Squark Contributions to Photon Structure Functions and Positivity Constraints

TL;DR

This paper investigates squark contributions to photon structure functions in supersymmetric QCD, confirming positivity constraints and exploring implications for polarized structure functions and potential experimental signatures.

Contribution

It provides the first detailed calculation of squark contributions to photon structure functions, verifying positivity constraints and analyzing polarized structure functions in supersymmetric QCD.

Findings

Squark contributions satisfy positivity constraints derived from Cauchy-Schwarz inequalities.

The polarized photon structure function $g_1^ ext{γ}$ for real photons obeys the vanishing first moment sum rule.

The constraint $|g_1^ ext{γ}| \,\leq\, F_1^ ext{γ}$ is upheld for real photons.

Abstract

Photon structure functions in supersymmetric QCD are investigated in terms of the parton model where squark contributions are evaluated. We calculate the eight virtual photon structure functions by taking the discontinuity of the squark massive one-loop diagrams of the photon-photon forward amplitude. The model-independent positivity constraints derived from the Cauchy-Schwarz inequalities are satisfied by the squark parton model calculation and actually the two equality relations hold for the squark contribution. We also show that our polarized photon structure function $g_1^\gamma$ for the real photon leads to the vanishing 1st moment sum rule, and the constraint $|g_1^\gamma|\leq F_1^\gamma$ is satisfied by the real photon. We also discuss a squark signature in the structure function $W_{TT}^\tau$.