Unintegrated parton distributions of pions and nucleons from the CCFM equations in the single-loop approximation

Abstract

The unintegrated quark and gluon distributions in the pion and nucleon are analyzed using the CCFM equations in the single-loop approximation. We utilize the transverse-coordinate (or impact-parameter) representation which diagonalizes the equations and study in detail the dependence on the transverse coordinate induced by the CCFM evolution. We find considerable broadening of the transverse-momentum distributions with an increasing magnitude of the hard scale Q. For instance, at the Bjorken $x=0.1$ the root mean squared transverse momentum of the gluons is enhanced by about 1 GeV when evolved from the initial low scale to ${Q}^{2}=10{\mathrm{GeV}}^{2},$ and by about 2 GeV when evolved up to ${Q}^{2}=100{\mathrm{GeV}}^{2}.$ The broadening effect is enhanced with decreasing Bjorken x, and is stronger for the gluons than for the quarks. Analytic solution for the average transverse momentum corresponding to the x moments of the distributions is obtained. The parton luminosities are also discussed.