Behavior Of Total Cross Sections Research Articles

Improvements to the Froissart bound from AdS/CFT

In this paper we consider the issue of the Froissart bound on the high energy behaviour of total cross sections. This bound, originally derived using principles of analyticity of scattering amplitudes, is seen to be satisfied by all the available experimental data on total hadronic cross sections. At strong coupling, gauge/gravity duality has been used to provide some insights into this behaviour. In this work, we find the subleading terms to the so-derived Froissart bound from AdS/CFT. We find that a $(\ln \frac{s}{s_0})$ term is obtained, with a negative coefficient. We see that the fits to the currently available data confirm improvement in the fits due to the inclusion of such a term, with the appropriate sign.

Outstanding features of reactions with halo nuclei

Recent results for total reaction and fusion excitation functions for halo systems are compiled. The striking similarity in the behavior of total cross sections for proton-halo (8B) and neutron-halo (6He) systems is pointed out. Static and dynamic halo effects are elucidated by comparing data for a neutron-halo nucleus and its core. Fusion cross sections are discussed in terms of a maximum angular momentum for fusion, Lf. A linear energy dependence for Lf is consistent with the data for all the existing measurements so this might actually be a characteristic feature of true halo systems. A qualitative difference between the fusion of neutro-halo and proton-halo systems also is pointed out.

Evidence for the saturation of the Froissart bound

It is well known that fits to high energy data cannot discriminate between asymptotic ln(s) and ln^2(s) behavior of total cross section. We show that this is no longer the case when we impose the condition that the amplitudes also describe, on average, low energy data dominated by resonances. We demonstrate this by fitting real analytic amplitudes to high energy measurements of the gamma p total cross section, for sqrt(s) > 4 GeV. We subsequently require that the asymptotic fit smoothly join the sqrt(s) = 2.01 GeV cross section described by Dameshek and Gilman as a sum of Breit-Wigner resonances. The results strongly favor the high energy ln^2(s) fit of the form sigma_{gamma p} = c_0 + c_1 ln(nu/m) + c_2 ln^2(nu/m) + beta_{P'}/sqrt(nu/m), basically excluding a ln(s) fit of the form sigma_{\gamma p} = c_0 + c_1 ln(nu/m) + beta_P'/sqrt(\nu/m), where nu is the laboratory photon energy. This evidence for saturation of the Froissart bound for gamma p interactions is confirmed by applying the same analysis to pi p data using vector meson dominance.

Analytic amplitudes for hadronic forward scattering and the Heisenberg ln2 s behaviour of total cross sections

We consider several classes of analytic parametrizations of hadronic scattering amplitudes (the COMPETE analysis), and compare their predictions to all available forward data ( pp, πp, Kp, γp, γγ, Σp ). Although these parametrizations are very close for √ s ≥ 9 GeV, it turns out that they differ markedly at low energy, where a universal Pomeron term ∼ ln 2 s enables one to extend the fit down to √ s = 4 GeV. We present predictions on the total cross sections and on the ratio of the real part to the imaginary part of the elastic amplitude ( ρ parameter) for present and future pp colliders, and on total cross sections for γp → hadrons at cosmic-ray energies and for itγγ → hadrons up to √ s = 1 TeV. The ln 2 s behaviour of total cross sections, first obtained by Heisenberg 50 years ago, receives now increased interest both on phenomenological and theoretical levels. We present a modification of the Heisenberg's model in connection with the presence of glueballs and we show that it leads to a realistic description of all existing hadron total cross-sections data, in agreement with the COMPETE analysis.

Heisenberg’s universalln2sincrease of total cross sections

The (lns)**2 behaviour of total cross-sections, first obtained by Heisenberg 50 years ago, receives now increased interest both on phenomenological and theoretical levels. In this paper we present a modification of the Heisenberg's model in connection with the presence of glueballs and we show that it leads to a realistic description of all existing hadron total cross-section data.

Total Cross Sections at High Energies — An Update

Current and future measurements for the total cross sections at E-811, PP2PP, CSM, FELIX, and TOTEM have been analyzed using various models. In the light of this study an attempt has been made to focus on the behavior of total cross section at very high energies.

High energy behaviour of total cross sections in weak interactions

We propose a new method for the computation of the high energy limit of the total cross section in spontaneously broken gauge theories. It is based on an evolution equation for effective couplings in dependence on the gauge boson mass. We apply this method to weak interactions in the leading logarithm approximation. Perturbation theory becomes invalid at very high energies since one of the couplings becomes strong. The obtained total cross sections obey Froissart's bound, in contrast to previous results not using the evolution equation.

Large-order perturbation theory for a physical quantity

Abstract We discuss renormalization scheme and normalization scale dependence of the large-order asymptotics of perturbative expansions due to renormalons based on an exact calculation of the Borel transform of the imaginary part of the electromagnetic current correlation function within an expansion in the number of fermions in quantum electrodynamics. Arguments are given that the leading uncertainty of perturbative series in quantum chromodynamics due to ultraviolet renormalons can be suppressed by an appropriate choice of normalization scale. Combining momentum analyticity with the Borel transformed renormalization-group equation, we relate the large-order behaviour of total cross sections to that of their polarization operator.

