On pi-pi Correlations in Polarized Quark Fragmentation Using the Linear Sigma Model

TL;DR

The paper investigates how a transversely polarized quark fragments into a two-pion final state using the linear sigma model. It shows that interference between continuum ππ production and the σ resonance generates a sizeable, leading-twist spin-dependent fragmentation function, providing a direct link between quark transverse spin and two-pion correlations in jets. The results highlight the potential to probe chiral symmetry breaking in QCD through jet fragmentation and motivate experimental measurements, while acknowledging the crude, model-dependent nature of the analysis. Overall, the work offers a theoretical basis for accessing quark transverse spin and chiral dynamics via polarized fragmentation into pion pairs.

Abstract

Using the linear sigma model to describe quark--pion interactions, we compute polarization asymmetries in quark fragmentation. We show that the effects of transverse quark polarizations appear in the correlation between the two leading pions in a jet produced by the fragmentation of a quark. Such asymmetries provide a window to the nature of chiral symmetry breaking in QCD.

Figures (3)

• Figure : The relevant Feynman rules obtained from the Sigma Model lagrangian.
• Figure : The fragmentation of a $\psi$ into hadron $A$.
• Figure : The four cut diagrams for the $u^{*}\to \pi ^{+}\pi ^{-} u$ fragmentation