[Paper Review] SIDIS in target fragmentation region

A.M. Kotzinian, M. Anselmino+1 more|arXiv (Cornell University)|Jul 12, 2011

Particle physics theoretical and experimental studies4 references3 citations

TL;DR

This paper develops a leading-twist formalism for spin and transverse-momentum dependent fracture functions in semi-inclusive deep inelastic scattering (SIDIS) in the target fragmentation region (TFR), demonstrating that single hadron production in the TFR only accesses a Sivers-like azimuthal asymmetry at leading order. It further shows that double hadron production—where one hadron is in the current fragmentation region and another in the TFR—provides access to all 16 leading-twist fracture functions, enabling a complete tomographic reconstruction of the nucleon's 3D spin structure.

ABSTRACT

We shortly describe the leading twist formalism of spin and transverse-momentum dependent fracture functions recently developed and present results for the production of spinless hadrons in the target fragmentation region (TFR) of SIDIS. In this case not all fracture functions can be accessed and only a Sivers-like single spin azimuthal asymmetry shows up at LO cross-section. Then, we demonstrate that the measurement of spin dependent azimuthal asymmetries in double hadron production in polarized SIDIS -- with one spinless hadron produced in the current fragmentation region (CFR) and another in the TFR -- would provide access to all 16 leading twist fracture functions.

Motivation & Objective

• To extend the theoretical framework of spin and transverse-momentum dependent (STMD) fracture functions to the target fragmentation region (TFR) of SIDIS.
• To address the limitation of single hadron production in the TFR, which only accesses a single Sivers-like azimuthal asymmetry at leading order.
• To propose double hadron production in SIDIS (DSIDIS) as a means to access all 16 leading-twist fracture functions.
• To demonstrate that measuring spin-dependent azimuthal asymmetries in DSIDIS enables a complete reconstruction of the nucleon's 3D spin-dependent partonic structure.
• To identify future experimental facilities—JLab 12 and the Electron-Ion Collider (EIC)—as optimal settings for testing the proposed framework.

Proposed method

• Adapts the TMD factorization formalism to SIDIS in the TFR using STMD fracture functions, which describe the probability of producing a hadron in the TFR after a hard scattering on a quark from the target nucleon.
• Derives the leading-order (LO) cross-section for single hadron production in the TFR, showing it depends only on a Sivers-like azimuthal asymmetry due to limited access to fracture functions.
• Introduces double hadron production (DSIDIS) with one hadron in the current fragmentation region (CFR) and one in the TFR, leveraging the Collins effect to probe quark transverse polarization.
• Constructs the full LO cross-section for DSIDIS as a convolution of STMD fracture functions and unpolarized/fragmentation functions, including spin-dependent terms for longitudinal and transverse target polarization.
• Identifies the presence of terms involving ${\bf P}_{T1} \cdot {\bf P}_{T2}$ correlations in the structure functions, which generate long-range azimuthal correlations between hadrons in CFR and TFR.
• Demonstrates that the DSIDIS cross-section structure allows access to all 16 leading-twist fracture functions through spin asymmetries in the azimuthal angles of the two hadrons.

Experimental results

Research questions

• RQ1 Why is single hadron production in the TFR of SIDIS insufficient for accessing the full set of spin and transverse-momentum dependent fracture functions?
• RQ2 How can double hadron production in SIDIS (DSIDIS) provide access to all 16 leading-twist fracture functions in the TFR?
• RQ3 What role does the Collins effect play in enabling the measurement of quark transverse polarization in the TFR?
• RQ4 What novel spin-dependent azimuthal asymmetries emerge in DSIDIS that are absent in standard SIDIS in the CFR?
• RQ5 How do correlations between the transverse momenta of hadrons in the CFR and TFR affect the azimuthal structure of the DSIDIS cross-section?

Key findings

• Single hadron production in the TFR of SIDIS at leading order only accesses a Sivers-like single spin azimuthal asymmetry, limiting the information on the nucleon's spin structure.
• The DSIDIS process—where one hadron is produced in the CFR and another in the TFR—provides access to all 16 leading-twist fracture functions through spin-dependent azimuthal asymmetries.
• The LO cross-section for DSIDIS includes terms proportional to $\lambda D_{ll}(y) \sigma_{LU}$ and $\lambda S_T D_{ll} \sigma_{LT}$, which correspond to beam-spin single-spin asymmetries not present in standard SIDIS in the CFR.
• The presence of ${\bf P}_{T1} \cdot {\bf P}_{T2}$ correlations in the structure functions leads to azimuthal correlations between hadrons in the CFR and TFR, which can complicate the analysis but also provide new physics.
• The structure function $\sigma_{LU}$ is proportional to $\sin(\phi_1 - \phi_2)$, indicating a direct sensitivity to the relative azimuthal angle between the two hadrons.
• The proposed DSIDIS framework is ideally suited for testing at future facilities such as the upgraded JLab 12 and the Electron-Ion Collider (EIC).