Resummation of Jet Mass at Hadron Colliders

TL;DR

This paper develops a threshold-resummed framework for the jet mass distribution in hadron collisions, focusing on a simple photon+jet topology. Using Soft-Collinear Effective Theory, it factorizes the partonic cross section into hard, jet, and soft components with a novel two-scale soft function that separates in-jet and out-of-jet radiation, enabling RG evolution and systematic improvements. The authors achieve NLL resummation of jet-mass logarithms and NNLL treatment of global logs, while explicitly addressing non-global logarithms through modeling and discussion, and demonstrating good agreement with PYTHIA for phenomenologically relevant kinematics. The work highlights the practical importance of multi-scale soft radiation management and provides a path toward fully NNLL predictions, with clear directions for future refinements and extensions to broader jet-topologies.

Abstract

A method is developed for calculating the jet mass distribution at hadron colliders using an expansion about the kinematic threshold. In particular, we consider the mass distribution of jets of size R produced in association with a hard photon at the Large Hadron Collider. Expanding around the kinematic threshold, where all the energy goes into the jet and the photon, provides a clean factorization formula and allows for the resummation of logarithms associated with soft and collinear divergences. All of the large logarithms of jet mass are resummed at next-to-leading logarithmic level (NLL), and all the global logarithms at next-to-next-to-leading logarithmic level (NNLL). A key step in the derivation is the factorization of the soft function into pieces associated with single scales and a remainder which contains non-global structure. This step, which is standard in traditional resummation, is implemented in effective field theory which is then used to resum the large logarithms using the renormalization group in a systematically improvable manner.

Figures (13)

• Figure 1: Event topology of direct photon production.
• Figure 2: The photon's momentum and rapidity is denoted by $p_\gamma$ and $y$, respectively. The jet cone of half angle $R$, centered around the direction of the jet $n_J = (1, \hat{n}_J)$. The restrictions on the jet rapidity $y_J$ is shown by the dashed gray line. Soft radiation inside the jet contributes to $k_{\rm in} = n_J \cdot P_{X_s^{{\rm in}}}$, whereas the radiation outside contributes to $k_{\rm out} = n_J \cdot P_{X_s^{{\rm out}}}$
• Figure 3: The integration region $\mathcal{R}$ is shown by the red lines. When the jet rapidity is restricted, the region is further constrained to be inside the blue lines, shown here for $y_{\rm cut}=1$. The dashed green line outlines the region that most strongly contributes. This is demonstrated by the right hand plot, which shows the rapid fall off of $x_1 f_{u/P}(x_1) x_2 f_{\bar{u}/P}(x_2)$.
• Figure 4: The non-vanishing diagrams that contribute to the one-loop soft function.
• Figure 5: The renormalization group evolution of the hard, jet and soft functions, as shown schematically. Each function is calculated at fixed order at its natural scale, and they are evolved to a common scale $\mu$. Two scales emerge in the soft sector which results in the refactorization of the soft function.