Regge Parametrization Research Articles

Toward complete pion nucleon amplitudes

We compare the low-energy partial wave analyses $\pi N$ scattering with a high-energy data via finite energy sum rules. We construct a new set of amplitudes by matching the imaginary part from the low-energy analysis with the high-energy, Regge parametrization and reconstruct the real parts using dispersion relations.

Chiral-dispersive calculations of ππ scattering confront experiment

In a series of papers we have applied several sum rules and forward dispersion relations, to ππ scattering. We have found that some widely used data sets fail to satisfy these constraints, and we have provided an amplitude that describes data consistently with the dispersive tests. Furthermore, we noted that the input and precision claimed in a Roy equation analysis by Colangelo, Gasser and Leutwyler (CGL), lead to several mismatches with some sum rules. Subsequently, Caprini, Colangelo, Gasser and Leutwyler claimed that our Regge parametrization was incorrect. We collect here the answers to their various claims, and try to clarify the points of agreement and disagreement, showing experimental evidence that substantiates our results, and that, in addition, their representation fails to satisfy all three forward dispersion relations up to s ⩽ 800 MeV by several standard deviations.

THEORETICAL ASPECTS OF THE PION-PION INTERACTION

We give a brief review of the theoretical description of low energy pion-pion scattering by the combined use of Chiral Perturbation Theory and Roy equations, an update of the Regge parametrization of ππ cross sections at high energies, and a short discussion of the scalar radius of the pion.

Nucleon form factors from generalized parton distributions

We discuss the links between Generalized Parton Distributions (GPDs) and elastic nucleon form factors. These links, in the form of sum rules, represent powerful constraints on parametrizations of GPDs. A Regge parametrization for GPDs at small momentum transfer, is extended to the large momentum transfer region and it is found to describe the basic features of proton and neutron electromagnetic form factor data. This parametrization is used to estimate the quark contribution to the nucleon spin.

Deeply exclusive processes and generalized parton distributions

We discuss how generalized parton distributions (GPDs) enter into hard exclusive processes, and focuss on the links between GPDs and elastic nucleon form factors. These links, in the form of sum rules, represent powerful constraints on parametrizations of GPDs. A Regge parametrization for the GPDs at small momentum transfer –t is extended to the large-t region and it is found to catch the basic features of proton and neutron electromagnetic form factor data. This parametrization allows to estimate the quark contribution to the nucleon spin. It is furthermore discussed how these GPDs at large-t enter into two-photon exchange processes and resolve the discrepancy between Rosenbluth and polarization experiments of elastic electron nucleon scattering. PACS: 12.38.Bx Perturbative calculations – 13.60.Fz Elastic and Compton scattering

Generalized parton distributions, nucleon form factors, and large‐t processes*

AbstractThe connection of generalized parton distributions (GPDs) to processes at large momentum transfer (high‐t), and the links between GPDs and elastic nucleon form factors are discussed here. These links, in the form of sum rules, represent powerful constraints on parametrizations of GPDs. A Regge parametrization for the GPDs at small‐t, which is surprisingly observed from the chiral quark soliton model results, is extended to the large‐t region and it is found to catch the basic features of proton and neutron electromagnetic form factor data. It is furthermore discussed how these GPDs at large‐t enter into two‐photon exchange processes and resolve the discrepancy between Rosenbluth and polarization experiments of elastic electron nucleon scattering.

On the precision of the theoretical predictions forππscattering

In a recent paper, Pelaez and Yndurain evaluate some of the low energy observables of pi pi scattering and obtain flat disagreement with our earlier results. The authors work with unsubtracted dispersion relations, so that their results are very sensitive to the poorly known high energy behaviour of the scattering amplitude. They claim that the asymptotic representation we used is incorrect and propose an alternative one. We repeat their calculations on the basis of the standard, subtracted fixed-t dispersion relations, using their asymptotics. The outcome fully confirms our earlier findings. Moreover, we show that the Regge parametrization proposed by these authors for the region above 1.4 GeV violates crossing symmetry: Their ansatz is not consistent with the behaviour observed at low energies.

QCD saturation and photoproduction on proton and nuclei targets

We calculate inclusive photoproduction cross sections for both proton and nuclei targets, using a saturation model derived from an approximate solution to the Balitsky-Kovchegov nonlinear evolution equation. This paper extends our hypothesis that one can successfully use the dipole picture and saturation models to describe soft processes, instead of the soft Pomeron Regge parametrization. Our fit is compatible with our previous fit to deep inelastic scattering data, and utilizes the same phenomenological parameters as in our paper devoted to soft hadronic interactions. Using the Glauber formalism and no additional parameters, we calculate the cross sections for photoproduction on various nuclei, and compare our results with the relevant data.

