Longitudinal quark polarization in transversely polarized nucleons.

Intrinsic transverse momentum (kT) plays an important role in the quark distribution functions ~DF’s! used to describe a polarized nucleon @1,2#. For the leading ~twist-two! part of the deep inelastic scattering cross section one already needs six DF’s to describe the quark state in a polarized nucleon. They depend on x and kT 2 , which parametrize the quark momentum in a nucleon with momentum P , k5xP1kT . We will adopt the notation of Ref. @2# for these ‘‘new’’ six independent DF’s: f 1 q , g1L q , g1T q , h1T q , h1L q' , and h1T q' (q denotes the quark flavor!. For a polarized nucleon the spin vector is written as SN 5 lP/M1ST , satisfying l2ST 51. The probability PN (x ,kT), the longitudinal spin distribution l(x ,kT), and the transverse spin distributions sT (x ,kT) of the quark in a polarized nucleon are given by PN ~x ,kT !5 f 1~x ,kT !, ~1!