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Showing papers on "Pseudoscalar published in 1968"


Journal ArticleDOI
TL;DR: In this article, the authors investigated the behavior under SU3×SU3 of the hadron energy density and the closely related question of how the divergences of the axial-vector currents and the strangeness-changing vector currents transform under SU 3×SU 3.
Abstract: We investigate the behavior under SU3×SU3 of the hadron energy density and the closely related question of how the divergences of the axial-vector currents and the strangeness-changing vector currents transform under SU3×SU3. We assume that two terms in the energy density break SU3×SU3 symmetry; under SU3 one transforms as a singlet, the other as the member of an octet. The simplest possible behavior of these terms under chiral transformations is proposed: They are assigned to a single (3,3*)+(3*,3) representation of SU3×SU3 and parity together with the current divergences. The commutators of charges and current divergences are derived in terms of a single constant c that describes the strength of the SU3-breaking term relative to the chiral symmetry-breaking term. The constant c is found not to be small, as suggested earlier, but instead close to the value (-sqrt[2]) corresponding to an SU2×SU2 symmetry, realized mainly by massless pions rather than parity doubling. Some applications of the proposed commutation relations are given, mainly to the pseudoscalar mesons, and other applications are indicated.

1,475 citations


Journal ArticleDOI
TL;DR: In this article, a nonlocal coupling is introduced by considering thej-th partial-wave projection of an inhomogeneous Bethe-Salpeter equation in the ladder approximation (exchange of mass-κ scalar boson).
Abstract: We are concerned with vertex functions to be used in the peripheral model and treat the vertex of two pseudoscalar mesons coupled to a spin-j resonance. A nonlocal coupling is introduced by considering thej-th partial-wave projection of an inhomogeneous Bethe-Salpeter equation in the ladder approximation (exchange of mass-κ scalar boson). An approximate resonance solution of this equation is expressed in terms of the first Fredholm determinants, and vertex functionsV j are derived. By interpolating between several partial waves according to the Regge model we arrive at the form factorV j /V 0, which for relative momentum |P|→0 or for κ→∞ (local coupling) turns into the Born-term vertex function (∞|P| j ) and for |P|/κ→∞ goes to 1. ThisV j /V 0 we call a kinematical form factor, because it is equal to 1 forj=0. In the case of peripheral processes with pseudoscalar-meson exchange it corresponds to the nonrelativistic penetration factor considered by Durr and Pilkuhn (1). But moreover it can be continued analytically into the crossed channel corresponding to, spin-j exchange peripheral processes. The mass κ is a fitting parameter.

41 citations


Journal ArticleDOI
P. Narayanaswamy1, A. Pagnamenta1
TL;DR: In this article, the Bethe-Salpeter equation for a fermion-antifermion system for the dynamical generation of a bound state via the exchange of a pseudoscalar particle leads to a set of coupled integral equations for the stateJP=0− and a system of eight for 1−.
Abstract: The Bethe-Salpeter equation for a fermion-antifermion system for the dynamical generation of a bound state via the exchange of a pseudoscalar particle leads to a set of four coupled integral equations for the stateJP=0− and a system of eight for 1−. It is argued that physically sensible solutions exist only after the introduction of a cut-off. These equations are solved with high accuracy by expanding the invariant amplitudes in terms of hyperspherical harmonics and then retaining the lowestn contribution only. It is found that for weakly bound systems the 1− state is always lighter than the 0− while for strong couplings the situation is reversed. Considering this solution as a relativistic quark model to form mesons as quark-antiquark bound states, the ratio 4∶1 between the masses of the vector and the pseudoscalar mesons occurs for quark masses of about two nucleon masses. For the case of scalar particles we obtain an algebraic perturbation formula which is very accurate in the limit of small exchange masses.

26 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that a vector meson field should be proportional to the corresponding current if the bare meson mass is infinite, provided the bare masses are both infinite.
Abstract: Using a finite form of local field equations some consequences of infinite mass renormalization are studied in a rigorous manner. The method is applied to various models. For pseudoscalar meson-nucleon interaction sufficient conditions are given for the equivalence to a direct Fermi coupling. Confirming a recent result byKroll, Lee, andZumino it is shown that a vector meson field should be proportional to the corresponding current if the bare meson mass is infinite. In the conventional treatment of neutral vector meson theories this causes certain difficulties which are analyzed in detail. In case of two vector fields coupled to the same current it is found that the fields must be proportional provided the bare masses are both infinite. In the Appendix finite local field equations are discussed for the coupling of a neutral vector meson field to the current of a spin 1/2 field.

