PHENOMENOLOGICAL ANALYSIS OF pp AND $\bar{p}p$ ELASTIC SCATTERING DATA IN THE IMPACT PARAMETER SPACE

Abstract

We use an almost model-independent analytical parameterization for pp andpp elastic scattering data to analyze the eikonal, profile, and inelastic overlap functions in the impact parameter space. Error propagation in the fit parameters allows estimations of uncertainty regions, improving the geometrical description of the hadron-hadron interaction. Several predictions are shown and, in particular, the prediction for pp inelastic overlap function at √ s = 14 TeV shows the saturation of the Froissart-Martin bound at LHC energies.

Eikonal model analysis of elastic proton–proton collisions at 52.8 GeV and 8 TeV

“…In the majority of published analyses of experimental data the corresponding freedom has been, however, strongly limited by the choice of amplitude parameterization. The imaginary part has been usually assumed to be dominant in a great interval of t and vanishing in the region around diffractive minimum; with the real part determining the non-zero value of differential cross section in the diffractive minimum; see, e.g., the earlier papers [73,75,[84][85][86][87][88][89], [90][91][92] and also recent papers [5][6][7][8][9][10][12][13][14][15][16][17][18][19]22,93,94]. Description of elastic hadronic amplitude corresponding to these widely used assumptions has been fitted to experimental data at energy of 52.8 GeV and 8 TeV in Sects.…”

“…It has concerned nearly all contemporary models of elastic (hadronic) scattering including the most recently published papers, see, e.g. [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] (in some papers the t-dependence of the phase of F N (s, t) has not been discussed at all). These additional assumptions constraining hadronic amplitude F N (s, t) have never been sufficiently reasoned (up to our knowledge) in the literature.…”

The Tsallis entropy and the BKT-like phase transition in the impact parameter space for pp and $\bar{p}p$ collisions

“…Here it is used the optical theorem s −1 ImF (s, 0) = σ tot (s) [28,29]. Also the unitarity condition demands Imχ(s, b) ≥ 0, implying that G inel (s, b) represents the probability of an elastic scattering in the 2D kinematic space (s, b) and this quantity is given by [30]…”

Eikonal model analysis of elastic proton-proton collisions at 52.8 GeV and 8 TeV

“…Similar amplitude characteristics have been used as a starting point of many analyses concerning the elastic pp and pp scattering at different energies; see, e.g., [4,[8][9][10][11][12][13][14][15][16][17][18][19]. These authors have tried to determine the elastic hadronic amplitude directly from the experimental data of dσ dt provided the following assumptions were accepted [7]: the elastic hadronic amplitude has been taken as smoothly energy dependent and purely imaginary.…”

“…It has been almost generally assumed (under the influence of the WY approach) that imaginary part of hadronic amplitude has been dominant in a broad region of t around forward direction and that it has vanished around the region of diffractive minimum. It has concerned nearly all contemporary models of elastic (hadronic) scattering including the most recently published papers, see e.g., [4,[7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26].…”