1,241 research outputs found
Exact treatment of dispersion relations in pp and p\=p elastic scattering
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 for the real parts and for their derivatives at based on given
inputs for the energy dependence of the total cross sections and of the slopes
of the imaginary parts. The results are prepared for application in the
analysis of forward scattering data of the pp and p\=p systems at all energies,
where exact and precise representations can be written.Comment: 23 pages, 1 figur
Elastic amplitudes studied with the LHC measurements at 7 and 8 TeV
Recent measurements of the differential cross sections in the forward region
of pp elastic scattering at 7 and 8 TeV show precise form of the
dependence. We propose a detailed analysis of these measurements including the
structures of the real and imaginary parts of the scattering amplitude. A good
description is achieved, confirming in all experiments the existence of a zero
in the real part in the forward region close to the origin, in agreement with
the prediction of a theorem by A. Martin, with important role in the observed
form of . Universal value for the position of this zero and
regularity in other features of the amplitudes are found, leading to
quantitative predictions for the forward elastic scattering at 13 TeV.Comment: 22 pages, 17 figures and 4 table
Photon and Pomeron -- induced production of Dijets in , and collisions
In this paper we present a detailed comparison of the dijet production by
photon -- photon, photon -- pomeron and pomeron -- pomeron interactions in
, and collisions at the LHC energy. The transverse
momentum, pseudo -- rapidity and angular dependencies of the cross sections are
calculated at LHC energy using the Forward Physics Monte Carlo (FPMC), which
allows to obtain realistic predictions for the dijet production with two
leading intact hadrons. We obtain that \gamma \pom channel is dominant at
forward rapidities in collisions and in the full kinematical range in the
nuclear collisions of heavy nuclei. Our results indicate that the analysis of
dijet production at the LHC can be useful to test the Resolved Pomeron model as
well as to constrain the magnitude of the absorption effects.Comment: 11 pages, 6 figures, 1 table. Improved and enlarged version published
in European Physical Journal
Structure of Forward pp and p\=p Elastic Amplitudes at Low Energies
Exact analytical forms of solutions for Dispersion Relations for Amplitudes
and Dispersion Relations for Slopes are applied in the analysis of pp and scattering data in the forward range at energies below
\sqrt(s)\approx 30 \GeV. As inputs for the energy dependence of the imaginary
part, use is made of analytic form for the total cross sections and for
parameters of the dependence of the imaginary parts, with exponential and
linear factors.
A structure for the dependence of the real amplitude is written, with
slopes
and a linear factor that allows compatibility of the
data with the predictions from dispersion relations for the derivatives of the
real amplitude at the origin. A very precise description is made of all
data, with regular energy dependence of all quantities. It is
shown that a revision of previous calculations of total cross sections, slopes
and parameters in the literatures is necessary, and stressed that only
determinations based on data covering sufficient range using
appropriate forms of amplitudes can be considered as valid.Comment: 28 pages and 26 figure
New properties of the Lerch's transcendent
A new representation of the Lerch''s transcendent F(z, s, a), valid for positive integer s=n=1, 2, … and for z and a belonging to certain regions of the complex plane, is presented. It allows to write an equation relating F(z, n, a) and F(1/z, n, 1-a), which in turn provides an expansion of F(z, n, a) as a power series of 1/z, convergent for |z|>1
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