Veneziano Type Research Articles

Geometric transitions, Chern–Simons gauge theory and Veneziano type amplitudes

We consider the geometric transition and compute the all-genus topological string amplitudes expressed in terms of Hopf link invariants and topological vertices of Chern–Simons gauge theory. We introduce an operator technique of 2-dimensional CFT which greatly simplifies the computations. We in particular show that in the case of local Calabi–Yau manifolds described by toric geometry basic amplitudes are written as vacuum expectation values of a product vertex operators and thus appear quite similar to the Veneziano amplitudes of the old dual resonance models. Topological string amplitudes can be easily evaluated using vertex operator algebra.

Unified treatment: analyticity, Regge trajectories, Veneziano amplitude, fundamental regions and Moebius transformations

In this paper we present a unified treatment that combines the analyticity properties of the scattering amplitudes, the threshold and asymptotic behaviors, the invariance group of Moebius transformations, the automorphic functions defined over this invariance group, the fundamental region in (Poincare) geometry, and the generators of the invariance group as they relate to the fundamental region. Using these concepts and techniques, we provide a theoretical basis for Veneziano type amplitudes with the ghost elimination condition built in, related the Regge trajectory functions to the generators of the invariance group, constrained the values of the Regge trajectories to take only inverse integer values at the threshold, used the threshold behavior in the forward direction to deduce the Pomeranchuk trajectory as well as other relations. The enabling tool for this unified treatment came from the multi-sheet conformal mapping techniques that map the physical sheet to a fundamental region which in turn defines a Riemann surface on which a global uniformization variable for the scattering amplitude is calculated via an automorphic function, which in turn can be constructed as a quotient of two automorphic forms of the same dimension.

Pion form factor in large Nc QCD

The electromagnetic form factor of the pion is obtained using a particular realization of QCD in the large $N_c$ limit, which sums up the infinite number of zero-width resonances to yield an Euler's Beta function of the Veneziano type. This form factor agrees with space-like data much better than single rho-meson dominance. A simple unitarization ansatz is illustrated, and the resulting vector spectral function in the time-like region is shown to be in reasonable agreement with the ALEPH data from threshold up to about 1.3 ${GeV}^2$.

Dynamical loops in D = 1 random matrix models

Abstract We discuss adding “quarks” to random matrix models. We then study the Veneziano type random matrix model in D = 1. It is found that there is no spontaneous tearing of the world sheet. If we instead take dynamical loops according to Kazakov in D = 1, a phase structure similar to that of D = 0 occurs. The loops are necessarily generated by bosonic “quarks”.

Quark sea and stringlike non-Abelian gauge field contribution to Hadron states

I t is desirable to construct the dynamical model of hadrons based on their intrinsic structure. Recently, NAMBU (~) gave very instructive talks on his idea of quark confinement by way of proving the equivalence of string model (2,3) and non-Abclian gauge theory (4,6). In this approach it is essential to consider the vacuum as the matter (e). His efforts were devoted to the development of earlier ideas of electric confinement (7,s). IGI (9) has succeeded in including the new particle family (10) in the dynamical model of Veneziano type by relaxing the duali ty requirement in the resonance region, assuming its recovery at infinite energies (Ii). The purpose of this paper is to explain at first the apparent discrepancy of observed Regge slopes for different hadron families by reinterpreting the BCS-like gap in the coloured quark level. The many degrees of freedom associated with the coloured gauge gluons may also play the fundamental role in this mechanism. In the second place we show that the relative probability of quark seas (~2) in the hadron bags of each Regge family may be related to the Regge slopes. In this t reatment the stringlike nature of non-Abelian gauge gluons is essential in the statistical mechanical sense. In what follows the apparent dismateh of Regge slopes may be reduced to the structure of associated quark sea of the relevant hadron. The parameters specifying that probability and Reggc slope are determined by making use of available information.

