Momentum sum rules for fragmentation functions

TL;DR

This paper proves a momentum sum rule for the Collins fragmentation function, clarifies the non-existence of similar rules for related functions, and supports findings with a simple field-theoretical model.

Contribution

It provides a general proof of the Sch"afer-Teryaev sum rule for the transverse momentum dependent Collins function and discusses the absence of similar sum rules for related functions.

Findings

Proof of the Sch"afer-Teryaev sum rule for the Collins function

Argument against the existence of sum rules for related fragmentation functions

Model calculations supporting the theoretical analysis

Abstract

Momentum sum rules for fragmentation functions are considered. In particular, we give a general proof of the Sch\"afer-Teryaev sum rule for the transverse momentum dependent Collins function. We also argue that corresponding sum rules for related fragmentation functions do not exist. Our model-independent analysis is supplemented by calculations in a simple field-theoretical model.