Determining probabilities and momentum fractions from distribution amplitudes

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Abstract
We study what various distribution amplitudes suggest for probability and momentum-fraction sharing among valence quarks of given flavor and helicity. If only because squaring and integrating are done in different orders, a strong asymmetry seen in distribution amplitude moments need not imply a strong asymmetry when probabilities or expectation values of momentum fractions are calculated, or even an asymmetry in the same direction. For example, regardless of the moments an asymmetric wave function always gives a lower probability for finding positive-helicity up quarks in a positive-helicity proton than a symmetric wave function gives. We calculate, using a factored approximation for the wave function, the distribution of probability and momentum fraction for several popular distribution amplitudes.