Factorization and Resummation for Jet Processes

TL;DR

The paper tackles non-global logarithms in cone-jet cross sections by developing an all-order factorization within Soft-Collinear Effective Theory (SCET) that retains a multi-Wilson-line structure for soft emissions and introduces a novel coft radiation mode for narrow jets.It derives factorization theorems for both wide-angle and narrow-jet regimes, lays out the corresponding renormalization-group evolution, and performs explicit NNLO checks against fixed-order results, providing analytic control over logarithmic terms in the cross sections.The RG framework reproduces the leading non-global logarithms in the large-$N_c$ limit and connects to the Banfi-Marchesini-Smye (BMS) equation, offering a pathway to higher-order resummations of non-global observables.These results pave the way for improved predictions in jet cross sections and jet-substructure studies, with potential extensions to hadronic collisions and Glauber effects.

Abstract

From a detailed analysis of cone-jet cross sections in effective field theory, we obtain novel factorization theorems which separate the physics associated with different energy scales present in such processes. The relevant low-energy physics is encoded in Wilson lines along the directions of the energetic particles inside the jets. This multi-Wilson-line structure is present even for narrow-cone jets due to the relevance of small-angle soft radiation. We discuss the renormalization-group equations satisfied by these operators. Their solution resums all logarithmically enhanced contributions to such processes, including non-global logarithms. Such logarithms arise in many observables, in particular whenever hard phase-space constraints are imposed, and are not captured with standard resummation techniques. Our formalism provides the basis for higher-order logarithmic resummations of jet and other non-global observables. As a nontrivial consistency check, we use it to obtain explicit two-loop results for all logarithmically enhanced terms in cone-jet cross sections and verify those against numerical fixed-order computations.

Figures (15)

• Figure 1: Definition of the parameters $\delta$ and $\beta$ of the dijet cross section. We use the thrust axis $\vec{n}$ as the jet axis.
• Figure 2: Momentum regions relevant for narrow-angle jet production. The plot shows the scaling of the light-cone components $n\cdot p$ and $\bar{n}\cdot p$, and we assume that $\beta\ll \delta$ (we use $\beta\sim\delta^2$ in the narrow-jet case to ensure this condition). The meshed gray area shows the veto in the out-of-jet region which forbids the presence of energetic modes. In the wide-angle limit $\delta \sim 1$, soft and coft modes coincide and the collinear and hard scalings are the same.
• Figure 3: Momentum modes and associated scales for wide-angle (left) and narrow-angle (right) jet production.
• Figure 4: Feynman diagrams contributing to the one-loop coft function $\bm{\mathcal{U}}_{2}$. For each of the three diagrams, there is also an equal, mirrored contribution. We use a double-line notation to represent the Wilson lines.
• Figure 5: Sample Feynman diagrams contributing to the jet function $\bm{\mathcal{J}}_1$ at different orders in perturbation theory. Note that only a single propagator is cut.