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Soft-collinear effects in prompt photon production

Rahul Basu, Eric Laenen, Anuradha Misra, Patrick Motylinski

TL;DR

Problem: Prompt photon production at hadron colliders is affected by large soft and collinear corrections; existing threshold and joint resummation controls these logs but neglects soft-collinear $\ln N/N$ terms. Approach: The authors extend both threshold and joint resummation to include leading $\ln N/N$ terms by (i) evolving initial-state partons to a soft scale to capture non-diagonal evolution, and (ii) modifying final-state jet functions to include soft-collinear radiation. Findings: The $\ln N/N$ corrections are generally small but non-negligible, with initial-state contributions sometimes suppressing the cross section and other times enhancing it, and final-state contributions typically small; the effects depend on kinematics (Tevatron vs fixed-target). Significance: This work improves theoretical control of prompt-photon spectra and motivates deeper study of soft-collinear subleading terms and their structure, including potential fragmentation contributions.

Abstract

We extend next-to-leading logarithmic threshold and joint resummation for prompt photon production to include leading collinear effects. The impact of these effects is assessed for both fixed-target and collider kinematics. We find them in general to be small, but noticeable.

Soft-collinear effects in prompt photon production

TL;DR

Problem: Prompt photon production at hadron colliders is affected by large soft and collinear corrections; existing threshold and joint resummation controls these logs but neglects soft-collinear terms. Approach: The authors extend both threshold and joint resummation to include leading terms by (i) evolving initial-state partons to a soft scale to capture non-diagonal evolution, and (ii) modifying final-state jet functions to include soft-collinear radiation. Findings: The corrections are generally small but non-negligible, with initial-state contributions sometimes suppressing the cross section and other times enhancing it, and final-state contributions typically small; the effects depend on kinematics (Tevatron vs fixed-target). Significance: This work improves theoretical control of prompt-photon spectra and motivates deeper study of soft-collinear subleading terms and their structure, including potential fragmentation contributions.

Abstract

We extend next-to-leading logarithmic threshold and joint resummation for prompt photon production to include leading collinear effects. The impact of these effects is assessed for both fixed-target and collider kinematics. We find them in general to be small, but noticeable.

Paper Structure

This paper contains 8 sections, 43 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Threshold and joint resummation for prompt photon production
  3. Including leading $\ln N/N$ terms
  4. Initial state
  5. Final state
  6. Results
  7. Conclusions
  8. Appendix

Figures (8)

  • Figure 1: $\ln N/N$ contributions for Tevatron kinematics. Left pane: LL without $\ln N/N$ ($a$, solid), NLL without $\ln N/N$ ($b$, dashed), NLL with $\ln N/N$ ($c$, short-dashed). Right pane: ratio of NLL to LL (solid), ratio of NLL with $\ln N/N$ to NLL without (dashed).
  • Figure 2: $\ln N/N$ effects for $q{\bar{q}}$ channel at LL, Tevatron kinematics. Ratio to LL without $\ln N/N$ of initial state (solid) and final state (dashed) effects, and both (short-dashed).
  • Figure 3: $\ln N/N$ effects for $qg$ channel at LL, Tevatron kinematics. Labels as in Fig. \ref{['fig2']}.
  • Figure 4: $\ln N/N$ contributions for E706 kinematics. Labels as in Fig. \ref{['fig1']}.
  • Figure 5: $\ln N/N$ effects for $q\bar{q}$ channel at LL, E706 kinematics. Labels as in Fig. \ref{['fig2']}.
  • ...and 3 more figures