Rise Of Cross Section Research Articles

The odderon: myths and reality

In the framework of a Regge-pole model, we discussthe forward phase of the proton-proton elastic scattering amplitude (ρ(13 TeV) = 0.1 ± 0.01), recently measured at the LHC. Our model includesa dipole pomeron, odderon and secondary reggeon exchanges. It accommodetes forthe low- |t| «break» (departure from the exponential behavior of the diffraction cone), the accelerating rise with energy of the forward slope B(s, t = 0) and absence of secondary dips and bumps. Contrary to the majority of Regge-pole models, our approach is based on he use of a dipole (double pole) pomeron (DP). It has a number of advantages over the conventional simple pole pomeron: DP generates rising cross sections even at unit pomeron intercept and, what is even more important, it produces a single diffraction minimum and maximum in the differential cross section, in accord with the experimental data. Relative contributions from different components to the scattering amplitude are evaluated from the fitted model.

Upper limit on the scale of new physics phenomena from rising cross sections in high multiplicity Higgs and vector boson events

In very high energy scattering events production of multiple Higgs and electroweak gauge bosons becomes possible. Indeed the perturbative cross section for these processes grows with increasing energy, eventually violating perturbative unitarity. In addition to perturbative unitarity we also examine constraints on high multiplicity processes arising from experimentally measured quantities. These include the shape of the Z-peak and upper limits on scattering cross sections of cosmic rays. We find that the rate of high multiplicity electroweak processes will exceed these upper limits at energies not significantly above what can be currently tested experimentally. This leaves two options: 1) The electroweak sector becomes truly non-perturbative in this regime or 2) Additional physics beyond the Standard Model is needed. In both cases novel physics phenomena must set in before these energies are reached. Based on the measured Higgs mass we estimate the critical energy to be in the range of $10^3$ TeV but we also point out that it can potentially be significantly less than that.

0+states in deformed actinide nuclei by the(p,t)reaction

By means of the $(p,t)$ reaction we study the excitation spectra of ${0}^{+}$ states in the deformed nuclei $^{228}\mathrm{Th}$, $^{230}\mathrm{Th}$, and $^{232}\mathrm{U}$, using the Q3D magnetic spectrograph facility at the Munich tandem accelerator. At small reaction angles the ${0}^{+}$ transfer angular distributions have steeply rising cross sections which allow us to identify these states in otherwise very complicated and dense spectra. For each of these nuclei we resolve typically about ten excited states with safe ${0}^{+}$ assignments. The studied excitation energies range up to 2.5, 2.7, and $2.3\phantom{\rule{0.3em}{0ex}}\text{MeV}$, respectively, and the summed transfer strengths add to more than $60%$ of the ground state strength. As in a recent study of $^{158}\mathrm{Gd}$ we compare with interacting boson approximation (IBA) calculations in the $spdf$ boson space. This highly schematic collective model description, including octupole collectivity, but neglecting other relevant degrees of freedom, gives numbers of excited ${0}^{+}$ states in these actinide nuclei that are rather close to the observed ones.

Photoproduction of vector mesons in the soft dipole Pomeron model

Exclusive photoproduction of all vector mesons by real and virtual photons is considered in the soft dipole Pomeron model. It is emphasized that, the Pomeron in this model being a double Regge pole with an intercept equal to 1, we are led to rising cross sections but the unitarity bounds are not violated. It is shown that all available data for $\ensuremath{\rho},\ensuremath{\omega},\ensuremath{\varphi},J/\ensuremath{\psi},$ and $\ensuremath{\Upsilon}$ in the region of energies $1.7<~W<~250\mathrm{GeV}$ and photon virtualities $0<~{Q}^{2}<~35{\mathrm{GeV}}^{2},$ including the differential cross sections in the region of transfer momenta $0<~|t|<~1.6{\mathrm{GeV}}^{2},$ are well described by the model.

The nucleon-airnucleus interaction probability law with rising cross section

The diffusion equation of cosmic-ray nucleons is exactly integrated usingthe successive approximation method for a general distribution of theprimary component, and taking into account the rising nucleon-aircross sections with energy. The interaction probability law for thenucleon in the atmosphere is obtained as a consequence of the respectivediffusion equation. If the nucleon-air cross sections rise logarithmically,this probability law assumes a binomial form, and for the constant crosssection, it is purely Poissonian. The well known approximate solution iscompared with our exact solution. It is found that the former always givesa nucleon number greater than ours by, for example, 15-25% in theenergy region 30-10 000 GeV at sea level in the case of the meaninelasticity ⟨κ⟩ = 0.60. It is also shown that a fairlyaccurate description of nucleon flux at sea level (1030 g cm-2) and hadron intensities at 840 g cm-2 and at1030 g cm-2 are obtained with ⟨κ⟩varying between 0.55 and 0.60.