Extrema bounds for the soft Pomeron intercept

By using an extended Regge parametrization and taking into account the discrepancies in the high-energy pp and p̄p total cross section data in both accelerator and cosmic-ray regions, we estimate extrema bounds for the soft Pomeron intercept. First we consider two ensembles of data with either the CDF or the E710 and E811 results for σtotp̄p at 1.8 TeV, from which we obtain the bounds 1.102 and 1.081, respectively. These ensembles are then combined with the highest and lowest estimations for σtotpp from cosmic-ray experiments (6–40 TeV), leading to the upper and lower bounds 1.109 and 1.082, respectively. The effects of simultaneous fits to σtot and ρ, individual fits to σtot, and the influence of the subtraction constant in the dispersion relations are also presented. Our global results favor the E710 and E811 data.

Analyses of single-pion photoproduction up to a centre-of-mass energy of 2.5 GeV

The previous Glasgow single-pion energy-dependent photoproduction analysis from protons and neutrons has been extended to include more recent experimental data. This analysis uses fixes- t dispersion relations with a resonance parametrization at low centre of mass energies and a Regge parametrization at high energies. An energy-dependent analysis has also been performed beneath 1.75 GeV for proton targets. Resonance mass, width and couplings are presented for 26 resonances.

Neutron-proton charge exchange revisited

It is shown that a simple Regge parametrization with π, ϱ and A2 t-channel exchanges and their associated cuts account rather well for the I = 1 (t-channel exchange) nucleon-nucleon data available at incoming momenta up to 300 GeV/c. The polarization data on pp → nn at 8 GeV/c may require additional input. Critical comparison with other investigations are presented.

A possible pomeron building mechanism in the fragmentation region

By the use of a Regge parametrization of the one-particle inclusive cross section in the fragmentation region, an integral equation is obtained for the high-energy hadron–hadron inelastic cross section. The main assumptions used in the derivation of this integral equation are: (i) When two hadrons collide with sufficiently high energy, the elastic, inelastic, and total cross sections have the same energy dependence and (ii) Unitarity and factorization of Regge residues hold also for Reggeon–hadron 'amplitudes'. The solution of the integral equation, i.e., the function σinel(s) can be made constant or slowly increasing. For 'reasonable' values of all the parameters involved, it is in very good agreement with the high energy pp data.

Structure of tensor-exchange amplitudes and polarization ofπ−+p→η+n

The structure of amplitudes of ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}\ensuremath{\eta}n$ is investigated by two methods: (a) fixed-$t$ dispersion relations and effective Regge parametrization of the high-energy imaginary parts and (b) two Regge poles and finite-energy sum rules. In both cases the resulting imaginary part of the nonflip amplitude deviates from the dualabsorptive-model form. Similarities with the conclusions of other amplitude analyses involving tensor exchange are discussed. The question of ${A}_{2}\ensuremath{-}\ensuremath{\rho}$ exchange degeneracy is also investigated. An important outcome of the work is that both methods (a) and (b) require a ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}\ensuremath{\eta}n$ polarization of very small magnitude throughout.

Regge parametrization of angular distributions for heavy-ion transfer reactions

A two-pole one-zero Regge parametrization of the l-window for transfer reactions is employed in conjunction with a chi-squared search program to obtain high-quality fits to a wide variety of transfer data. The data employed include both direct and multi-step transfers.

The Adler Sum Rule and Quark Parton Distribution Functions in Nucleon

The behaviour of the quark parton distribution functions is discussed through the phenomenological analysis of the deep inelastic e-p and e-n data under constraint of the saturation of the Adler sum rule. It is concluded that in the region 0≤x ≤x0 where the Regge parametrization can be applied, u(x) is equal to d(x), and both behave as const/x, (x0 will be 0.04 ∼ 0.05); for x0 ≪ x ≤1, both u(x) and d(x) reduce rapidly to sufficiently small values as x increases and u(x)≪d(x) holds; and s(x) and s(x) have roughly the similar behaviour to u(x) and d(x). One possible explanation of u(x)≪d(x) for x≪x0 is given. The rate of convergence of the Adler sum rule is also discussed.

Regge parametrization for low-energy πN scattering

It is shown that the complementary aspect of high-energy Regge behaviour and low-energy resonance saturation known as « duality » from finite-energy sum rules can be advanced in a unifying direction. The Regge parametrization of low-energy partial waves is deduced reversing the path leading to asymptotic Regge behaviour in the crossed channel by means of the Khuri-Jones representation. TheP11 andS11 waves in πN scattering are analysed. They show evidence for a pattern of trajectories characteristic for a model of oscillatory excitations.

Vector Dominance, Regge Poles, andπ0Photoproduction

The presently accepted Regge parametrization of ${\ensuremath{\pi}}^{0}$ photoproduction claims that the $t\ensuremath{\sim}0.5$ ${\mathrm{BeV}}^{2}$ cross section is completely provided by $B$ exchange. We show that this statement disagrees with vector dominance by a factor of at least 4 and probably 10 or more. Additional $I=0$ poles or cuts are needed both in this process and in the $I=0$ $t$-channel combination of $\ensuremath{\pi}+N\ensuremath{\rightarrow}\ensuremath{\rho}+N$ cross sections.