Can Transversity Be Measured?

TL;DR

This paper analyzes methods to measure the quark transversity δq, a chiral-odd, leading-twist distribution difficult to access in standard DIS. It surveys existing proposals (Drell–Yan, twist-3 pion production, Collins-angle effects) and argues for a novel, leading-twist approach based on two-meson fragmentation with final-state interactions in DIS on polarized targets. The author and collaborators develop a formalism for interference between s- and p-waves in two-particle fragmentation, introducing interference fragmentation functions and deriving a measurable asymmetry that links δq to these functions. The work emphasizes the necessity of final-state interaction phases and keeping the two-meson mass differential to preserve the phase, with promising experimental prospects at HERMES/COMPASS and potential extensions to hadronic collisions.

Abstract

I review the ways that have been proposed to measure the quark transversity distribution in the nucleon. I then explain a proposal, developed by Xuemin Jin, Jian Tang and myself, to measure transversity through the final state interaction between two mesons ($ππ$, $K \bar K$, or $πK$) produced in the current fragmentation region in deep inelastic scattering on a transversely polarized nucleon.

Figures (5)

• Figure 1: Forward quark-hadron scattering. (a) The forward scattering amplitude with helicities of quarks and hadrons labelled. (b) The particular ($u$-channel) discontinuity that corresponds to the quark distribution function. It describes emission of a quark with helicity $h$ from a hadron of helicity $H$, and reabsorption of the quark with helicity $h'$ to give a hadron of helicity $H'$.
• Figure 2: Why $\delta q$ decouples from DIS. (a) A typical perturbative contribution to DIS. The chirality of the propagating quark is not changed by the coupling to gluons or photon, so it cannot be reabsorbed to form the outgoing hadron. (b) A mass insertion (marked with an $\times$) can flip chirality but give a contribution suppressed by ${\cal O}(1/Q^2)$.
• Figure 3: A generic process that could be sensitive to the nucleon's transversity. The presence of two soft processes is crucial since the chirality flip associated with $\delta q$ must be reversed by a second soft interaction.
• Figure 4: The factor, $\sin\delta_0 \sin\delta_1 \sin(\delta_0-\delta_1)$, as a function of the invariant mass $m$ of two-pion system. The data on $\pi\pi$ phase shifts are taken from Ref. ref1.
• Figure 5: Hard scattering diagram for $\pi^+\pi^- (K\overline{K})$ production in the current fragmentation region of electron scattering from a target nucleon. In perturbative QCD the diagram (from bottom to top) factors into the products of distribution function, hard scattering, fragmentation function, and final state interaction. Helicity density matrix labels are shown explicitly.