Impact-parameter analysis of TOTEM data at the LHC: Black disk limit exceeded

Abstract

We discuss the profile of the impact-parameter dependent elastic scattering amplitude. Extraction of impact-parameter dependence from the data set with inclusion of the experimental data on elastic scattering at the LHC energies helps to reveal the asymptotics of hadron interactions. Analysis of the data clearly indicates that the impact-parameter elastic scattering amplitude exceed the black disk limit at the LHC energy 7 TeV and the inelastic overlap function reaches its maximum value at b > 0.

The interaction region of high energy protons

“…2. This disagreement is especially surprising because the same model [12] was used in papers [11,15] to fit experimental results at 7 TeV. However, we see that the excess at impact parameters 0.1 -0.3 fm compared to the center pointed out in [15] reveals itself in the fourth digits only while the error bars of the slope B and the total cross section σ t are larger by an order of magnitude.…”

“…However, we see that the excess at impact parameters 0.1 -0.3 fm compared to the center pointed out in [15] reveals itself in the fourth digits only while the error bars of the slope B and the total cross section σ t are larger by an order of magnitude. This excess is so small that it can be explained either by insufficient precision in determining the values of B and σ t (and, consequently, of Z) and also by inaccuracy in account for different scales or by different procedures adopted in the papers [11,15] for extrapolations to the ranges of transferred momenta where there are no experimental data yet.…”

“…However, the comparison of the results of [11] and [15] shows that we are in the critical regime of elastic scattering with Z ≈ 1 at 7 TeV as was pointed out in [14]. Let us stress that at good precision of experimental data the proposed approach allows to analyse the fine structure of the core of the interaction region at the very small scales in distinction to the less precise correlation methods.…”

“…That is what was successfully done a'posteriori, for example, in papers [11,15,25]. First two of them used the model [12] proposed a long ago, while a completely new form of the amplitude was analyzed in [25].…”

“…However, the value of Z is close to 1 even at LHC energies, and this regime asking for Z < 0.5 is, surely, shifted to extremely high energies if it can be observed at all. The approach to asymptotics is argued as following the logarithmic dependences of cross sections σ t ∝ σ el ∝ ln 2 s and σ in ∝ ln s. The depletion of G(s, 0) in [15] was ascribed to this regime by mistake since the values of Z are near 1 at 7 TeV but not as small as 0.5.…”