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.
Highlights
For the purpose of the present work, it suffices to recall that the Ji decomposition is based on the kinetic momentum defined by the covariant derivative Dμ = ∂μ − ig Aμ, whereas the JM decomposition is based on the canonical momentum ∂√μ defined in the light-front (LF) gauge A+ = ( A0 + A3)/ 2 = 0
From a physical point of view, this potential angular momentum (AM) has been interpreted as the accumulated change in orbital angular momentum (OAM) experienced by the struck quark due to the color Lorentz forces as it leaves the target in high-energy scattering processes [8]
At one-loop level in the scalar diquark model (SDM), it has been shown that JM and Ji notions of OAM do coincide [53,54], implying a vanishing potential AM
Summary
A comparison of their magnitudes is motivated by Burkardt’s proposal of a lensing mechanism due to soft gluon rescattering in deep-inelastic and other high-energy scattering [16,17] Such mechanism describes the asymmetry in transverse momentum space (i.e. Sivers effect) as originating from an asymmetry of the parton distribution in the impact-parameter space (due to the orbital motion of partons) convoluted with a lensing function that accounts for the effects of attractive initial/final-state interactions (ISI/FSI). Despite being a simple model, the SDM provides analytic results that have been broadly explored in the literature It has the feature of maintaining explicit Lorentz covariance. For these reasons, the SDM provides an interesting framework for studying the relative magnitudes between the potential AM and the potential TM. Some details about the two-loop calculations are collected in the Appendices
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