Investigating the structure of gluon fluctuations in the proton with incoherent diffraction at HERA

Abstract

Impact parameter dependent dipole models are ideal tools for investigating the spatial structure of the proton. We investigate the incoherent ep cross section in exclusive $$J/\psi $$ J / ψ photoproduction as measured by HERA, and find that as |t| increases, the models need several levels of substructure of gluon density fluctuations in order to describe the measured data well. In lieu of a perturbative description, we add this substructure by hand. This substructure is modelled as hotspots within hotspots. This enables us to describe measurements for $$|t|> 1$$ | t | > 1 GeV$$^2$$ 2 , which is necessary for describing any observable which integrate over the t-spectrum, such as the rapidity or $$W_{\gamma p}$$ W γ p . We find that three levels of proton substructure are adequate for a good description of all available ep data up to $$|t|=30$$ | t | = 30 GeV$$^2$$ 2 . We note that the gluonic density fluctuation structure follows a scaling behaviour, such that the logarithms of the number of hotspots and their size fall on a line, effectively reducing the available parameter space of the model. Our findings systematically constrains and provides a benchmark for the development of a perturbative model of spatial gluon fluctuations in nucleons.

Evolution of eccentricities induced by geometrical and quantum fluctuations in proton-nucleus collisions

“…We also did not implement some physical ingredients that have been used in previous works using hot spots. These include: Q s fluctuations [12,[24][25][26][27], repulsion between hot spots [9,28] and hot spots within hot spots [29]. Another interesting addition to our model could be the inclusion of x-dependence through x-dependent hot spot size and number as in Ref.…”

“…Implementing this in our framework would require us to let the saturation scale of each hot spot fluctuate independently. There are other physics ingredients used in hot spot models that are not included in the model we use, such as the repulsive force between hot spots [9,28] and hot spots within hot spots [29]. Another possible extension to our model (and a way of making it more physically accurate) could be considering a fluctuating number of hot spots.…”

Evolution of initial state fluctuations in the hotspot model of the proton structure

“…This discrepancy indicates that fluctuations at large momentum transfers are missing in the model. To address this, additional small-scale fluctuations were introduced in [8] by incorporating more substructure into the hotspots manually. This modified model successfully described all available data [9,10] up to t≤30 GeV 2 .…”

“…• Hotspot model as the initial state for t = t 0 • Evolution of the initial state as splitting of the hotspots based on the resolution for t > t 0 Now for the evolution of initial state and splitting of the hotspots in the evolution we need to define a probability splitting function for which we have some hints from the scaling behavior in our previous study of J/ψ production at large momentum transfer. We refer to [8] for more details on the scaling behavior for the number of hotspots. The actual probability of splitting (P a ) is a product of probability of splitting (P split ) and probability of no-splitting(P no−split ).…”