Phenomenological relation between distribution and fragmentation functions

We study the relation between the quark distribution function q(x) and the fragmentation function Dq(z) based on a general form Dq(x)=C(z)zαq(z) for valence and sea quarks. By adopting two known parametrizations of quark distributions for the proton, we find three simple options for the fragmentation functions that can provide a good description of the available experimental data on proton production in e+e− inelastic annihilation. These three options support the revised Gribov–Lipatov relation Dq(z)=zq(z) at z→1, as an approximate relation for the connection between distribution and fragmentation functions. The three options differ in the sea contributions and lead to distinct predictions for antiproton production in the reaction p+p→p̄+X, thus they are distinguishable in future experiments at RHIC-BNL.