Collins function for pion-in-jet production in polarized $pp$ collisions: a test of universality and factorization

TL;DR

This work probes the universality and factorization of the Collins fragmentation function in a two-scale process, namely pion-in-jet production in polarized $pp$ collisions. It uses updated extractions of transversity $h_1^q$ and Collins FF $H_1^{\perp q}$ from SIDIS and $e^+e^-$ data within a simplified TMD framework at LO, with a collinear initial state and TMDs only in fragmentation, and computes the azimuthal asymmetry $A_N^{\sin(\phi_S-\phi^H_\pi)}$ for STAR kinematics at $\sqrt{s}=200$ GeV and $510$ GeV. The results show good agreement across key observables (e.g., distributions in $p_{\rm jT}$, $z$, $p_{\perp\pi}$, and $x_T$), supporting both Collins universality and a mild TMD evolution in these asymmetries, and also include predictions based on reweighted extractions in GPM/CGI-GPM. The findings bolster a unified TMD description of spin-dependent observables in two-scale processes and have implications for global analyses and future facilities such as an Electron-Ion Collider (EIC).

Abstract

We present an updated study of the Collins azimuthal asymmetries for pion-in-jet production in polarized $pp$ collisions. To this aim, we employ a recent extraction of the transversity and Collins fragmentation functions from semi-inclusive deep inelastic scattering and $e^+ e^-$ annihilation into hadron pairs processes, obtained within a simplified transverse momentum dependent (TMD) approach at leading order in the strong coupling constant $α_s$. In the present case we adopt a collinear configuration for the initial state, keeping transverse momentum effects only in the fragmentation mechanism. Our theoretical estimates, when compared against 200~GeV and 510~GeV data from the STAR Collaboration, show a generally good agreement for the distributions in the transverse momentum of the jet, the pion longitudinal momentum fraction and its transverse momentum with respect to the jet direction. While not being a proof, due the assumptions and limitations behind the entire approach, these findings corroborate the hypothesis of TMD factorization for such processes as well as of the universality of the Collins function and, once again, of a reduced impact of the proper TMD evolution on azimuthal asymmetries. We will also present predictions based on an extraction of the Collins and transversity distributions where information from data on single spin asymmetry for inclusive pion production in $p^\uparrow p$ collisions is included through a Bayesian reweighting procedure.

Figures (7)

• Figure 1: Estimates of the Collins azimuthal asymmetry for $p^\uparrow p\to {\rm jet}\, \pi\, X$, based on the extractions of Ref. Boglione:2024dal, as a function of $z$, integrated over $\eta_{\rm j}$ in the forward region, at $\sqrt s=200$ GeV and $\langle p_{{\text{j}}T}\rangle = 13.3$ GeV (upper panel) and $\sqrt s= 510$ GeV and $\langle p_{{\text{j}}T}\rangle = 32.3$ GeV (lower panel). Uncertainty bands at 2$\sigma$ CL are also shown. STAR data are from Refs. STAR:2022hqgSTAR:2025xyp.
• Figure 2: Estimates of the Collins azimuthal asymmetry for $p^\uparrow p\to {\rm jet}\, \pi\, X$, based on the extractions of Ref. Boglione:2024dal, as a function of $x_T$ at $\sqrt s=200$ GeV (upper panel) and $\sqrt s= 510$ GeV (lower panel), integrated over $z$ and over $\eta_{\rm j}$ in the forward region. Uncertainty bands at 2$\sigma$ CL are also shown. STAR data are from Refs. STAR:2022hqgSTAR:2025xyp.
• Figure 3: Estimates of the Collins azimuthal asymmetry for $p^\uparrow p\to {\rm jet}\, \pi\, X$, based on the extractions of Ref. Boglione:2024dal, as a function of $z$ at $\sqrt s= 200$ GeV (upper panels) and $\sqrt s= 510$ GeV (lower panels) integrated over $\eta_{\rm j}$ in the forward region, for different $p_{{\text{j}}T}$ bins. Uncertainty bands at 2$\sigma$ CL are also shown. STAR data are from Refs. STAR:2022hqgZhang:2024zuq.
• Figure 4: Estimates of the Collins azimuthal asymmetry for $p^\uparrow p\to {\rm jet}\, \pi\, X$, based on the extractions of Ref. Boglione:2024dal, as a function of $j_T$, at $\sqrt s=200$ GeV (left panels) and $\sqrt s= 510$ GeV (right panels) integrated over $\eta_{\rm j}$ in the forward region, for different $z$ bins. In both cases we use the corresponding $\langle p_{{\text{j}}T} \rangle$ values. Uncertainty bands at 2$\sigma$ CL are also shown. STAR data are from Refs. STAR:2022hqgSTAR:2025xyp.
• Figure 5: Estimates of the Collins azimuthal asymmetry for $p^\uparrow p\to {\rm jet}\, \pi\, X$, based on the extractions of Ref. Boglione:2024dal, as a function of $j_T$ at $\sqrt s= 200$ GeV (upper panels) and $\sqrt s= 510$ GeV (lower panels) for different $p_{{\text{j}}T}$ bins, integrated over $z$ and over $\eta_{\rm j}$ in the forward region. Uncertainty bands at 2$\sigma$ CL are also shown. STAR data are from Refs. STAR:2022hqgZhang:2024zuq.