Asymmetries in polarized hadron production in e^+e^- annihilation up to order 1/Q

TL;DR

This work provides the complete tree-level, $O(1/Q)$ description of inclusive two-hadron production in $e^+e^-$ annihilation with back-to-back jets, expressed in terms of a comprehensive set of fragmentation functions, including time-reversal odd ones like $H_1^ot$ and $D_{1T}^ot$. It reveals leading azimuthal asymmetries, such as a cos$(2\,oldsymbol{ heta})$ dependence arising from intrinsic transverse momentum, and systematically derives both unpolarized and polarized cross-sections for one- and two-hadron final states. The analysis shows how weighted cross-sections can access $k_T^2$-moments and links twist-3 functions to these moments, offering a framework to extract fragmentation functions and study hadron structure in $e^+e^-$ processes. The results underscore the potential of azimuthal observables to probe fragmentation dynamics and test factorization in high-energy annihilation.

Abstract

We present the results of the tree-level calculation of inclusive two-hadron production in electron-positron annihilation via one photon up to subleading order in 1/Q. We consider the situation where the two hadrons belong to different, back-to-back jets. We include polarization of the produced hadrons and discuss azimuthal dependences of asymmetries. New asymmetries are found, in particular there is a leading cos(2 phi) asymmetry, which is even present when hadron polarization is absent, since it arises solely due to the intrinsic transverse momenta of the quarks.

Figures (4)

• Figure 1: Kinematics of the annihilation process in the lepton center of mass frame for a back-to-back jet situation. $P_2$ is the momentum of a jet or of a fast hadron in a jet, $P_1$ is the momentum of a hadron belonging to the other jet.
• Figure 2: Correlation functions $\Delta$ and $\Delta_A$.
• Figure 3: Quark diagram contributing to $e^+ e^-$ annihilation in leading order. There is a similar diagram with reversed fermion flow.
• Figure 4: Diagrams contributing to $e^+ e^-$ annihilation at order $1/Q$.