On the Evolution of Sum Rules for T-Odd Distribution and Fragmentation Functions

TL;DR

This paper investigates the stability of sum rules for T-odd distribution and fragmentation functions under probabilistic evolution, revealing parallels with known sum rules in deep inelastic scattering.

Contribution

It provides a comparative analysis of the evolution stability of the Burkardt and Schaefer-Teryaev sum rules, linking them to fundamental conservation laws.

Findings

Burkardt sum rule for Sivers functions is stable under evolution.

Schaefer-Teryaev sum rule preservation mirrors the Burkhardt-Cottingham sum rule.

Sum rules exhibit stability similar to conservation of momentum and spin structure functions.

Abstract

We test stability against probabilistic evolution of sum rules for transverse-momentum-dependent distribution and fragmentation functions. We find that preservation of the Burkardt sum rule for Sivers distribution functions is similar to the conservation of longitudinal momentum related to spin-averaged parton distributions. At the same time, preservation of the Schaefer-Teryaev sum rule for Collins functions is similar to preservation of the Burkhardt-Cottingham sum rule for the spin-dependent g_2 structure function.