Inelastic Overlap Function Research Articles

The Invariance of Inelastic Overlap Function

In this study, we consider the symmetry property of the inelastic overlap function and its relation to the reflective scattering mode appearance. This symmetry property disfavors an exclusion of one of the scattering modes—the reflective mode—when approaching the asymptotic limit. Predominance of the particular mode correlates with the energy and impact parameters ranges.

Central elastic scattering

We comment on phase selection of the scattering amplitude, emphasizing that the elastic overlap function should have a central impact parameter profile at high energies and highlighting the role of the reflective scattering mode at the LHC energies. Emerging problems with the use of peripheral impact parameter dependence of the elastic overlap function are explicitly indicated. Their solution is an elimination of the phases connected to peripheral form of the elastic overlap function. Contrary, we adhere to a relative peripheral form of the inelastic overlap function with an additional new feature of a maximum at nonzero value of the impact parameter at the highest energies. Phenomenologically, the dynamics of hadron scattering is motivated by a hadron structure with a hard central core presence.

Hollowness effect and entropy in high energy elastic scattering

This paper presents a qualitative explanation for the hollowness effect based on the inelastic overlap function, claiming this result is a consequence of fundamental thermodynamic processes. Using the Tsallis entropy, one identifies the entropic index w with the ratio of the collision energy to critical one in the total cross-section. The integrated probability density function is replaced by the inelastic overlap function, which represents the probability of occurrence of an inelastic event depending on both the collision energy and impact parameter. The Coulomb potential, as well as the confinement potential, are used as naive approaches to describe the (internal) energy of the colliding hadrons. The Coulomb potential in the impact parameter picture is not able to furnish any reliable physical result near the forward direction. However, the confinement potential in the impact parameter space results in the hollowness effect shown by the inelastic overlap function near the forward direction.

The Tsallis entropy and the BKT-like phase transition in the impact parameter space for pp and collisions

In this paper, one uses the Tsallis entropy (TE) in the impact parameter space to study pp and inelastic overlap function and the energy density filling up mechanism responsible by the so-called black disk limit as the energy increases. The TE is non-additive and non-extensive and these features are of fundamental importance since the internal constituents of pp and are strongly correlated and also the existence of the multifractal character of the total cross-section. The entropy approach presented here takes into account a phase transition occurring inside the hadrons as the energy increases. This phase transition in the impact parameter space is quite similar to the Berezinskii–Kosterlitz–Thouless phase transition, possessing also a topological feature due to the multifractal dimension of the total cross-sections in pp and scattering.

A note on the relations between elastic and inelastic interactions and increasing ratio σel(s)/σtot(s) at the LHC

We comment briefly on relations between the elastic and inelastic cross-sections valid for the shadow and reflective modes of the elastic scattering. Those are based on the unitarity arguments. It is shown that the redistribution of the probabilities of the elastic and inelastic interactions (the form of the inelastic overlap function becomes peripheral) under the reflective scattering mode can lead to increasing ratio of [Formula: see text] at the LHC energies. In the shadow scattering mode, the mechanism of this increase is a different one, since the impact parameter dependence of the inelastic interactions probability is central in this mode. A short notice is also given on the slope parameter and the leading contributions to its energy dependence in both modes.

Impact-parameter analysis of TOTEM data at the LHC: Black disk limit exceeded

We discuss the profile of the impact-parameter dependent elastic scattering amplitude. Extraction of impact-parameter dependence from the data set with inclusion of the experimental data on elastic scattering at the LHC energies helps to reveal the asymptotics of hadron interactions. Analysis of the data clearly indicates that the impact-parameter elastic scattering amplitude exceed the black disk limit at the LHC energy 7 TeV and the inelastic overlap function reaches its maximum value at $b>0$.

APPLICABILITY OF A REPRESENTATION FOR THE MARTIN'S REAL-PART FORMULA IN MODEL-INDEPENDENT ANALYSES

Using a novel representation for the Martin's real-part formula without the full scaling property, an almost model-independent description of the proton–proton differential cross-section data at high energies (19.4 GeV–62.5 GeV) is obtained. In the impact parameter and eikonal frameworks, the extracted inelastic overlap function presents a peripheral effect (tail) above 2 fm and the extracted opacity function is characterized by a zero (change of sign) in the momentum transfer space, confirming results from previous model-independent analyses. Analytical parametrization for these empirical results are introduced and discussed. The importance of investigations on the inverse problems in high-energy elastic hadron scattering is stressed and the relevance of the proposed representation is commented. A short critical review on the use of Martin's formula is also presented.

