Proton Total Cross Sections Research Articles

The effects of the Tsallis entropy in the proton internal pressure

In this paper, one discusses the effects of Tsallis entropy on the radial pressure distribution in the proton. Using a damped confinement potential the pressure distribution is obtained from the Tsallis entropy approach, being the entropic-index [Formula: see text] connected with the proton temperature concerning some transition temperature. Then, the approach allows the study of the proton thermal evolution up to the Quark–Gluon Plasma regime. The von Laue stability condition, arising from the pressure distribution results in positive and negative energy regions. An analogy between the results for the radial pressure distribution and the proton–proton and the antiproton–proton total cross-section is performed. The negative energy region is identified with the odderon exchange while the positive represents the pomeron exchange dominance above some transition energy [Formula: see text]. The hollowness effect is also discussed in terms of the results obtained and the proposed analogy.

Bounds on the rise of total cross section from LHC7 and LHC8 data

Recent measurements of the proton–proton total cross section σtot at 7 and 8 TeV by the TOTEM and ATLAS Collaborations are characterized by some discrepant values: the TOTEM data suggest a rise of the cross section with the energy faster than the ATLAS data. Attempting to quantify these different behaviors, we develop new analytical fits to σtot and ρ data from pp and p¯p scattering in the energy region 5 GeV–8 TeV. The dataset comprises all the accelerator data below 7 TeV and we consider three ensembles by adding: either only the TOTEM data (T), or only the ATLAS data (A), or both sets (T + A). For the purposes, we use our previous RRPLγ parametrization for σtot(s), consisting of two Reggeons (RR), one critical Pomeron (P) and a leading log-raised-to-gamma (Lγ) contribution (with γ as a free fit parameter), analytically connected to ρ(s) through singly-subtracted derivative dispersion relations and energy scale fixed at the physical threshold. The data reductions with ensembles T and A present good agreement with the experimental data analyzed and cannot be distinguished on statistical grounds. The quality of the fit is not as good with ensemble T + A. The fit results provide γ∼2.3±0.1 (T), 2.0±0.1 (A), 2.2±0.2 (T+A), with χ2/DOF∼1.07 (T), 1.09 (A), 1.14 (T + A), suggesting extrema bounds for γ given by 1.9 and 2.4. Fits with γ=2 (fixed) are also developed and discussed.

AN UPDATED ANALYSIS ON THE RISE OF THE HADRONIC TOTAL CROSS-SECTION AT THE LHC ENERGY REGION

A forward amplitude analysis on pp and [Formula: see text] elastic scattering above 5 GeV is presented. The dataset includes the recent high-precision TOTEM measurements of the pp total and elastic (integrated) cross-sections at 7 TeV and 8 TeV. Following previous works, the leading high-energy contribution for the total cross-section (σ tot ) is parametrized as ln γ(s/sh), where γ and sh are free real fit parameters. Singly-subtracted derivative dispersion relations are used to connect σ tot and the rho parameter (ρ) in an analytical way. Different fit procedures are considered, including individual fits to σ tot data, global fits to σ tot and ρ data, constrained and unconstrained data reductions. The results favor a rise of the σ tot faster than the log-squared bound by Froissart and Martin at the LHC energy region. The parametrization for σ tot is extended to fit the elastic cross-section (σ el ) data with satisfactory results. The analysis indicates an asymptotic ratio σ el /σ tot consistent with 1/3 (as already obtained in a previous work). A critical discussion on the correlation, practical role and physical implications of the parameters γ and sh is presented. The discussion confronts the 2002 prediction of σ tot by the COMPETE Collaboration and the recent result by the Particle Data Group (2012 edition of the Review of Particle Physics). Some conjectures on possible implications of a fast rise of the proton–proton total cross-section at the highest energies are also presented.

On the rise of proton–proton cross-sections at high energies

The rise of total, elastic and inelastic hadronic cross sections at high energies is investigated by means of an analytical parametrization, with the exponent of the leading logarithm contribution as a free fit parameter. Using derivative dispersion relations with one subtraction, two different fits to proton–proton and antiproton–proton total cross section and ρ parameter data are developed, reproducing well the experimental information in the energy region 5 GeV–7 TeV. The parametrization for the total cross sections is then extended to fit the elastic (integrated) cross section data in the same energy region, with satisfactory results. From these empirical results we extract the energy dependence of several physical quantities: inelastic cross section, ratios elastic/total, inelastic/total cross sections, ratio total-cross-section/elastic-slope, elastic slope and optical point. All data, fitted and predicted, are quite well described. We find a statistically consistent solution indicating: (1) an increase of the hadronic cross sections with the energy faster than the log-squared bound by Froissart and Martin; (2) asymptotic limits 1/3 and 2/3 for the ratios elastic/total and inelastic/total cross sections, respectively; a result in agreement with unitarity. These indications corroborate recent theoretical arguments by Azimov on the rise of the total cross section.

