High-energy Total Cross Sections Research Articles

Perturbative Treatment of Diffractive Dissociation at High Energies

Two-component models have been quite successful in fitting multiplicity distributions in high-energy hadronic collisions. The fact that the diffractive component is considerably smaller than the short-range-correlation component suggests the possibility of a perturbative expansion of the high-energy total cross section. We develop such an expansion in this paper, and examine some of its consequences. Finally, prominent among these consequences are: (i) diffraction dissociation into high masses rises approximately logarithmically with energy at NAL-ISR (CERN Intersecting Storage Rings) energies, (ii) the short-range-correlation part of the cross section has high-energy behavior dominated by a bare Pomeron Regge pole, and (iii) the average multiplicity of particles produced in diffractive dissociation rises logarithmically with energy.

Scale Invariance, Fixed Poles, and Cuts in Compton and Deep-Inelastic Scattering

Finite-energy sum rules in Compton and deep-inelastic scattering are analyzed at ${q}^{2}=0$ and $\ensuremath{-}{q}^{2}=\ensuremath{\infty}$ on the basis of a Regge-pole model including cuts. It is found that the sum rules can be satisfied without the use of real fixed poles. Good fits are obtained to the data for the deep-inelastic structure functions in the Regge region, and to the data for the high-energy total and differential cross sections.

Solutions toπ−πandK−πScattering in a Model Satisfying Analyticity, Crossing Symmetry, and Approximate Unitarity

Phase shifts for $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ and $K\ensuremath{-}\ensuremath{\pi}$ scattering are obtained from a model satisfying analyticity, exact crossing symmetry, and approximate unitarity up to $\sqrt{s}\ensuremath{\sim}1.3$ GeV. Low-energy elastic as well as low- and high-energy total cross sections are calculated. The results are compared with available data on $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ and $K\ensuremath{-}\ensuremath{\pi}$ scattering, as well as general restrictions on $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ models.

High-Energy Total Cross Sections and Symmetry Relations

Recent Serpukhov measurements of meson-baryon total cross sections allow comparisons with the Johnson-Treiman and Barger-Rubin relations. For 25-55-GeV/c incident meson momenta, the Johnson-Treiman relation, $\frac{1}{2}\ensuremath{\Delta}(\mathrm{Kp})=\ensuremath{\Delta}(\ensuremath{\pi}p)$, is well satisfied. The less restrictive Barger-Rubin relation holds for most of the Serpukhov points. Linear extrapolation of Serpukhov fits for $\ensuremath{\Delta}(\mathrm{Kp})$ and $\ensuremath{\Delta}(\ensuremath{\pi}p)$ to high momenta leads to the prediction of large violations of the Johnson-Treiman relations.

Multiple scattering model for pion-nucleon scattering and the slope of the Pomeranchuk trajectory

The multiple scattering model of Frautschi and Margolis, with secondary trajectories included, is applied to pion-nucleon elastic and charge- exchange scattering. It is possible to explain the Serpukhov high energy total cross section data, but not other data such as the phase of the forward amplitude and the elastic scattering polarization.

Models for diffraction scattering with fixed pole and shielding cut

It is proposed that the nonshrinking πp diffraction peak is due to a fixed pomeron,t-channel unitarity being preserved by a shielding cut, which also explains the constancy of high-energy total cross-sections. Several models are discussed and used to fit πp and pp data; in some a new pole is assumed near the pomeron.

Shielded fixed-pole Pomeranchon model for high energy total and differential cross sections

A Regge model with a fixed-pole Pomeranchon and its associated shielding cut is used for π ±p, K ±p and pp scattering at small t and from 6 GeV to NAL and ISR energies. No additional parameters are associated with the cut. The model produces rising total cross sections and anti-shrinkage or non-shrinking diffraction peaks for some s and t. Good fits to total cross sections and to Serpukhov and ISR pp slope parameter data are obtained, and predictions about cross sections and shrinkage at NAL energies are made.

