Related papers: Comment on applying dispersion relations to amplit…
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…
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 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…
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 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 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 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…
In QCD sum rules with external fields, the double dispersion relation is often used to represent the correlation function. In this work, we point out that the double spectral density, when it is determined by successive applications of the…
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 the evaluation of the real part of the elementary amplitudes in the context of a multiple diffraction model for $pp$ elastic scattering earlier developed. The framework is based on the concepts of analyticity and polynomial…
Dispersion relations for the scattering of hadrons are considered within the framework of Quantum Chromodynamics. It is argued that the original methods of proof remain applicable. The setting and the spectral conditions are provided by an…
We use duality to relate resonances in missing mass $M$ to the large-mass diffraction dissociation of protons. In deep inelastic lepton-hadron scattering (DIS), hadronic resonances are related by duality in $Q^2$ to the low-$x$, smooth…
We present a short comment on resummation of double-logarithmic (DL) contributions to decays of W and Z -bosons into charged fermion pairs. We show that resummation of DL corrections to the Z -boson decay leads to standard Sudakov form…
We analyze the analytic continuation of the formally divergent one-loop amplitude for scattering of the graviton multiplet in the Type II Superstring. In particular we obtain explicit double and single dispersion relations, formulas for all…
Dispersion relations are nonperturbative formulas that relate the ultraviolet and infrared behavior of an observable with wide-ranging applications applications in linear response theory, quantum field theory scattering amplitudes, and…
These lecture notes give a pedagogical introduction to the use of dispersion relations in loop calculations. We first derive dispersion relations which allow us to recover the real part of a physical amplitude from the knowledge of its…
We derive dispersion relations for a system of identical particles confined in a two-dimensional annular harmonic well and which interact through a Yukawa potential, e.g., a dusty plasma ring. When the particles are in a single chain (i.e.,…
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…
In this letter we show that the dispersion relation for the dynamical modes of dislocations ("dislons") in solids is sensitive to the lattice symmetries. In particular, we show that in the IR, the dislon dispersion relation develops a…
Kramers-Kronig type dispersion relations for integer powers of complex reflection coefficient are introduced for testing the consistency of terahertz reflection spectra. By using numerical simulations we show that such dispersion relations…