Polarized hadron pair production from electron-positron annihilation

TL;DR

Addressing polarized hadron-pair production in $e^+e^-$ annihilation, the paper develops a model-independent decomposition of the hadronic tensor and a twist-2 TMD fragmentation-function description of the cross section, including electroweak effects. It provides explicit mappings between angular structure functions and convolutions of eight twist-2 TMD FFs, with frame-independent angular decompositions in Collins-Soper and Gottfried-Jackson frames. The work yields a comprehensive framework with 72 structure functions and a translation path to double-polarized Drell-Yan, enabling robust tests of TMD evolution at current and future colliders. These results facilitate simultaneous extraction and cross-checks of fragmentation functions such as $D_1$, $H_1^$, and $D_{1T}^{}$ from $e^+e^-$ data and Drell-Yan, with electroweak interference enriching the observable set.

Abstract

We study the production of two almost back-to-back hadrons from the annihilation of an electron and a positron, allowing for the polarization of all particles involved. In particular, we conduct a general (model-independent) structure function decomposition of the cross section for the case $e^+e^- \to γ^* \to h_ah_bX$. Moreover, using the parton model we calculate the relevant structure functions in terms of twist-2 transverse momentum dependent (TMD) fragmentation functions (FFs). We also give results for the situation $e^+e^- \to Z^* \to h_ah_bX$ (including $γ$-$Z$ interference) within this model. This is the first time a complete framework has been presented for the examination of TMD FFs within $e^+e^-\to h_ah_bX$. We also specify certain parts of our analysis that hold for the triple-polarized semi-inclusive deep-inelastic scattering process and for di-hadron fragmentation. Furthermore, we give an explicit prescription of how our work can be translated to the Drell-Yan reaction, which provides for the first time full results for double-polarized Drell-Yan that include electroweak effects. We further discuss the relevance of our $e^+e^-\to h_ah_bX$ results for future experiments at $e^+e^-$ machines.

Figures (5)

• Figure 1: Cross section for $e^+e^-\!\rightarrow h_a\, h_b\, X$ in terms of its leptonic and hadronic parts. The leptonic piece contains the (squared) electron-positron interaction, and the hadronic factor contains the (squared) decay of the virtual boson into the two detected hadrons and other (unobserved) particles. The former can be calculated perturbatively, while the latter is non-perturbative and can be parameterized. See text for details.
• Figure 2: Analogue of the Collins-Soper frame for $e^+e^-\!\!\rightarrow h_a h_b\, X$. The incoming electron makes an angle $\theta$ w.r.t. the $+z$-axis, and the plane spanned by the outgoing hadrons forms an angle $\phi$ w.r.t. the lepton plane. Note that both hadrons form the same angle $\beta$ w.r.t the $+z$-axis.
• Figure 3: Hadronic center-of-mass frame for $e^+e^-\!\!\rightarrow h_a h_b\, X$. The hadron $h_b$ ($h_a$) moves along the $+z$-axis ($-z$-axis), and the transverse momentum of the virtual photon defines the $+x$-axis.
• Figure 4: Cross section for $e^+e^-\!\!\rightarrow h_ah_b\, X$ in a partonic description for $q_{\perp,cm} \ll q$. The virtual photon decays into a quark-antiquark pair with (a) the quark (antiquark) fragmenting into $h_a$ ($h_b$) or (b) the antiquark (quark) fragmenting into $h_a$ ($h_b$).
• Figure 5: Analogue of the Gottfried-Jackson frame for $e^+e^-\!\!\rightarrow h_a h_b\, X$. The incoming electron makes an angle $\theta_2$ w.r.t. the $+z$-axis defined by $\vec{P}_b$, and the hadron $h_a$ moves in a plane that forms an angle $\phi_0$ w.r.t. the lepton plane.