An operator expansion for the elastic limit

TL;DR

The paper addresses the challenge of resumming logarithmic enhancements near the elastic limit in hard QCD processes by introducing a bi-local operator expansion that extends leading-twist descriptions to higher-dimension operators. It identifies a leading dimension-four operator that drives the longitudinal structure function $F_L$, introduces a new jet function $J'$, and derives its anomalous dimension to enable resummation of all leading $\ln^k N / N$ terms in moment space, with an infrared-finite relation connecting $F_L$ and $F_2$ coefficient functions to allow predictions of $C_L$ from $C_2$; the ${\cal O}(\alpha_s^2)$ results agree with known calculations. The framework yields a gauge-invariant, general method for edge-of-phase-space resummation applicable to DIS, Drell-Yan, thrust, and related observables, with potential impact on phenomenology and renormalon analyses.

Abstract

A leading twist expansion in terms of bi-local operators is proposed for the structure functions of deeply inelastic scattering near the elastic limit $x \to 1$, which is also applicable to a range of other processes. Operators of increasing dimensions contribute to logarithmically enhanced terms which are supressed by corresponding powers of $1-x$. For the longitudinal structure function, in moment ($N$) space, all the logarithmic contributions of order $\ln^k N/N$ are shown to be resummable in terms of the anomalous dimension of the leading operator in the expansion.

Figures (1)

• Figure 1: Momentum configurations that produce logarithmic enhancements near the elastic limit $x \rightarrow 1$ in DIS.