相关论文: Differential dispersion relations and elementary a…
We extend the use of derivative dispersion relations to the study of slopes of the real and imaginary amplitudes in pp and p-pbar elastic scattering. The new relations are tested against the solutions for the amplitudes obtained in the…
Based on a study of the properties of the Lerch's transcendent, exact closed forms of dispersion relations for amplitudes and for derivatives of amplitudes in pp and p\=p scattering are introduced. Exact and complete expressions are written…
An analysis of the data on forward $pp, \bar pp, \pi^{\pm}p$ and $K^{\pm}p$ scattering is performed making use of the single- and double-subtraction integral and comparing with derivative dispersion relations for amplitudes. Various pomeron…
Various forms of derivative dispersion relations, in which the dispersion integral is replaced by a series of derivatives of the imaginary part of a scattering amplitude, are reviewed. Conditions of their validity and practical…
We give a pedagogical introduction to the founding ideas of dispersion relations in particle physics. Starting from elementary mechanical systems, we show how the physical principle of causality is closely related to the mathematical…
We discuss some analytical and numerical aspects related to the replacement of integral dispersion relations by derivative relations and also the practical applicability of the derivative approach in the investigation of high-energy elastic…
We propose analytical forms, in both momentum transfer and impact parameter spaces, for the amplitudes of elastic pp scattering, giving coherent and accurate description of the observables at all energies $\sqrt{s}\geq 20$ GeV. The real and…
It is shown that, for a wide class of functions with physical interest as forward scattering amplitudes, integral dispersion relations can be replaced by derivative forms without any high-energy approximation. The applicability of these…
In the framework of multiple-scattering theory, we show that the dispersion relations of certain electromagnetic (EM) and elastic metamaterials can be obtained analytically in the long-wavelength limit. Specific examples are given to the…
Scenario for restoration of the real part of the elastic scattering amplitude has been proposed for the unitarity saturation case. Dependence of the real part of the elastic scattering amplitude on the transferred momentum $-t$ at the…
Integral and derivative dispersion relations (DR) are considered for the $pp$ and $\bar pp$ forward scattering amplitudes. A new representation for the derivative DR, valid at lower energies than the standard one, is obtained. The data on…
We investigate the high-energy behavior of the elastic scattering amplitude using the eikonal and $U$-matrix unitarization schemes. This work extends the analysis in [1] by exploring the sensitivity of the Pomeron and Odderon parameters to…
We discuss some formal and fundamental aspects related with the replacement of integral dispersion relations by derivative forms, and their practical uses in high energy elastic hadron scattering, in particular $pp$ and $\bar{p}p$…
Exact analytical forms of solutions for Dispersion Relations for Amplitudes and Dispersion Relations for Slopes are applied in the analysis of pp and $\rm {p \bar p}$ scattering data in the forward range at energies below $\sqrt(s)\approx…
Based on the behavior of the elastic scattering data, we introduce an almost model-independent parametrization for the imaginary part of the scattering amplitude, with the energy and momentum transfer dependences inferred on empirical basis…
We propose a new method for constructing the consistent space of scattering amplitudes by parameterizing the imaginary parts of partial waves and utilizing dispersion relations, crossing symmetry, and full unitarity. Using this framework,…
Dispersion Relations (DR) are known to be a powerful instrument for studying scattering amplitudes. In particular, they often apply to calculations in Perturbative QCD and Standard Model. We argue that applying DR to amplitudes with…
We analyse the tension between the (indirect) measurements of the total cross section, and show the impact of various assumptions on the extraction of the parameters from the elastic scattering amplitude, with a special attention to the…
Making use of a recursive approach, derivative dispersion relations are generalized for an arbitrary number of subtractions. The results for both cross even and odd amplitudes are theoretically consistent at sufficiently high energies and…
The high energy elastic nucleon cross section is treated from the viewpoint of the basic principles of local field theory. The connection between the energy dependence of $\sigma_{tot}$ and the $\rho$ - ratio of the real to imaginary parts…