Dual Amplitude Research Articles

Triple-Pomeron couplings in dual models

By examining the dual amplitudes for external Pomerons in the triple-Regge region, we extract the triple-Pomeron couplings ${g}_{\mathrm{PPP}} (t)$ corresponding to the dual models of Veneziano and of Neveu and Schwarz. We also verify the expected central region plateau in Pomeron production and isolate the ${p}_{\ensuremath{\perp}}$ dependence.

Dual Amplitudes with Two Off-Shell Lines

An integral-representation is explicitly established for the dual-resonance amplitudes with two off-the-mass-shell states which interact with several unexcited states within the framework of Schwarz's off-shell dual scalar (orbital) theory. The procedure to be employed is based on a functional-integral method and shares its most steps in common with those of the functional method used in the on-shell theory: One crucial difference is the presence of the Carrigan-Fairlie boundary condition. The main ingredients of the formula are compactly written in terms of Jacobi's theta functions which also play a judicious role in other various stages of the present formulation. The representation established is shown to be valid only when the intercept of the leading trajectory is one and the transverse degree of space-time dimensions is twenty-four. It is also demonstrated how our amplitudes reduce to the totally on-shell Bardak'ii-Ruegg amplitudes if both of the two-off-shell particles are put on the ground state shells: We also obtain the amplitudes with one off-shell line in the course.

Towards a Satisfactory Invariant Measure of Dual-Resonance Amplitudes

An attempt is made, in the context of the integral representations of the four-point dual amplitudes, to lower the critical degree of space-time dimensions on which dual amplitudes are established. The critical dimension and the intercept of the leading Regge trajectory are determined by an invariancy (under a dual operation) of a differential form (including a volume element), which thus plays a role of measure. A derivation is given of a measure a la Nahm which yields the worldly dimensions in such a way that it appears as a natural generalization of that of the Neveu-Schwarz model, hence still suffering from a presence of tachyon. Its relevancy is studied within the simplest case of two off-shell dual amplitudes. Also specified is the modular group associated with the new volume element. The volume element points to a new pair of the fermi-type dynamical fields, whose construction has not, however, been tried.

Old and New Mesons in Dual Resonance Amplitudes and PCAC

Old and New Mesons in Dual Resonance Amplitudes and PCAC

Dual amplitudes of baryonium interaction

It is shown that the interaction of the M 0 J-baryonium can be described by Brower-Goddard dual amplitudes with n=3, where n is the dimension of “Koba-Nielsen” variables.

Functional Method for the Off-Shell Dual Amplitudes

By adopting Corrigan and Fairlie's interpretation of the off·the·mass·shell states of Schwarz, we give a general framework to establish the dual amplitudes for off·shell particles in terms of purely functional-integral formalism. In our framework, the amplitudes with one·particle off-shell are derived, whose representation is of the Bardak~i-Ruegg type, only when the number of effective dimensions is 24 and the intercept of the leading trajectory is one. There is an involved problem around the effective dimensionality (in connection with the integration measure), but the origin of magic number 16 of Schwarz is undiscovered.

Asymptotic energy scale factors for pseudoscalar meson scattering and charmed meson couplings

Energy scale factors ν 0 for PP → PP scattering amplitudes are related via the absence of exotic resonances to ratios of tensor to vector coupling strengths. These same ratios are extracted from FESR's for non-exotic reactions. The scale factors obtained are all of the order of 1.0 GeV 2 or less, independent of quantum numbers. This contradicts the expectations of dual amplitudes in which ν 0 = 1/ α′, and trajectory slopes are smaller for charmed mesons. Decay widths for tensor mesons are predicted. An observed SU(3) violation for the ratio A 2 → K K / K ∗∗ → Kπ is shown to be consistent with the FESR results. Charmed meson decays are predicted to be factors of 2–3 larger than those predicted by SU(4).

Regge spectra, symmetry-breaking effects, and decays of old and new mesons in dual resonance amplitudes

Single-term Veneziano dual amplitudes with nondegenerate Regge slopes are examined in detail. Factorization of parent resonance residues and the equal-spacing rule extracted from the universal-slope case are used to determine all the leading-meson-trajectory parameters in terms of that of the $\ensuremath{\rho}$. Relations between nondegenerate slopes and SU(4)-symmetry-breaking effects are discussed. The predicted meson mass spectra and the partial decay widths into two pseudoscalars are shown to agree well with data for the cases in which data exist.

Constraints on reggeon amplitudes from analyticity and planar unitarity

Using planar dual amplitudes as a guide, we discuss some features of reggeon amplitudes which are relevant in the context of the topological expansion. We look into the analytic properties and, in particular, discuss the validity of finite-mass sum rules for reggeon-reggeon scattering. We investigate the form taken by planar unitarity when a multiperipheral assumption is added. The integral equations obtained are not of the standard Chew-Goldberger-Low type. We find that pure pole-type solutions (i.e. without Regge cuts) to planar unitarity are possible in a way consistent with the symmetry and factorization properties of reggeon-reggeon amplitudes. The appearance of “good” FMSR in the unitarity integrals follows from a careful treatment of phase space — all possible configurations are counted uniquely — and is crucial in achieving the cut cancellation. Throughout the paper we emphasize various subtle points that have been overlooked in the literature.