Total hadronic cross section and the elastic slope: An almost model-independent connection

An almost model-independent parametrization for the ratio of the total cross section to the elastic slope, as function of the center of mass energy, is introduced. The analytical result is based on the approximate relation of this quantity with the ratio R of the elastic to total cross section and empirical fits to the R data from proton–proton scattering above 10 GeV, under the conditions of asymptotic unitarity and the black-disk limit. This parametrization may be useful in studies of extensive air showers and the determination of the proton–proton total cross section from proton–air production cross section in cosmic-ray experiments.

Measurement of the energy dependence of the total photon–proton cross section at HERA

The energy dependence of the photon–proton total cross section, σtotγp, was determined from e+p scattering data collected with the ZEUS detector at HERA at three values of the center-of-mass energy, W, of the γp system in the range 194<W<296 GeV. This is the first determination of the W dependence of σtotγp from a single experiment at high W. Parameterizing σtotγp∝W2ϵ, ϵ=0.111±0.009(stat.)±0.036(syst.) was obtained.

Calculation of proton total reaction cross sections for some target nuclei in incident energy range of 10–600 MeV

In this study, proton total reaction cross sections have been investigated for some isotopes such as 12C, 27Al, 9Be, 16O, 181Ta, 197Au, 6Li, and 14N by a proton beam up to 600 MeV. Calculation of the proton total cross sections has been carried out by the analytic expression formulated by M.A. Alvi by using Coulomb-modified Glauber theory with the Helm model nuclear form factor. The obtained results have been discussed and compared with the available experimental data and found to be in agreement with each other.

Modeling pion and proton total cross-sections at LHC

To settle the question whether the growth with energy is universal for different hadronic total cross-sections, we present results from theoretical models for πp, and (pp, pp¯) total cross-sections. We show that present and planned experiments at LHC can differentiate between different models, all of which are consistent with presently available (lower energy) data. This study is also relevant for the analysis of those very high energy cosmic ray data which require reliable πp total cross-sections as seeds. A preliminary study of the total ππ cross-sections is also made.

Calculation of the physical proximity function t(x) for electrons, protons and carbon ions using Geant4.

When a same quantity of energy is transfered to a biological medium, strong difference in the effects can be observed, if this energy is transfered by high or low-LET (Linear Energy Transfer) particles. This difference is mainly due to the track structure geometry and to the more substantial density of energy deposit in the case of high LET particles. This leads to complex DNA damages, much more difficult to repair by the cell. Therfore, a spatial distribution of energy seems more relevant to characterize the energy deposits in the medium, for biological purposes. Lea’s work on the formation of chromosome aberrations have led to the « Dual Radiation Action » theory. In this theory, Lea suggested that the final biological “lesions” were formed by the interaction of pair of “sublesions” issued from the initial energy transfer in the medium. Later on, Kellerer and Rossi[1] proposed a general formulation of this theory using the concept of proximity functions. In their formulation, Kellerer and Rossi expressed the average number of lesions as the integral of the product of two functions: the physical proximity function t(x) that characterizes the microdosimetric distribution of energy transfers in a medium, and the biological proximity function that characterizes the biological system (cell). In this work we calculate the physical function t(x) for electron, proton and carbon tracks simulated in water with a low energy package of the Geant4 Monte Carlo toolkit. This version of Geant4 (Geant4DNA) includes specific physical processes for low energy protons and electrons. In addition, carbon tracks are calculated by scaling with Z²eff (carbon effective charge) the proton total cross section in water. The function t(x) is thus calculated for electron tracks of 125 eV, 1 KeV and 10 KeV, and compared to Chen and Kellerer [2] results. The function t(x) is also calculated for 0.5, 5 and 20 MeV protons and for 5 and 20 MeV/n carbons. The characteristics of this function are then analysed and discussed. Finally, the variation of the dose mean lineal energy depending on the size of the sensitive site is deduced from t(x). [1]:A. M. Kellerer and H. H. Rossi, A generalized formulation of dual radiation action. Radiat. Res 75, 471-488 (1978). [2]: J. Chen and A. M. Kellerer, Proximity Functions for electrons from 100 eV to 10 MeV. Rad. Prot. Dos. 122, 1-4, pp 56-60 (2006).

Proton–proton total cross-sections at VHE from accelerator data

Up-to-date estimates of proton–proton total cross-sections, σtotpp, at very high energies in the literature were obtained from cosmic rays (>1017 eV) by approximations using the measured proton–air cross-section at these energies. As σtotpp are measured with present day high energy colliders up to nearly 2 TeV in the centre of mass (∼1015 eV in the laboratory), several proven theoretical, empirical and semi-empirical parametrizations for interpolation at accelerator energies were used to extrapolate these measured values to get reasonable estimates of cross-sections at higher cosmic ray energies (∼1017 eV). The cross-section estimates from these two methods disagree by a discrepancy beyond statistical error. Here we use a phenomenological model based on the ‘multiple diffraction’ approach to successfully describe data at accelerator energies. Using this model, we then estimate σtotpp at cosmic ray energies. The model free-parameters used in the fit depend on only two physical observables: the differential cross-section and the parameter ρ. The model estimates of σtotpp are then compared with total cross-section data. Using regression analysis, we determine confidence error bands, analysing the sensitivity of our predictions to the data used in the extrapolations. This work reduces the width of the confidence band around ‘multiple diffraction’ model fits of accelerator data. With the data at 546 GeV and 1.8 TeV, our extrapolations are compatible with only the Akeno cosmic ray data, predicting a slower rise with energy than do other cosmic ray results and other extrapolation methods. We discuss our results within the context of constraints expected from future accelerator and cosmic ray experimental results.

