Self-consistent description of HERA data at low $Q^2$ and soft hadron production at LHC

Using the analytical expression for transverse momentum dependent (TMD) gluon density in a proton, a self-consistent simultaneous description of low $Q^2$ data on proton structure function $F_2(x,Q^2)$, reduced cross section for the electron-proton deep inelastic scattering at HERA and soft hadron production in $pp$ collisions at the LHC is achieved in the framework of color dipole approach and modified quark-gluon string model.