A Survey on Dual Tree and Loop Amplitudes

A Survey on Dual Tree and Loop Amplitudes

The structure of dual green functions

We exhibit a simple relationship between the position space and momentum space singularity structure of off-shell dual amplitudes. This scheme is naturally described in terms of amplitudes which couple to the external sources via pairs of “confined” states.

Phenomenological description of the reaction [formula omitted] using a dual fermion model

Using the Neveu-Schwarz-Ramond model as a starting point, attempts have been made to construct a phenomenological dual amplitude for the reaction K − p→ K ∗0(890)(π − p) . The amplitude contains trajectories of both natural and unnatural spin-parity in the exchange channel as well as N α, N γ and Δ trajectories in the production channel. Furthermore, it has the correct Regge behaviour in both meson and fermion channels. Reasonable agreement between the predictions and the data with respect to differential cross sections and density matrix elements has been found.

New Representation of Gauge Operator and Off-Mass-Shell Dual Amplitude

A new representation for gauge operators of a dual model with L-gauge is used for constructing off-mass-shell dual amplitude. The essential point is the inclusion of linear terms in newly introduced scalar mode operators into the gauge operators. By the use of Schwarz's method the off-mass-shell state and its ghost free scattering amplitudes are constructed for any space-time dimensions including 4. Integral representations of some off-mass-shell amplitudes turn out to be well-defined.

ππ and π– p → π0n Scattering in a Multiple-Reggeon-Cut Dual Absorptive Model

A dual absorptive amplitude, in which s-channel resonances are generated by summing up t-channel n-Reggeon cuts, is constructed. Adjusting the two free parameters of the model in the resonance region of π π scattering, the various π π differential high energy cross sections are calculated. The model is also applied to π N charge exchange, where a fit to the high energy data is obtained even without Reggeon-Pomeron cuts

Impact parameter analysis of DAMA

Dual amplitudes with Mandelstam analyticity (DAMA) are analysed in the impact parameter plane. The consequences of elastic unitarity and duality are exhibited by studying the behaviour of the transformed amplitude in thes andb variables. An example is given where the features of the model, relevant to phenomenological applications, are discussed.

TVVandTTPcouplings and related strong and electromagnetic decays of tensor mesons

Equations for $\mathrm{TVV}$ and $\mathrm{TTP}$ couplings are derived from dual amplitudes for the processes $P+V\ensuremath{\rightarrow}P+V$ and $P+T\ensuremath{\rightarrow}P+P$. The couplings are expressed in terms of other mesonic couplings, known from experiment. With the aid of these couplings we calculate the decay rates of ${A}_{2}\ensuremath{\rightarrow}\ensuremath{\omega}\ensuremath{\pi}\ensuremath{\pi}$, $f\ensuremath{\rightarrow}\ensuremath{\rho}\ensuremath{\pi}\ensuremath{\pi}$, ${K}^{**}\ensuremath{\rightarrow}{K}^{*}\ensuremath{\pi}\ensuremath{\pi}$ and the electromagnetic decays ${A}_{2}$, $f\ensuremath{\rightarrow}V\ensuremath{\gamma}$,, and $\ensuremath{\gamma}\ensuremath{\gamma}$.. The calculated rates for ${A}_{2}\ensuremath{\rightarrow}\ensuremath{\omega}\ensuremath{\pi}\ensuremath{\pi}$ and $f\ensuremath{\rightarrow}\ensuremath{\rho}\ensuremath{\pi}\ensuremath{\pi}$ are smaller (by about a factor of 4) than the average experimental data. This discrepancy is analyzed in terms of a consistent picture for all the decays studied in this paper.

Simple quark-duality-diagram description ofn−pcharge-exchange scattering

A precise one-parameter fit has been made to $n\ensuremath{-}p$ charge-exchange data in the non-pion region [$|t|\ensuremath{\ge}0.2$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$]. The dual amplitude corresponds to a simple quark duality diagram for baryon-baryon scattering. The exotic trajectory in such a description provides a large Regge scale factor for the $\ensuremath{\rho}\ensuremath{\omega}f{A}_{2}$ exchange, so that the experimentally observed effective trajectory is flat.

Dual four-point functions

The properties of a phenomenologically useful dual amplitude and its similarity with composite-particle scattering amplitudes are discussed. (AIP)

The superoperator formalism of the Neveu-Schwarz-Ramond model

The Neveu-Schwarz-Ramond model is rewritten in terms of a new operator formalism where the old ones are combined into superoperators, i.e. we will use an extra set of variables, anticommuting Grassman variables, besides the usual Koba-Nielsen variables to describe external legs in dual amplitudes. We show that many formulae become more compact and transparent and find an operator formalism closer to a spinning string picture. We also show that the fermion emission vertex appears in a more natural way in a formalism like this.

Nucleon exchange: A simple description

It is shown that the high-energy behaviour of exclusive and inclusive processes dominated by nucleon exchange can be described by simple forms suggested by dual amplitudes. The energy, momentum transfer and mass dependences of the differential cross sections are reproduced. The value of the triple-Regge NNF coupling is obtained. The role of MacDowell partners and of exotic exchanges are discussed.