Super-leading logarithms in non-global observables in QCD?

TL;DR

The paper identifies a theoretical mechanism by which non-global QCD observables may exhibit a breakdown of coherence through Coulomb-phase induced miscancellation in out-of-gap radiation, producing super-leading logarithms at order $\alpha_s^4$. It develops an all-orders framework for a single out-of-gap gluon, showing that imaginary Coulomb terms spoil real-virtual cancellations in certain collinear configurations and lead to a new $\ln^5(Q/Q_0)$ enhancement. A detailed analysis reveals final-state collinear emissions cancel, while initial-state collinear emissions do not, producing the leading super-leading contribution with a precise coefficient and dependence on rapidity $Y$. Numerical results indicate the effect is numerically modest for typical log-values but non-global logarithms remain significant, and the work motivates extending the calculation to multiple out-of-gap emissions and exploring connections to small-$x$ dynamics and pomeron-loop structure.

Abstract

We reconsider the calculation of a non-global QCD observable and find the possible breakdown of QCD coherence. This breakdown arises as a result of wide angle soft gluon emission developing a sensitivity to emission at small angles and it leads to the appearance of super-leading logarithms. We use the `gaps between jets' cross-section as a concrete example and illustrate that the new logarithms are intimately connected with the presence of Coulomb gluon contributions. We present some rough estimates of their potential phenomenological significance.

Figures (7)

• Figure 1: Illustrating the cancellation (and miscancellation) of soft gluon corrections.
• Figure 2: $L$ dependence of the out-of-gap cross-section (normalized to the in-gap cross-section) at two different values of $Y$.
• Figure 3: $Y$ dependence of the out-of-gap cross-section (normalized to the in-gap cross-section) at two different values of $L$.
• Figure 4: $L$ dependence of the out-of-gap cross-section (normalized to the in-gap cross-section) at two different values of $Y$ and plotted out to very large $L$.
• Figure 5: The $Y$ dependence of the large $L$ behaviour of the out-of-gap cross-section normalized to the in-gap cross-section at two different values of $\alpha_{s}$.