fully the possible effects of higher-order corrections on DY asymmetries, a DIS definition for transversity is devised using a hypothetical scalar (Higgs-like) vertex. The results show that some care may be required in interpreting experimentally extracted partonic transversity, in particular when comparing with model calculations or predictions.

Paper Structure

This paper contains 14 sections, 25 equations, 4 figures.

Table of Contents

  1. Introduction
  2. 1.
  3. 2 + 3.
  4. The Calculation
  5. Drell--Yan cross-section and asymmetries
  6. The Drell--Yan Process
  7. Deeply Inelastic Scattering
  8. Real-gluon contributions
  9. Virtual-gluon contributions
  10. The K-Factor Results
  11. Cross-checks
  12. Conclusions
  13. Plus-regularised distributions
  14. Modified minimal subtraction scheme: implementation

Figures (4)

  • Figure 1: The DIS "handbag" diagram for a photon--Higgs interference process.
  • Figure 2: The two diagram types contributing to the NLO DIS hard partonic $q\gamma^*(H^*)\to{}gq$ scattering subprocess, the dotted line represents either a virtual photon or Higgs.
  • Figure 3: The DY--DIS difference in the Mellin moments of the Wilson coefficients (, the $K$ factor) for the three leading-twist densities.
  • Figure 4: The doubly polarised $p\bar{p}$ helicity and transversity asymmetries $A_{LL}$ and $A_{TT}$ for purely valence-driven DY at LO and NLO as functions of $\tau=Q^2/s$, for $\sqrt{s}=200$ GeV.