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Partial-wave analysis of two-hadron fragmentation functions

Alessandro Bacchetta, Marco Radici

TL;DR

This paper develops a unified framework for accessing the transversity distribution h1 through interference fragmentation functions in two-hadron production within the same jet. It introduces a partial-wave expansion of the two-hadron system (focusing on s- and p-waves) and derives positivity bounds for the relevant fragmentation functions, including chiral-odd, T-odd partners. The authors show two distinct leading-twist SSAs: one arising from s-p interference and another from pure p-wave (spin-1) fragmentation, both coupling to h1 but with different physical origins and invariant-mass dependencies. They further extend the formalism to include intrinsic transverse momentum, providing a comprehensive, angle- and momentum-dependent description that subsumes prior approaches and offers a practical path for experimental extraction of transversity via two-hadron SIDIS.

Abstract

We reconsider the option of extracting the transversity distribution by using interference fragmentation functions into two leading hadrons inside the same current jet. To this end, we perform a new study of two-hadron fragmentation functions. We derive new positivity bounds on them. We expand the hadron pair system in relative partial waves, so that we can naturally incorporate in a unified formalism specific cases already studied in the literature, such as the fragmentation functions arising from the interference between the s- and p-wave production of two mesons, as well as the production of a spin-one hadron. In particular, our analysis clearly distinguishes two different ways to access the transversity distribution in two-hadron semi-inclusive leptoproduction.

Partial-wave analysis of two-hadron fragmentation functions

TL;DR

This paper develops a unified framework for accessing the transversity distribution h1 through interference fragmentation functions in two-hadron production within the same jet. It introduces a partial-wave expansion of the two-hadron system (focusing on s- and p-waves) and derives positivity bounds for the relevant fragmentation functions, including chiral-odd, T-odd partners. The authors show two distinct leading-twist SSAs: one arising from s-p interference and another from pure p-wave (spin-1) fragmentation, both coupling to h1 but with different physical origins and invariant-mass dependencies. They further extend the formalism to include intrinsic transverse momentum, providing a comprehensive, angle- and momentum-dependent description that subsumes prior approaches and offers a practical path for experimental extraction of transversity via two-hadron SIDIS.

Abstract

We reconsider the option of extracting the transversity distribution by using interference fragmentation functions into two leading hadrons inside the same current jet. To this end, we perform a new study of two-hadron fragmentation functions. We derive new positivity bounds on them. We expand the hadron pair system in relative partial waves, so that we can naturally incorporate in a unified formalism specific cases already studied in the literature, such as the fragmentation functions arising from the interference between the s- and p-wave production of two mesons, as well as the production of a spin-one hadron. In particular, our analysis clearly distinguishes two different ways to access the transversity distribution in two-hadron semi-inclusive leptoproduction.

Paper Structure

This paper contains 18 sections, 71 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Two-particle inclusive deep inelastic scattering
  3. Kinematics and hadronic tensor
  4. The quark-quark correlator $\Phi$
  5. The quark-quark correlator $\Delta$ and positivity bounds
  6. Cross section and transverse spin asymmetry
  7. Partial-wave expansion for the two-hadron system
  8. Partial-wave expansion of the quark-quark correlator $\Delta$ and positivity bounds
  9. Cross section and transverse spin asymmetries
  10. Explicit dependence on the transverse momenta
  11. Partial-wave expansion with transverse momenta
  12. Conclusions
  13. Unpolarized lepton beam and unpolarized target
  14. Polarized lepton beam and unpolarized target
  15. Unpolarized lepton beam and longitudinally polarized target
  16. ...and 3 more sections

Figures (3)

  • Figure 1: The usual quark handbag diagram contributing at leading twist to the semi-inclusive DIS into two leading hadrons: a) hadron and parton momenta are shown, in particular the total momentum $P_h=P_1+P_2$ and relative momentum $R=(P_1-P_2)/2$ of the two-hadron system; b) target helicity, parton chirality and two-hadron partial wave indices are shown.
  • Figure 2: Kinematics for the SIDIS of the lepton $l$ on a transversely polarized target leading to two hadrons inside the same current jet.
  • Figure 3: The hadron pair in the cm frame; $\theta$ is the cm polar angle of the pair with respect to the direction of $P_h$ in the target rest frame.