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Register a new userCoulomb and hadronic scattering in elastic high-energy nucleon collisions
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The commonly used West and Yennie model approach to the description of the interference between Coulomb and hadronic scattering of nucleons is critically examined and its deficiencies are clarified. The preference of the more general eikonal model approach is summarized.
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The functional dependence of the high-energy observables of total cross section and slope parameter on the sizes of the colliding hadrons predicted by the model of the stochastic vacuum and the corresponding relations used in the geometric model of Povh and Hufner are confronted with the experimental data. The existence of a universal term in the expression for the slope, due purely to vacuum effects, independent of the energy and of the particular hadronic system, is investigated. Accounting for the two independent correlation functions of the QCD vacuum, we improve the simple and consistent description given by the model of the stochastic vacuum to the high-energy pp and pbar-p data, with a new determination of parameters of non-perturbative QCD. The increase of the hadronic radii with the energy accounts for the energy dependence of the observables.
This paper presents a qualitative explanation for the hollowness effect based on the inelastic overlap function, claiming this result is a consequence of fundamental thermodynamic processes. Using the Tsallis entropy, one identifies the entropic index $w$ with the ratio of the collision energy to critical one in the total cross-section. The integrated probability density function is replaced by the inelastic overlap function, which represents the probability of occurrence of an inelastic event depending on both the collision energy and impact parameter. The Coulomb potential, as well as the confinement potential, are used as naive approaches to describe the (internal) energy of the colliding hadrons. The Coulomb potential in the impact parameter picture is not able to furnish any reliable physical result near the forward direction. However, the confinement potential in the impact parameter space results in the hollowness effect shown by the inelastic overlap function near the forward direction.
Elastic lepton scattering off of a nucleon has proved to be an efficient tool to study the structure of the hadron. Modern cross section and asymmetry measurements at Jefferson Lab require effects beyond the leading order Born approximation to be taken into account. Availability of unpolarized beams of both electrons and positrons in respective experiments would enable to reduce systematic uncertainties due to higher-order charge-odd contributions. In addition, information on an unpolarized electron-to-positron cross section ratio could serve as a test for theoretical models that provide predictions for charge-dependent radiative corrections to elastic lepton-nucleon scattering. Availability of polarized beams of leptons would allow for even more comprehensive study of higher-order effects as some of them are dominant in polarized lepton-nucleon scattering asymmetries. We present a brief overview of effects due to the leptons charge and targets polarization on elastic lepton-nucleon scattering measurements.
A parameterization of the nucleon-nucleon elastic scattering amplitude is needed for future experiments with nucleon and nuclear beams in the beam momentum range of 2 -- 50 GeV/c/nucleon. There are many parameterizations of the amplitude at $P_{lab} >$ 25--50 GeV/c, and at $P_{lab} leq$ 5 GeV/c. Our paper is aimed to cover the range between 5 -- 50 GeV/c. The amplitude is used in Glauber calculations of various cross sections and Monte Carlo simulations of nucleon-nucleon scatterings. Usually, the differential nucleon-nucleon elastic scattering cross sections are described by an exponential expression. Corresponding experimental data on $pp$ interactions at $|t|>$ 0.005 (GeV/c)$^2$ and $|t|leq$ 0.125 (GeV/c)$^2$ have been fit. We propose formulae to approximate the beam momentum dependence of these parameters in the momentum range considered. The same was done for $np$ interactions at $|t|leq$ 0.5 (GeV/c)$^2$. Expressions for the momentum dependence of the total and elastic cross sections, and the ratio of real to imaginary parts of the amplitude at zero momentum transfer are also given for $pp$ and $np$ collisions. These results are sufficient for a first approximation of the Glauber calculations. For more exact calculations we fit the data at $|t|>$ 0.005 (GeV/c)$^2$ without restrictions on the maximum value of $|t|$ using an expression based on two coherent exponential. The parameters of the fits are found for the beam momentum range 2 -- 50 GeV/c.
Neutrino oscillation experiments at accelerator energies aim to establish CP violation in the neutrino sector by measuring the energy-dependent rate of $ u_e$ appearance and $ u_mu$ disappearance in a $ u_mu$ beam. Extracting the correct oscillation rate demands control over QED radiative corrections at the percent level. Focusing on the critical charged-current neutrino-nucleon scattering process, we show that the cross section factorizes into two pieces. The first piece depends on hadron structure but is universal for $ u_e$ and $ u_mu$, and hence constrained by high-statistics $ u_mu$ data. The second piece is nonuniversal and suffers large logarithm enhancements, but is computed to high precision using renormalization group improved perturbation theory. Our results provide a missing ingredient for the robust interpretation of current NOvA and T2K experiments, and can be applied to future experiments such as DUNE and HyperK.
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