Possible evidence for deconfinement in hadron collisions

The collision of hadrons at very high energies produces an entity whose energy density is extremely large resulting in the emission of a large number of hadrons. Though the entity may not have transited into the deconfined parton phase, the very high energy density may cause more than one charged hadron to be emitted at any instant. This yields a new multiplicity distribution, termed the GS distribution which fits the data as well as the popular negative binomial distribution. Neither the GS nor the NB distribution alone agrees with the data beyond 200 GeV, but a weighted sum of GS and NB distributions fits the experimental results exceedingly well. Since the negative binomial distribution arises from the branching of partons, we interpret the increase with energy of the negative binomial component in the weighted sum as the onset of a deconfined phase. The rising cross section for the negative binomial component parallels very closely the inclusive cross section for hadron jets which also is considered a consequence of parton branching.

Pomeron and odderon in high energypp and $$p\bar p$$ elastic scattering

High energypp and\(p\bar p\) data on elastic scattering and total cross sections are analyzed in a model including the pomeron, odderon and secondary reggeons. A dipole model is used for the pomeron and for the odderon. By construction, our (bare) pomeron ansatz produces a single dip, as observed experimentally. The model reproduces the logarithmically rising cross sections with a unit pomeron intercept, but better fits are obained when a small non-zero value of the parameter δ = αp (0) is allowed for. Predictions for the future accelerators (UNK, LHC, SSC) are given.

Probing ultraheavy quanta with photon-photon or gluon-gluon scattering.

The existence of ultraheavy quanta too heavy to produce directly may be probed by means of the rising cross sections they would induce in scattering at the TeV energy scale of photon or gluon pairs to weak boson pairs, for instance \ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\rightarrow}ZZ or gg\ensuremath{\rightarrow}ZZ.

Possibility of a locally, strongly increasing total cross section and related large real amplitude for $$\bar p$$ (p)−p scattering up to 1000 TeV

Using a new form for the diffractive amplitude, we show the possibility of a local increase above asymptotic behavior in the\(\bar p\)(p)−p total cross section well up in the TeV range with values of about 180 mb reached at 100 TeV and 316 mb at 1000 TeV. Use of this locally, relatively strongly rising cross section in the dispersion relation leads to evaluation of the real to imaginary part ratio ϱ, for the forward scattering amplitude up into the TeV range. This quantity increases; we obtain ϱ=18% at 40 TeV. On the basis of a physical picture involving the growth of average multiplicities, it appears possible that asymptotic, bounded growth for the cross section may be reached only at collision energies in the vicinity of 1000 TeV. In this domain, certain global measures of partonic behavior come close to the behavior of the produced physical hadrons.

Rising cross sections in QCD and the cosmic ray data

QCD suggested pattern of the Pomeron is applied to an analysis of asymptotic properties of the proton-proton total cross section. There is an accumulating evidence for the QCD Pomeron having an intercept δ = αp(0) - 1 = 0.2–0.4: 1. i)Large ϱ p p = Re/Im = +0.24 ≠ 0.04 at √s = 546 GeV from UA4 , 2. ii)Large p p total cross section of 85.5 ≠ 6.7 mb from E710, 3. iii)The Akeno & Fly's Eye data on the p-air absorption cross section. After comments on the phenomenology of the ACD Pomeron and onset of the Froissart asymptotics of σ tot ( pp), I will concentrate on evaluation of the Cosmic Ray data. I emphasize that, before commissioning SSC, the Cosmic Ray experiments will remain a unique, and reliable , source of information on the very High Energy behavior of σ in ( pp). Major observation is that, in view of the unitarity enforced correlation between the pp diffraction slope and σ in ( pp), determination of σ in( pp) from σ abs( p- air) is virtually uncertainty free.

Rising cross sections in QCD and the cosmic-ray data.

