# Parity odd Fragmentation Functions

## TL;DR

This paper introduces and analyzes parity odd fragmentation functions in quantum chromodynamics, showing their properties, bounds, and how they relate to parity violation effects induced by the QCD vacuum.

## Contribution

It provides a detailed decomposition of the quark-quark correlator into parity odd and even fragmentation functions, including their operator definitions and positivity bounds.

## Key findings

- Parity odd fragmentation functions are explicitly defined and characterized.
- Positivity bounds for these functions are established.
- Parity odd functions vanish when summed over all hadrons.

## Abstract

Quantum chromodynamics is a non-Abelian gauge theory of strong interactions, in which the parity symmetry can be violated by the non-trivial $\theta$-vacuum tunneling effects. The $\theta$-vacuum induces the local parity odd domains. Those reactions that occur in these domains can be affected by the tunneling effects and quantities become parity odd. In this paper we consider the fragmentation process where parity odd fragmentation functions are introduced. We present the fragmentation functions by decomposing the quark-quark correlator. Among the total 16 fragmentation functions, 8 of them are parity conserved, and the others are parity violated. They have a one-to-one correspondence. Positivity bounds of these one dimensional fragmentation functions are shown. To be explicit, we also introduce a operator definition of the parity odd correlator. According to the definition, we give a proof that the parity odd fragmentation functions are local quantities and vanish when sum over all the hadrons h.