Helicity correlation of dihadron in current and target fragmentation regions of unpolarized SIDIS

TL;DR

The paper investigates how the helicity correlation ${ m C}_{LL}$ of a dihadron produced in unpolarized SIDIS, with one hadron in the CFR and the other in the TFR, probes spin-dependent hadronization through the polarized fragmentation function $G_{1Lq}$ and the polarized fracture function $l_{1q}^L$. It develops a theoretical framework for the cross section, defines ${ m C}_{LL}$ as the ratio of the polarized to unpolarized contributions, and performs perturbative matching of fracture functions onto proton PDFs and $\,\Lambda$ fragmentation functions in the region $_{ m QCD} rt P_{2ot} rt Q$. Numerical predictions, using CTEQ18 PDFs and DSV $\\Lambda$ FFs across three polarized FF scenarios, show strong flavor and kinematic sensitivity: scenario-1 yields negligible ${ m C}_{LL}$, while scenario-3 can reach percent-level values in certain $\xi_2$ and $z_1$ regions, with energy-scale evolution modestly enhancing the signal. The results indicate that high-precision SIDIS experiments, especially at the EIC, can constrain the flavor structure of spin-dependent fragmentation and fracture functions, offering new insights into spin transfer in both CFR and TFR and advancing our understanding of spin-dependent hadronization.

Abstract

We study the helicity correlation of two $Λ$ hyperons produced in unpolarized semi-inclusive deep inelastic scatterings (SIDIS), with one hyperon detected in the current fragmentation region and the other in the target fragmentation region. This observable provides direct access to the spin-dependent fragmentation function $G_{1Lq}$ and the spin-dependent fracture function $l_{1q}^L$ even in unpolarized lepton nucleon collisions. Utilizing the perturbative matching of the fracture function, we present numerical predictions for the helicity correlation, revealing significant variations with flavor and kinematic regions. This observable offers a unique way to investigate the spin-dependent hadronization mechanism across both the current and target fragmentation regions. It also provides new insights into the spin transfer effects in SIDIS processes.

Figures (3)

• Figure 1: Feynman diagram of the hadronic tensor at the tree level of perturbative QCD. Similar antiquark contribution is not shown.
• Figure 2: Diagrams for the matching of quark fracture functions at the leading order of $\alpha_s$.
• Figure 3: Numerical estimations for helicity correlation of $\Lambda$ hyperons in the CFR and TFR as a function of $\xi_2$ for different values of $x_B$ and $z_1$. The typical values of factorization scales are chosen to $\mu_f^2 = 10{\rm GeV}^2$ or $100{\rm GeV}^2$ for experiments at low or high energy scales. Results are shown for three DSV scenarios of polarized $\Lambda$ FFs.