Novel features of the QCD-implied growth of the total cross sections are discussed. Specifically, Lipatov's QCD Pomeron is a series of poles above unity, so that the center of gravity of the QCD Pomeron---the effective intercept---moves to higher j with rising energy. The higher the energy the steeper is the predicted rate of growth of the cross section, until unitarity enforces saturation of the growth rate and the onset of the Froissart asymptotics at extremely high energies. We demonstrate that the QCD-predicted rapid rise of the p(p\ifmmode\bar\else\textasciimacron\fi{})p total cross section agrees perfectly with the recent CERN Sp\ifmmode\bar\else\textasciimacron\fi{}pS datum on the phase of the p\ifmmode\bar\else\textasciimacron\fi{}-p forward amplitude. Further evidence for the QCD-predicted rise of the total cross section comes from the published Akeno and Fly's Eye data on the extensive air showers. Our principal observation is that in view of the unitarity-enforced slope--cross-section correlation one can determine proton-proton inelastic cross section from the proton-air absorption cross section to a very high accuracy. The published Fly's Eye result ${\ensuremath{\sigma}}_{\mathrm{abs}(\mathrm{p}}$-air)=540\ifmmode\pm\else\textpm\fi{}40 mb corresponds to ${\ensuremath{\sigma}}_{\mathrm{in}(\mathrm{p}\mathrm{\ensuremath{-}}\mathrm{p}{)=113}_{\mathrm{\ensuremath{-}}15}^{+16}}$ mb and ${\ensuremath{\sigma}}_{\mathrm{tot}(\mathrm{p}\mathrm{\ensuremath{-}}\mathrm{p}{)=164}_{\mathrm{\ensuremath{-}}27}^{+32}}$ mb. All of the previous determinations of ${\ensuremath{\sigma}}_{\mathrm{tot}(\mathrm{p}\mathrm{\ensuremath{-}}\mathrm{p}}$) from ${\ensuremath{\sigma}}_{\mathrm{abs}(\mathrm{p}}$-air) have grossly underestimated ${\ensuremath{\sigma}}_{\mathrm{tot}(\mathrm{p}\mathrm{\ensuremath{-}}\mathrm{p}}$). We present predictions for Fermilab Tevatron, \ensuremath{\surd}s =1.8 TeV, and Superconducting Super Collider, \ensuremath{\surd}s =40 TeV, energies. We give a functional form of correlation of the scaling violations in proton-air collisions with ${\ensuremath{\sigma}}_{\mathrm{abs}(\mathrm{p}}$-air), allowance for which could greatly improve the reliability of determination of ${\ensuremath{\sigma}}_{\mathrm{abs}(\mathrm{p}}$-air) from data on extensive air showers.

Exact solution of the diffusion equation of cosmic-ray nucleons with rising cross section

The diffusion equation of cosmic-ray nucleons is exactly solved, taking into account the rising cross section of the form sigma 0(1+a ln(E/ epsilon )). Grigorov's well known approximate solution (1977) is compared with the authors' exact solution; it is found that the former overestimates the nucleon flux by, for example, 10-20% in the energy region 1-1000 TeV at mountain altitudes in case of a=0.06. Their solution is compared with the hadron fluxes of emulsion chamber data; they find a good consistency with a=0.06.

QCD and rising cross sections.

We show that parton-parton scattering processes in QCD drive a rapid increase in the proton-proton scattering cross section at high energies, and use a diffraction-scattering formalism to obtain quantitative predictions for ${\ensuremath{\sigma}}_{\mathrm{tot}}$, ${\ensuremath{\sigma}}_{\mathrm{inel}}$, and ${\ensuremath{\sigma}}_{\mathrm{el}}$ at Superconducting Super Collider and cosmic-ray energies. We also predict a very rapid increase in the number of minijet events with \ensuremath{\surd}s .

Charge transfer into the metastable2Slevel of hydrogen by protons colliding with K and Na

We measure the charge transfer cross section for protons in potassium and sodium with the final state being $\mathrm{H}(2s)+{A}^{+}$. Using a crossed-beam experimental method we look at this cross section as a function of proton beam energy from 500 to 2500 eV. Our results for potassium agree with previous experiments and theories in showing two main peaks in the cross section: one of (3.9 \ifmmode\pm\else\textpm\fi{} 1.5)\ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}15}$ ${\mathrm{cm}}^{2}$ at a proton beam energy of 800 eV, and another of (2.8\ifmmode\pm\else\textpm\fi{} 1.1)\ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}15}$ ${\mathrm{cm}}^{2}$ at a proton beam energy of 2.5 keV. Our results for sodium show a steadily rising cross section with a value of (7.3\ifmmode\pm\else\textpm\fi{} 2.5)\ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}15}$ ${\mathrm{cm}}^{2}$ at a proton beam energy of 2.5 keV in agreement with the prediction of Kubach and Sidis; we do not find the maximum at 700 eV reported by Nagata that agrees with the theory of Kimura, Olson, and Pascale.

