Dual-resonance Amplitudes Research Articles

Regge Spectra of Charmed Baryons in Dual Resonance Amplitudes

Regge Spectra of Charmed Baryons in Dual Resonance Amplitudes

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.

Old and New Mesons in Dual Resonance Amplitudes and PCAC

Old and New Mesons in Dual Resonance Amplitudes and PCAC

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.

Dynamical Theory of Hadron Interactions Based upon Extended Particle Picture. I: Basic Formulation and Its Application to - Scattering

A dynamical theory of hadron interaction is developed and applied to π-π scattering by taking the extended particle picture as its basis. It is shown that if the excitation energy is not so large, the motion of an extended particle can be described by two kinds of variables describing respectively the quark-like mode and the string-like mode. Thus our model allows us to derive the dual-resonance amplitude for particles with arbitrary spin,unitary spin, etc. according to the first principle . The actual form of the model is severly restricted by requiring the covariance under an arbitrary transformation of the Lagrange coordinate labeling each material point of the body, and we are led to the following predictions: δ 0 /δ 2 =-2, a 0 /a 2 =-2, where δ 0 (δ 2 ) and a0 ( a2 ) denote respectively the phase shift of the D -wave and the scattering length of the S -wave for I =0(2).

A dual description of the reactions K±p → K*0π±p for incident momenta from 2.7 to 12.7 GeV/cfor incident momenta from 2.7 to 12.7 GeV/c

A model is considered in which the reactions K±p → K*0π±p are simultaneously described in terms of a dual five-point function forp-wave exchanges plus dual-resonance amplitudes for pion exchange and pomeron exchange. Various versions of the model are considered. A convenient parametrization of the imaginary parts of Regge trajectories is introduced. Four free parameters are adapted to obtain good agreement with a vast amount of experimental data, containing effectivemass and four-momentum transfer distributions. These cover the incident-momentum interval from 2.7 to 12.7 GeV/c, and have been subjected to a variety of kinematical cuts in the different experiments which are taken into account in the analysis. Total cross-sections and their composition in terms of contributions of the various amplitudes are predicted. The Q-bump is reproduced out of K*(1420), diffraction dissociation of the K-meson (Q(1300)) and also nondiffractive pion exchange background. The L-bump is shown to be particularly sensitive to interference between pomeron exchange and the remaining part of the amplitude.

Symmetric vertex couplings for all spins and parities

Interaction Hamiltonians for three particles having arbitrary spins and parities are constructed based on the rather stringent requirement of permutation symmetry. There are only two free parameters in each Hamiltonian: an overall coupling constant and a scaling parameter (identified as the inverse slope of a Regge trajectory). Vertex functions are evaluated in lowest order purturbation theory and their use in formulating Reggeized scattering amplitudes is reviewed. In the particular case of three normal-parity bosons the calculated vertex functions coincide with the vertices extracted from a 6-point dual resonance amplitude. The results presented here may be used, for example, to predict the two-body decay characteristics of resonances and, in a more theoretic vein, to serve as a base upon which to build dual resonance amplitudes for particles of all spins and parities.

How to calculate low-energy partial-wave parameters of dual resonance amplitudes

It is shown that the low-energy parameters for all classes of dual, elastic scattering amplitudes can be readily derived by simple use of Rodrigues's formula for the Legendre polynomials.

On the connection between smoothed and narrow-resonance discontinuities of dual-resonance amplitudes

It is shown, for the case of the beta-function and the Bardakci-Ruegg five- and six-point functions, that the high-energy « smoothed » and « narrow resonance »s-channel discontinuitiesΔ′ andΔ are asymptotically equivalent in the sense that in both the Regge and deep inelastic domains lim\(\mathop {\lim }\limits_{n \to \infty } \int\limits_{n - \frac{1}{2}}^{n + \frac{1}{2}} {dss^\lambda } \Delta /\int\limits_{n - \frac{1}{2}}^{n + \frac{1}{2}} {dss^\lambda } \Delta ' = 1\) for all realλ.

Single-particle spectra at fixed angle and duality

A dual resonance amplitude with satellites is applied in order to study the inclusive reactions a + b → x + anything at high energies and at fixed c.m.s. angle of the produced particle. Comparing the asymptotic expansion in this deep inelastic region with the one in the triple-Regge region, it turns out that the contributions of the satellite terms can be expressed by a function which is the same, but which appears with different arguments, in both limits. On the basis of this relationship between small- and large-angle scattering, a dependence of the shapes of single-particle distributions at large angles on the quantum numbers of the channel (a x ) can be predicted.

A new derivation of the off-shell dual-resonance amplitudes

A new derivation of the off-shell dual-resonance amplitudes

Physical States, Spurious States and Projection Operator in the Dual Resonance Model

Physical states of each mass level of the dual resonance amplitudes are completely characterized. Ghost states in the physical states are extracted from the parent, the first daughter and the second daughter trajectories. There exist six particles with positive metric and only one particle with negative metric at each level on the second daughter trajectory. Some geometric properties of the projection operators are studied. The investigations are made throughout for general cases where α(0)≪0.

