The Phillips - Barger model for the elastic cross section and the Odderon

Inspired by the recent TOTEM data for the elastic proton -- proton ($pp$) scattering at $\sqrt{s} =$ 8 and 13 TeV, we update previous studies of the differential cross sections using the Phillips -- Barger (PB) model, which parametrizes the amplitude in terms of a small number of free parameters. We demonstrate that this model is able to describe the recent $pp$ data on a statistically acceptable way. Additionally, we perform separate fits of the $pp$ data for each center - of - mass energy and propose a parametrization for the energy dependence of the parameters present in the PB model. As a consequence, we are able to present the PB predictions for the elastic proton - proton cross section at $\sqrt{s} = 546$ GeV and $1.8$ TeV, which are compared with the existing antiproton -- proton ($\bar{p}p$) data. We show that the PB predictions, constrained by the $pp$ data, are not able to describe the $\bar{p}p$ data. In particular, the PB model predicts a dip in the differential cross section that is not present in the $\bar{p}p$ data. Such result suggests the contribution of the Odderon exchange at high energies.Comment: 6 pages, 4 tables, 2 figures, results updated, matches published versio

Quantum Electro and Chromodynamics treated by Thompson's heuristic approach

In this work we apply Thompson's method (of the dimensions and scales) to study some features of the Quantum Electro and Chromodynamics. This heuristic method can be considered as a simple and alternative way to the Renormalisation Group (R.G.) approach and when applied to QED-lagrangian is able to obtain in a first approximation both the running coupling constant behavior of alpha(mu) and the mass m(mu).The calculations are evaluated just at d_c=4, where d_c is the upper critical dimension of the problem, so that we obtain the logarithmic behavior both for the coupling alpha and the excess of mass Delta m on the energy scale mu. Although our results are well-known in the vast literature of field theories,it seems that one of the advantages of Thompson's method, beyond its simplicity is that it is able to extract directly from QED-lagrangian the physical (finite) behavior of alpha(mu) and m(mu), bypassing hard problems of divergences which normally appear in the conventional renormalisation schemes applied to field theories like QED. Quantum Chromodynamics (QCD) is also treated by the present method in order to obtain the quark condensate value. Besides this, the method is also able to evaluate the vacuum pressure at the boundary of the nucleon. This is done by assumming a step function behavior for the running coupling constant of the QCD, which fits nicely to some quantities related to the strong interaction evaluated through the MIT-bag model.Comment: RevTex, 25 pages, no figure