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(x), and its Bjorken-x position as a function Q$^{\mathrm{2}}$. 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 the Q$^{\mathrm{2}}$- range covering four-orders of magnitude. 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$^{\mathrm{2}}$ range of valence PDFs being considered. A similar relation is observed also for pions, indicating that the obtained relation may be universal. The observed ``height - position" correlation is used 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 xq(x) distribution, thereby in the hadron structure function, F$_{\mathrm{2}}$(x).