Accessing transversity with interference fragmentation functions

TL;DR

This work proposes accessing the nucleon transversity distribution $h_1(x)$ through interference fragmentation functions in two-hadron production within the same jet, focusing on $ ext{π}^+ ext{π}^-$ pairs near the $ ho$ resonance. By exploiting a novel interference FF, $H_1^{<{ )}}$, and a new azimuthal angle that links quark transverse polarization to the hadron-pair relative motion, the authors derive a leading-twist SSA in semi-inclusive DIS that cleanly factors $h_1$ with the FF. A spectator-model calculation for the fragmentation functions demonstrates measurable, predominantly negative asymmetries across $x$ and the two-hion mass $M_h$, with modest dependence on model inputs, and highlights experimental prospects at current and future facilities. The approach offers a collinear, less dilution-prone alternative to Collins-based methods, and provides a practical framework for constraining $h_1$ with forthcoming spin-physics experiments.

Abstract

We discuss in detail the option to access the transversity distribution function $h_1(x)$ by utilizing the analyzing power of interference fragmentation functions in two-pion production inside the same current jet. The transverse polarization of the fragmenting quark is related to the transverse component of the relative momentum of the hadron pair via a new azimuthal angle. As a specific example, we spell out thoroughly the way to extract $h_1(x)$ from a measured single spin asymmetry in two-pion inclusive lepton-nucleon scattering. To estimate the sizes of observable effects we employ a spectator model for the fragmentation functions. The resulting asymmetry of our example is discussed as arising in different scenarios for the transversity.

Figures (7)

• Figure 1: Quark diagram contributing in leading order to two-hadron inclusive DIS when both hadrons are in the same quark current jet. There is a similar diagram for anti-quarks.
• Figure 2: The kinematics for the final state where a quark fragments into two leading hadrons inside the same current jet.
• Figure 3: The definition of azimuthal angles, in the frame where $q_\perp = 0$, with respect to the scattering plane and the laboratory plane, whose relative oriented angle is $\phi^L = -\phi_{S_\perp}$.
• Figure 4: The diagrams considered for the quark fragmentation into $\pi^+ \pi^-$ at leading twist and leading order in $\alpha_s$ in the context of the spectator model.
• Figure 5: The FF $D_1 (z)$ (left) and $H_{1\, (R)}^{{<{ )}}} (z)$ (right). Solid line for $N_{q\rho} = 0.9$ GeV$^3$, and the integral (\ref{['eq:sumrule']}) amounting to 0.14; dashed line for $N_{q\rho} = 1.6$ GeV$^3$, and the integral equals 0.48.