On the rise of proton–proton cross-sections at high energies

Abstract

The rise of total, elastic and inelastic hadronic cross sections at high energies is investigated by means of an analytical parametrization, with the exponent of the leading logarithm contribution as a free fit parameter. Using derivative dispersion relations with one subtraction, two different fits to proton-proton and antiproton-proton total cross section and ρ parameter data are developed, reproducing well the experimental information in the energy region 5 GeV-7 TeV. The parametrization for the total cross sections is then extended to fit the elastic (integrated) cross section data in the same energy region, with satisfactory results. From these empirical results we extract the energy dependence of several physical quantities: inelastic cross section, ratios elastic/total, inelastic/total cross sections, ratio total-cross-section/elasticslope, elastic slope and optical point. All data, fitted and predicted, are quite well described. We find a statistically consistent solution indicating: (1) an increase of the hadronic cross sections with the energy faster than the logsquared bound by Froissart and Martin; (2) asymptotic limits 1/3 and 2/3 for the ratios elastic/total and inelastic/total cross sections, respectively; a result in agreement with unitarity. These indications corroborate recent theoretical arguments by Azimov on the rise of the total cross section.

Can Froissart bound explain hadron cross-sections at high energies?

“…Let us note that we can not take for granted that the form (1.1) will persist much longer beyond currently accessible scales. Indeed there is some evidence σ pp may grow faster than the "logarithm square" growth of (1.1) [15][16][17][18][19][20]. This conclusion is in agreement with an alternative fit of experimental data [21][22][23],…”

“…It is likely that both "power law" (1.3) and "log squared" behavior (1.1) fail to capture true asymptotic of σ pp . While the "power law" will ultimately violate Froissart-Martin bound, there is also some circumstantial evidence that "log squared" behavior of σ pp does not continue at very high energies [15][16][17][18][19][20]. The Froissart-Martin bound should apply once σ pp becomes significantly larger than 2σ FM 0 130 mb, i.e.…”

pp interactions in extended air showers

“…Equation (8) indicates that this ratio converges to 0.3588 for √ s → ∞, which is far from the value 1/2 that is characteristic of the idea of a black disk. Our results show that there is no such black disk behaviour [10]. This point will be discussed later in b-space representations.…”

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

“…The bound reduced by factor of 4 for the total inelastic cross section has also been derived [3]. Several asymptotic limits have been treated in [4] in an almost model-independent way, but also for the forward scattering data only. As well, Eq.…”