Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Hard Scattering Factorization from Effective Field Theory

Christian W. Bauer, Sean Fleming, Dan Pirjol, Ira Z. Rothstein, Iain W. Stewart

TL;DR

This paper demonstrates how gauge symmetries within soft-collinear effective theory (SCET) simplify proofs of factorization for high-energy hadronic processes, including back-to-back jets. By separating collinear, soft, and usoft modes and employing field redefinitions and Wilson lines, factorization emerges at the operator level to all orders in αs at leading power, applicable to exclusive (π-γ and meson form factors) and inclusive (DIS, Drell-Yan, DVCS) observables. The approach yields concise, gauge-invariant derivations of factorized forms, expressing amplitudes as hard coefficients convolved with universal nonperturbative matrix elements (DAs, PDFs, and NFPDFs). The results reproduce known limits (e.g., Brodsky-Lepage, Callan-Gross) within the SCET framework and set the stage for systematic power corrections and resummations in a broad class of processes.

Abstract

In this paper we show how gauge symmetries in an effective theory can be used to simplify proofs of factorization formulae in highly energetic hadronic processes. We use the soft-collinear effective theory, generalized to deal with back-to-back jets of collinear particles. Our proofs do not depend on the choice of a particular gauge, and the formalism is applicable to both exclusive and inclusive factorization. As examples we treat the pi-gamma form factor (gamma gamma* -> pi^0), light meson form factors (gamma* M -> M), as well as deep inelastic scattering (e- p -> e- X), Drell-Yan (p pbar -> X l+ l-), and deeply virtual Compton scattering (gamma* p -> gamma(*) p).

Hard Scattering Factorization from Effective Field Theory

TL;DR

This paper demonstrates how gauge symmetries within soft-collinear effective theory (SCET) simplify proofs of factorization for high-energy hadronic processes, including back-to-back jets. By separating collinear, soft, and usoft modes and employing field redefinitions and Wilson lines, factorization emerges at the operator level to all orders in αs at leading power, applicable to exclusive (π-γ and meson form factors) and inclusive (DIS, Drell-Yan, DVCS) observables. The approach yields concise, gauge-invariant derivations of factorized forms, expressing amplitudes as hard coefficients convolved with universal nonperturbative matrix elements (DAs, PDFs, and NFPDFs). The results reproduce known limits (e.g., Brodsky-Lepage, Callan-Gross) within the SCET framework and set the stage for systematic power corrections and resummations in a broad class of processes.

Abstract

In this paper we show how gauge symmetries in an effective theory can be used to simplify proofs of factorization formulae in highly energetic hadronic processes. We use the soft-collinear effective theory, generalized to deal with back-to-back jets of collinear particles. Our proofs do not depend on the choice of a particular gauge, and the formalism is applicable to both exclusive and inclusive factorization. As examples we treat the pi-gamma form factor (gamma gamma* -> pi^0), light meson form factors (gamma* M -> M), as well as deep inelastic scattering (e- p -> e- X), Drell-Yan (p pbar -> X l+ l-), and deeply virtual Compton scattering (gamma* p -> gamma(*) p).

Paper Structure

This paper contains 15 sections, 129 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Formalism
  3. Soft-Collinear Effective Theory
  4. SCET for $n$ and ${\bar{n}}$ collinear fields
  5. Non-perturbative Matrix Elements
  6. Symmetries for collinear fields
  7. Exclusive Processes
  8. $\pi$-$\gamma$ Form Factor
  9. The large $Q^2$ meson form factor
  10. Inclusive Processes
  11. Deep inelastic scattering
  12. Drell-Yan, $p \bar{p} \to \ell^+\ell^- X$
  13. Deeply Virtual Compton Scattering, $\gamma^* p\to \gamma^{(*)} p'$
  14. Conclusion
  15. Factorization of soft and collinear $n$ & ${\bar{n}}$ modes

Figures (4)

  • Figure 1: Tree level matching onto $O_{j}$ in the Breit Frame. The graphs on the left include $u$ and $d$ quarks.
  • Figure 2: Tree level matching onto $C_{0,8}$. The QCD graphs on the left plus the analogous graphs with the current on the bottom quark line are matched onto the collinear operator on the right.
  • Figure 3: Tree level matching onto the operator $O_j^{(i)}$ in DIS.
  • Figure 4: Tree level matching onto the operators in Drell-Yan.