Related papers: Integral and derivative dispersion relations, anal…
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 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…
Integral and derivative dispersion relations (IDR and DDR) are considered for the proton-proton and antiproton-proton forward scattering amplitudes. A scheme for calculation of the corrections to asymptotic form for the DDR is presented.…
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…
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 $\bar{p}p$…
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…
We discuss some formal and practical aspects related to the replacement of Integral Dispersion Relations (IDR) by derivative forms, without high-energy approximations. We first demonstrate that, for a class of functions with physical…
The representation of the usual integral dispersion relations (IDR) of scattering theory through series of derivatives of the amplitudes is discussed, extended, simplified, and confirmed as mathematical identities. Forms of derivative…
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…
Making use of a derivative dispersion approach, we investigate the behavior of the the total cross section and the rho parameter for pp and p(bar)p scattering from accelerator to cosmic ray energies. The discrepancies in the cosmic ray…
We review various applications of dispersion relations (DRs) to the electromagnetic structure of hadrons. We discuss the way DRs allow one to extract information on hadron structure constants by connecting information from complementary…
Deeply Virtual Compton Scattering and electroproduction of mesons involve amplitudes that are analytic in energy. Analyticity enables Dispersion Relations (DR's) for such amplitudes, relating real and imaginary parts. Lately it has been…
We present the results of several parametrizations to two different ensemble of data on $pp$ total cross sections $\sigma_{tot}^{pp}$ at the highest center-of-mass energies (including cosmic-ray information). The results are statistically…
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…
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…
A new derivation is given for the representation, under certain conditions, of the integral dispersion relations of scattering theory through local forms. The resulting expressions have been obtained through an independent procedure to…
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 present the results of fitting all data for $pp$ and $\bar pp$ scattering at $\sqrt s \geq 9.7$ Gev and up to the collider energy with various analytic parametrizations of the elastic forward scattering amplitudes based on the derivative…
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 $\sqrt(s)\approx…
Few composite exponential models for the differential cross section are proposed to analyse the proton-proton ($pp$) elastic scattering at several energies. These proposed models are fitted to the data for $pp$ elastic differential cross…