QCD distributions for SEMD and spectral shape observables

Determine whether analytic Quantum Chromodynamics calculations can be performed for the distributions of the p = 2 Spectral Energy Mover’s Distance (SEMD) metric and SEMD-derived shape observables introduced in this work, extending beyond the existing fixed-order results for the p = 1 SEMD, and thereby compute their distributions in QCD.

Background

This work develops closed-form expressions for the p = 2 Spectral Energy Mover’s Distance (SEMD) and introduces a suite of spectral event and jet shape observables, together with an efficient implementation (Specter) enabling large-scale computations.

While prior analytic progress exists only for fixed-order calculations of the p = 1 SEMD, no corresponding QCD predictions are established for the p = 2 SEMD or for the distributions of the spectral shapes introduced here. Establishing such results would enable precision theoretical control and facilitate comparisons with experimental data.

The authors explicitly identify as an open direction the task of computing these distributions in QCD and question whether one can go beyond the fixed-order p = 1 SEMD results to more general analytic control for the p = 2 case and associated observables.