Wouter J. Waalewijn

A bstract: We present a factorization formula for the e + h → e + jet + X cross section at small transverse momenta up to next-to-leading power (NLP), derived using the background field method (BFM) with explicit inclusion of soft modes. We discuss the relation between soft modes and overlap subtractions at NLP, showing that the inclusion of soft modes enables a definition of twist-3 operators with properly subtracted rapidity and endpoint divergences. We also derive the effective current operator at NLP and identify additional structures compared to previous approaches based on soft-collinear effective theory and the BFM without soft modes. Nevertheless, for the hadronic tensor, we find agreement at the perturbative order that we are working at, and identify a condition that needs to be satisfied for this agreement to extend to higher orders. Furthermore, we construct the most general form factors for this process, taking into account the polarization of the initial states. These involve perturbatively-calculable jet functions, opening a path to precise determinations of twist-3 hadronic distributions. Finally, our formalism is illustrated with phenomenological results for a specific azimuthal asymmetry, whose leading-logarithmic contribution depends solely on a twist-3 hadronic distribution and a twist-2 jet function.

Modern collider phenomenology requires unprecedented precision for the theoretical predictions, for which slicing techniques provide an essential tool at next-to-next-to-leading order (NNLO) in the strong coupling. The most popular slicing variable is based on the transverse momentum q T of a color-singlet final state, but its generalization to final states with jets is known to be very difficult. Here we propose two generalizations of q T that can be used for jet processes, providing proof of concept with an NLO slicing for p p → 2 jets. We present factorization formulas that enable our approach to NNLO, calculate the NNLO collinear-soft function, and demonstrate slicing at this order for e + e − → 2 jets. One of these generalizations of q T only applies to planar Born processes, such as p p → 2 jets, but offers a dramatic simplification of the soft function. We also discuss how our approach can directly be extended to obtain predictions for the fragmentation of hadrons. This presents a promising path for high-precision QCD calculations with multijet final states.

A bstract: Energy correlators are theoretically simple and physically intuitive observables that bridge experimental and theoretical particle physics. They have for example enabled the most precise jet substructure determination of the strong coupling constant to date, and recent proposals suggest that they may be used to precisely determine the top quark mass with calculable, small theoretical uncertainties. However, existing energy correlators all measure correlations in angles between particles, from which other observables such as mass must be inferred through potentially complicated procedures. In this work, we generalize energy correlators to enable straightforward measurements of non-angular correlations, which we call Energy Weighted Observable Correlations (EWOCs). To enforce collinear safety, EWOCs quantify correlations between subjets rather than particles. The subjet radius can be tuned to control both the physical scales probed by EWOCs and their sensitivity to non-perturbative physics. We focus on the phenomenologically relevant example of the mass EWOC, which measures mass correlations between pairs of subjets, in the task of extracting mass scales from jets. In jet substructure determinations of the mass of a hadronically-decaying W boson, we show that the mass EWOC outperforms the angle-based energy correlator, and performs comparably to the soft-drop groomed jet mass. As a first exploration of the theoretical properties of EWOCs, we also calculate the mass EWOC on light-quark jets and compare to results obtained with Pythia 8.309.

Energy correlators have recently come to the forefront of jet substructure studies at colliders due to their remarkable properties: they naturally separate physics at different scales, are robust to contamination from soft radiation, and offer a direct connection with quantum field theory. The current parametrization used for energy correlators, however, is based on redundant pairwise angles with complex phase space restrictions. In this Letter, we introduce a new parametrization of energy correlators that features a simpler phase space structure and preserves information about the orientation of jet constituents. Further, our parametrization drastically reduces the computational cost to compute energy correlators on experimental data; whereas the time to compute a traditional projected N -point energy correlator scales as M N / N ! on a jet with M particles, our new parametrization achieves a scaling of M 2 ln M , remarkably independently of N . Even for N = 3 , this improved scaling is particularly important for studies of heavy ion collisions, and higher values of N will enable new qualitative understanding of gauge theories. Theoretical calculations for our new energy correlators differ from those of traditional parametrizations only at next-to-next-to-leading logarithmic accuracy and beyond, and we expect that our simpler phase space structure will simplify those calculations. We also discuss how to extend our parametrization to resolved N -point energy correlators that encode angular distances between greater numbers of particles, yielding intuitive visualizations of jet substructure that are qualitatively different for different jet samples. We propose two possible generalizations for probing multiprong jets and testing jet scaling behavior. Published by the American Physical Society 2025

Renormalization group evolution equations describing the scale dependence of quantities in quantum chromodynamics play a central role in the interpretation of experimental data. Arguably the most important evolution equations for collider physics applications are the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) equations, which describe the evolution of a quark or gluon fragmenting into hadrons, with only a hadron identified at a time. In recent years, the study of the correlations of energy flow within jets has come to play a central role at collider experiments, necessitating an understanding of correlations, going beyond the standard DGLAP paradigm. In this paper we derive a general renormalization group equation describing the collinear dynamics that account for correlations in the fragmentation. We compute the kernel of this evolution equation at next-to-leading order, where it involves the 1 → 3 splitting functions, and develop techniques to solve it numerically. We show that our equation encompasses all previously known collinear evolution equations, namely DGLAP and the evolution of multihadron fragmentation functions. As an application of our results, we consider the phenomenologically relevant example of energy flow on charged particles, computing the energy fraction in charged particles in e + e − → hadrons at next-to-next-to-leading order. Our results are an important step toward improving the understanding of the collinear dynamics of jets, with broad applications in jet substructure, ranging from the study of multihadron correlations, to the description of inclusive (sub)jet production, and the advancement of modern parton showers.