Extraction of Quark Transversity Distribution and Collins Fragmentation Functions with QCD Evolution (1505.05589v1)

Abstract: We study the transverse momentum dependent (TMD) evolution of the Collins azimuthal asymmetries in $e^+e^-$ annihilations and semi-inclusive hadron production in deep inelastic scattering (SIDIS) processes. All the relevant coefficients are calculated up to the next-to-leading logarithmic (NLL) order accuracy. By applying the TMD evolution at the approximate NLL order in the Collins-Soper-Sterman (CSS) formalism, we extract transversity distributions for $u$ and $d$ quarks and Collins fragmentation functions from current experimental data by a global analysis of the Collins asymmetries in back-to-back di-hadron productions in $e^+e^-$ annihilations measured by BELLE and BABAR Collaborations and SIDIS data from HERMES, COMPASS, and JLab HALL A experiments. The impact of the evolution effects and the relevant theoretical uncertainties are discussed. We further discuss the TMD interpretation for our results, and illustrate the unpolarized quark distribution, transversity distribution, unpolarized quark fragmentation and Collins fragmentation functions depending on the transverse momentum and the hard momentum scale. We make detailed predictions for future experiments and discuss their impact.

Overview of Quark Transversity and Collins Fragmentation Functions With QCD Evolution

The paper presents an in-depth examination of the extraction of quark transversity distributions and Collins fragmentation functions by employing Quantum Chromodynamics (QCD) evolution principles. This paper provides a comprehensive analysis of transverse momentum-dependent (TMD) evolution applied to experimental data from electron-positron scattering and semi-inclusive deep inelastic scattering (SIDIS). Utilizing this evolution framework within the Collins-Soper-Sterman (CSS) formalism, the paper focuses on extracting these key functions for $u$ and $d$ quarks.

Key Contributions

1. Application of TMD Evolution: This research is pivotal in utilizing approximate next-to-leading logarithmic (NLL) order accuracy for TMD evolution, allowing for a more precise understanding of the transversity distributions and Collins fragmentation functions. The approach leverages data from multiple experimental collaborations, including BELLE, BABAR, HERMES, COMPASS, and JLab HALL A.
2. Integration of QCD Techniques: The paper systematically incorporates CSS-based QCD evolution to explore transverse momentum dependencies within the Collins asymmetries observed in various scattering experiments. This integration is vital for deriving consistent transversity distributions and unraveling fragmentation dynamics in $e^+e^-$ annihilation contexts.
3. Detailed Theoretical Framework: The authors meticulously articulate the theoretical foundations necessary for addressing chirality-odd transversity within the nucleon spin structure. They emphasize that extracting transversity requires coupling to another chirality-odd function, highlighting the importance of Collins fragmentation functions within this context.

Strong Numerical Results and Claims

The paper provides a robust numerical framework for the extraction processes, supporting its findings with detailed mathematical formulations and convolutions of pertinent quantities like spin-averaged and spin-dependent structure functions. The authors claim improved consistency with experimental data and previous phenomenological studies by implementing the TMD evolution framework—a significant advancement in precise evaluations of quark transversity and fragmentation functions.

Theoretical and Practical Implications

This in-depth analysis yields several critical implications for both theoretical and practical applications in high-energy physics:

• Understanding Spin Asymmetries: The approach deepens insights into nucleon tensor charge and its fundamental characteristics, offering a clearer picture of associated spin-related asymmetries evident in high-energy scattering experiments.
• Predictive Capabilities for Future Experiments: The framework provided opens new avenues for predicting outcomes of future experiments across different energy scales, enhancing the utility of theoretical models in actual experimental settings.
• Potential Research Directions: The methodologies and analyses in this research lay a solid foundation for further exploration of nucleon structure through planned experiments at facilities such as the Electron-Ion Collider (EIC).

Conclusion

By rigorously applying QCD evolution techniques to the extraction of quark transversity distributions and Collins fragmentation functions, this paper makes significant strides towards refining our understanding of complex spin phenomena in high-energy physics. Through rigorous data analysis and theoretical advancements, it paves the way for future experimental and phenomenological inquiries into the subtle intricacies of nucleon structure. This research stands as a critical contribution to the ongoing exploration of spin dynamics and QCD behavior at the quantum level.