16 citations


Journal ArticleDOI
TL;DR: In this article, the authors considered the unified field theory of Heisenberg and co-workers in the framework of Bethe-Salpeter dynamics and proposed a non-canonical quantization procedure, which predicts the existence of spin-parity 0− mesons, a strongly bound family of solutions: a pion triplet, an eta singlet and a kaon doublet.
Abstract: The unified field theory of Heisenberg and co-workers is considered in the framework of Bethe-Salpeter dynamics. The approach suggests, in contrast to the Tamm-Dancoff formulations, the use of a Green’s function involving the baryon mass, in order to rectify deficiencies in the analytic properties of solutions hitherto found. On the basis of a noncanonical quantization procedure, the theory predicts the existence of two families of spin-parity 0− mesons,a) a strongly bound family of solutions: a pion triplet, an eta singlet and kaon doublets, supporting previous results of the unified field theory, andb) a new family of nearly degenerate mesons in the proximity of the baryon mass. The dynamical theory of the mutual baryon-baryon coupling constants to the pseudoscalar mesons is presented. The results are compared to experiment where available. It is pointed out that the dynamical solutions possess superconducting properties. In particular, the dynamical results for the pseudoscalar meson masses can be interpreted in analogy to the gap equations which arise in many-body fermion systems.

14 citations


Journal ArticleDOI

13 citations


Journal ArticleDOI
TL;DR: In this article, the authors proposed to extend the Cabibbo theory to the radiative leptonic decays by extending Vaks and Ioffe's relation for π→l+νl+γ showing that it is a good approximation for all physical values of the momentum transfer.
Abstract: We propose to extend the Cabibbo theory to the radiative leptonic decays As an application, we study the π(K)→l+νl+γ decay The axial part is determined by using conservation of electromagnetic current and assuming A1-dominance For the vector part, assuming ρ-dominance, we extend Vaks and Ioffe's relation for π→l+νl+γ showing that it is a good approximation for all physical values of the momentum transfer Furthermore, we show that the relative phase between the vector and axial parts can be determined The available experimental data on π→e+νe+γ are compared with the predictions

11 citations


Journal ArticleDOI
TL;DR: In this article, a universal vector and axial-vector interaction theory is proposed for strong-interaction phenomena, which leads to a definite relation between vector and pseudoscalar coupling constants, which predict the S- and P-wave pion-nucleon scattering lengths.
Abstract: A primary universal vector and axial-vector interaction theory is proposed for strong-interaction phenomena. It is shown that such a hypothesis leads to a definite relation between vector and pseudoscalar coupling constants, which predict the S- and P-wave pion-nucleon scattering lengths, in good agreement with experiments. The ratio of π-meson to ρ-meson masses is also predicted, which agrees well with the observed value.

8 citations



Journal ArticleDOI
TL;DR: In this article, the authors investigated low-energy pseudoscalar-meson-pseudoscalarmeson scatterings in terms of the forward dispersion relations and showed that there exists one general feature common to the scattering amplitudes in the nonet states, namely, that the effective-range functions decrease rather rapidly above threshold.
Abstract: The low-energy pseudoscalar-meson-pseudoscalar-meson scatterings are investigated phenomenologically in terms of the forward dispersion relations. Using the scattering lengths given by the current algebra, it is shown that there exists one general feature common to the scattering amplitudes in the nonet states, namely, that the effective-range functions $(\frac{2p}{W})cot\ensuremath{\delta}$ decrease rather rapidly above threshold. It is suggested that this behavior can be explained by assuming the existence of a zero in the scattering amplitude. Another argument which requires these nonet zeros is given in the framework of the theory of complex angular momenta.

3 citations


Journal ArticleDOI
TL;DR: In this paper, the strong decays of baryonic resonances 32− in baryons and pseudoscalar mesons were studied in the framework of SU(3) symmetry.

