Dipole amplitude with uncertainty estimate from HERA data and applications in Color Glass Condensate phenomenology

We determine the initial condition for the small-$x$ evolution equation (BK) from the HERA deep inelastic scattering data using a new parametrization that also keeps the unintegrated gluon distribution positive. The obtained dipole amplitude and its uncertainty estimate can be used to compute single inclusive particle production in proton-proton and proton-nucleus collisions. We argue that one has to use consistently the proton transverse area measured in DIS and the total inelastic cross section when calculating the single inclusive cross section. This leads to a midrapidity nuclear modification factor $R_{pA}$ that approaches unity at large transverse momentum, independently of the center-of-mass energy.