  A large number of double parton scatterings have been recently measured by
CDF. The double parton scattering process measures $\sigma_{eff}$, a non
perturbative quantity related to the hadronic transverse size and with the
dimensions of a cross section. The actual value measured by CDF is considerably
smaller as compared with the naive expectation, namely the value of the
inelastic non diffractive cross section. The small value of $\sigma_{eff}$ may
be an effect of the hadron structure in transverse plane. We discuss the
problem by taking into account, at all orders, the two-body parton correlations
in the many-body parton distributions.
