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Register a new userLocal one-dimensional reggeon model of the interaction of pomerons and odderons
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We propose the one-dimensional reggeon theory describing local pomerons and odderons. It generalizes the well-known one-dimensional theory of pomerons (the Gribov model) and includes only triple interaction vertices. The proposed theory is studied by numerical methods: the one-particle pomeron and odderon propagators and the pA amplitude are found as functions of rapidity by integrating the evolution equation.
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The effective reggeon field theory in zero transverse dimension (the toy model) is studied. The transcendental equation for eigenvalues of the Hamiltonian of this theory is derived and solved numerically. The found eigenvalues are used for the calculation of the pomeron propagator.
Hadron-nucleus amplitudes at high energies are studied in the toy Regge model in zero transverse dimension for finite nuclei, when the standard series of fan diagrams is converted into a finite sum and looses physical sense at quite low energies. Taking into account all the loop contributions by numerical methods we find a physically meaningful amplitudes at all energies. They practically coincide with the amplitudes for infinite nuclei. A surprizing result is that for finite nuclei and small enough triple pomeron coupling the infinite series of fan diagrams describes the amplitude quite well in spite of the fact that in reality the series should be cut and as such deprived of any physical sense at high energies.
Recent data from LHC13 by the TOTEM Collaboration on $sigma_{tot}$ and $rho$ have indicated disagreement with all the Pomeron model predictions by the COMPETE Collaboration (2002). On the other hand, as recently demonstrated by Martynov and Nicolescu (MN), the new $sigma_{tot}$ datum and the unexpected decrease in the $rho$ value are well described by the maximal Odderon dominance at the highest energies. Here, we discuss the applicability of Pomeron dominance through fits to the textit{most complete set} of forward data from $pp$ and $bar{p}p$ scattering. We consider an analytic parametrization for $sigma_{tot}(s)$ consisting of non-degenerated Regge trajectories for even and odd amplitudes (as in the MN analysis) and two Pomeron components associated with double and triple poles in the complex angular momentum plane. The $rho$ parameter is analytically determined by means of dispersion relations. We carry out fits to $pp$ and $bar{p}p$ data on $sigma_{tot}$ and $rho$ in the interval 5 GeV - 13 TeV (as in the MN analysis). Two novel aspects of our analysis are: (1) the dataset comprises all the accelerator data below 7 TeV and we consider textit{three independent ensembles} by adding: either only the TOTEM data (as in the MN analysis), or only the ATLAS data, or both sets; (2) in the data reductions to each ensemble, uncertainty regions are evaluated through error propagation from the fit parameters, with 90 % CL. We argument that, within the uncertainties, this analytic model corresponding to soft Pomeron dominance, does not seem to be excluded by the textit{complete} set of experimental data presently available.
The Ising one-dimensional (1D) chain with spin $S=1/2$ and magnetoelastic interactions is studied with the lattice contribution included in the form of elastic interaction and thermal vibrations simultaneously taken into account. The magnetic energy term and the elastic (static) energy term based on the Morse potential are calculated exactly. The vibrational energy is calculated in the Debye approximation, in which the anharmonicity is introduced by the Gr{u}neisen parameter. The total Gibbs potential, including both the magnetic field, as well as the external force term, is constructed and from its minimum the equation of state is derived. From the Gibbs energy all the thermodynamic properties are calculated in a self-consistent manner. The comprehensive numerical calculations are performed in a full temperature range, i.e., from zero temperature up to the vicinity of melting. In particular, a role of magneto-elastic coupling is emphasized and examined. The numerical results are illustrated in figures and discussed.
The hard pomeron component needed to reproduce small-x data seems to be present in elastic scattering at moderate energy. If this is the case, it is likely that the total cross section at the LHC will be appreciably larger than previously expected.
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