A Novel Feature of Valence Quark Distributions in Hadrons

We report an observation of a strong correlation between the height of the maximum of valence quark structure function, $xq_V(x)$, and its Bjorken-$x$ position as a function of four-momentum transfer square $-Q^2$. The observed correlation is used to derive a new model independent relation which connects the partial derivative of the valence parton distribution functions(PDFs) in $x$ to the QCD evolution equation through the $x$-derivative of the logarithm of the correlation function. The numerical analysis of this relation using empirical PDFs results in a constant factor for $Q^2$-range covering four-orders of magnitude for leading and next (or next to next) order logarithmic approximations in QCD evolution. The obtained constant factor allows us to express the height-position correlation function in a simple exponential form which is valid for the all $Q^2$ range of valence PDFs being considered. The very similar correlation function is observed also for pions, indicating that the obtained relation may be universal. The observed height-position correlation is used also to prove the mean field theorem according to which no fixed number constituent exchanges can be responsible for the valence quark distributions that produce a peak in the $x q_V(x)$ distribution, thereby in the hadron structure function, $F_{2}(x)$.