Hot spots and the hollowness of proton–proton interactions at high energies

Abstract

We present a dynamical explanation of the hollowness effect observed in proton-proton scattering at √ s = 7 TeV. This phenomenon, not observed at lower energies, consists in a depletion of the inelasticity density at zero impact parameter of the collision. Our analysis is based on three main ingredients: we rely gluonic hot spots inside the proton as effective degrees of freedom for the description of the scattering process. Next we assume that some non-trivial correlation between the transverse positions of the hot spots inside the proton exists. Finally we build the scattering amplitude from a multiple scattering, Glauber-like series of collisions between hot spots. In our approach, the onset of the hollowness effect is naturally explained as due to the diffusion or growth of the hot spots in the transverse plane with increasing collision energy.The analysis of experimental data on the elastic proton-proton differential cross-section at collision energy √ s = 7 TeV measured by the TOTEM Collaboration[1] has revealed a new, intriguing feature of hadronic interactions: at high energies, the inelasticity density of the collision does not reach a maximum at zero impact parameter. Rather, peripheral collisions, where the effective geometric overlap of the colliding protons is smaller, are more inelastic or, equivalently, are more effective in the production of secondary particles than central ones. This phenomenon, not observed before at lower collision energies, has been referred to as hollowness [2] or grayness [3-5] of proton-proton collisions by the authors of the first analyses where it was identified.Our own independent analysis of LHC and ISR data, to be described below, confirms that the inelasticity density of the collisionwhere T el (s, b) is the scattering amplitude in the impact parameter representation, reaches a maximum at b = 0 for a collision energy √ s = 7 TeV, as shown in Fig. 1.The hollowness effect challenges the standard geometric interpretations of proton-proton collisions. In particular, it precludes models where the scattering amplitude is built in terms of a positive dependence on the convolution of the density profiles of the two colliding protons. Indeed, it can be shown that the inelasticity density associated to any elastic scattering amplitude thus constructed presents a maximum at zero impact parameter, regardless how intricate the internal structure of one individual proton may be [2]. These observations suggest that the scattering problem may be best formulated in terms of sub nucleonic degrees of freedom which internal dynamics and correlations should be non-trivial with increasing collision energy. Such is the view adopted in this work, where we consider hot spots to be the effective degrees of freedom in terms of which to discuss the properties of the scattering amplitude.The idea that the gluon content of the proton is con-× 2 |t|[GeV 2 ] dσ/dt [GeV −4 ]

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