We present the numerical solution of the leading order QCD evolution equation for the orbital angular momentum distributions of quarks and gluons and discuss its implications for the nucleon spin sum rule. We observe that at small-x, the gluon helicity and orbital angular momentum distributions are roughly of the same magnitude but with opposite signs, indicating a significant cancellation between them. A similar cancellation occurs also in the quark sector. We explain analytically the reason for this cancellation. PACS numbers: 12.38.Bx, 14.20.Dh 1 0 dxx j−1 L q,g (x, Q 2 ) and performing the inverse Mellin transformation. Now that we know the fully gauge invariant definitions of L q,g (x, Q 2 ) and their detailed twist structure [12], we think it is timely and worthwhile to revisit this problem, by numerically solving the DGLAP-like evolution equation for L q,g (x, Q 2 ) directly in the x-space.

We find a novel mechanism for generating transverse single-spin asymmetry (SSA) in semiinclusive deep inelastic scattering, distinct from the known ones which involve the Sivers and Collins functions, or their collinear twist-three counterparts. It is demonstrated that a phase needed for SSA can be produced purely within a parton-level cross section starting at two loops. We identify the complete set of two-loop diagrams for SSA, and discuss their gauge invariance and collinear factorization which features the gT distribution function. In the kT factorization framework, many more sources for SSA exist, and contributions from all possible two-parton transverse-momentumdependent parton distribution functions are presented up to two loops and twist three.

We derive gluon fragmentation functions in the Nambu-Jona-Lasinio (NJL) model by treating a gluon as a pair of color lines formed by fictitious quark and anti-quark (qq). Gluon elementary fragmentation functions are obtained from the quark and anti-quark elementary fragmentation functions for emitting specific mesons in the NJL model under the requirement that the qq pair maintains in the flavor-singlet state after meson emissions. An integral equation, which iterates the gluon elementary fragmentation functions to all orders, is then solved to yield the gluon fragmentation functions at a model scale. It is observed that these solutions are stable with respect to variation of relevant model parameters, especially after QCD evolution to a higher scale is implemented. We show that the inclusion of the gluon fragmentation functions into the theoretical predictions from only the quark fragmentation functions greatly improves the agreement with the SLD data for the pion and kaon productions in e + e − annihilation. Our proposal provides a plausible construct for the gluon fragmentation functions, which are supposed to be null in the NJL model.

We have calculated the unpolarized dihadron fragmentation functions (uDiFFs) of pions and kaons using the nonlocal chiral-quark model (NLChQM) and evolved our results to the transferred momentum scale Q 2 =4GeV 2 by the QCD evolution equations. These uDiFFs have also been computed in the Nambu-Jona-Lasinio-jet (NJL-jet) model for the sake of comparison. We find that there is substantial difference between the results of these two models. Furthermore, the DiFFs of u → π + π − and g → π + π − at Q 2 = 109 GeV 2 in these two models are presented in comparison with the parametrizations fitted by the Monte Carlo event generator JETSET.

We derive the fragmentation function (FF), which describes the probability for a charm quark to emit a D meson with a certain momentum fraction, in the Nambu-Jona-Lasinio model. The corresponding elementary FF is calculated with the quark-meson coupling determined in the Nambu-Jona-Lasinio model involving charm quarks. The FF in the infinite momentum frame is constructed through the jet process governed by the elementary FF, and then evolved to the charm scale, at which it is defined. To prepare the FF suitable for an analysis of D meson production at CLEO, we further match the above FF to that in the finite momentum frame at one loop in QCD. It is shown that the charm quark FF, including the finite momentum effects, leads to theoretical results in agreement with the CLEO data.