Angular-Momentum Cuts and Scaling of Total Cross Sections at High Energies

High-energy total cross sections for the ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}p$, ${K}^{\ifmmode\pm\else\textpm\fi{}}p$, $\overline{p}p$, and $\mathrm{pp}$ reactions are analyzed using a Regge-pole model combined with an odd-signature cut. It is found that the asymptotic cross sections, when plotted versus $\ensuremath{\omega}=\frac{s}{2{M}_{1}{M}_{2}}$, satisfy a scaling law within specified normalization constants.

Regge cuts and high energy πN and KN scattering

A phenomenological analysis of πN and KN elastic and charge exchange scattering is made in the framework of convolutions models. The pomeron trajectory is taken with a non-zero slope which allows one to describe high-energy total cross sections (without violating the Pomeranchuk conjecture) together with d σ/d t and P o . For the Regge contribution strong exchange degeneracy and Gell-Mann's ghost killing mechanism are used. A rather good fit to the data ( σ T, d σ/d t, P o for | t| < 1.5 GeV 2/ c 2) is obtained. The slope of the pomeron is found to be the same as for pp scattering ( α′ P = 0.33 GeV −2/ c −2). In πp scattering no cut should be present in the helicity flip amplitude.

Low-Energy Zeros and Regge Poles from an Extended Amati-Bertocchi-Fubini-Stanghellini-Tonin Multiperipheral Model

By inserting the elastic absorptive part from a multiperipheral model into a fixed-momentum-transfer dispersion relation, it is possible to obtain the low-energy amplitude in the crossed channel. We use the ABFST (Amati-Bertocchi-Fubini-Stanghellini-Tonin) version of this model so that the amplitude satisfies a BS (Bethe-Salpeter) equation. The Veneziano model for the $\ensuremath{\pi}\ensuremath{\pi}$ amplitude is used to calculate the ABFST input kernel, for which off-shell effects are neglected. We go beyond the usual pion-exchange dominance of the ABFST model by including an "inelasticity" factor in our BS equation. The strength of this factor is fixed by requiring that the Chew-Mandelstam $\ensuremath{\pi}\ensuremath{\pi}$ symmetry-point crossing condition is satisfied. It is then found that zeros arise in the $S$-wave amplitudes, which can presumably be identified with the zeros which are predicted from the Adler self-consistency condition. As a by-product, we also calculate the leading Regge trajectories in our model. These have no difficulty in rising to fairly high angular momenta and lead to relatively narrow reduced widths for the $\ensuremath{\rho}$ and ${f}^{0}$ resonances, as well as a high-energy total cross section in approximate agreement with experiment.

Compton Scattering at High Energies

Using the continuous moment sum rule it is found that the third vacuum pole P is im­ portant for the forward proton Compton scattering, and the residue of the fixed pole at J =0 is also estimated. The third vacuum pole P has zero intercept ap(0)~-0.5. The prediction of the high energy total cross section is consistent with recent experimental results.

Magnitude of High-Energy Meson-Meson Total Cross Sections

The total cross section for meson-meson scattering at high energy is calculated using a simple, but plausible, $\mathrm{SU}(n)$-symmetric multiperipheral model. The resulting ${\ensuremath{\sigma}}_{T}$ is of the order $\frac{16{\ensuremath{\pi}}^{3}}{NM_{V}^{}{}_{}{}^{2}}$, where ${M}_{V}$ is the central mass of the dominant low-energy resonance multiplet in elastic meson-meson scattering and $N$ is the dimensionality of the multiplet of the incident mesons. The nongeometric character of this result is discussed.

Some remarks forπ-N scattering towards nearly constant bounds for high-energy total cross-sections and the Pomeranchuk theoremscattering towards nearly constant bounds for high-energy total cross-sections and the Pomeranchuk theorem

Some remarks forπ-N scattering towards nearly constant bounds for high-energy total cross-sections and the Pomeranchuk theoremscattering towards nearly constant bounds for high-energy total cross-sections and the Pomeranchuk theorem

High-energy total cross-sections and the adler-weisberger relation

The Adler-Weisberger relation and other similar relations are re-examined without assuming unsubtracted dispersion relations. The results are essentially unchanged for any reasonable behavior of the high-energy cross-sections, even if that behavior would cause the original dispersion integrals to diverge.

