[Paper Review] The concept of phenomenological light-front wave functions -- Regge improved diquark model predictions

D. Müller, Dae Sung Hwang|arXiv (Cornell University)|Jul 7, 2014

Quantum Chromodynamics and Particle Interactions9 references9 citations

TL;DR

This paper introduces a unified framework for modeling generalized parton distributions (GPDs), parton distribution functions (PDFs), and their form factors using effective light-front wave functions (LFWFs) within a phenomenological diquark model. It derives model-independent relations between GPDs and unintegrated PDFs, incorporates Regge behavior for improved high-energy dynamics, and provides explicit expressions for twist-two GPDs—including chiral-odd components—using a 'spherical' LFWF ansatz, offering a consistent description of nucleon structure with orbital angular momentum effects.

ABSTRACT

We introduce a classification scheme for parton distribution models and we model generalized parton distributions (GPDs), their form factors, and parton distribution functions (PDFs), integrated and unintegrated ones, in terms of unintegrated double distributions that are obtained from the parton number conserved overlap of effective light-front wave functions. For a so-called "spherical" model we present general expressions for all twist-two related non-perturbative quantities in terms of one effective light-front wave function, including chiral-odd GPDs. We also discuss the Regge improvement of such quark models from the $s$-channel point of view and study the relations between zero-skewness GPDs and unintegrated PDFs on a more general ground. Finally, we provide a few phenomenological applications that emphasize the role of orbital angular momenta.

Motivation & Objective

• To develop a systematic classification scheme for parton distribution models based on light-front wave functions (LFWFs).
• To model generalized parton distributions (GPDs), form factors, and parton distribution functions (PDFs) using unintegrated double distributions derived from LFWF overlaps.
• To incorporate Regge behavior into quark-diquark models from the s-channel perspective to improve high-energy behavior.
• To clarify the relations between zero-skewness GPDs and unintegrated PDFs, especially in the context of orbital angular momentum contributions.
• To provide phenomenological applications highlighting the role of orbital angular momentum in GPDs and PDFs.

Proposed method

• Uses the LFWF overlap representation to express unintegrated PDFs (uPDFs) and GPDs as matrix elements of two-body wave functions.
• Introduces a 'spherical' model with a single effective LFWF to describe all twist-two GPDs and PDFs, including chiral-odd components.
• Applies Regge trajectory behavior to the diquark sector to model high-energy scattering behavior and improve the s-channel unitarity.
• Derives double distribution (DD) representations for GPDs using LFWF overlaps, enabling model constraints and duality relations.
• Constructs model-specific relations between uPDFs, nfPDFs, and GPDs, including sum rules and symmetry constraints.
• Uses helicity amplitudes and momentum-space wave functions to compute chiral-odd GPDs such as $H_T$, $E_T$, $\tilde{H}_T$, and $\tilde{E}_T$ via LFWF overlaps with transverse momentum dependence.

Experimental results

Research questions

• RQ1 How can generalized parton distributions (GPDs) and parton distribution functions (PDFs) be systematically modeled using effective light-front wave functions?
• RQ2 What are the model-independent relations between zero-skewness GPDs and unintegrated PDFs, and how do they constrain non-perturbative dynamics?
• RQ3 Can Regge behavior be consistently implemented in a diquark model from the s-channel perspective to improve high-energy predictions?
• RQ4 What role does orbital angular momentum play in the structure of chiral-odd GPDs, and is there a 'pretzelosity' sum rule?
• RQ5 How do different LFWF ansätze (e.g., power-law, exponential) affect the predictions for GPDs and PDFs, and which recover known double distribution forms?

Key findings

• The paper derives general expressions for all twist-two GPDs—including chiral-odd components—using a single effective 'spherical' light-front wave function.
• It establishes that the Radyushkin double distribution ansatz can be recovered from the LFWF overlap representation under specific model assumptions.
• The model shows that the $| abla L^z| = 1$ sector exhibits mismatches in standard inclusive-exclusive relations, suggesting new model-dependent constraints.
• The authors find that the $H_T$ and $E_T$ GPDs are related to LFWF overlaps involving transverse momentum and spin structure, with explicit expressions in Eqs. (B.36)–(B.39).
• The Regge-improved diquark model successfully incorporates high-energy behavior through $s$-channel unitarity, improving the description of hard exclusive processes.
• The study confirms that orbital angular momentum effects are non-trivial and manifest in the chiral-odd GPDs, particularly in the $| abla L^z| = 1$ sector, with implications for the nucleon spin structure.