Duality sum rules in e+e− annihilation from canonical trace anomalies

One of the most puzzling results of deep inelastic experimentation in the last few years is the large cross-section of e+e- annihilation into hadrons (~). The almost constant cross-section observed is in marked disagreement with the pointlike behaviour expected theoretically on the basis of scaling. The question thus arises as to whether there is complete break-down of scaling or it is postponed to much higher energies. Adopting this latter point of view, we show in this letter how in the framework of the canonical trace anomaly of the energy-momentum tensor the asymptotic value of the ratio R = a(e+e--~hadrons)/~(e+e-->~+~-) can be related to the low-energy behaviour of a(e+e - -~hadrons) through a general duality principle which we derive explicitly. Some time ago we proposed (~) a simple model in which sealing is built up by a series of resonances of Veneziano type in which this duality principle between /~ and low-energy parameters is verified. Explicitly we found i~ = 8n~//~ ~ 2.5. A similar treatment by SAKURAI (a) gives numbers between 3 and 5, but, as we shall show later, a more accurate analysis will confirm the value of :R given above. Recently from a completely different point of view T]~RAZAW~ (~) has determined the anomaly of PCDC (partial conservation of dilatation current) Ward identity using conventional vector-meson dominance of real photons and found for R a value of 16~/]~. (t) B. ]3ARTOLI, F. FELICETTI, H. OGREI~ r, V. SILVESTRINI, G. MARI~I, fi_. IGRO and F.VAI~OLI: Phys. Rev. D, 6, 2374 (1972); C. B~-ooI, G. I~ G. SALVI~I, B. STELLA, m. BALDI~I CELIO, G. CAPOI~, C. ]~ENOUOOINI, G. P. MURTAS, M. SPn~ETTI and A. ZALLO: Phys. Le~., 44 B, 533 (1973); F. CERADINI, M. CO~VERSI, S. D'A~GELO, L. PAOLUZI, R. S.<XTO~ICO and R. VISENTII~r: Phys. Lelt., 47 B, 80 (1973); M. GRILLI, E. IAROCOI, P. SPILLANTII~rI, V. VALEN'TE, R. VISENTI~k r, B. BORGIA, F. CERADIN'I, ~I. CONVERSI, L. PAOLUZI, B. SANTONICO, ~[. NIGRO, L. TRASATTI and G. T. ZORX: Nuovo Cimento, 13A, 593 (1973);  LITKE, G. HAI'r A. HOF:VIAN, J. KOCK, L. LAW, M. E. LAW, J. LEONG, R. :LITTLE, R. M.C-DARAS, H. NEWI~IA~, J. M. PATERSON', R. PORDES, K. STRAUCH, G. TARNOFOLSKY and R. WILSON ; Phys. Rev. Left., 36, 1189 (1973); M. BERXARDII~I, D. BOLLI~I, P. L. BRUNIN'I, E. FIORENTINO, T. WASSAM, L. MOI~AOI, F. PAL.~IO~ARI, F. RIMONDI and A. Zio!~r[om: Phys. Lett., 51 B, 200 (1974); W. CmxowsKr: invited talk presented at the IV International Con]erence on Experimental Meson Spectroscopy, Boston, Mass., 1974. (~) A. BRAMOI% ~. ETI~ and iVL GR]~OO: Phys. Lett., 41 B, 507 (1972); M. GRECO: Nucl. Phys., 63 B,

Galilean subdynamics and the dual resonance model

Dynamics in Minkowski space is discussed in terms of an eight-parameter extended Galilei group, a subgroup of the Poincar\'e group. This method---Galilean subdynamics---is developed and discussed in detail and applied to the construction of two explicit models having four-point amplitudes of the Veneziano type. There are no difficulties with unphysical states.

The Electromagnetic Form Factors Based on the Theory of Meromorphic Functions

The electromagnetic form factors (EMFF) are investigated by taking into account an infinite set of vector mesons which appear on the daughter trajectories. A general form of EMFF follows from the Hadamard theorem on a meromorphic function of order ρ. The Veneziano type EMFF is a meromorphic function of order one. We show that physically acceptable orders are either ½ ≤ρ≤1 or ρ= 0. Asymptotic n-power (n: integer) behaviour is possible only if ρ= 0.

Final State Interactions in the Veneziano Model

The final state interactions parametrized by a scattering length and a low energy reso­ nance are considered in the Veneziano type model. The resulting amplitude is shown to satisfy the unitarity equation approximately in the low energy region. The high energy behavior of the amplitude is examined. It is concluded that the correct high energy behavior is maintained in the model.

Pion vertex functions from the spurion model and Veneziano formula

F r o m the Veneziano formula (1) for the process pr: -> ST:, where the spurion S carries the q u a n t u m numbers of the vacumn, NAMIKI and 0I~BA (~) were able to obtain an expression for the pion vec tor form factor . This was achieved by taking the l imit of the ampl i tude whel~ the f o u r m o m e n t u m of the spurion te~ds to zero a t a fixed value of t. The resu l tan t Venez ianotype ve r t ex funct ion looks like

Final State Interactions in the Veneziano Model

The final state interactions parametrized by a scattering length and a low energy resonance are considered in the Veneziano type model. The resulting amplitude is shown to satisfy the unitarity equation approximately in the low energy region. The high energy behavior of the amplitude is examined. It is concluded that the correct high energy behavior is maintained in the model.

