# Parity-odd Parton Distribution Functions from $\theta$-Vacuum

## TL;DR

This paper introduces parity-odd parton distribution functions arising from the QCD $ heta$-vacuum, exploring their properties and potential experimental signatures in high-energy scattering processes.

## Contribution

It defines and analyzes the properties of parity-odd parton distribution functions in the context of the QCD $ heta$-vacuum, a novel approach to understanding parity violation inside hadrons.

## Key findings

- Eight parity-odd PDFs at leading twist for spin-1/2 hadrons.
- Parity-odd effects vanish in macroscopic observables.
- Potential to observe effects via single spin asymmetries in scattering.

## Abstract

Quantum chromodynamics is a fundamental non-abelian gauge theory of strong interactions. The physical quantum chromodynamics vacuum state, $|\theta\rangle$, is a linear superposition of the $n$-vacua states with different topological numbers. Because of the configuration of the gauge fields, the tunneling events can induce the local parity-odd domains. Those interactions that occur in these domains can be affected by these effects. Considering the hadron (nucleon) system, we introduce the parity-odd parton distribution functions in order to describe the parity-odd structures inside the hadron in this paper. We obtain 8 parity-odd parton distribution functions at leading twist for spin-1/2 hadrons and present properties of these parton distribution functions. By introducing the parity-odd quark-quark correlator, we find the parity-odd effects vanish from the macroscopic point of view. Since the parity-odd effects are confined in small domains, we consider the high energy semi-inclusive deeply inelastic scattering process to investigate these effects by calculating the single spin asymmetries.