3D structure of nucleon with virtuality distributions

We describe a new approach to transverse momentum dependence in hard processes. Our starting point is coordinate representation for matrix elements of operators (in the simplest case, bilocal ${\cal O} (0,z)$) describing a hadron with momentum $p$. Treated as functions of $(pz)$ and $z^2$, they are parametrized through {\it parton virtuality distribution} (PVD) $\Phi (x, \sigma)$, with $x$ being Fourier-conjugate to $(pz)$ and $\sigma$ Laplace-conjugate to $z^2$. For intervals with $z^+=0$, we introduce the {\it transverse momentum distribution} (TMD) $f (x, k_\perp)$, and write it in terms of PVD $\Phi (x, \sigma)$. The results of covariant calculations, written in terms of $\Phi (x, \sigma)$ are converted into expressions involving $f (x, k_\perp)$. We propose models for soft PVDs/TMDs,and describe how one can generate high-$k_\perp$ tails of TMDs from primordial soft distributions.