Describing the incoherent exclusive diffraction t-spectrum with hotspot evolution

We present a model of proton geometry where the number and size of gluon density hotspots in the proton's thickness function evolves with the resolution scale of the event, given by the Mandelstam $t$ variable in exclusive diffractive $ep$ collisions. We use the impact-parameter dependent saturation dipole model bSat (IPsat), as well as its linearised (non-saturated) version bNonSat. In the latter the proton thickness has a clear interpretation as a thickness and in the former it is directly related to the saturation scale. The resulting phenomenological model for the splitting of hotspots, making full use of earlier experimental and phenomenological studies, is able to describe the entire incoherent $t$-spectrum for $1.1<|t|<25~$GeV$^2$ with a single phenomenological parameter. As such, this is a useful model for investigating saturation physics at large $t$ at future colliders such as the EIC, LHeC, or $\mu$IC for both proton and nuclear targets.