Showing papers on "Pseudoscalar published in 1972"

Partial-Wave Analysis of Spinor Bethe-Salpeter Equations for Single-Particle Exchange

Abstract: The Bethe-Salpeter equation for spin-$\frac{1}{2}$ particles is analyzed by the use of helicity amplitudes. Decomposition into partial-wave amplitudes reduces the equation into three subsets of eight coupled integral equations, one set for singlet states, one set for triplet states ($L=J$), and one set for the coupled triplet states ($L=J\ifmmode\pm\else\textpm\fi{}1$). Both positive- and negative-energy states are included. Matrix elements are written for interaction kernels that come from single-particle exchange. The cases treated are scalar, pseudoscalar, and photon exchanges. Detailed expressions are given in the general case when all particles are off the mass shell, both for the full Bethe-Salpeter equation and for all the partial-wave equations.

Six-dimensional formulation of meson equations

Abstract: The structure of the conformal group is studied by a generalisation of quaternion methods to six dimensions. Some simpleSO(4,2) covariant equations are shown to correspond to the Kemmer formulation for pseudoscalar and vector mesons, and the matrix elements of the irreducible representations of the Kemmer algebra are expressed as traces of products of Dirac matrices.

Nonlinear realizations of brokenSU 3 ×SU 3 for pseudoscalar mesons

Abstract: A nonlinear realization ofSU3×SU3 for the pseudoscalar mesons is constructed. First, theSU3×SU3 symmetry is broken, while keepingSU2×SU2 exact, by letting the K and η mesons acquire a mass. This model provides a generalization of K-π effective Lagrangians consistent with the Callan-Treiman relations. The symmetry is further broken toSU2×U1 by allowing the pion to have a mass. This is achieved through a one-parameter unitary transformation which has a structure similar to a generalized Cabibbo rotation. This « mass rotation » introduces a part which transforms as the « 27 » representation into the symmetry-breaking term. This term breaks the Gell-Mann-Okubo mode ofSU3 violation and leads to an alternative, accurate mass formula. Divergences of the currents are calculated in both broken-symmetry schemes.

Capture of μ−-mesons by polarized proton target

Abstract: Differential capture sections are calculated of longitudinally polarized or unpoiarizedμ −-mesons by polarized proton target of low order in weak (V, A, P)-interaction. It is shown that the presence of pseudoscalar interaction in the effective Hamiltonian results in the appearance in the angular distribution of neutrons emitted in the longitudinal capture of polarized muons polarized by proton target; the latter is characteristic for the interference term ∼cos2 θ but for high-energy right-polarizedμ −-mesons the capture section by unpolarzed or polarized protons is only proportional to G p 2 and may be used to determine the strength and the sign of the pseudoscalar interaction. It is also shown that in the (V-λA)-variant of the interaction between muon and nucleon currents the predictions of two-component and fourcomponent neutrino theory diverse.

a Relativistic Quark Model for Mesons Based on Numerical Solutions of the Bethe-Salpeter Equation.

Abstract: A study is made to determine if the results of the nonrelativistic quark model can be reproduced by a fully relativistic model of deeply bound spin - 1 2 quarks. It is found that the relativistic model does not reproduce the nonrelativistic results, even when the quarks have nonrelativistic momenta. However, the model is rather successful in accounting for the known properties of mesons. Numerical solutions to the Bethe-Salpeter equation are obtained for pseudoscalar and vector bound states of equal mass quark-antiquark pairs, with either a scalar, pseudoscalar, or neutral vector exchange interaction. The interaction function corresponds to single particle exchange, with the addition of either one or two regulating terms. It is found that the second regulator allows the internal quark momentum to be nonrelativistic, but that the spinor structure of the wave function remains highly relativistic. Only the scalar interaction can account for the observed spectrum of states. The pseudoscalar interaction yields a vector state of lower mass than the pseudoscalar state, and the vector interaction leads to a vector state which lies approximately one quark mass above the pseudoscalar state. The λ quark is taken as slightly heavier than the p and n, and the perturbation treatment of the mass difference leads to a quadratic mass formula. The decay amplitudes for π, K → μν are calculated, and it is found, independent of parameters, that ƒ π ≈ ƒ K for either a scalar or vector interaction, in agreement with experiment and in contrast with the nonrelativistic model. The amplitudes for ϱo, ω, φ → e+e−, μ+μ− are also calculated, but in this case the ratios (again parameter independent) are in minor discrepancy with experiment. The question of the additivity of quark amplitudes is examined by calculating (with significant restrictions) the magnetic moments of the vector mesons and the amplitudes for magnetic transitions such as ω → πoγ. The magnetic moments of the vector mesons have the same (trivial) ratios to each other as in the nonrelativistic model, but they are strongly enhanced over the sum of the quark magnetic moments. The amplitude for magnetic transitions, however, is related to the quark magnetic moments in approximately the same ratio as in the nonrelativistic model. The model is also used to obtain parameter dependent predictions for the masses and decay amplitudes. These predictions are not experimentally correct, but are generally well within an order of magnitude for a wide range of the parameters. The most significant defect discovered of the model is the presence of ghost states (the daughters of the vector mesons, with JPC = 0+−) with masses of about 2 BeV.

