The transverse momentum dependent statistical parton distributions revisited

The extension of the statistical parton distributions to include their transverse momentum dependence (TMD) is revisited by considering that the proton target has a finite longitudinal momentum. The TMD will be generated by means of a transverse energy sum rule. The new results are mainly relevant for electron-proton inelastic collisions in the low $Q^2$ region. We take into account the effects of the Melosh-Wigner rotation for the helicity distributions.