Resummation of double collinear logs in BK evolution versus HERA data

We present a global fit to HERA data on the reduced cross section measured in electron-proton collisions in the region of small Bjorken-$x$: $x\le x_0=10^{-2}$ and moderate to high values of the virtuality $Q^2<Q^2_{max}=650$ GeV$^2$. The main dynamical ingredients in the fits are two recently proposed improved BK equations for the description of the small-$x$ evolution of the dipole scattering amplitude. These two new equations provide an all-order resummation of double collinear logarithms that arise beyond leading logarithmic accuracy. We show that a very good description of data is possible in both cases, provided the parent dipole or smallest dipole prescriptions are employed for the running of the coupling.