Pion Valence Quark Distributions from Maximum Entropy Method

Valence quark distributions of pion at very low resolution scale $Q^{2}_0 \sim 0.1~GeV^2$ are deduced from a maximum entropy method, under the assumption that pion consists of only a valence quark and a valence anti-quark at such a low scale. Taking the obtained initial quark distributions as the nonperturbative input in the modified Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (with the GLR-MQ-ZRS corrections) evolution, the generated valence quark distribution functions at high $Q^2$ are consistent with the measured ones from a Drell-Yan experiment. The maximum entropy method is also applied to estimate the valence quark distributions at relatively higher $Q^2$ = 0.26 GeV$^{2}$. At this higher scale, other components (sea quarks and gluons) should be considered in order to match the experimental data. The first three moments of pion quark distributions at high $Q^2$ are calculated and compared with the other theoretical predictions.