Differential Cross Sections For Pp Research Articles

Scaling laws of elastic proton-proton scattering differential cross sections

We show that elastic scattering pp→pp differential cross sections as function of the four-momentum transfer square |t| have a universal property, such that the ratio of bump-to-dip positions is constant from the energies of the ISR to the LHC, from tens of GeV and up to the TeV scale. We explore this property to compare the geometrical scaling observed at the ISR with the recently proposed scaling law at the LHC. We argue that, at the LHC, within present experimental uncertainties, there is in fact a family of scaling laws. We discuss the constraints that the scaling laws impose on the parametrization of the elastic pp→pp scattering amplitude.

Oscillations in the elastic high energy amplitude

We discuss the oscillations in the elastic pp differential cross section seen in the TOTEM data at s=13\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{s}=13$$\\end{document} TeV on the top of the usual smooth behaviour.

Simple Lévy α-Stable Model Analysis of Elastic pp and pp¯ Low-|t| Data from SPS to LHC Energies

A simple Lévy α-stable (SL) model is used to describe the data on elastic pp and pp¯ scattering at low-|t| from SPS energies up to LHC energies. The SL model is demonstrated to describe the data with a strong non-exponential feature in a statistically acceptable manner. The energy dependence of the parameters of the model is determined and analyzed. The Lévy α parameter of the model has an energy-independent value of 1.959 ± 0.002 following from the strong non-exponential behavior of the data. We strengthen the conclusion that the discrepancy between TOTEM and ATLAS elastic pp differential cross section measurements arises only in the normalization and not in the shape of the distribution of the data as a function of t. We find that the slope parameter has different values for pp and pp¯ elastic scattering at LHC energies. This may be the effect of the odderon exchange or the jump in the energy dependence of the slope parameter in the energy interval 3 GeV ≲s≲ 4 GeV.

Evolution equation for elastic scattering of hadrons

We turn high energy elastic scattering of hadrons into an initial value problem using an evolution equation based on the Regge Field Theory, which has a form of the complex nonlinear reaction–diffusion equation, with time being played by the logarithm of energy. The initial conditions are provided by the data-driven models for the real and imaginary parts of the amplitude. Numerical calculations of pp differential cross sections and forward quantities for LHC energies agree very well with experimental data extending up to, and including the diffractive cone. Furthermore, we show that at current accessible energies the non-linear effects play an important role, as the impact parameter space profiles approach the unitarity bound. The equation also predicts some other effects discussed in the literature, like the hollowness of nuclear matter or existence of stationary points in momentum transfer t.

Elastic differential cross-section measurement at sqrt{s}=13\xa0TeV by TOTEM

The TOTEM collaboration has measured the elastic proton-proton differential cross section mathrm{d}sigma /mathrm{d}t at sqrt{s}=13 TeV LHC energy using dedicated beta ^{*}=90 m beam optics. The Roman Pot detectors were inserted to 10sigma distance from the LHC beam, which allowed the measurement of the range [0.04 GeV^{2}; 4 GeV^{2}] in four-momentum transfer squared |t|. The efficient data acquisition allowed to collect about 10^{9} elastic events to precisely measure the differential cross-section including the diffractive minimum (dip), the subsequent maximum (bump) and the large-|t| tail. The average nuclear slope has been found to be B=(20.40 pm 0.002^{mathrm{stat}} pm 0.01^{mathrm{syst}})~GeV^{-2} in the |t|-range 0.04–0.2 GeV^{2}. The dip position is |t_{mathrm{dip}}|=(0.47 pm 0.004^{mathrm{stat}} pm 0.01^{mathrm{syst}})~GeV^{2}. The differential cross section ratio at the bump vs. at the dip R=1.77pm 0.01^{mathrm{stat}} has been measured with high precision. The series of TOTEM elastic pp measurements show that the dip is a permanent feature of the pp differential cross-section at the TeV scale.

