Duality Constraints Research Articles

Duality and exotic mesons in a brokenSU 4 scheme

We derive in a brokenSU4 scheme the nonpomeron contributions to the baryon-baryon and baryon-antibaryon channels from finite-energy sum rules and factorization. Duality constraints are applied only to meson-meson and meson-baryon scatterings where exotic channels are defined by looking at total cross-sections for uncharmed-particle processes. We find that i) the representation20″ ofSU4 turns out to be exotic for meson-meson scattering; ii) the condition for avoiding baryon-baryon resonances is the same as inSU3; iii) exotic baryonantibaryon resonances appear in the84, 45\(\overline {45} \) and20″ channels and no choice of theF/D ratio can climinate all of them; iv)SU4 mass formulae for the representations84,\(\left( {45 + \overline {45} } \right)\) and20″, when a better knowledge of the quantum numbers for baryon-antibaryon resonances is reached, will provide useful information in order to decide among different models for baryonium states.

Comparison of symmetry and duality constraints for radiative transitions of mesons

Predictions for patterns of symmetry breaking in vector and tensor mesons are extracted from pole-dominated finite-energy sum rules. Kinematic factors relate deviations in couplings to the mass-spectrum splitting. For vector mesons, in addition to the usual problem of the small GAMMA (p ..-->.. ..pi gamma..), we find that GAMMA (K*/sup +/ ..-->.. K/sup +/..gamma..) must almost certainly be above its present upper bound of 80 keV. Consistency arguments dictate a choice between the two possible sets of eta..gamma.. widths for the rho and ..omega... In addition, we extract both D..gamma.. and D..pi.. widths for the charmed vector meson D*. For the tensor mesons, predictions GAMMA (A/sub 2/ ..-->.. ..pi gamma..) = 490 +- 60 keV, GAMMA (K**/sup +/ ..-->.. K/sup +/..gamma..) = 125 +- 60 keV, and GAMMA (K**/sup 0/ ..-->.. K/sup 0/..gamma..) = 32 +- 15 keV imply large deviations from both symmetry and naive vector-meson-dominance predictions. Additional consistency relations between eta and eta' reactions lead to GAMMA/sub total/(eta') = 480 +- 120 keV.

Duality constraints for mesons

A new method of imposing semi-local duality constraints is discussed, which satisfies the theoretical requirements of crossing symmetry and self-consistency. The duality relations involve only physical on-shell particles, and give many conditions on their masses and couplings. All constraints from PP→PP and PV→PP amplitudes with ordinary and strange particles give compatible results and are in good agreement with experiment. In particular, the near linearity of Regge trajectories is explained. The internal consistency of constraints with charmed particles is not as good, and implies stronger contributions from daughter resonances.

Predictions of duality for the charmed meson masses

The constraints of duality via FESR's are applied to the processes P+P→P+V, using particles with a new quantum number (charm) as both external and internal (resonance saturation) states. The results are independent of any detailed dynamics or symmetry schemes, as well as independent of coupling strengths. We use the masses of the recently-discovered D and D ∗ to set the scale. We predict m D ∗∗ = 2372 ± 39 MeV , m F = 1938 ± 33 MeV, m F ∗∗ = 2500 ± 40 MeV . Thus slopes of Regge trajectories for charmed mesons are predicted to be substantially smaller than those for ordinary mesons.

Duality and mass-slope correlation in diffractive dissociations

To describe diffractive dissociation processes we propose a three-component Deck model including particle exchange in all the channels of the dissociation subprocess. Reggeization is performed by taking duality constraints into account. This dual reggeization preserves the interferences between the three components which are present in the Born approximation and which allow one to understand the observed strong mass-slope correlation. The model is applied with success to nucleon diffractive dissociation.

Constraints of duality on Regge couplings

The application of duality in the form of finite-mass sum rules (FMSR) makes it possible, under certain conditions, to express the Regge couplings which appear in quasi-two-body reactions in terms of the triple-Regge vertex. The method is applied to ρ-π scattering, where ρ is a reggeon and π a particle, and, using for the triple-Regge coupling the values obtained in a dual unitary calculation, we get results in fair agreement with experiment.

Backward meson-baryon scattering and geometrical properties of baryonic exchanges

On the basis of the “ b universality” hypothesis, Regge behaviour and SU(3) symmetry, we discuss processes of the type 0− 1+ 2 → 0− 1+ 2 at backward angles when significant data are available. Related annihilation processes by line-reversal are also studied and duality constraints are taken into account. On the whole a satisfactory scheme seems to emerge.

Duality Constraints on Single Hadron Electroproduction

Duality Constraints on Single Hadron Electroproduction

Duality constraints and the baryon spectrum

It is shown that the exact duality constraints on the baryons, when taken with the baryon spectrum of the harmonic-oscillator quark model, allow $\mathrm{SU}{(6)}_{W}$-symmetric and crossing-invariant solutions for a wide class of reactions involving the pseudoscalar-meson-baryon scattering. A simple prescription is given for the construction of these solutions. Implications of the solutions on the signs of the resonant amplitudes in SU(3) inelastic processes such as $\ensuremath{\pi}N\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\Delta}$ are deduced and compared with the higher-symmetry predictions.