Measurement of the photon–proton total cross section at a center-of-mass energy of 209 GeV at HERA

The photon–proton total cross section has been measured in the process e + p→ e + γp→ e + X with the ZEUS detector at HERA. Events were collected with photon virtuality Q 2<0.02 GeV 2 and average γp center-of-mass energy W γp =209 GeV in a dedicated run, designed to control systematic effects, with an integrated luminosity of 49 nb −1. The measured total cross section is σ tot γp =174±1 (stat.)±13 (syst.) μb. The energy dependence of the cross section is compatible with parameterizations of high-energy pp and p p ̄ data.

The modified additive quark model applied to the elastic and charge exchange pion proton reaction

The modified additive quark model (MAQM) successfully used in pp and p p elastic scattering and also in pion proton total cross section is applied to the description of differential cross section in pion proton scattering (elastic and charge exchange). The spin-flip components of pomeron and secondary reggeons are included permitting to describe polarization.

Antineutron–proton total cross section from 50 to 400 MeV/ c

The antineutron–proton total cross section has been measured in the low momentum range 50–400 MeV/ c (below 100 MeV/ c for the first time). The measurement was performed at LEAR (CERN) by the OBELIX experiment, thanks to its unique antineutron beam facility. A thick target transmission technique has been used. The measured total cross section shows an anomalous behaviour below 100 MeV/ c. A dominance of the isospin I=0 channel over the I=1 one at low energy is clearly deduced.

Diffractive contribution to the elasticity and to the nucleonic flux in the atmosphere

We perform an analysis of the nucleonic and hadronic fluxes in the atmosphere by considering two components for the nucleon scattering, namely non-diffractive and diffractive interactions. It is shown that, albeit small, the diffractive component is really necessary to get good agreement with data. An analysis of the proton - proton total cross section and proton - air inelastic cross section, both extracted from cosmic-ray data, is also presented.

Nuclear Ramsauer effect and the isovector potential.

The simple nuclear Ramsauer model is extended to include explicitly the isovector potential. This model predicts large differences between proton and neutron total nuclear cross sections. When this model is applied to isotope/isotone total neutron cross section differences, it gives a good description of the measured data in the mass 140 region. Non-isospin-dependent differences in the isotopic imaginary potential are observed which totally obscure the contribution from the isovector imaginary potential. Additional measurements further from closed nuclear shells may yield useful information on the isovector imaginary potential.

Cosmic ray results on total cross section

This talk is a review of the methods used to estimate the proton total cross section in the SSC energy range from observations of air showers with energies of order 10 18 eV. The relation between this kind of measurement and the cross section is rather indirect. I briefly describe each of the essential steps and discuss the uncertainty that it introduces.

Coulomb effects on parity violation in proton total cross sections

The Holdeman-Thaler modified optical theorem is used to compute Coulomb contributions to the parity-violating helicity dependence of proton total cross sections. For 15-MeV protons incident on hydrogen, the result is a modest (perhaps 20%) reduction in the experimental signal, while for 6-GeV protons on water, there is a comparable (15%) enhancement. The large experimental signal reported at 6 GeV is shown to imply an order-of-magnitude enhancement by strong interactions of the weak forward scattering amplitude. A phase convention is proposed to facilitate application of the modified optical theorem to the general problem of measuring total cross sections in the presence of Coulomb forces.

Strong Enhancement of Weak Amplitudes and Helicty Dependence of Proton Total Cross Sections

Received 6 November 1981DOI:https://doi.org/10.1103/PhysRevLett.48.214©1982 American Physical Society

Proton total cross sections on 1H, 2H, 4He, 9Be, C and O in the energy range 180 to 560 MeV

Proton total cross sections have been measured for the nuclei 1H, 2H, 4He, 9Be, C and O from 180 to 560 MeV (610 to 1170 MeV/c). The standard transmission technique was used with a resulting total error of 1 % to 2 %. Statistical errors were small (< 1 %) and the major contribution to the final error comes from uncertainties in applying the correction for Coulomb-nuclear interference in elastic scattering at small angles. For 4He, 9Be, 12C. and 16O this experiment also gives new information on the real part of the spin-independent forward scattering amplitude for proton-nucleus elastic scattering. Total cross sections have been calculated using a Glauber model approach and poor agreement with the data is obtained, even for deuterium.

The proton total cross section on 12C and the α-particle model

The proton total cross section on 12C has been calculated in the energy range 0.15 to 1 GeV using the α-particle model and Glauber multiple scattering theory. Taking the experimental p- 4He amplitude as the input information we find that the experimental total cross section data are nicely reproduced. The work also sheds light on the likely causes for the failure of the independent-particle model calculation of the total cross section.