Odderon effects in the differential cross-sections at Tevatron and LHC energies

In the present paper, we extend the Froissaron-Maximal Odderon (FMO) approach at t different from 0. Our extended FMO approach gives an excellent description of the 3266 experimental points considered in a wide range of energies and momentum transferred. We show that the very interesting TOTEM results for proton–proton differential cross-section in the range 2.76–13 TeV, together with the Tevatron data for antiproton–proton at 1.8 and 1.96 TeV give further experimental evidence for the existence of the Odderon. One spectacular theoretical result is the fact that the difference in the dip-bump region between {bar{p}}p and pp differential cross-sections is diminishing with increasing energies and for very high energies (say 100 TeV), the difference between {bar{p}}p and pp in the dip-bump region is changing its sign: pp becomes bigger than {bar{p}}p at |t| about 1 GeV^2. This is a typical Odderon effect. Another important – phenomenological – result of our approach is that the slope in pp scattering has a different behavior in t than the slope in {bar{p}}p scattering. This is also a clear Odderon effect.

Colisiones elásticas y sección eficaz total hadrón - hadrón a altas energías

We present a study of the differential cross section for pp and pp collisions based on the use of a parametrization of the scattering amplitude as a function of two exponential terms with a phase difference. This parametrization describes correctly the experimental data, including the diffraction minimum which is different for both processes.Also, a detailed study of the total cross section, σT, for pp, pp, π±p and K±p collisions is presented. This study uses a parametrization based on the logaritmic increase of σT with the energy of the collision. Integral dispersion relations are used in order to maximize the data sample tudied. All the existing experimental data up to date (including datafrom the TOTEM experiment) are taken into account. The study concludes that σT increases with energy as ln 2(s) and predicts a value for σT in pp collisions at the energy of 14 TeV of σpp = 109,1 ± 1,6 mb.T The document aditionally presents a review of the methods used to study elastic collis. © 2014. Acad. Colomb. Cienc. Ex. Fis. Nat. All rights reserved.

Phenomenological analysis of the double-pion production in nucleon-nucleon collisions up to2.2GeV

With an effective Lagrangian approach, we analyze several NN \to NN\pi\pi channels by including various resonances with mass up to 1.72 GeV. For the channels with the pion pair of isospin zero, we confirm the dominance of N*(1440)\to N\sigma in the near threshold region. At higher energies and for channels with the final pion pair of isospin one, we find large contributions from N*(1440)\to \Delta\pi, double-Delta, \Delta(1600) \to N*(1440)\pi, \Delta(1600) \to \Delta\pi and \Delta(1620) \to \Delta\pi. There are also sizeable contributions from \Delta \to \Delta\pi, \Delta \to N\pi, N \to \Delta\pi and nucleon pole at energies close to the threshold. We well reproduce the total cross sections up to beam energies of 2.2 GeV except for the pp\to pp\pi^0\pi^0 channel at energies around 1.1 GeV and our results agree with the existing data of differential cross sections of pp \to pp\pi^+\pi^-, pp \to nn\pi^+\pi^+ and pp \to pp\pi^0\pi^0 which are measured at CELSIUS and COSY.

Eikonal zeros in the momentum transfer space from proton–proton scattering: an empirical analysis

By means of improved empirical fits to the differential cross section data on pp elastic scattering at \(19.4 \le\sqrt{s}\le62.5GeV\) and making use of a semi-analytical method, we determine the eikonal in the momentum transfer space (the inverse scattering problem). This method allows for the propagation of the uncertainties from the fit parameters up to the extracted eikonal, providing statistical evidence that the imaginary part of the eikonal (real part of the opacity function) presents a zero (change of signal) in the momentum space, at q2≈7±1 GeV2. We discuss the implication of this change of signal in the phenomenological context, showing that eikonal models with one zero provide good descriptions of the differential cross sections in the full momentum transfer range, but that is not the case for models without zero. Empirical connections between the extracted eikonal and results from a recent global analysis on the proton electric form factor are also discussed, in particular the Wu–Yang conjecture. In addition, we present a critical review on the pp differential cross section data presently available at high energies.

