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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 2
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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.
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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.
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.
The precise determination of the proton radius from recent elastic scattering electron-proton data is discussed. The necessary precision on the elastic cross section to discriminate among the values coming from atomic spectroscopy is scrutinized in terms of the relevant quantity, i.e., the derivative of the form factor. It is shown that such precision is two orders of magnitude higher than the precision on the cross section, that is the measured observable. Different fits on the available data and of their discrete derivative, with analytical constraints are shown. The systematic error associated to the radius is evaluated taking into account the uncertainties from different sources, as the extrapolation to the static point, the choice of the class of fitting functions and the range of the data sample. This error is shown to be even orders of magnitude larger than commonly assumed.
Background: The neutron skin thickness $R_{rm skin}^{rm PV}$ of PREX-II is presented in Phys. Rev. Lett. {bf 126}, 172502 (2021). The reaction cross section $sigma_R$ is useful to determine the matter radius $R_m$ and $R_{rm skin}$. For proton scattering, the reaction cross section $sigma_R$ are available for $E_{rm in} > 400$ MeV. Method and results: We determine $R_n^{rm exp}=5.727 pm 0.071$ fm and $R_m^{rm exp}=5.617 pm 0.044$ fm from $R_p^{rm exp}$ = 5.444 fm and $R_{rm skin}^{rm PV}$. The $R_p^{rm GHFB}$ calculated with Gongny-D1S HFB (GHFB) with the angular momentum projection (AMP). agrees with $R_p^{rm exp}$. The neutron density calculated with GHFB+AMP is scaled so as to $R_n^{rm scaling}=5.727$ fm. The Love-Franey $t$-matrix model with the scaled densities reproduces the data on $sigma_R$. Aim: Our aim is to find the $sigma_R$ of proton scattering consistent with $R_{rm skin}^{rm PV}$. Conclusion: The $sigma_R$ of proton scattering consistent with $R_{rm skin}^{rm PV}$ are $sigma_R^{rm exp}$ at $E_{rm in} = 534.1, 549, 806$ MeV.
The production of the Lambda and Sigma0 hyperons has been measured via the pp->pK+Lambda / Sigma0 reaction at the internal COSY-11 facility in the excess energy range between 14 and 60 MeV. The transition of the Lambda/Sigma0 cross section ratio from about 28 at Q<=13 MeV to the high energy level of about 2.5 is covered by the data showing a strong decrease of the ratio between 10 and 20 MeV excess energy. Effects from the final state interactions in the p-Sigma0 channel seem to be much smaller compared to the p-Lambda one. Estimates of the effective range parameters are given for the N-Lambda and the N-Sigma systems.
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