[Paper Review] Momentum Sum Rules in QCD for a Photon Target

L. Frankfurt, E. G. Gurvich|ArXiv.org|May 29, 1995

Particle physics theoretical and experimental studies2 references3 citations

TL;DR

This paper derives momentum sum rules for parton structure functions in a photon target using non-perturbative QCD, with contributions from the hadronic vacuum polarization and gauge invariance. It establishes that the unresolved photon's contribution is unambiguously determined by renormalizability, asymptotic freedom, and gauge invariance, providing a rigorous framework for testing parton distribution parametrizations in photons.

ABSTRACT

We deduce momentum sum rules for the parton structure functions of a photon target. Non-perturbative QCD contribution to the momentum sum rules follows from conservation of the energy--momentum tensor and it is calculated through the hadronic part of the photon vacuum polarization operator. The contribution of the unresolved photon unambiguously follows from gauge invariance, renormalizability and asymptotic freedom in QCD. We also compare available parametrizations of parton distribution in a photon with the deduced sum rules.

Motivation & Objective

• To derive momentum sum rules for parton structure functions in a photon target within the framework of non-perturbative QCD.
• To identify the non-perturbative contribution to the momentum sum rule via the hadronic part of the photon vacuum polarization operator.
• To clarify the role of the unresolved photon contribution using gauge invariance, renormalizability, and asymptotic freedom in QCD.
• To compare existing parametrizations of photon parton distributions with the derived sum rules for consistency validation.

Proposed method

• Uses conservation of the energy-momentum tensor to derive momentum sum rules for a photon target in QCD.
• Calculates the non-perturbative contribution through the hadronic component of the photon vacuum polarization tensor.
• Applies gauge invariance and renormalizability to uniquely determine the unresolved photon contribution to the sum rule.
• Utilizes asymptotic freedom in QCD to ensure the consistency of the perturbative and non-perturbative contributions.
• Employs a field-theoretic approach to relate the sum rules to the matrix elements of the energy-momentum tensor.
• Compares theoretical sum rules with phenomenological parametrizations of parton distributions in photons.

Experimental results

Research questions

• RQ1 What is the non-perturbative contribution to the momentum sum rule for parton distributions in a photon target?
• RQ2 How does gauge invariance constrain the unresolved photon contribution in the momentum sum rule?
• RQ3 To what extent do existing parametrizations of photon parton distributions satisfy the derived momentum sum rules?
• RQ4 Can the sum rules be used as a consistency check for parton distribution models in photons?
• RQ5 What role does the hadronic vacuum polarization play in determining the momentum sum rule for a photon?

Key findings

• The non-perturbative contribution to the momentum sum rule is fully determined by the hadronic part of the photon vacuum polarization operator.
• The unresolved photon contribution is unambiguously fixed by gauge invariance, renormalizability, and asymptotic freedom in QCD.
• The derived sum rules provide a stringent consistency check for phenomenological parametrizations of parton distribution functions in photons.
• The sum rules are consistent with the expectation that the total momentum fraction carried by partons in a photon must sum to one, under the given theoretical constraints.
• The framework allows for a model-independent determination of the momentum sum rule, independent of specific ansätze for parton distributions.
• The results demonstrate that the sum rule is saturated by both the resolved and unresolved photon contributions, with the latter being uniquely fixed by fundamental symmetries.