Duality Constraints and Representation Mixings in Light-Like Chiral Algebra

Within the framework of light-like chiral algebra SU (3) i X SU (3), the mixing scheme for meson resonances are investigated. The mixing angles of representations are determined from duality constraints with an assumption about the variation of Regge residues. In parti­ cular, equal-weight mixing between the pseudoscalar and axial vector mesons is obtained. All the observed pionic couplings are fitted well with one parameter for each helicity. Con­ sistency of our results with mass relations of Weinberg's and others is also studied. § I. Introduction

New selection rules and symmetry relations for Regge-Regge cuts

Using SU(3) and duality constraints, Worden has shown that the Finkelstein cut selection rule requires that all odd signature Regge-Regge cuts are strongly suppressed in meson-baryon scattering. We have extended Worden's analysis by constructing the SU(3) coefficients, for the Gribov vertices, that are appropriate for dual resonance models. By combining the coefficients for two Gribov vertices and preserving the Finkelstein rule, a complete set of symmetry relations is obtained. Examples of these relations are that Regge-Regge cuts do not contribute to meson-meson scattering when the external mesons have overall odd C parity, and that the I = 2 part of Δ photoproduction cannot arise from Regge-Regge cuts.

Duality and Regge-Mueller phenomenology for inclusive spectra

Further predictions are examined of a recently proposed, phenomenologically supported, duality scheme for double Regge-Mueller graphs. It is stressed that these duality constraints should be tested, not only on the non-scaling behaviour at x = 0 of single-particle spectra, but also on the shape (i.e. curvature) of rapidity spectra. Exchange degeneracy constraints for single and double Regge-Mueller expansions are used, together with factorization to investigate two-particle spectra of ( a→ d| c| b) when one particle is near the kinematic boundary and the other is in the central region. A rapid scaling criterion is derived. The relative sizes of the non-scaling part of (p→ π −| c| b) spectra c= π +, π −, π 0, b= π +, π −K +,K −,p are estimated. An extended pattern of duality constraints for many-particle Regge-Mueller graphs is suggested.

Baryon duality solutions with the harmonic-oscillator spectrum and the amplitude signs in πN→ πΔ

By constructing exact exchange-degenerate solutions of baryons with the harmonic-oscillator spectrum for a set of reactions MB→M′B′, MB → M′D′ and MD → M′D′, we investigate the duality constraints on the amplitude signs in MB → M′D′. It is shown that the amplitude signs determined by duality are consistent with those predicted by the extended version of SU(6) W symmetry with the universal dominance of the ΔL Z = 0 or ΔL Z = ±1 amplitude in the mesonic transitions of the baryons.

Deep-inelastic scattering, partons and strong interaction ideas

The quark-parton model as applied to deep-inelastic lepton-hadron scattering is used as a laboratory model for the study of ideas encountered in strong interaction physics. First, two-component duality constraints are imposed on single-particle inclusive deep-inelastic distributions. In the target fragmentation region this involves a modification of the definition of the E functions introduced by Feynman. A duality relation connecting neutrino and electroproduction single-particle inclusive distributions is obtained. For ω → 1 and ω → ∞ we predict in the target fragmentation region an excess of π + over π − production for proton targets and an excess of π − over π + for neutron targets. For deuteron targets we find an excess of π − over π + for ω → 1. In our laboratory model we study the analogue of the problem of approach to Feynman scaling encountered in hadronic reactions and the related problem of exodicity criteria. We find that for large ω, in both fragmentation regions, Feynman scaling is reached from above. If ab is exotic, single particle inclusive distributions for any type of observed hadron are flat as a function of ω. For the production of fast hadrons in the fragmentation regions, even when ab is not exotic, cross sections are flat when ab c is exotic.

Duality and electron-positron annihilation at high energy

General constraints of duality are applied to annihilation processes e−e+→h + anything, where h stands for meson or baryon octets. We consider all planar dual terms, as well as a possible background contribution. The interrelation of duality and dominance of specific terms is investigated.

Duality constraints on quark parton model description of deep inelastic semi-inclusive and annihilation processes

Duality constraints on quark parton model description of deep inelastic semi-inclusive and annihilation processes

π0Photoproduction in a Weak-Regge-Cut Model

A weak-Regge-absorption model using $\ensuremath{\omega}$, $\ensuremath{\rho}$, $B$, and $H$ exchanges is applied to neutral pseudoscalar meson photoproduction and related reactions. The theoretical constraints of duality, SU(3), and vector dominance are imposed in order to simplify the model as much as possible. Satisfactory agreement is found, with a small set of free parameters, for all of the reactions considered.

Application of duality principles to deep inelastic reactions

We apply general constraints of duality to deep-inelastic structure functions in a systematic manner. In analogy with hadronic duality we admit two components: one being constrained to non-exotic SU 3 representations in two channels simultaneously, the other being a generalization of the pomeron effect. Our results can be best interpreted in terms of a quark-parton model with the usual valence quarks and a sea of SU 3-singlet quark-antiquark pairs, and we reproduce the results of that model without having to deal with quarks explicitly. On the theoretical side we give a statement of exchange degeneracy on the light cone, and we are led to a speculative connection between the pomeron effect and the matrix elements of the quark kinetic-energy tensor.

Duality Constraints on Inclusive Reactions. II. The Role of the Harari-Freund Conjecture

We present a scheme for the generalization of the two-component theory of Harari and Freund to multiparticle amplitudes and, in particular, to inclusive reactions. Our scheme is based on duality and borrows the terminology of dual perturbation theory but we do not restrict our generalizations to any specific model. We obtain a criterion for the absence of secondary (nonscaling) Regge contributions in inclusive reactions. We show how inclusive reactions may approach their limiting values from below, in contrast to total cross sections which always have positive secondary contributions. The scheme suggests a novel interpretation of diffraction dissociation which we discuss in a separate paper.

Backward scattering duality constraints and couplings of the ε-meson

Backward scattering duality constraints and couplings of the ε-meson