Potential linear and angular momentum in the scalar diquark model

TL;DR

This paper analytically calculates the potential linear and angular momenta in the scalar diquark model at two loops, clarifying their relation to different definitions of momentum and exploring their connection to the Sivers asymmetry.

Contribution

It provides the first two-loop analytic calculation of potential linear and angular momenta in the scalar diquark model, linking them to the Jaffe-Manohar and Ji definitions.

Findings

Potential transverse momentum matches the Jaffe-Manohar definition.

Potential angular momentum's relation to initial/final-state interactions is examined.

The calculation confirms symmetry constraints on the momenta.

Abstract

We present an analytic two-loop calculation within the scalar diquark model of the potential linear and angular momenta, defined as the difference between the Jaffe-Manohar and Ji notions of linear and angular momenta. As expected by parity and time-reversal symmetries, a direct calculation confirms that the potential transverse momentum coincides with the Jaffe-Manohar (or canonical) definition of average quark transverse momentum, also known as the quark Sivers shift. We examine whether initial/final-state interactions at the origin of the Sivers asymmetry can also generate a potential angular momentum in the scalar diquark model.