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  1. On the axial vector current and PCAC in the σ-model

    Maurer, R. H. ; Willey, R. S. - Annals of Physics
    Here an explicit operator construction of the axial vector current in the boson σ model is given in perturbation theory. This current is finite and satisfies the PCAC condition with the renormalized pion field. It also (at least formally) satisfies the SU2 × SU2 equal-time time-component current algebra.

  2. SU3 mass differences in fifth interaction and tadpole results

    Goyal, Ashok - Nuovo Cimento, A
    Here we examine the medium strong mass splittings for pseudo-scalar mesons, vector mesons and spin-2/3 baryons in the framework of the «fifth interaction» proposed by Ne’eman. In addition to the resonance contributions from the low-lying states, we write an expression for the contribution from f8 Regge exchange in terms of contributions to electromagnetic mass differences from $$\text{A}^0_2$$ Regge exchange. Assuming that the $$\text{A}^0_2$$ Regge pole gives the correct contribution to the e.m. mass differences, we estimate the contribution of the f8-meson. In the approximation of neglecting the continuum spectrum, the ratio of tadpole contributions is given by the ratio ofmore » coupling constants of the f8-meson with hadrons. The results of the tadpole model are in agreement with the subtraction scheme of Segrè. We also find that in the presence of such anSU3-symmetry-breaking term, the renormalization of the hadronic weak-strangeness-changing vector current vertex, to second order in such a term, is quadratically divergent.« less

  3. Field-Theoretic Model of High-Energy Scattering. III. Inelastic Electron-Proton Scattering

    Fried, H. M. ; Gaisser, T. K. - Physical Review. D, Particles Fields
    In this study, a field-theoretic model of soft, neutral-meson production is used to bracket recent deep-inelastic electron-proton scattering data.

  4. Eikonal Model for Large-Angle $np$ and $pp$ Elastic Scattering

    Fried, H. M. ; Raman, K. - Physical Review. D, Particles Fields
    An eikonal model is described for large-angle $np$ and $pp$ elastic scattering at medium energies. Further, each amplitude is parametrized as a sum of one-boson exchanges modulated by the multiple virtual emission of soft neutral $$I$$=0 and $$I$$=1 vector mesons. Fits to the data are presented.

  5. Current-Commutator Derivation of Mass-Difference Relations

    Goyal, Ashok ; Li, Gino Fong ; Segrè, Gino - Physical Review. D, Particles Fields
    Here we investigate the consequences of the vanishing of certain double commutators to examine the consistency of SU⁡(3) × SU⁡(3)-breaking models. We also calculate the contribution to ΔI = 2 mass differences of isospin-violating terms other than the electromagnetic interactions, in the Hamiltonian.

  6. Field-Theoretic Model for High-Energy Scattering. II. Regge and Non-Regge Damping in πN Scattering

    Fried, H. M. - Physical Review. D, Particles Fields
    A field-theoretic formulation of πN scattering, combining soft virtual neutral vector-meson exchange with simple nucleon, 3-3 resonance, and ρ poles, is shown to produce damped amplitudes containing both fixed and Regge poles, yielding polarizations and differential cross sections with a qualitative resemblance to recent experiments.

  7. Application of a Relativistic Resonance Formula to the e+⁢e-→π+⁢π- Experiment

    Parkinson, Michael - Physical Review. D, Particles Fields
    The present data for the reaction e+⁢e-→π+⁢π- are analyzed with the aid of a general effective-range resonance formula for the ρ meson. It is concluded that (a) mρ = 769 ± 5 MeV and Γρ = 109 ± 10 MeV provide a reasonable explanation of the present experimental points; (b) the full width at half-maximum regardless of the peak height should give an excellent estimate of the ρ width; (c) it is hard to escape $$|F_π$$$$(m_ρ$$$$^2|$$^2$ $$= m_ρ$$$$^2$$$$/Γ_ρ$$$$^2$; (d) the effects of final-state interactions on resonance shape ought to be investigated.

  8. A dynamical derivation of meson mass formulae

    Pakvasa, S. ; Papastamatiou, N. J. - Nuovo Cimento, A
    Using asymptotic SU(3) and superconvergence relations, the ω-φ mixing angle is determined and mass formulas for pseudoscalar and vector mesons are derived.

  9. Analyticity Properties of the Meson-Deuteron Elastic-Scattering Amplitudes at Low Energy

    Ando, Fujio ; Feldman, David - Progress of Theoretical Physics, Supplement
    A dispersion-theoretic treatment of the elastic scattering at low energy of mesons by deuterons is presented. The loosely bound nature of the deuteron results in small anomalous thresholds of the scattering amplitudes in the t channel and justifies the use of selected Feynman diagrams in the determination of the general analyticity properties of the amplitudes. The impulse approximation, binding corrections, and multiple-scattering terms are defined in terms of both triangle and box diagrams, and the dispersion relations with fixed s for these terms are derived by the method of analytic continuation with respect to the deuteron mass and with respectmore » to s. Further, it is found that the anomalous parts of the deuteron-baryon vertices play important roles in the derivation of the dispersion relations, and that the double-scattering amplitudes have no complex singularities. The general method has been applied to a determination of the angular distributions for π+d and K-d elastic scattering. In the former case, the binding correction due to N*3/2 is the main correction to the impulse approximation. In the latter case, the impulse approximation has been determined in terms of the $$\overline{K}$$N scattering amplitudes which are approximated by two complex poles.« less

  10. Theory of Low-Energy π ω Scattering

    Kang, Kyungsik - Physical Review
    The πω problem, as the simplest case of the pseudoscalar-meson and vector-meson system, is discussed from the standpoint of the S-matrix approach. A general procedure of constructing invariant amplitudes in spin and isospin space of the pseudoscalar-vector system is given, and for πω scattering, a set of invariant amplitudes are conveniently chosen and their crossing properties are discussed. These amplitudes are expressed by one-dimensional representations which are derived from the Mandelstam representations by the Cini-Fubini technique. Partial-wave expansions as well as projections are done by the use of the Jacob-Wick helicity amplitudes. A prescription for calculating the driving forces frommore » the exchange of particles is presented and applied to the exchange of the ρ and B mesons in states of the two possible quantum numbers JP =1+ and 2–. The procedure consists of a zero-width approximation to the transition amplitudes in states of given J and L, crossing-symmetric relations, and the one-dimensional dispersion representations of the invariant amplitudes. The relationship between the invariant amplitudes and the helicity amplitudes greatly facilitates this procedure. The t-channel reaction is also analyzed. A method of solution of the partial-wave dispersion relations is discussed based on a recently developed formalism, and is extended further to avoid the difficulty associated with the zeros of the driving forces. A systematic program to understand the quantum numbers of the B meson as a πω resonance is also discussed. The qualitative nature of the forces due to the B exchange in states of each possible quantum number is briefly sketched. Finally, a model calculation which favors a 2– state of the B meson is presented.« less
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