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Register a new userMechanisms of proton-proton inelastic cross-section growth in multi-peripheral model within the framework of perturbation theory. Part 3
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We develop a new method for taking into account the interference contributions to proton-proton inelastic cross-section within the framework of the simplest multi-peripheral model based on the self-interacting scalar phi^3 field theory, using Laplaces method for calculation of each interference contribution. We do not know any works that adopted the interference contributions for inelastic processes. This is due to the generally adopted assumption that the main contribution to the integrals expressing the cross section makes multi-Regge domains with its characteristic strong ordering of secondary particles by rapidity. However, in this work, we find what kind of space domains makes a major contribution to the integral and these space domains are not multi-Regge. We demonstrated that because these interference contributions are significant, so they cannot be limited by a small part of them. With the help of the approximate replacement the sum of a huge number of these contributions by the integral were calculated partial cross sections for such numbers of secondary particles for which direct calculation would be impossible. The offered model qualitative agrees with experimental dependence of total scattering cross-section on energy {sqrt s} with a characteristic minimum in the range {sqrt s approx 10} GeV. However, quantitative agreement was not achieved; we assume that due to the fact that we have examined the simplest diagrams of phi^3 theory.
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We demonstrate a possibility of computation of inelastic scattering cross-section in a multi-peripheral model by application of the Laplace method to multidimensional integral over the domain of physical process. The constrained maximum point of scattering cross-section integral under condition of the energy-momentum conservation has been found. In the vicinity of this point the integrand is substituted for an expression of Gaussian type, which made possible to compute this integral numerically. The paper has two parts. The hunting procedure of the constrained maximum point is considered and the properties of this maximum point are discussed in the given part of the paper. It is shown that virtuality of all internal lines of the comb diagram reduced at the constrained maximum point with energy growth. In the second part of the paper we give some arguments in favor of consideration of the mechanism of virtuality reduction as the mechanism of the total hadron scattering cross-section growth, which is not taken into account within the framework of Regge theory.
We demonstrate a new technique for calculating proton-proton inelastic cross-section, which allows one by application of the Laplace method replace the integrand in the integral for the scattering amplitude in the vicinity of the maximum point by expression of Gaussian type. This in turn, allows one to overcome the computational difficulties for the calculation of the integrals expressing the cross section to sufficiently large numbers of particles. We have managed to overcome these problems in calculating the proton-proton inelastic cross-section for production (n le 8) number of secondary particles in within the framework of phi^3 model. As the result the obtained dependence of inelastic cross-section and total scattering cross-section on the energy sqrt{s} are qualitative agrees with the experimental data. Such description of total cross-section behavior differs considerably from existing now description, where reggeons exchange with the intercept greater than unity is considered.
The description of the inelastic proton -- nucleus cross section at very high energies is still an open question. The current theoretical uncertainty has direct impact on the predictions of the cosmic ray and neutrino physics observables. In this paper we consider different models for the treatment of $sigma_{inel}^{pA}$, compare its predictions at ultrahigh cosmic ray energies and estimate the prompt neutrino flux at the neutrino energies that have been probed by the IceCube Observatory. We demonstrate that depending of the model used to describe $sigma_{inel}^{pA}$, the predictions for the prompt neutrino flux can differ by a factor of order of three. Such result demonstrate the importance of a precise measurement of the inelastic proton -- nucleus cross section at high energies.
The differential cross section for proton-proton elastic scattering has been measured at a beam energy of 1.0 GeV and in 200 MeV steps from 1.6 to 2.8 GeV for centre-of-mass angles in the range from 12-16 degrees to 25-30 degrees, depending on the energy. Absolute normalisations of typically 3% were achieved by studying the energy losses of the circulating beam of the COSY storage ring as it passed repeatedly through the windowless hydrogen target of the ANKE magnetic spectrometer. It is shown that the data have a significant impact upon a partial wave analysis. After extrapolating the differential cross sections to the forward direction, the results are broadly compatible with the predictions of forward dispersion relations.
Study of the elastic scattering can produce a rich information on the dynamics of the strong interaction. The EPECUR collaboration is aimed at the research of baryon resonances in the second resonance region via pion-proton elastic scattering and kaon-lambda production. The experiment features high statistics and better than 1 MeV resolution in the invariant mass thus allowing searches for narrow resonances with the coupling to the pi p channel as low as 5%. The experiment is of formation type, i.e. the resonances are produced in s-channel and the scan over the invariant mass is done by the variation of the incident pion momentum which is measured with the accuracy of 0.1% with a set of 1 mm pitch proportional chambers located in the first focus of the beam line. The reaction is identified by a magnetless spectrometer based on wire drift chambers with a hexagonal structure. Background suppression in this case depends on the angular resolution, so the amount of matter in the chambers and the setup was minimized to reduce multiple scattering. The measurements started in 2009 with the setup optimized for elastic pion-proton scattering. With 3 billions of triggers already recorded the differential cross section of the elastic pi p-scattering on a liquid hydrogen target in the region of the diffraction minimum is measured with statistical accuracy about 1% in 1 MeV steps in terms of the invariant mass. The paper covers the experimental setup, current status and some preliminary results.
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