Angular dependences in inclusive two-hadron production at BELLE

TL;DR

The paper develops a comprehensive theoretical framework for azimuthal asymmetries in inclusive two-hadron production at BELLE, aiming to extract the Collins fragmentation function and, via its universality, access transversity. It combines leading-twist Collins-Soper factorization with higher-twist, electroweak interference, radiative corrections, and frame choices, and then extends to nonperturbative Sudakov effects and weighted observables. Key contributions include explicit LO and TMD formulations, a detailed treatment of scale dependence and Sudakov suppression, and practical strategies (weighted moments, asymmetry ratios, jet-frame analyses) to isolate the Collins signal in BELLE data. The results highlight that Sudakov effects significantly suppress the asymmetry at higher Q^2, underscoring the need for nonperturbative inputs and careful observable design to robustly extract the Collins function and transversity from experiments. Overall, the work provides essential theoretical tools for interpreting BELLE measurements and for linking e+e- data to SIDIS extractions of transversity.

Abstract

A collection of results is presented relevant for the analysis of azimuthal asymmetries in inclusive two-hadron production at BELLE. The aim of this overview is to provide theoretical ingredients necessary to extract the Collins effect fragmentation function. The latter arises within the Collins-Soper factorization formalism, which describes both the transverse momentum and Q^2 dependence of the cross section and its angular dependences at low and moderate transverse momentum. Since the Collins effect is not the only source of angular dependences, a discussion of various other effects is included. This concerns higher twist contributions, photon-Z-boson interference effects, radiative corrections, beam polarization and weak decays. Furthermore, different frames, transverse momentum weighting and ratios of asymmetries are discussed. These issues are all of relevance for the unambiguous measurement of the Collins effect.

Figures (7)

• Figure 1: Kinematics of the annihilation process in the lepton center of mass frame (the analogue of the Gottfried-Jackson frame) for a back-to-back jet situation. $P_2$ is the momentum of a hadron in one jet, $P_1$ is the momentum of a hadron belonging to the other jet.
• Figure 2: Kinematics of the annihilation process in the lepton center of mass frame, the analogue of the Collins-Soper frame.
• Figure 3: Factorized 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 $1/Q$.
• Figure 5: The asymmetry factor ${\cal A}(Q_T)$ (in units of $M^2$) at $Q=10 \, \text{GeV}$ and $Q = 90 \, \text{GeV}$. The solid curves are obtained with the method explained in the text; the dashed-dotted curves are from the earlier analysis of Ref. Boer01.