Quark fragmentation in the $\theta$-vacuum

TL;DR

This paper investigates how topologically non-trivial QCD vacuum structures induce novel parity-odd quark fragmentation functions, leading to unique dihadron correlations observable in high-energy collision experiments.

Contribution

It introduces two new parity-odd fragmentation functions arising from the $ heta$-vacuum in QCD, and estimates their magnitudes and experimental signatures.

Findings

Discovery of two new $ ext{P}$-odd fragmentation functions.

Prediction of azimuthal correlations in dihadron production.

Estimation of effects in $e^+e^-$ collisions and implications for other experiments.

Abstract

The vacuum of Quantum Chromodynamics is a superposition of degenerate states with different topological numbers that are connected by tunneling (the $\theta$-vacuum). The tunneling events are due to topologically non-trivial configurations of gauge fields (e.g. the instantons) that induce local $\p$-odd domains in Minkowski space-time. We study the quark fragmentation in this topologically non-trivial QCD background. We find that even though QCD globally conserves $\p$ and $\cp$ symmetries, two new kinds of $\p$-odd fragmentation functions emerge. They generate interesting dihadron correlations: one is the azimuthal angle correlation $\sim \cos(\phi_1 + \phi_2)$ usually referred to as the Collins effect, and the other is the $\p$-odd correlation $\sim \sin(\phi_1 + \phi_2)$ that vanishes in the cross section summed over many events, but survives on the event-by-event basis. Using the chiral quark model we estimate the magnitude of these new fragmentation functions. We study their experimental manifestations in dihadron production in $e^+e^-$ collisions, and comment on the applicability of our approach in deep-inelastic scattering, proton-proton and heavy ion collisions.