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Non-factorizable contributions to deep inelastic scattering at large x

Ben D. Pecjak

TL;DR

The paper investigates DIS near the endpoint $1-x \sim \Lambda_{\rm QCD}/Q$ using soft-collinear effective theory (SCET) and a regions analysis in the Breit frame. It identifies hard, anti-hard-collinear, collinear, and soft-collinear modes as essential, and shows that soft-collinear interactions couple soft and collinear sectors in a way that prevents a clean perturbative factorization into hard, jet, and soft functions. One-loop matching reveals that finite pieces entail convolutions among jet, soft, and soft-collinear structures, while UV poles cancel only after accounting for soft-collinear contributions, signaling a breakdown of factorization driven by soft-collinear dynamics. Consequently, for $1-x$ in the region $\Lambda_{\rm QCD}/Q$, DIS cannot be factorized perturbatively into independent scale-separated functions; a multi-scale effective theory or non-perturbative input is required, though standard factorization may still hold away from the endpoint. The work also contrasts the SCET-based findings with diagrammatic endpoint analyses and with prior SCET treatments, highlighting the central role of the soft-collinear mode in redefining endpoint factorization in DIS.

Abstract

We use soft-collinear effective theory (SCET) to study the factorization properties of deep inelastic scattering in the region of phase space where 1-x = O(Lambda_{QCD/Q}). By applying a regions analysis to loop diagrams in the Breit frame, we show that the appropriate version of SCET includes anti-hard-collinear, collinear, and soft-collinear fields. We find that the effects of the soft-collinear fields spoil perturbative factorization even at leading order in the 1/Q expansion.

Non-factorizable contributions to deep inelastic scattering at large x

TL;DR

The paper investigates DIS near the endpoint using soft-collinear effective theory (SCET) and a regions analysis in the Breit frame. It identifies hard, anti-hard-collinear, collinear, and soft-collinear modes as essential, and shows that soft-collinear interactions couple soft and collinear sectors in a way that prevents a clean perturbative factorization into hard, jet, and soft functions. One-loop matching reveals that finite pieces entail convolutions among jet, soft, and soft-collinear structures, while UV poles cancel only after accounting for soft-collinear contributions, signaling a breakdown of factorization driven by soft-collinear dynamics. Consequently, for in the region , DIS cannot be factorized perturbatively into independent scale-separated functions; a multi-scale effective theory or non-perturbative input is required, though standard factorization may still hold away from the endpoint. The work also contrasts the SCET-based findings with diagrammatic endpoint analyses and with prior SCET treatments, highlighting the central role of the soft-collinear mode in redefining endpoint factorization in DIS.

Abstract

We use soft-collinear effective theory (SCET) to study the factorization properties of deep inelastic scattering in the region of phase space where 1-x = O(Lambda_{QCD/Q}). By applying a regions analysis to loop diagrams in the Breit frame, we show that the appropriate version of SCET includes anti-hard-collinear, collinear, and soft-collinear fields. We find that the effects of the soft-collinear fields spoil perturbative factorization even at leading order in the 1/Q expansion.

Paper Structure

This paper contains 12 sections, 48 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Power counting and momentum regions
  3. Matching onto SCET
  4. SCET Lagrangian
  5. SCET current at one loop
  6. Matching onto parton distributions at tree level
  7. Matching onto parton distributions at one loop
  8. Soft-collinear effects and factorization
  9. Comparison with previous work
  10. Diagrammatic Approach
  11. SCET based approach
  12. Conclusions

Figures (4)

  • Figure 1: The triangle diagram. The momentum $p_p$ is collinear and the momentum $p_x$ is anti-hard-collinear.
  • Figure 2: One-loop corrections to the SCET current. The long-dashed lines are collinear and the short-dashed lines anti-hard-collinear. The gluon scaling is indicated explicitly.
  • Figure 3: Tree-level contribution to the current correlator in SCET, evaluated in terms of collinear fields $\xi_c$ (a), and soft-collinear fields $\xi_{Q,sc}$ (b). The short-dashed propagator is anti-hard-collinear.
  • Figure 4: One-loop corrections to the current correlator. The long-dashed lines are collinear and the short-dashed lines anti-hard-collinear. The gluon scaling is labeled explicitly. The mirror image graphs are not shown. The part of (e) involving collinear exchange, (h), and (i) should not be included in the effective theory.