Polarization of Spin-1/2 Particles in Scattering Processes

Abstract: For a beam of spin-12 particles with definite momentum, a complete description of the spin state is provided by a single three-space vector, the polarization. This paper shows how the polarization-vector description provides a clear and vivid picture of spin effects in scattering processes. Explicit results are given for three types of interaction with a fixed source in first order: Coulomb, scalar, and pseudoscalar. The effect of a scattering is given by a vector-algebra formula, in which the final polarization is given in terms of the initial polarization and the momenta. In the Coulomb case, for example, the result of the scattering is that the polarization is rotated through an angle β about the normal to the scattering plane, in the same direction that the momentum is rotated. The rotation of the polarization is less than that of the momentum and the lag angle is given by cos(θ−β) = 1 − [(m/E) tan;12θ]21 + [(m/E) tan;12θ]2 where E is the electron energy and θ is the scattering angle.

Exchange-degenerate and exotic trajectories in a multiperipheral model with veneziano-type production amplitudes.

Abstract: The implications of duality and absence of exotics are investigated in a multiperipheral model of pseudoscalar meson-meson scattering. An exchange-degenerate leading trajectory is obtained besides low lying ones in exotic and non-exotic channels.

New scalar and conserved vector currents in dual-resonance models

Abstract: S U1.1 invarianee of an ampl i tude guarantees i ts dual character (1), while conformal invariance allows the elimination of all ghosts (~). Faetor izable dual models are buil t from irreducible fields ~d,~ Of the conformal group in two dimensions (3). The ~Yd,t'S are labelled by their dimension d and eonformal spin j. In this let ter , s tar t ing from conformal scalar and spinor fields, we present a new class of dual models of scalar and vector currents. Our work stems from the notion (a) tha t off-shell mesons (currents) are emit ted from the interior of the Kova-Nielsen disc, while on-shell mesons are emit ted from the unit circle. We choose to work in the upper half-plane Z = X ~ iY , which is simply related to the Nambu-Susskind str ip w = ~ ~i0 by the mapping Z = e% Let us consider two d= ] : 0 fields tha t obey the eonformally invar iant Laplace equation (~2/~Z~Z) q~,= 0 (***)

Multiperipheral bootstrap model withSU3 multiplets

Abstract: The ABFST multiperipheral bootstrap model, studied recently by various authors withSU2 multiplets (ρ and f mesons etc., exchanged between π-mesons), is enlarged to useSU3 multiplets (octets of vector mesons, nonets of tensor mesons etc., exchanged between octets of pseudoscalar mesons). It is found that this increases the effective strength of the interaction slightly, but not enough to yield output trajectories with the correct intercepts. The calculation appears to yield f and f′ trajectories but no pomeron trajectory. Exchange degeneracy is broken for the output trajectories in this type of model in which an interaction potential is iterated, and this seems to be a serious difficulty.

Nonlinear chiral lagrangians and the ΔI=1/2 rule

Abstract: A nonlinear chiral Lagrangian with symmetry breaking describing vector, pseudovector and pseudoscalar mesons is constructed. The weak currents deduced via field-current identities are used to compute to zeroth order in (mπ2/mρ2) the K → 2π decays. The ΔI=1/2 rule is found to hold and an estimate for the mass of the intermediate vector boson is given.