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

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 GeV2, and by about 2 GeV when evolved up to Q(2)=100 GeV2. 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.