Transverse momentum distribution in hadrons: What can we learn from QCD?

We discuss some strict QCD constraints on the light-cone {π} meson wave function {ψ}(k→_⊥²,x). The analysis is based on such general methods as dispersion relations, duality, and partial conservation of axial-vector current. We calculate the asymptotic behavior of the wave function (WF) at the end-point region (x{→}1 and k→_⊥²{→}{∞}) by analyzing the corresponding large nth moments in transverse 〈k→_⊥²ⁿ〉{~}n! and longitudinal 〈(2x-1)ⁿ〉{~}1/n² directions. This information fixes the asymptotic behavior of the WF at large k→_⊥² (which turns out to be the Gaussian commonly used in phenomenological analyses). We discuss one particular application of the obtained results. We calculate the nonleading ``soft'' contribution to the pion form factor at intermediate momentum transfer. We argue that, due to the specific properties of {ψ}(k→_⊥²,x), the corresponding contribution can temporarily simulate the leading twist behavior in the extent region of Q²: 3 GeV²{≤}Q²{≤}40 GeV², where Q²F(Q²){~}const. Such a mechanism, if it is correct, would be an explanation of the phenomenological success of the dimensional counting rules at available, very modest energies for many different processes. We discuss some inclusive amplitudes (such as Drell-yan and deep inelastic) where the intrinsic {π} meson structure might be essential. The relation to the valence quark model is also discussed.