The Veneziano transform and the high-energy behavior of dual-resonance amplitudes

The Veneziano beta-function transform technique is generalized to the case in which there are several asymptotic variables. The multiple transform of a dual-tree amplitude is found to be again a dual-tree amplitude apart from a well-defined redefinition of the trajectories. The asymptotic behavior of dual amplitudes is discussed, with particular emphasis on the analytic structure in the complex-angular-momentum like plane.

Functional-Integral Approach to Dual-Resonance Theory

It is shown that dual-resonance amplitudes can be expressed in terms of rudimental amplitudes defined by functional integrals which correspond to transition amplitudes of quantum-mechanical systems of strings with imaginary time. The equivalence between the path-integral and operator formulation of quantum mechanics is used to establish the connection between this approach and the usual operator approach. The factorization of rudimental amplitudes is studied to obtain the Feynman-like rules for dual-resonance amplitudes. This allows us to express $N$-Reggeon vertices in terms of rudimental amplitudes, and to determine the propagator, which is shown to be the usual spurious-free twisted propagator. $N$-loop orientable diagrams are calculated. In general, the functional integrals considered can be calculated by solving appropriate Neuman's boundary-value problems of corresponding bounded Riemann surfaces. This provides a generalization of the analog model to the case of external Reggeons which are described by extended momentum distributions on the boundaries.

Unstable particle and a dual-cut model

The unstable-particle solution has been obtained from the Bethe-Salpeter equation. The solution is connected with a timelike potential, and is due to a continuous cut contribution. A dual-cut model has been introduced, and the scattering amplitude is obtained by adding a series of dual-cut amplitudes to the dual-resonance amplitude.

The dual-resonance model with unequal intercepts

The dual-resonance operator formalism is extended to the case of unequal intercepts in all channels. By imposing factorization we get a parametrization of the Regge trajectories and are forced into a quark picture of the dual model. Whereas some of the operators of the theory remain unchanged in the unequal-intercept case, others such as the gauge operator are modified. These modifications have effects that reinforce our quark interpretation of the dual-resonance amplitude. Ghost compensation on the first daughter trajectory is still valid providing certain conditions on the quark « masses » are satisfied. Finally, anSU1,1 analysis of theN-point amplitude is displayed by couplingN «vertex fields», each with differentSU1,1 spin, to anSU1,1 scalar.

Dual-Resonance Amplitude as a Generalization of Feynman's Propagator

With the aid of the dual four-position fields, the Veneziano amptlitude is shown to have a functional integral representation whose prototype is found as the conventional Feynman propagator. The method of dual positions leads us to the boundary-value problem of Dirichlet's type and enables us to decompose easily the Koba-Nielsen kernel in correspondence with a factorization of the corresponding physical process.

Unitarization of the Dual-Resonance Amplitude. III. General Rules for the Orientable and Nonorientable Multiloop Amplitudes

We complete the Kikkawa-Sakita-Virasoro unitarization scheme for the dual-resonance amplitude by presenting the nonorientable and overlapping multiloop amplitudes. We also present rules for writing down arbitrarily mixed planar, nonplanar, nonorientable, and overlapping multiloop amplitudes by inspection.

Dual Resonance Amplitude Corresponding to Globular Feynman Diagrams

Following the conjecture on the correspondence between the dual resonance amplitude and the very high order Feynman diagram, we calculate the dual resonance amplitude cor­ responding to the globular Feynman diagram. We find that it develops essential singularities in the Lorentz-invariant variables. It has been suggested by several authors 1 l' 2 l that amplitudes in the dual res­ onance model can be obtained by taking the continuum limit of the F eynman amplitudes corresponding to the very high order planar diagrams. It seems rather peculiar that only the planar Feynman diagram can lead to the dual reso­ nance amplitude. In general any Feynman diagram can be drawn in a three­ dimensional topological space. However, we need higher dimensional topolo­ gical spaces in order to discuss the continuum limits of the very high order Feynman diagrams. For example, the Klein-bottle-like Feynman diagram can be drawn in the three-dimensional space before taking the continuum limit. But, once we take the continuum limit, we need the four-dimensional space to draw

Off-mass-shell extrapolation of the dual-resonance amplitude

A still open quest ion in the t heo ry of dual-resonance models is how to ex t rapola te the dual ampl i tude off t he mass shell (1). The p rob lem is par t icu la r ly re levant if we believe tha t currents , scalar and pseudoscalar densi t ies are domina ted by resonances, so tha t any dual ampl i tude involv ing quant i t ies of this k ind should na tura l ly p rov ide an ex t rapola t ion off the mass shell (2). In this l e t t e r we propose an off-mass-shell ex t rapola t ion of the dual-resonance ampl i tude . L e t us give a precise defini t ion of dual-resonance ampl i tude off the mass shell. By this we mean a func t ion of all the subenergies s i , . . i a = (k 1 + .. . § k~) ~, including the ex te rna l masses si = k~, which