Evolution, probabilistic interpretation and decoupling of orbital and total angular momenta in nucleon

Abstract

The leading order evolution of parton orbital angular momenta is treated in the probabilistic manner. As a result, the splitting probability matrix, while coinciding with the recent explicit calculations, is expressed in the terms of the standard spin-dependent and spin-averaged kernels. The implied relations between spin and orbital angular momenta evolution kernels may be interpreted as resulting from the ambiguity in the separation of the angular momenta to the spin and orbital contributions and are likely to be valid for higher orders and twists. Consequently, the orbital and total angular momenta may be considered as decoupling from the spin ones, the latter being the only elements of nucleon structure accessible via the hard scattering of polarized particles. In particular, the partition of the total angular momenta of quarks and gluons should be analogous to that of their momentum at any $Q^2$, generalizing the earlier finding for asymptotic limit by Ji, Tang and Hoodbhoy.