[Paper Review] Single-spin asymmetries with two-hadron fragmentation functions

Alessandro Bacchetta, Marco Radici|ArXiv.org|Jul 29, 2004

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper proposes using two-hadron fragmentation functions in semi-inclusive deep inelastic scattering to measure quark transversity and other spin-dependent distributions with reduced theoretical ambiguities. By integrating over intrinsic transverse momenta, it avoids factorization and evolution issues plaguing single-hadron asymmetries, enabling cleaner extraction of transversity via azimuthal and angular correlations in hadron pair production.

ABSTRACT

Using the formalism of two-hadron fragmentation functions, we discuss single-spin asymmetries occurring in the production of two hadrons in the current region of deep inelastic scattering, with a particular emphasis on transversity measurements.

Motivation & Objective

• To overcome theoretical challenges in single-spin asymmetries from single-hadron production, such as lack of factorization and unknown evolution equations for transverse-momentum-dependent functions.
• To exploit two-hadron fragmentation functions to access the quark transversity distribution $ h_1(x) $ in a way less sensitive to competing contributions and intrinsic transverse momentum dependencies.
• To provide a framework for measuring interference fragmentation functions, which are T-odd and sensitive to spin-orbit correlations.
• To enable experimental extraction of transversity and other spin distributions through angular and invariant mass distributions of hadron pairs.
• To support ongoing HERMES measurements and future studies in $e^+e^-$ and $pp$ collisions using partial-wave expansions and azimuthal angle correlations.

Proposed method

• The study employs a leading-twist and subleading-twist formalism for two-hadron fragmentation functions in semi-inclusive DIS ($ lp \to l' h_1 h_2 X $), integrating over transverse momenta to avoid factorization issues.
• It introduces the total and relative momenta of the hadron pair, $ P_h = P_1 + P_2 $ and $ R = (P_1 - P_2)/2 $, with $ |R| $ defined via the invariant mass $ M_h $, enabling kinematic separation of spin-dependent effects.
• The cross-sections are differential in $ d ext{cos} heta \, dM_h^2 \, d\varphi_R \, dz \, dx \, dy \, d\varphi_S $, with azimuthal angles $ \varphi_R $ and $ \varphi_S $ defined using the virtual photon momentum and spin/orientation vectors.
• The formalism includes Wandzura-Wilzcek approximation, where T-odd fragmentation functions with tilde (e.g., $ \widetilde{D}^{<\kern-2.1pt{\scriptscriptstyle)}} $) vanish, simplifying expressions.
• Partial-wave expansions of $ D_1 $ and $ H_1^{<\kern-2.1pt{\scriptscriptstyle)}} $ are used, truncated at $ p $-wave level, to separate contributions from $ s $- and $ p $-wave components.
• The analysis uses specific kinematic functions $ A(y), B(y), V(y), W(y) $ to express cross-sections in terms of scaling variables and spin asymmetries.

Experimental results

Research questions

• RQ1 Can two-hadron fragmentation functions provide a cleaner access to the quark transversity distribution $ h_1(x) $ than single-hadron production?
• RQ2 To what extent do single-spin asymmetries in two-hadron production avoid the theoretical drawbacks of transverse-momentum-dependent observables, such as lack of factorization and unknown evolution?
• RQ3 How can the partial-wave decomposition of two-hadron fragmentation functions isolate contributions from $ H_{1,ut}^{<\kern-2.1pt{\scriptscriptstyle)}} $ and $ H_{1,lt}^{<\kern-2.1pt{\scriptscriptstyle)}} $, especially near the $ \rho $ resonance?
• RQ4 What role do interference fragmentation functions—T-odd and odd under naive time reversal—play in the observed asymmetries?
• RQ5 Can the $ \rho $-resonance peak in $ M_h^2 $ be used to isolate $ H_{1,lt}^{<\kern-2.1pt{\scriptscriptstyle)}} $ contributions via invariant mass integration, while preserving $ \cos\theta $ dependence?

Key findings

• Single-spin asymmetries in two-hadron production are proportional to the product of a parton distribution function and a two-hadron fragmentation function, avoiding convolutions and competing contributions that plague single-hadron observables.
• The asymmetry in transverse target polarization ($ d^7\sigma_{UT} $) contains a term proportional to $ h_1 H_1^{<\kern-2.1pt{\scriptscriptstyle)}} $, which survives integration over $ \cos\theta $ due to partial-wave decomposition, enabling clean extraction of transversity.
• The $ H_{1,lt}^{<\kern-2.1pt{\scriptscriptstyle)}} $ component exhibits a Breit-Wigner shape near the $ \rho $-resonance mass, allowing its isolation via $ M_h^2 $-bin integration.
• The $ H_{1,ut}^{<\kern-2.1pt{\scriptscriptstyle)}} $ component, while not resonant, can be accessed by measuring $ \cos\theta $ dependence in separate $ M_h^2 $ bins.
• The longitudinal beam polarization asymmetry $ d^7\sigma_{LU} $ is proportional to $ e H_1^{<\kern-2.1pt{\scriptscriptstyle)}} $, providing a direct probe of the distribution function $ e(x) $.
• The formalism is experimentally viable and currently being tested at HERMES, with extensions to $ e^+e^- $ and $ pp $ collisions also feasible, as demonstrated by BELLE, PHENIX, and STAR collaborations.