Related papers: Representation of Integral Dispersion Relations by…
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…
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…
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…
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…
Many models of electroweak symmetry breaking predict new particles with masses at or just beyond LHC energies. Even if these particles are too massive to be produced on-shell at the LHC, it may be possible to see evidence of their existence…
We develop a dynamical formulation of one-dimensional scattering theory where the reflection and transmission amplitudes for a general, possibly complex and energy-dependent, scattering potential are given as solutions of a set of dynamical…
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…
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 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…
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 $\bar{p}p$…
We introduce a general framework for constructing dispersion relations using crossing-symmetric variables, leading to infinitely many distinct representations of the 2-to-2 scattering amplitude of identical scalars. Classical formulations…
We derive a local, crossing symmetric dispersion relation (CSDR) for 2-2 scattering amplitudes with a parametric ambiguity motivated by string theory. Various limits of the parameter lead to the fixed-t, fixed-s, and other known CSDRs. We…
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 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…
The extension of the Dirac Delta distribution (DD) to the complex field is needed for dealing with the complex-energy solutions of the Schr\"odinger equation, typically when calculating their inner products. In quantum scattering theory the…
The scattering theory of the integrable statistical models can be generalized to the case of systems with extended lines of defect. This is done by adding the reflection and transmission amplitudes for the interactions with the line of…
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…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
Forward amplitude analyses constitute an important approach in the investigation of the energy dependence of the total hadronic cross-section $\sigma_{tot}$ and the $\rho$ parameter. The standard picture indicates for $\sigma_{tot}$ a…
We present a generalization of the discrete Lehmann representation (DLR) to three-point correlation and vertex functions in imaginary time and Matsubara frequency. The representation takes the form of a linear combination of judiciously…