Quark Fragmentation in the $\theta$ Vacuum

QCD vacuum is a superposition of degenerate states with different topological numbers that are connected by tunneling (the $\theta$ vacuum). The tunneling events are due to configurations of gauge fields (e.g., the instantons) that induce local $\mathcal{P}$-odd domains in Minkowski space-time. We study the quark fragmentation in this topologically nontrivial QCD background. We find that even though QCD globally conserves $\mathcal{P}$ and $\mathcal{C}\mathcal{P}$ symmetries, two new kinds of $\mathcal{P}$-odd fragmentation functions emerge. We study their experimental manifestations in dihadron production in $e^{+}{e}^{-}$ collisions, and find two interesting dihadron correlations: the $\cos ({\varphi }_1+{\varphi }_2)$ correlation usually referred to as the Collins effect, and a $\mathcal{P}$-odd $\sim \sin ({\varphi }_1+{\varphi }_2)$ correlation that vanishes in the cross section summed over many events, but survives on the event-by-event basis.

Figure 1

Lowest-order Feynman diagram for a quark with momentum $k$ fragmenting into a $\pi$ meson with momentum $p$.