Nested-GPT for variable-multiplicity parton showers: A case study in the resummation of non-global logarithms

TL;DR

Nested-GPT is a hierarchical Transformer architecture designed to simulate variable-multiplicity parton-shower histories, effectively modeling complex emission processes in high-energy physics.

Contribution

It introduces Nested-GPT, a novel autoregressive Transformer framework that enforces physical constraints and dynamically predicts emissions, advancing surrogate modeling of parton showers.

Findings

Nested-GPT accurately reproduces reference shower observables within uncertainties.

It outperforms flow-matching baseline in modeling emission sequences.

The approach is validated for leading-logarithmic resummation of non-global logarithms.

Abstract

We introduce Nested-GPT, a hierarchical autoregressive Transformer architecture for simulating the variable-multiplicity parton-shower histories. As a controlled benchmark, we study the leading-logarithmic resummation of non-global logarithms in the large-$N_c$ limit, utilizing a stochastic Monte Carlo dipole shower to generate reference training data. We systematically evaluate Nested-GPT against a Transformer flow-matching baseline. The flow-matching framework successfully parameterizes the joint distribution of emission kinematics at fixed multiplicity. Its phase-space representation, however, requires the final number of emissions to be specified externally rather than generated dynamically. Conversely, Nested-GPT strictly enforces the ordered Markovian branching structure, predicting emissions sequentially and dynamically evaluating a learned sequence-termination condition. We benchmark both approaches using gap fraction observables under two complementary training regimes: direct training on vetoed histories and inclusive training followed by an analysis-level veto. The resulting generated samples agree with the reference shower within statistical uncertainties for the observables considered. These results establish Nested-GPT as a physically consistent autoregressive surrogate for variable-multiplicity shower generator and motivate extensions to subleading-logarithmic resummation and finite-$N_c$ color evolution.