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arXiv · 2605.18360

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

Wanchen Li·Ding Yu Shao·Hao-Zhe Shi·Yu-Xuan Sun
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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.

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Wanchen Li, Ding Yu Shao, Hao-Zhe Shi, Yu-Xuan Sun. 2026-05-20. Nested-GPT for variable-multiplicity parton showers: A case study in the resummation of non-global logarithms. https://arxiv.org/abs/2605.18360

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