Evolution equation for soft physics at high energy

Brogueira, P.; Deus, J. Dias de

doi:10.1088/0954-3899/37/7/075006

Cited by 11 publications

(9 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Email addresses: pedro.brogueira@ist.utl.pt (P. Brogueira), jorge.dias.de.deus@ist.utl.pt (J. Dias de Deus) Letters B June 14, 2018 In [9] we have argued that the evolution with the energy, √ s, of ImG(s, b 2 ) -or of the Fourier-Bessel transform, ImF (s, t) -qualitatively describe the evolution of the differential elastic cross-section, dσ/dt, in particular in the small |t| region. Here we present quantitative tests for the approach of ImF (s, t) to the black disk in the region |t| |t 0 |, t 0 being the position of the first diffractive zero.…”

Section: Introductionmentioning

confidence: 99%

Testing the black disk limit inppcollisions at very high energy

Brogueira¹,

Deus²

2012

J. Phys. G: Nucl. Part. Phys.

Self Cite

View full text Add to dashboard Cite

We use geometric scaling invariant quantities to measure the approach, or not, of the imaginary and real parts of the elastic scattering amplitude, to the black disk limit, in pp collisions at very high energy. Keywords:Cross-sections, Differential elastic cross-section, pp collisions at high energy, Evolution equation, Geometric scaling.Saturation phenomena are expected to dominate QCD physics at high energy and high matter density [1,2]. At LHC and at ultra high energy cosmic rays these effects should become easily detected. One of the possible consequences of such physics is the setting up of the black disk regime in the description of soft physics, namely total cross-section, elastic cross-section, elastic differential cross-section, etc., as discussed for instance in [3,4] (see also [5]).Non linear differential equations include, in a natural way, saturation effects. This happens with the well known logistic equation, which can be seen as a simplified version of the B-K equation [6]. For a general discussion on evolution and saturation, in the present context see [7] and [8]. In this paper we apply the logistic equation to the evolution of the imaginary part of the impact parameter elastic amplitude, ImG(s, b2 ).Email addresses: pedro.brogueira@ist.utl.pt (P. Brogueira), jorge.dias.de.deus@ist.utl.pt (J. Dias de Deus) Letters B June 14, 2018 In [9] we have argued that the evolution with the energy, √ s, of ImG(s, b 2 ) -or of the Fourier-Bessel transform, ImF (s, t) -qualitatively describe the evolution of the differential elastic cross-section, dσ/dt, in particular in the small |t| region. Here we present quantitative tests for the approach of ImF (s, t) to the black disk in the region |t| |t 0 |, t 0 being the position of the first diffractive zero. As most of the cross-sections are concentrated in the small |t| region, any test for the approach to the black disk has, at least, to work at small |t|. Preprint submitted to PhysicsWe study next the evolution of the profile function Γ(s, b 2 ), or the imaginary part of the impact parameter elastic amplitude,and we consider the logistic equationwhere γ > 0 is a positive constant, and b ≃ 2 √ s ℓ, ℓ being the angular momentum and √ s the center of mass energy. As, from unitarity,∂Γ/∂b ≤ 0, which means that Γ is a decreasing function of b, becoming eventually constant at small b. This means that saturation occurs first at small b. At large b, Γ decreases exponentially (Γ ∼ exp(−b/γ)). The parameter γ, which we take as a constant, controls the long range behaviour of the strong forces and can be associated to the two pion exchange diagram. A solution of (2) -not the most general one -isR being a positive quantity, R > 0. In comparisons with data, for √ s 50 GeV, we shall fix γ, γ = 1.1 mb 1/2 , which means that the dependence of Γ on √ s is exclusively contained in R → R(s). One sees that R is a radial scale parameter, in fact the only relevant parameter in the black disk limit. It is then clear, from (4), that there is also an evolution equation in R...