Journal ArticleDOI
Hugh Osborn1
TL;DR: In this article, the vanishing of renormalization constants Z3 and Z1 as conditions for compositeness is examined from the viewpoint of dispersion theory and field theory, and the theory of a pseudoscalar field coupled to a spinor field is examined in detail.

Journal ArticleDOI
TL;DR: In this article, the decay of K20 → 2γ is studied in the framework of a pole model with vectors and axial particles as poles, and the usual treatment which considers only intermediate pseudoscalar particles is considered.
Abstract: The decay K20 → 2γ is studied in the framework of a pole model. In addition to the usual treatment which considers only intermediate pseudoscalar particles, we also discuss models with vectors and axial particles as poles.

Journal ArticleDOI
TL;DR: In this article, the general Regge-pole formalism for axial mesons was developed in detail, and the effects of possible meson mixings were examined under SU3 and exchange degeneracy.
Abstract: The reactions pseudoscalar+nucleon→axial+nucleon and pseudoscalar+nucleon→axial+3/2+-resonance, are discussed. The general Regge-pole formalism is first developed in detail. It is subsequently specialized in the following steps: i) production near the forward direction, ii) validity ofSU3 (with breakings for meson mixings); iii) validity of exchange degeneracy. Two nonets of produced axial mesons are considered: theA-nonet (JPC=1++) and theB-nonet (JPC=1+−) and the effects of the possibleA-B mixings are examined. The most specific model, assumingSU3 and exchange degeneracy, gives rise to a large number of restrictions (mostly inequalities) among cross-sections which should be testable. The value ofD/F for the couplings of theR-trajectories to nucleons is a relevant unknown parameter; we calculate its value in the kinetic supermultiplet model for a possible indication. The problem of KA-KB interference is discussed and the implied shape of the K* mass spectra is examined.

Journal ArticleDOI
TL;DR: The relativistic Schrodinger equation is applied to the multichannel problem of pseudoscalar meson-baryon scattering in the two lowest partial waves as discussed by the authors, and actual physical masses are used in the calculation so that SU3 symmetry is broken.
Abstract: The relativistic Schrodinger equation is applied to the multichannel problem of pseudoscalar meson-baryon scattering in the two lowest partial waves. Actual physical masses are used in the calculation so thatSU3 symmetry is broken. The potential is obtained by computing allowed single-particle exchange processes for which the exchanged particles have spin less than or equal to 3/2, following some simple rules. The model accounts for most of the experimentally known baryon resonances in these partial waves.


Journal ArticleDOI
TL;DR: In this paper, the symmetry breaking based on Okubo's ansatz is considered to modify Weinberg's spectral function sum rules (particularly the second), and the modified sum rules are applied to the chiral $U(3)$ and obtain physically interesting results for the mass relation and mixing angles of the vector mesons, a nonet assignment of the axialvector mesons and the decay constants of the pseudoscalar mesons.
Abstract: The symmetry breaking based on Okubo's ansatz is considered to modify Weinberg's spectral-function sum rules (particularly the second). We then apply the modified sum rules to the chiral $U(3)\ifmmode\times\else\texttimes\fi{}U(3)$ and obtain physically interesting results for the mass relation and mixing angles of the vector mesons, a nonet assignment of the axial-vector mesons, and the decay constants of the pseudoscalar mesons.


Journal ArticleDOI
TL;DR: In this paper, a tadpole model for non-leptonic decays based on a scalar κ field proportional to the divergence of the strangeness-changing vector current-density, and on the pseudoscalar mesons π and K satisfying PCAC, is studied by use of the current-algebra and spectral function sum rules.
Abstract: A tadpole model for the nonleptonic decays based on a scalar κ field proportional to the divergence of the strangeness-changing vector current-density, and on the pseudoscalar mesons π and K satisfying PCAC, is studied by use of the current-algebra and spectral-function sum rules. A reasonably good fit to the hyperon decay data is obtained.


Journal ArticleDOI
M.A. Ahmed1
TL;DR: In this paper, the authors derived a number of sum rules from the axial-vector current with a pseudoscalar density and derived a value for the coupling constant to nucleons of the "hypothetical" σ-meson.


