Transverse deformation of parton distributions and transversity decomposition of angular momentum

Abstract

Impact parameter dependent parton distributions are transversely distorted when one considers transversely polarized nucleons and/or quarks. This provides a physical mechanism for the $T$-odd Sivers effect in semi-inclusive deep-inelastic scattering. The transverse distortion can also be connected with Ji's quark angular momentum relation. The distortion of chirally odd impact parameter dependent parton distributions is related to chirally odd generalized parton distributions (GPDs). This result is used to provide a decomposition of the quark angular momentum with respect to (w.r.t.) quarks of definite transversity. Chirally odd GPDs can thus be used to determine the correlation between quark spin and quark angular momentum in unpolarized nucleons. Based on the transverse distortion, we also suggest a qualitative connection between chirally odd GPDs and the Boer-Mulders effect.