Conservation laws and effective hadronization models

TL;DR

This paper introduces a formalism that models hadronization as a conditioned stochastic diffusion process, revealing how conservation laws induce non-Markovian correlations and enabling a systematic effective theory approach.

Contribution

It develops a novel mathematical framework for hadronization that incorporates conservation laws via a Doob $h$-transform, establishing a Wilsonian tower of effective theories with scale separation.

Findings

Reveals non-Markovian correlations from conservation laws in hadronization.

Establishes a Wilsonian effective theory hierarchy with scale-invariant and running regimes.

Provides a framework for improved theoretical analysis and simulation of hadronization.

Abstract

Hadronization models based on local string-breaking dynamics are typically Markovian by construction, yet the physical ensemble of final states is shaped by global constraints that couple the entire fragmentation trajectory. Recasting hadronization as a conditioned stochastic diffusion process provides a precise mathematical resolution to this tension. In particular, this language reveals explicitly that constraints stemming from conservation laws induce non-Markovian correlations between otherwise independent fragmentation steps, and that these correlations can be absorbed exactly into a renormalization of the local dynamics through a Doob $h$-transform. We develop this formalism for a $q\bar{q}$ string in the chiral limit, where the longitudinal-transverse factorization of the Lund kernel becomes exact, enabling systematic power counting and clean ultraviolet (UV)/infrared (IR) separation. The dynamics organize naturally into a tower of effective theories distinguished by the remaining string mass, spanning a UV fixed point with scale-invariant transport coefficients, an intermediate regime where transverse phase space induces controlled running, and an IR boundary layer where non-local effects enter at leading order. The tower exhibits genuine Wilsonian structure, including $\beta$-functions, anomalous dimensions, and systematic matching conditions. The resulting framework achieves a clean factorization of universal microscopic fragmentation dynamics from infrared constraint effects, and opens new directions for both the theoretical analysis and practical simulation of hadronization.