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Register a new userScaling laws for the elastic scattering amplitude
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The partial differential equation for the imaginary part of the elastic scattering amplitude is derived. It is solved in the black disk limit. The asymptotical scaling behavior of the amplitude coinciding with the geometrical scaling is proved. Its extension to preasymptotical region and modifications of scaling laws for the differential cross section are considered.
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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.
Colliding high energy hadrons either produce new particles or scatter elastically with their quantum numbers conserved and no other particles produced. We consider the latter case here. Although inelastic processes dominate at high energies, elastic scattering contributes considerably (18-25%) to the total cross section. Its share first decreases and then increases at higher energies. Small-angle scattering prevails at all energies. Some characteristic features are seen that provide informationon the geometrical structure of the colliding particles and the relevant dynamical mechanisms. The steep Gaussian peak at small angles is followed by the exponential (Orear) regime with some shoulders and dips, and then by a power-law drop. Results from various theoretical approaches are compared with experimental data. Phenomenological models claiming to describe this process are reviewed. The unitarity condition predicts an exponential fall for the differential cross section with an additional substructure to occur exactly between the low momentum transfer diffraction cone and a power-law, hard parton scattering regime under high momentum transfer. Data on the interference of the Coulomb and nuclear parts of amplitudes at extremely small angles provide the value of the real part of the forward scattering nuclear amplitude. The real part of the elastic scattering amplitude and the contribution of inelastic processes to the imaginary part of this amplitude (the so-called overlap function) at nonforward transferred momenta are also discussed. Problems related to the scaling behavior of the differential cross section are considered. The power-law regime at highest momentum transfer is briefly described.
Theoretical predictions for elastic neutrino-electron scattering have no hadronic or nuclear uncertainties at leading order making this process an important tool for normalizing neutrino flux. However, the process is subject to large radiative corrections that differ according to experimental conditions. In this paper, we collect new and existing results for total and differential cross sections accompanied by radiation of one photon, $ u e to u e (gamma)$. We perform calculations within the Fermi effective theory and provide analytic expressions for the electron energy spectrum and for the total electromagnetic energy spectrum as well as for double- and triple-differential cross sections with respect to electron energy, electron angle, photon energy, and photon angle. We discuss illustrative applications to accelerator-based neutrino experiments and provide the most precise up-to-date values of neutrino-electron scattering cross sections. We present an analysis of theoretical error, which is dominated by the $sim 0.2 - 0.4%$ uncertainty of the hadronic correction. We also discuss how searches for new physics can be affected by radiative corrections.
Neutrino-nucleus elastic scattering provides a unique laboratory to study the quantum mechanical coherency effects in electroweak interactions, towards which several experimental programs are being actively pursued. We report results of our quantitative studies on the transitions towards decoherency. A parameter ($alpha$) is identified to describe the degree of coherency, and its variations with incoming neutrino energy, detector threshold and target nucleus are studied. The ranges of $alpha$ which can be probed with realistic neutrino experiments are derived, indicating complementarity between projects with different sources and targets. Uncertainties in nuclear physics and in $alpha$ would constrain sensitivities in probing physics beyond the standard model. The maximum neutrino energies corresponding to $alpha$>0.95 are derived.
Recent data from LHC13 by the TOTEM Collaboration have indicated an unexpected decrease in the value of the $rho$ parameter and a $sigma_{tot}$ value in agreement with the trend of previous measurements at 7 and 8 TeV. These data at 13 TeV are not simultaneously described by the predictions from Pomeron models selected by the COMPETE Collaboration, but show agreement with the maximal Odderon dominance, as recently demonstrated by Martynov and Nicolescu. Here we present a detailed analysis on the applicability of Pomeron dominance by means of a general class of forward scattering amplitude, consisting of even-under-crossing leading contributions associated with single, double and triple poles in the complex angular momentum plane. We carry out fits to $pp$ and $bar{p}p$ data in the interval 5 GeV - 13 TeV. The data set comprises all the accelerator data below 7 TeV and we consider two independent ensembles by adding either only the TOTEM data or TOTEM and ATLAS data at the LHC energy region. In the data reductions to each ensemble the uncertainty regions are evaluated with both one and two standard deviation ($sim$ 68 % and $sim$ 95 % CL, respectively). Besides the general analytic model, we investigate four particular cases of interest, three of them typical of outstanding models in the literature. We conclude that, within the experimental and theoretical uncertainties and both ensembles, the general model and three particular cases are not able to describe the $sigma_{tot}$ and $rho$ data at 13 TeV simultaneously. However, if the discrepancies between the TOTEM and ATLAS data are not resolved, one Pomeron model, associated with double and triple poles and with only 7 free parameters, seems not to be excluded by the complete set of experimental information presently available.
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