ω production inppcollisions

A model-independent irreducible tensor formalism that was developed earlier to analyze measurements of $\stackrel{\ensuremath{\rightarrow}}{p}\stackrel{\ensuremath{\rightarrow}}{p}\ensuremath{\rightarrow}\mathit{pp}{\ensuremath{\pi}}^{\ifmmode^\circ\else\textdegree\fi{}}$ is extended to present a theoretical discussion of $\stackrel{\ensuremath{\rightarrow}}{p}\stackrel{\ensuremath{\rightarrow}}{p}\ensuremath{\rightarrow}pp\ensuremath{\omega}$ and of \ensuremath{\omega} polarization in $\mathit{pp}\ensuremath{\rightarrow}\mathit{pp}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\omega}}$ and in $p\stackrel{\ensuremath{\rightarrow}}{p}\ensuremath{\rightarrow}pp\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\omega}}$. The recent measurement of an unpolarized differential cross section for $pp\ensuremath{\rightarrow}pp\ensuremath{\omega}$ is analyzed by use of this theoretical formalism.

Singlet and triplet differential cross sections forpp→ppπ0

The singlet and triplet differential cross sections for pp-> pp pi^0 have been estimated for the first time at 325, 350, 375 and 400 MeV using the results of the recent experimental measurements [Phys. Rev. C 63, 064002 (2001)] of Meyer et al.

An examination of pp elastic analyzing power using the diquark cluster model

An examination of pp elastic analyzing power is conducted using a semi-phenomenological approach based on the diquark cluster model. It is shown that the structures observed empirically can be closely reproduced using the present approach. The elastic pp differential cross-section at θc.m. = 90 ° is also calculated and compared with the experimental data.

Baryon exchange and meson pole diagrams in [formula omitted], π+π−

The pp → KK and π + π − annihilation reactions are consistently investigated in a model with both the baryon-exchange diagrams and the meson pole diagrams. The main feature, the backward enhancement, of the observed differential cross sections for pp → KK and π + π − between 360 to 1550 MeV/ c is well understood in this model while the analyzing powers are reasonably reproduced. Specific to the strangeness aspect in pp → KK is that the meson pole diagrams are more important than the baryon-exchange diagrams. Among the meson pole diagrams the tensor meson f 2 dominates the back angle behaviour of differential cross sections.

Differential cross sections for pp-->pn pi + near threshold.

Differential cross sections from kinematically complete measurements of $\mathrm{pp}\ensuremath{\rightarrow}\mathrm{pn}{\ensuremath{\pi}}^{+}$ production are presented for proton beam energies of 294.2, 299.5, and 319.5 MeV. Total cross sections are given for 294.2, 299.5, 306.5, 314.3, and 319.5 MeV. The two angular distributions close to threshold are dominated by $s$ wave contributions. Total cross sections within the first 30 MeV of threshold show qualitative agreement with an early theoretical prediction based on PCAC.

Differential cross section for proton-proton bremsstrahlung at 294 MeV.

The differential cross section for pp\ensuremath{\rightarrow}pp\ensuremath{\gamma} has been measured at an average bombarding energy of 294 MeV and for proton laboratory angles between 5\ifmmode^\circ\else\textdegree\fi{} and 12\ifmmode^\circ\else\textdegree\fi{}. The absolute normalization of the data is based on the concurrent measurement of pp elastic scattering. The experiment has been carried out with the Indiana University Cyclotron Facility Cooler Ring using an internal gas jet target in an electron-cooled beam. The data cover a region of the kinematic space where off-shell contributions of the NN interaction are expected to be enhanced. The shape of the measured cross sections as a function of the photon angle agrees fairly well with the expectation from phase space alone.

A measurement of p̄p and pp elastic scattering at ISR energies

We have measured the differential cross section for pp and p̄p elastic scattering at √ s = 31, 53 and 62 GeV in the interval 0.05 < | t| < 0.85 GeV 2 at the CERN ISR using the Split Field Magnet detector. At 53 and 62 GeV, for 0.17 < | t| < 0.85 GeV 2 both pp and p̄p data show simple exponential behaviour in t; at √ s = 31 GeV the data for 0.05 < | t| < 0.85 GeV 2 are consistent with a change in slope near | t| = 0.15 GeV 2.