PHENOMENOLOGICAL ANALYSIS OF pp AND $\bar{p}p$ ELASTIC SCATTERING DATA IN THE IMPACT PARAMETER SPACE

We use an almost model-independent analytical parametrization for pp and [Formula: see text] elastic scattering data to analyze the eikonal, profile and inelastic overlap functions in the impact parameter space. Error propagation in the fit parameters allows estimations of uncertainty regions, improving the geometrical description of the hadron–hadron interaction. Several predictions are shown and, in particular, the prediction for pp inelastic overlap function at [Formula: see text] shows the saturation of the Froissart–Martin bound at LHC energies.

Scaling violations: Connections between elastic and inelastic hadron scattering in a geometrical approach

Starting from a short range expansion of the inelastic overlap function, capable of describing quite well the elastic pp and $\bar{p}p$ scattering data, we obtain extensions to the inelastic channel, through unitarity and an impact parameter approach. Based on geometrical arguments we infer some characteristics of the elementary hadronic process and this allows an excellent description of the inclusive multiplicity distributions in $pp$ and $\bar{p}p$ collisions. With this approach we quantitatively correlate the violations of both geometrical and KNO scaling in an analytical way. The physical picture from both channels is that the geometrical evolution of the hadronic constituents is principally reponsible for the energy dependence of the physical quantities rather than the dynamical (elementary) interaction itself.

Elastic pp- and pp-scattering and the inelastic overlap function model

A combined description of the pp- and pp-scatterings is provided in the wide range of energies\(\sqrt s = 4 - 1800{\text{ GeV}}\) and for a momentum transfer -t between 0 and 10 GeV2, on the basis of the inelastic overlap function model. The calculated cross sections are compared with the experimental measurements and theoretical predictions are obtained for large values of the momentum transfer.

Scaling behavior of average multiplicities from large hadronic masses and increase of inelasticity with energy

For processes p+p → M x+p, there is an empirical approximate scaling property for the average multiplicity of charged particles, 〈 n( M x 2, s)〉, observed in large missing masses, M x. We use this and an impact-parameter representation for the distribution of the directly measurable variable, M x s , which is related to the collision inelasticity, to predict an increase in the mean inelasticity in going from s ⋍ 30 to 540 GeV , due to the empirically more opaque inelastic overlap function at 540 GeV.

What is elastic scattering past the diffraction dip telling Us?

The elastic scattering of protons on protons at CERN's Intersecting Storage Rings and at FNAL, after the famous diffraction dip, yields a high crosssection when compared to the trend of the diffraction peak before the dip. What do these experimental results tell us? We will be justifying these principal answers: (1) the inelastic overlap function (which controls elastic scattering) can be explained in terms of the characteristics of certain experimentally measured crosssections (more precisely, semi-inclusive cross-sections), (2) a precise mechanism exists which, by bringing into play the inner part of the proton, builds up after-the-dip scattering from before-the-dip scattering, with corresponding predictions, in particular, for CERN's SPS Collider, and (3) after-the-dip scattering is no direct signal of the proton's constituents.

On elastic proton-proton diffraction scattering and its energy dependence

Recent FNAL and CERN ISR data on proton-proton elastic scattering and total cross sections at momenta q L = 200−2000 GeV/ c and momentum transfers up to | t| = 14(GeV/ c) 2 are discussed in terms of a short range expansion (SRE) of the inelastic overlap function (IOF). Model independence of the conclusions is established, which are also shown to be unaffected by real part and spin effects. The main results and conclusions are the following: (i) the SRE of the IOF is able to describe well all above data; (ii) the energy dependences of the parameters of the SRE are well reproduced by linear functions of ln sor 1/ln s as may apply; (iii) interpolating predictions of d σ/d t are made at q L = 300, 400, 500 and 1000, where experiments on the t-dependence are being done presently, as well as an extrapolating prediction at ISABELLE energy q L = 10 000; (iv) the IOF is “more diffractive” than d σ/d t and has two diffraction zeros near | t| = 0.645 and 3.83; (v) at all | t| ≳ 3.5, d σ/d t is practically equal to the square of the elastic overlap function, which overshadows the second zero of the IOF such that only the single well-known diffraction zero appears in d σ/d t; (vi) this implies that at all | t| ≳ 3.5, d σ/d t is practically built up by s-channel unitarity rescattering, and a high cross section at these t-values is hence not necessarily indicative of proton constituent effects; (vii) concavities (“breaks”) of d σ/d t as observed experimentally at | t| values 0−0.5, as well as larger than 3, are predicted features of the SRE in combination with rescattering; (viii) the ratio 5 of the forward slope of d σ/d t to the overall slope after the 2nd maximum can be understood qualitatively with the SRE.