Journal ArticleDOI
TL;DR: In this paper, the vector-meson exchange force is assumed to be SU3 symmetric, and the S11 resonance is interpreted as a bound state of the KΣ system.
Abstract: Several very interesting effects have begun to manifest themselves in the difficult data analysis of πNS-waves. All of these involve the influence of inelastic channels coupled to πN. Since the σ-exchange force has been very successful in the understanding of the low-energy phenomena, it seems worth-while to pursue the implications of this force to higher energies in a many-channel formalism. Wyld has done this in a Schrodinger model; here it is undertaken in a dispersion theory framework. All of the relevant pseudoscalar meson-baryon channels are included and the vector-meson exchange force is prescribed to beSU3 symmetric. For degenerate masses a bound unitary singlet and two degenerate bound octets occur. For physical mass splittings only oneS11 resonance survives. A curious extinction phenomenon suppresses the ππN component in the wave function of the resonance so that it does not show up strongly in ππN clastic scattering. TheS11 resonance is found at 1690 MeV and is interpreted as a bound state of the KΣ system.

Journal ArticleDOI
TL;DR: In this article, the production of neutral vector and pseudoscalar mesons in a quark model is studied and the mixing-angle-dependent and mixingangle-independent sum rules are compared with experiment.
Abstract: The production of neutral vector and pseudoscalar mesons is studied in a quark model. The mixing-angle-dependent as well as mixing-angle-independent sum rules are obtained and compared with experiment. For pseudoscalar mesons both possibilities, namely, ν-Xo and E-ν mixing, are discussed and using the present model, expected cross-sections for E-production in π−p (π+n) processes are calculated.

Journal ArticleDOI
TL;DR: In this article, the collinear production of a vector meson is considered in the scattering of pseudoscalar mesons on baryons, and relations between the experimental quantities, following from the symmetry [SU(3) ⊗SU (3)]coll, are obtained.
Abstract: The collinear production of a vector meson is considered in the scattering of pseudoscalar mesons on baryons. Relations between the experimental quantities, following from the symmetry [SU(3) ⊗SU(3)]coll, are obtained.


Journal ArticleDOI
Ahmad B. Khalil1
TL;DR: In this paper, an approximate bootstrap solution for the mass of degenerate vector mesons and their SU(3)-invariant coupling to degenerate pseudoscalar mesons is presented.

Journal ArticleDOI
TL;DR: In this paper, an extensive comparison of the O(31)-model with experimental information was made and the fit which obtained is quite good and the SU(3) symmetry breaking is described in much better agreement with experiment than in an approach which, instead of O( 31)-form factors, takes only the correct threshold behavior into account.
Abstract: The notion of dynamical groups [1] has been introduced into hadron physics in order to relate amplitudes of particles of many different spins In particular the O(31)-model of BARUT and KLEINERT [5a, 6] gives the pseudoscalar form factors of all the strange and non-strange baryons in terms of a few adjustable coupling constants and claims that they furnish a good approximation in the region of not too large physical momentum transfers Here we report on an extensive comparison of this O(31)-model with experimental information For one such comparison we take the known partial decay widths [7] of baryon resonances into members of the nucleon and pseudoscalar meson octet The fit which we obtain is quite good and the SU(3) symmetry breaking is described in much better agreement with experiment than in an approach which, instead of O(31)-form factors, takes only the correct threshold behavior into account Further we look at baryon decays with two final mesons and calculate theoretical Dalitz-plots Very good agreement with some recent results on Δ(1920) Δ Kπ is achieved Finally we give some closed functional form for the form factors which approximate the complicated O(31) form factors well in the region relevant for phenomenological calculations

Journal ArticleDOI
TL;DR: In this article, a modification of the quark model for annihilation permits the calculation of the relative probabilities of all observed channels with pseudoscalar mesons, and agreement with the experimental data on proton-antiproton annihilations at rest into three and more mesons is obtained.
Abstract: A modification of the quark model for annihilation permits the calculation of the relative probabilities of all observed channels with pseudoscalar mesons. Agreement with the experimental data on proton-antiproton annihilations at rest into three and more mesons is obtained.