show abstract

Section: Introductionmentioning

confidence: 99%

Testing the black disk limit inppcollisions at very high energy

Brogueira¹,

Deus²

2012

J. Phys. G: Nucl. Part. Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

“…This idea to introduce a Fermi function in b space has been considered by several authors [14][15][16] and also in momentum space with a Tsallis function [17,18]. 1 However, most authors consider a global opaqueness which does not discriminate between the quark components, and we will see that in our approach the properties of each of them reflect their importance inside the proton and that their associated thermodynamical potentials remain valid for light nuclei elastic reactions.…”

Section: Introductionmentioning

confidence: 93%

An analysis of elastic scattering reactions with a Fermi–Dirac pomeron opaqueness in impact parameter space

Bourrely

2014

Eur. Phys. J. C

View full text Add to dashboard Cite

In the Bourrely-Soffer-Wu model we introduce for the pomeron a new opaqueness in impact parameter space in terms of different quark contributions described by a Fermi-Dirac distribution. In order to check the validity of this assumption we consider p p,p p, and π ± p elastic scattering. We emphasize the role of the gluon above the diffraction peak in the differential cross sections. Once these contributions are determined we extend the model to light nuclei elastic reactions like p d, p 4 He and π ± 4 He. The results obtained show a good description of all these elastic processes over the available experimental energy range and moderate momentum transfer.

show abstract

“…Thus the scaling law is predicted not for the differential cross section itself but for its product to t 2 . Let us note that the often used ratio (see, e.g., [46]) of dσ/dt to dσ/dt| t=0 ∝ σ 2 t is also a scaling function. However, the expression (32) is more suitable for comparison with experiment.…”

Section: Scaling Lawsmentioning

confidence: 99%

Hadron Structure and Elastic Scattering

Dremin

2014

Pomeranchuk 100

View full text Add to dashboard Cite

Prelude.It was in September 1954 when I met Pomeranchuk. He lectured Theory of Relativity. Next year he became a tutor of our "theoretical group". In some time he proposed me to learn the book of Flügge on nuclear physics. After struggling with difficult subject written in German I asked him some questions. He liked it and one by one proposed several problems to be solved. In parallel, he insisted on passing through the series of famous Landau exams. It was a good school. Its lessons I described in the book of reminiscences about Pomeranchuk. As a supervisor, he advised my diploma paper to be published in JETP Letters and recommended me to Prof. Tamm as a PhD student. Soon I proposed the one-pion exchange model which was later extended to multiperipheral and multireggeon models. Pomeranchuk got interested in it and asked me to come for discussion. He was deeply interested in properties of hadron collisions. Our contacts lasted till his death.In this paper I describe some new findings about elastic scattering of hadrons studied now up to LHC energies. I briefly reviewed this at the Pomeranchuk centennial seminar at ITEP. This would be extremely interesting subject for him. Let me just mention Pomeron and famous Pomeranchuk theorem to remind you his basic contributions in this field. I dedicate the paper to the memory of my teacher Isaak Pomeranchuk. AbstractWhen colliding, the high energy hadrons can either produce new particles or scatter elastically without change of their quantum numbers and other particles produced. Namely elastic scatterings of hadrons are considered in this paper. The general machinery of their theoretical treatment is described. Some new experimental data are presented and confronted to phenomenological approaches. The internal structure of hadrons is the main subject of these studies. Its impact on properties of their interactions is reviewed. It is shown that protons become larger and darker with increase of their collision energy and reveal some substructure. The violation of the geometric scaling in the diffraction cone and new problems of description of differential cross sections outside it are described.

show abstract

Evolution equation for soft physics at high energy

Cited by 11 publications

References 38 publications

Testing the black disk limit inppcollisions at very high energy

Testing the black disk limit inppcollisions at very high energy

An analysis of elastic scattering reactions with a Fermi–Dirac pomeron opaqueness in impact parameter space

Hadron Structure and Elastic Scattering

Contact Info

Product

Resources

About