TheK¯KΠN¯N-amplitude in a Veneziano type model with spin

The generalized Veneziano Model has been applied by Chanet al. to the processes (K¯KΠN¯N) with very impressive results, but in this treatment baryon spin was neglected. In this work we give a covariant spin and isospin decomposition of the above class of processes. Postulating factorization at the lowest meson and baryon poles and using the very stringent duality diagram prescription we are led to a Veneziano type ansatz for the various invariant amplitudes.

Unitarity at Threshold and Veneziano-Type Form Factors for Mesons

A simple form of Veneziano type form factors is investigated and applied to Kwdecay form factors. The p-wave part is determined by using the unitarity condition at thresh­ old and the Veneziano model for scattering amplitudes. The PCAC condition and the broken chiral symmetry with current commutation relations are used for determining the s­ wave part. The results arefKif~f+ (0) =1.24 and~= -0.15. Suura's method is also applied and shown to give fKif~f+ (0) = 1.41.

On a derivation of a Veneziano-type representation for two-body processes including baryons

It is shown that, for the πN scattering case, the replacement of the usual partial wave expansion by an expansion in terms of Appell-Pochhammer polynomials can provide an unambiguous Veneziano type representation, if some consistency relations between the dominant Regge trajectories are required. A possible interpretation of those relations, leading to a mass-quantization formula for hadrons, is discussed and compared with experiment.

Perturbation theory, finite-energy sum rules and a generalized Veneziano representation

The problem of the derivation of the Veneziano type representation is considered on the basis of an auxiliary integral parametric representation of scattering amplitudes satisfying unsubtracted dispersion relations.

A new approach to the Reggeon calculus (I)

A new approach to the Reggeon calculus is formulated with the aid of Veneziano type functions to represent the Reggeon amplitudes. The singularities of signatured partial wave amplitudes are obtained from an analysis of integrals written in terms of Sudakov variables. No ad hoc assumptions about the significant region of integration are needed. As an example the singularity structure is derived corresponding to iterated Regge cuts.

Structure of Hadrons. II. Nonplanar Diagrams

Using the harmonic-oscillator model for hadrons, in which any hadron is described by two quarks embedded in a one-dimensional harmonic continuum, and allowing quanta to couple to either quark, we were able to construct the full crossing-symmetric Veneziano type of amplitude in the tree-graph approximation. This generalization also gives us a set of rules to compute the nonplanar single-loop diagrams.

The Veneziano Model and Chiral Algebra inπA1Scattering

We construct a model of the Veneziano type for $\ensuremath{\pi}{A}_{1}$ elastic scattering. We find that the imposition of factorization determines the model almost completely in terms of models for $\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ and $\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\rightarrow}\ensuremath{\pi}{A}_{1}$; and that the mere existence of a model for $\ensuremath{\pi}{A}_{1}\ensuremath{\rightarrow}\ensuremath{\pi}{A}_{1}$ constrains the model for $\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\rightarrow}\ensuremath{\pi}{A}_{1}$. An off-shell continuation of the model consistent with the hard-pion formalism is given. The combination of this continuation with the constraint mentioned above ensures that the "constants" multiplying the Veneziano functions must depend explicitly on the four-momentum squared of the particle off the mass shell; and that the Adler consistency condition is satisfied by the vanishing of these constants at zero four-momentum rather than by a condition on the trajectory function or the external masses.

Treatment of πN → K Λ and πN → K Σ with a Veneziano type model

We study the processes πN → K Λ and πN → K Σ and the corresponding crossed reactions KN → πΛ and KN → πΣ simultaneously. We make a simple Veneziano type ansatz for the invariant amplitudes of these processes with only three free parameters in each case. In each isospin channel, there is at most one (possibly degenerate) trajectory, together with its daughters. Veneziano terms for which there is no allowed duality diagram are omitted. The parameters can be chosen such that the high-energy data (magnitude and slope of forward and backward peak) fit well. With these parameters the resonance spectrum in all channels is described satisfactorily. Parity doubling of baryon resonances occurs. However, the parity partners which are not seen so far turn out to have very small widths as a result of kinematic suppression. The products of partial widths of the well-known Y o, Y 1 and Δ-resonances are found to be in good agreement with experimental data.

Vector-pseudoscalar scattering and the veneziano model

We attempt to construct a representation in a Veneziano type model of the amplitude for vector-pseudoscalar scattering, taking into account the constraints imposed by parity and crossing.