Elastic scattering of protons and their structure

The experimental data about elastic scattering of protons and their theoretical interpretations are briefly reviewed. The time delay between the conference and preparation of the manuscript allowed me to modify it and include more recent important results. Some modern problems of elastic scattering of hadrons newly revealed by experimental data obtained at the LHC are discussed. Among them are the curious findings about the behavior of real and imaginary parts of the elastic scattering amplitude at non-forward scattering. The comparison with experiment at LHC energies shows that their ratio in this region can be drastically different from its values measured at low transferred momenta. Also, it is shown how the shape and the darkness of the interaction region of colliding protons change with increase of their energies. In particular, the collisions become fully absorptive at small impact parameters at LHC energies that results in some special features of inelastic processes. These problems ask for further careful treatment in a wide energy interval. 1. Few words about Alexei Kaidalov Aliosha Kaidalov was a talented and generous person highly respected by physics community. He left important traces in high energy physics, especially, in the field of inelastic (in particular, diffractive) processes and elastic scattering of hadrons. It is a honour for me to give a talk to his memory. 2. Introduction Elastic scattering of protons is one of the sources to learn the strong interaction forces which were the main object of studies of Aliosha Kaidalov (e.g., see the papers [1, 2, 3]). This particular topic has been reviewed recently in my paper [4]. To shorten the presentation, I omit many details contained in there and presented during the talk but concentrate here on two problems which became quite actual nowadays. Namely, I’ll discuss the behavior of the elastic scattering amplitude at non-forward direction and our knowledge of the shape and opacity of the interaction region of two colliding protons. 3. Elastic scattering At the first sight, the experimental data about elastic scattering seem to look very simplified. The only information about this process consists of the measurement of the differential cross section of the process related to the scattering amplitude f(s, t) in a following way dσ dt = |f(s, t)|. (1) 1st International Kaidalov Workshop on the Phenomenology of High Energy Particle Physics IOP Publishing Journal of Physics: Conference Series 607 (2015) 012005 doi:10.1088/1742-6596/607/1/012005 Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by IOP Publishing Ltd 1 Fig. 1. The differential cross section of elastic proton-proton scattering at √ s=7 TeV measured by the TOTEM collaboration [5]. The region of the diffraction cone with the |t|-exponential decrease is shown. It is a function of two variables: s = 4E, where E is the energy of protons in the center of mass system, and the four-momentum transfer squared −t = 2p(1 − cos θ) with θ denoting the scattering angle and p the momentum in the center of mass system. The amplitude f is normalized at t = 0 by the optical theorem such that Imf(s, 0) = σt/ √ 16π. (2) Moreover, one can find out the real part of the amplitude at very small t (practically at t = 0) from experimental data using the interference of the Coulomb and nuclear contributions to f . Even though the real and imaginary parts are, in general, related at any t by the dispersion relations as parts of a single analytic function, this treatment asks for some assumptions about their energy dependence, and the conclusions strongly depend on them. Thus, from experiment, we get the knowledge only about the modulus of the amplitude at the available values of s and t and about the real and imaginary parts separately just in forward direction t = 0 but not at any other values of t. The theoretical approaches differ in ascribing different roles for their relative contributions at t 6= 0. Unfortunately, the available tools are rather moderate and can not exploit the power of QCD at full strength. Mostly, the phenomenological models and some insights from the unitarity relation are used. The typical shapes of the differential cross section at small and larger values of |t| are demonstrated in Figs 1 and 2. The most prominent feature of these plots is the fast decrease of the differential cross section with increasing transferred momentum |t|. As a first approximation at present energies, it can be described at comparatively small transferred momenta by the exponential shape with the slope B such that dσ dt ∝ exp(−B|t|). (3) This region is called the diffraction peak. Its slope B increases with energy approximately as ln s. Moreover, it slightly depends on t at more careful fits of experimental data as seen in Fig. 1st International Kaidalov Workshop on the Phenomenology of High Energy Particle Physics IOP Publishing Journal of Physics: Conference Series 607 (2015) 012005 doi:10.1088/1742-6596/607/1/012005