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Factorization and soft-gluon divergences in isolated-photon cross sections

S. Catani, M. Fontannaz, E. Pilon

TL;DR

The paper proves that isolated-photon cross sections obey an all-orders factorization where collinear singularities are absorbed into universal photon fragmentation functions $D_{\\gamma/a}(z,\mu^2)$, while the isolation constraints modify only short-distance coefficient functions that depend on the isolation parameters. It provides a detailed NLO calculation for the fragmentation component in $e^+e^-$ annihilation, revealing large double logarithms near the critical point $x_\\gamma=x_c$ due to the non-smooth isolation criterion and LO step behavior. The authors attribute these Sudakov-type divergences to soft/collinear radiation constrained by isolation and argue that all-order resummation is required to obtain finite, physically sensible predictions, with resummation expected to smooth the cross section across the critical region. They also discuss the extension to hadroproduction, the interpretation of the divergences, and the role of non-perturbative fragmentation, outlining a path toward practical, resum incorporating predictions for isolated-photon production. Overall, the work clarifies factorization structure for isolated photons and highlights the importance of resummation in controlling soft-gluon effects within experimentally imposed isolation criteria.

Abstract

We study the production of isolated photons in $e^+e^-$ annihilation and give the proof of the all-order factorization of the collinear singularities. These singularities are absorbed in the standard fragmentation functions of partons into a photon, while the effects of the isolation are consistently included in the short-distance cross section. We compute this cross section at order $\as$ and show that it contains large double logarithms of the isolation parameters. We explain the physical origin of these logarithms and discuss the possibility to resum them to all orders in $\as$.

Factorization and soft-gluon divergences in isolated-photon cross sections

TL;DR

The paper proves that isolated-photon cross sections obey an all-orders factorization where collinear singularities are absorbed into universal photon fragmentation functions , while the isolation constraints modify only short-distance coefficient functions that depend on the isolation parameters. It provides a detailed NLO calculation for the fragmentation component in annihilation, revealing large double logarithms near the critical point due to the non-smooth isolation criterion and LO step behavior. The authors attribute these Sudakov-type divergences to soft/collinear radiation constrained by isolation and argue that all-order resummation is required to obtain finite, physically sensible predictions, with resummation expected to smooth the cross section across the critical region. They also discuss the extension to hadroproduction, the interpretation of the divergences, and the role of non-perturbative fragmentation, outlining a path toward practical, resum incorporating predictions for isolated-photon production. Overall, the work clarifies factorization structure for isolated photons and highlights the importance of resummation in controlling soft-gluon effects within experimentally imposed isolation criteria.

Abstract

We study the production of isolated photons in annihilation and give the proof of the all-order factorization of the collinear singularities. These singularities are absorbed in the standard fragmentation functions of partons into a photon, while the effects of the isolation are consistently included in the short-distance cross section. We compute this cross section at order and show that it contains large double logarithms of the isolation parameters. We explain the physical origin of these logarithms and discuss the possibility to resum them to all orders in .

Paper Structure

This paper contains 7 sections, 39 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Factorization
  3. $e^+e^-$ annihilation
  4. Hadroproduction and photoproduction collisions
  5. Fixed-order calculation in $e^+e^-$ annihilation
  6. Divergent behaviour for $x_\gamma \sim x_c$
  7. Outlook: higher orders, resummation and non-perturbative effects

Figures (2)

  • Figure 1: The divergent behaviour of the isolated-photon cross section in the vicinity of the critical point $x_\gamma=x_c$ at LO (solid), NLO (dotted) and as expected after resummation (dot-dashed).
  • Figure 2: Divergent behaviour at a critical point with single-sided singularities: LO (solid), NLO (dotted). The dot-dashed line denotes the Sudakov shoulder obtained after all-order resummation.