Towards nearly constant bounds for high-energy total cross-sections

Some rigorous results of quantum field theory suggest further assumptions restricting the behaviour of scattering amplitudes at high energies and small momentum transfers in such a way as to ensure the existence of some weighted averages both of the real and imaginary parts of the forward amplitude. The latter prevent the total cross-sections from saturating high-energy bounds of the type (logs)s, (log logs)s,\(\left( {\underbrace {\log (\log \ldots \log s) \ldots }_{p times}} \right)^\varepsilon \),p integer,ɛ>0. If the property that total cross-section cannot saturate nearly constant bounds at infinity is violated there exist within our framework two possibilities. On one hand the amplitudes could be indefinitely oscillating. If not, there would appear particular zeros in linear combinations of the real and imaginary parts of the amplitudes. These zeros would be always present in the nearly forward asymptotic domain with energy as large and transfer as small as we want.

Multiperipheral model suggestion of a damped oscillatory component in high energy total cross sections

We use a simplified multiperipheral model to illustrate the possibility of complex Regge poles that contribute damped oscillations to the total cross section. The model suggests a relation between the period of the oscillations and the rate of growth of average multiplicity with energy.

Formula omitted] elastic scattering and the shadow of generalized annihilation processes

The differences between the high-energy total cross sections and elastic scatterings of K − p and pp and their counterparts under crossing, K +p or pp, are analysed in terms of the inelastic channels open for the former and closed for the latter system. For pp these channels are mainly baryon annihilation. For K − p we introduce the concept of hypercharge annihilation K − p → hypercharge-zero particles (mainly one Y = 0 hyperon and Y = 0 mesons) and a vaguer notion of charge annihilation, and we propose that these generalized annihilation channels are the main ones open to K − p and closed to K +p. The contribution of the generalized annihilation processes to the overlap function of the overall collision is derived from the σ T and d σ el/d t data, using various simple model assumptions. The results, which are insensitive to the latter, predict the total annihilation cross sections and their high-energy dependence, as well as the range of the annihilation processes. The annihilation cross sections compare well with the few measured values. The annihilation ranges are predicted to be equal for K − p and pp , with a value close to the range of elastic scattering of pp and pp. The elastic range of Kp is smaller by about a factor two.

Certain Implications for High-Energy Total Cross Sections from the Multiperipheral Model

The multiperipheral model is used to relate the experimental fact, ${{\ensuremath{\sigma}}_{N\overline{N}}}^{\mathrm{tot}}&gt;{{\ensuremath{\sigma}}_{\mathrm{NN}}}^{\mathrm{tot}}$, to the possibility that the $N\overline{N}$ channel can annihilate into purely meson final states by exchange of $N$ or $\overline{N}$ trajectories, whereas the $\mathrm{NN}$ channel cannot do so. Our argument shows that from the multi-Regge bootstrap point of view, the combination of baryon and antibaryon trajectories will generate a pair of exchange-degenerate trajectories ${P}^{\ensuremath{'}}$ and $\ensuremath{\omega}$. The same line of reasoning can easily be generalized to include strange particles, as well as the (${K}^{\ensuremath{-}}N, {K}^{+}N$) and (${\ensuremath{\pi}}^{\ensuremath{-}}p, {\ensuremath{\pi}}^{+}p$) systems.

Low-EnergyK¯NScattering and Finite-Energy Sum Rules

Finite-energy sum rules are used to test the consistency of Kim's multichannel effective-range analysis of low-energy $\overline{K}N$ data with high-energy total cross sections.

High Energy Total Cross Sections and 36-plet 2+-Mesons

High Energy Total Cross Sections and 36-plet 2⁺-Mesons