Overlap function and regge cut in a self-consistent multi-regge model

We present a self-consistent multi-Regge model with unit intercept for the input trajectory. Violation of unitarity is avoided in the model by assuming the vanishing of the pomeron-pomeron-hadron vertex, as the mass of either pomeron tends to zero. The model yields an output Regge pole in the inelastic overlap function which fort>0 lies on the r.h.s. of the moving branch point in the complexJ-plane, but fort<0 moves to unphysical sheets. The leading Regge-cut contribution to the forward diffraction amplitude can be negative, so that the total cross-section predicted by the model attains a limiting value from below.

Elastic and Inelastic Diffraction and Two-Component Overlap Function

We show that, as a consequence of the s-channel unitarily, non-diffractive part of inelastic overlap function in high-energy hadron-hadron scattering should have a longer range than diffractive one, and discuss impact and energy-dependence structure of p-p overlap function at FNAL-ISR energies. Apparently elastic and inelastic diffraction is a prominent feature 111 high energy hadron phenomena, and one recongnizes it to be important in hadron physics that the diffraction is made clear in terms of multi-particle production. As is well known the multi-particle production may be classified into two distinct components; the dif­ fractive and the non-diffractive production.!) Implications of those components in elas­ tic P-P diffraction or, more precisely, in inelastic overlap function in the unitarity sum have been discussed by many people. Roughly speaking, there are two kinds of opposite arguments for impact profile of the overlap function: Diffractive part is more peripheral ;2l non-diffractive part is more peripheral. 31 4l In this paper we point out that, as a consequence of the s-channel unitarity, non-diffractive part of the inelastic overlap function should have a longer range than diffractive one, and discuss structure of P-P inelastic overlap function at FNAL­ ISR energies.

On the energy dependence of elastic scattering

The energy dependence of elastic scattering is discussed and it is shown that it is compatible with geometrical scaling of the inelastic overlap function. The importance of the real part of the elastic amplitude for the energy dependence is emphasized.

Structure of Inelastic Overlap Function for the 30 1500 GeV Proton-Proton Scattering

Structure of Inelastic Overlap Function for the 30 1500 GeV Proton-Proton Scattering

Geometrical scaling and the real part of the Pomeron

Consequences of the hyptohesis of geometrical scaling of the inelastic overlap function applied to the Pomeron amplitude are discussed. From analyticity and crossing symmetry some predictions are given for the asymptotic real part of the Pomeron.

Proton-Proton Elastic Scattering at High Energy and Multiple Scattering. III

The angular distribution of proton-proton elastic scattering in ISR energy region, 23 ≲√s ≲62 GeV, is analyzed on the basis of composite model of hadrons. The inward moving of the position of dip and the growth of second bump with energy are explained in terms of the multiple scattering process between constituents (urbaryons), by using the diffractive amplitude of urbaryons which is phenomenologically determined so as to be dependent on energy. The characteristic radius √≪r2 >, root mean square distance between centers of a proton and its constituent urbaryons, is well fixed to be 0.6 fermi in the whole ISR energy range, which results in the growth of second bump when combined with the shrinking forward peak of urbaryon scattering. The behavior of dip and bump is predicted at much higher energies. The inelastic overlap function is also discussed both in momentum and in impact parameter space.

Geometrical scaling — A property of the inelastic overlap function?

Geometrical scaling (GS) of the inelastic overlap function and GS of the imaginary part of the elastic nonflip amplitude are discussed and their consequences are compared. Since the corresponding real part does not scale both types of GS are not equivalent. It is shown that the energy dependences of the slope parameters and of the total cross sections for pp, p̄p, πp and Kp scattering are compatible with GS of the overlap functions.