A comparison between pp and [formula omitted] diffractive peaks at and beyond ISR energies

Although a substantial difference between pp differential cross section at ISR energies and pp differential cross section at SPS energy has been reported, we demonstrate that both differential cross sections, at least up to | t| ∼ 1.2 GeV 2, can be satisfactory accounted for within the usual eikonal model in which the diffractive component is crossing even. Thus at a given ultra high energy, there is no suggestive evidence for a difference between pp and pp diffractive peaks.

P - p and pp elastic scattering from 10 GeV to 1000 GeV centre-of-mass energy

Antiproton-proton and proton-proton elastic scattering are studied simultaneously over the energy range\(\sqrt s \) ≃ (10÷1000) GeV in a nucleon valence core model proposed earlier. The scattering is described as primarily due to two processes: diffraction and hard scattering. The latter originates from the scattering of a nucleon core off another core. Destructive interference between the two processes produces dips inp-p and pp differential cross-sections. As energy increases beyond the ISR range (\(\sqrt s \) = (23÷62) GeV), the dips get filled up, and eventually transform into shoulders or breaks at collider energies. Differences betweenp-p and pp differential cross-sections persist even at collider energies. Comparison with ISR data shows that the model provides a quantitative description of pp elastic scattering in this energy range. Predictions ofp-p and pp differential cross-sections at future collider energies\(\sqrt s \)=800 and 2000 GeV are given. In order to distinguish between competing models, need for measuring thep-p differential cross-section at the ISR and SPS collider in the |t|-range (0.5÷2.0) (GeV)2 is stressed.

πNNform factor, chiral-symmetry breaking, and three-pion resonances

The extraction of the ..pi..NN form factor F/sub piN/N(t) from Reggeized one-pion-exchange (OPE) fits to hadronic cross sections is reexamined. The objective is to explain the Goldberger-Treiman discrepancy ..delta../sub ..pi../ which is determined from the extrapolation of F/sub piN/N to t = 0. Until now Reggeized OPE analyses have led to values of ..delta../sub ..pi../ that disagree with experiment by a factor of 2. It is argued that this failure is likely due to an insensitivity of the OPE amplitudes to heavy-pion (three-pion-resonance) contributions, at small t, when F/sub piN/N is parametrized by standard forms, e.g., the monopole or the dual model. A new functional form is proposed for F/sub piN/N(t) which has the virtue of enhancing these contributions at small momentum transfers, thus leading to OPE amplitudes more sensitive to 3..pi..-resonance effects. This form factor is then used to reanalyze differential cross sections for pp..-->..n..delta../sup + +/, pp..-->..p..delta../sup +/, np..-->..pn, p-barp..-->..n-barn, and ..gamma..p..--> pi../sup +/n, as well as asymmetries for ..gamma..p..--> pi../sup +/n, at high energies (E/sub L/approx. =5--25 GeV) and Vertical BartVertical Bar< or approx. =0.3 (GeV/c)/sup 2/. The results show that a self-consistent fit to all these data, with the correct value of ..delta../sub ..pi../, is indeedmore » possible.« less

Comparison of small-angle pp̄ and pp elastic scattering at 52.8 GeV center-of-mass energy at the CERN intersecting storage rings

Proton-antiproton and proton-proton elastic scattering have been measured in the four-momentum transfer range 0.001⩽| t|⩽0.06 GeV 2 for center-of-mass energy 52.8 GeV at the CERN Intersecting Storage Rings (ISR). Using the known pp total cross section, a simultaneous fit to the pp̄ and pp differential cross sections yields the pp̄ total cross section; in addition, we obtain the ratio of the real-to-imaginary part of the forward nuclear-scattering amplitude and the nuclear-slope parameter for both pp̄ and pp. Our results show conclusively that the pp̄ total cross section is rising at ISR energies and lend support to conventional theories in which the difference between the pp̄ and pp total cross section vanishes at very high energy.