Instanton induced cross sections below the sphaleron

We study the S-matrix and the total cross section of high-energy collisions in the one-instanton sector of purely bosonic theories with instantons. Making use of the coherent state formalism, we develop the perturbation theory around the instanton. We find that in the limit g2 → 0, E/Esph fixed, the leading behaviour of the total cross section is σtot ∼ exp[g−2(−2S0 + F(E/Esph))], where S0 is the instanton action. In the eelectroweak theory at E/Esph ⪡ 1, the function F(E/Esph) is determined by the gauge boson part of the instanton configuration and its explicit form is found. Our results suggest that there may exist a semiclassical type of procedure for evaluating the leading behaviour of the one-instanton total cross section at E≳Esph and g2 → 0.

Analysis of Experimental Semi-Inclusive Distributions at the SPS-Collider Energies

The experimental data on hadron-hadron interactions at high up to SPS-collider energies are analysed carefully within a multicomponent approach based on the renormalization group method. In particular, the behaviour of total cross sections and forward-backward correlations of scattered particles is described as well as the broadening of pT-spectra with increasing multiplicity of charged particles and the “sea-gull” effect for η-distributions observed at small multiplicities.

Conformal mapping in the energy variable and nuclear coupling constants

Abstract Conformal mapping techniques are combined with forward dispersion relations. Applications are made to nα and nd scattering. Legendre and Tchebycheff extrapolations to the nuclear poles lead to consistent values for the 4 He 3 Hen, the dpn and tdn coupling constants. The new method is insensitive to the strength of competing nuclear cuts and to the asymptotic behavior of total cross sections. Cutkosky type truncation errors can be estimated.

On the asymptotic behaviour of total cross section in the Reggeon field theory

A suggestion is given, based on earlier results of Bronzan and Cardy, that the Reggeon field theory predicts total cross section increasing like (log s)2 or falling as a power of s (depending on the value of the bare intercept) and that the renormalization group solutions are asymptotically valid only in the unphysical case when the bare intercept takes exactly the “critical” value.

Constraints on the asymptotic behaviour of total cross sections

We derive constraints on the asymptotic behaviour of total cross sections which follow from dispersion relations and measured real parts of the forward scattering amplitudes. For πN and pp scattering, these constraints are calculated using recent results from FNAL and Serpukhov. The relation to other methods is discussed.

High temperature expansion and the reggeon calculus

Abstract We show that in the framework of Reggeon calculus the use of “high temperature expansion” may produce an accurate determination of the asymptotic behaviour of total cross sections.

Renormalizability and the high energy behaviour of total cross sections in the Weinberg salam model

Abstract It is discussed how the violation of the Pomeranchuk theorem in the Weinberg Salam model of weak and electromagnetic interactions upsets current ideas about the convergence of dispersion relations in renormalizable field theories.

High-mass diffraction and Regge behavior of total cross sections

Abstract We consider a modified two-component model of particle production in which diffractive excitation into high mass states gives a contribution to K±p, π±p and pp total cross sections of sufficient magnitude and with the proper associated threshold to be a possible explanation of deviations of σtot from Regge pole model fits at Serpukhov energies. We present tests of the model. for K+p scattering by extrapolating σtot to National Accelerator Laboratory energies and by calculating the high mass diffraction contribution to the forward peak in inclusive reactions. The consistency of this scheme is discussed in relation to the pomeron intercept and the form of the triple-pomeron coupling.

Comments on the high energy behaviour of total cross-sections based on light-cone algebra

Based on considerations of the light-cone algebra of currents and pseudoscalar densities, it is suggested that either the high energy meson-nucleon cross-sections are constants (even though the pp-cross-section increases indefinitely) or that they deviate from constancy by logarithmic terms whose scale is set by a mass, of the order of at least tens of Gev, and which also characterises the consequent logarithmic violations of Bjorken scaling.

High energy behavior of total cross sections for e +e − scattering and the slope at q2=0 of the Dirac form factor

The slope at q 2 =0 of the fourth order Dirac form factor is expressed in terms of various exclusive high energy cross sections for e + e − scattering. The agreement between high energy and low energy calculations is obtained.

Proof of the Pomeranchuk Theorem and Related Theorems Deduced from Unitarity

A new general proof of the Pomeranchuk theorem in the form of the average behavior of total cross sections is given. It contains the features of the Martin and Meiman proof and is more precise. By considering the integral of the forward amplitude, this proof can be extended to cover slowly increasing and decreasing total cross sections. The unitarity restriction on the relative behavior of particle-antiparticle total cross sections is studied in general, again without making the smoothness assumption. In particular, using unitarity, it is shown that a modified form of the Pomeranchuk theorem is valid when the total cross sections are asymptotically unbounded.

Sum Rules and Bounds on Scattering Amplitudes

Using sum rules obtained from crossing and analyticity, and unitarity bounds on scattering amplitudes, we show how new relations between low-energy and high-energy scattering can be derived. These relations can provide tests of a wide range of theoretical ideas. As examples, we discuss several inequalities obtained for $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ and $\ensuremath{\pi}\ensuremath{-}N$ scattering. For $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ scattering, a number of relations involving the asymptotic behavior of total cross sections are presented, including bounds limiting the size of violations of the Pomeranchuk theorem. Using finite-energy sum rules for $\ensuremath{\pi}\ensuremath{-}N$ scattering, we derive new types of bounds and show how they can be used to probe such things as the nature of the Pomeranchuk trajectory and the assumption of $s$-channel helicity conservation. Finally, we introduce inequality constraints between partial-wave amplitudes of different isospin, and indicate how they can be used to explore the nature of exchange degeneracy, absence of exotics, and duality.