Monte Carlo Implementation of Polarized Hadronization

TL;DR

This paper develops a Monte Carlo framework for polarized quark hadronization based on an extended quark-jet model, validating it through explicit calculations and presenting detailed results for pion fragmentation functions and analyzing powers.

Contribution

It introduces a self-consistent Monte Carlo implementation of polarized hadronization using TMD splitting functions, addressing positivity violations in models, and providing detailed pion fragmentation function results.

Findings

Validated the MC framework against explicit analytical results.

Demonstrated opposite sign Collins functions for favored and unfavored channels.

Produced detailed pion fragmentation functions and analyzing powers with different model inputs.

Abstract

We study the polarized quark hadronization in a Monte Carlo (MC) framework based on the recent extension of the quark-jet framework, where a self-consistent treatment of the quark polarization transfer in a sequential hadronization picture has been presented. Here, we first adopt this approach for MC simulations of hadronization process with finite number of produced hadrons, expressing the relevant probabilities in terms of the eight leading twist quark-to-quark transverse momentum dependent (TMD) splitting functions (SFs) for elementary $q \to q'+h$ transition. We present explicit expressions for the unpolarized and Collins fragmentation functions (FFs) of unpolarized hadrons emitted at rank two. Further, we demonstrate that all the current spectator-type model calculations of the leading twist quark-to-quark TMD SFs violate the positivity constraints, and propose quark model based ansatz for these input functions that circumvents the problem. We validate our MC framework by explicitly proving the absence of unphysical azimuthal modulations of the computed polarized FFs, and by precisely reproducing the earlier derived explicit results for rank two pions. Finally, we present the full results for pion unpolarized and Collins FFs, as well as the corresponding analyzing powers from high statistics MC simulations with a large number of produced hadrons for two different model input elementary SFs. The results for both sets of input functions exhibit the same general features of opposite signed Collins function for favored and unfavored channels at large $z$, and at the same time demonstrate the flexibility of the quark-jet framework by producing significantly different dependences of the results at mid- to low-$z$ for the two model inputs.