On the form factor of physical mesons and their distribution function

Abstract

This work addresses more to the technical rather than to the physical problem, how to calculate analytically the form factor $F(Q)$, the associated mean-square radius $<r^2>$, and the distribution function $\Phi(x,Q^2)$ for a given light-cone wave function $\Psi_{q\bar q}(x,\vec k_{\perp})$ of the pion. They turn out to be functions of only one dimensionless parameter, which is the ratio of the constituent quark mass and an effective Bohr momentum which measures the width of the wave function in momentum space. Both parameters are subject to change in the future, when the presently used solution for the over simplified $\uparrow\downarrow$-model will be replaced by something better. Their relation to and agreement with experiment is discussed in detail. The procedure can be generalized also to other hadrons.