Transverse-momentum spectrum of inclusive reactions in the geometrical picture

The geometrical model of hadron elastic scattering is generalized to encompass the transverse-momentum spectrum of inclusive reactions. The model is capable of explaining the rapidly rising cross section at large momentum transfer squared as a result of the rising total cross section. We fit all data from $\sqrt{s}\ensuremath{\cong}5 \mathrm{to} 540$ GeV and from ${{P}_{t}}^{2}=0 \mathrm{to} 25$ Ge${\mathrm{V}}^{2}$.

The relation of Cerenkov time profile widths to the distance to maximum of air showers

The authors provide information to enable experimenters to interpret measurements of Cerenkov pulse widths (FWHM) in terms of the distance along the axis to air-shower maximum. The relations were calculated from Monte Carlo simulations for protons using a scaling model and rising cross sections. Primary energies of 1015, 1016, 1017 eV and zenith angles from 0 degrees to 40 degrees are covered. The results will be useful for radii of observation from 200 to 350 m and refer to sea level. The relations are sensitive to marked deviations from scaling-model behaviour on the approach to maximum; however, reasonable aerosol variations to not invalidate the results. The procedure frequently used to obtain the true widths by correcting the measured widths for the impulse response of the detector can lead to appreciable errors near a radius of 200 m. An alternative method is described.

Cosmic Rays in the Energy Range 1014?1017 eV

It is possible to explain the gross features of extensive air showers using very different alternative assumptions about the character of particle interactions, provided that different assumptions are made about the primary particle flux and composition. From this fact it is first shown that a very consistent set of fairly direct measurements on primary flux now exists (subject to the acceptance of a systematic bias in one set of data), together with constraints on the composition. (Protons and other nuclei however turn out not to have the same rigidity spectrum.) The gross features of showers mostly fit a scaling model with rising cross sections, but there are contrary indications (particularly from y-ray flux, particle spread and core structure at the higher energies) that a change in the nature of interactions occurs above 10'5 eV, and this puzzle has not been solved.

The confinement of massless non-Abellian gluons and rising total cross section

It is argued that the critical pomeron solution of the reggeon field theory (RFT) occurs in massless Yang-Mills theories with an SU( N) gauge group. A proviso is that gluon confinement must allow a principal-value regularization of the Regge limit infrared divergences. The supercritical RFT phase occurs when the gauge symmetry is spontaneously broken down to a U(1) symmetry. SU(3) seems to be the minimum structure for the (broken) gauge group in the supercritical phase. The method used is to extend the multi-Regge dispersion relation calculations of Fadin, Kuraev and Lipatov to a full RFT of the pomeron applicable to Yang-Mills. The presence of a pomeron satisfying RFT is closely related to the regularization procedure used. Since the critical pomeron is the only known unitary ( s- and t-channel) description of rising cross sections, the results imply that their experimental observation is direct evidence for a non-abelian gauge symmetry underlying strong interactions. The results also imply that diffraction scattering is precisely calculable in QCD.

Scaling, the energy dependence of the total inelastic p-air cross section and the hadron energy spectrum

The sea-level hadron spectrum has been redetermined. From comparison with the primary spectrum it is shown that the effective p-air total cross section is rising faster than 1nE in the energy region 1-100 TeV. Comparison with calculations by Hillas shows that simulations using a scaling model and incorporating a rising cross section are in agreement with the experimental data if the inelasticity is constant in this energy region.

Unified Model for Elastic Scattering and Inclusive Reactions

A unitary model for the particle production is presented on the basis of the eikonal for­ malism and the Regge theory. The elastic and production processes are treated in a unified way and the diffraction in the former is described explicitly as a shadow of the latter. In our model, the exchange of the Regge cut is important in the particle production and the self-consistency is retained between the input and output forward two-body amplitudes. Our model reproduces rising cross sections and the shrinkage effect in the forward slope parameter. As for the production processes, the increasing average multiplicity, the sharp cutoff of the transverse momentum and the wide rapidity plateau with a bump structure in inclusive spectra are reproduced. High energy experiments at FNALn and at CERN-ISR2J have revealed several regularities in hadronic processes. In proton-proton collisions in the range 300<s <3000 Ge V 2 , s being c.m.s. energy squared, rises of total, elastic and inelastic cross sections are observed. In addition, the forward peak in the elastic differential cross section shrinks and the dip position decreases correspondingly. Variations of all these quantities are approximately the same. The forward real to imaginary ratio of the elastic amplitude is positive but close to zero. It follows from these facts that the effective interaction range between hadrons expands at high energies. In other words, the elastic amplitude in the impact parameter space T(b, s) has an asymptotic behavior of the form