Current Algebra Approach Research Articles

Radiative partial width of A1 in current-algebra approach.

The width for A/sub 1/..--> pi gamma.. is calculated in a current-algebra approach and is found to be consistent with its recent experimental estimate.

Current algebra approach to conformal invariant two-dimensional models

A critical chiral QFT in 1 + 1 dimensions is determined by conformal and internal symmetry properties of the basic fields. The free parameters multiplying the Schwinger terms in the current and stress-energy tensor commutators are related in a non-linear fashion. For a semi-simple (compact) internal symmetry group, the effective coupling constant is found to be a (computable) integer number.

Boson-Fermion equivalence in a two-dimensional anomalous chiral model

A current algebraic approach is taken to realise the two-dimensional chiral model having anomaly analogous to that of Wess and Zumino. The conserved currents are shown to be a combination of bosonic and fermionic ones. The equations of motion of the fermions are realised through its commutation algebra with the Sugawara-like energy-momentum tensor. Quantisation of the anomaly parameter is shown to be a consequence of consistent statistics.

Current algebra and PCAC-application to p̄p→ K+K-π0π0π0

Current algebra and the partially conserved axial-vector current (PCAC) hypothesis are employed to arrive at the amplitude for the emission of three neutral soft pions in the annihilation process p-bar p to K+K-. All final-state pi - pi scattering effects coming out of the current-algebra approach are taken into account. The differential rate for the process is normalised to the rate of the original reaction without the soft pions. Branching ratios w(pp to K+K- pi 0 pi 0 pi 0)/w(pp to K+K-) are computed for different centre-of-mass energies. A comparison with the existing experimental data is made and the agreement is found to be reasonable.

η→3πdecays and theρηπcoupling constant

An approach to the eta..-->..3..pi.. decays based on eta-..pi../sup 0/ mixing and resonant final-state interactions is presented. It successfully accounts for the experimental data and circumvents the difficulties of the traditional (current-algebra) approach. The value for the G-parity-violating coupling constant Vertical Barg/sub rhoetapi/Vertical Bar = 0.067 +- 0.013 is deduced from the data.

Current Algebra Approach to Tensor Meson Decays

Current Algebra Approach to Tensor Meson Decays

Current algebra applied to properties of the light Higgs boson

We present a general current algebra approach to the study of the new light Higgs boson h. In particular we apply it to the Weinberg-Salam model for both standard and non-standard Yukawa couplings. The partially conserved axial-vector current for his explicitly constructed and used to calculate its mass and lifetime.

Non-Leptonic decays of hyperons in the quartet model

The non-leptonic hyperon decays are investigated in the framework of the colored quartet model with GIM current. We take two octet components of the weak Hamiltonian which belong to 15 and 20″ representations of SU(4) symmetry. The 15 Hamiltonian arising from the symmetry breaking is assumed to have the universal spurion coupling. We obtain remarkable fits to s- and p-wave amplitudes both in the current algebra approach and the dispersion theory. It is shown that the standard arguments for s-wave decays based on the K ∗ pole dominance, on the duality arguments and on the current algebra lead to different physical consequences with one another.

An improved determination ofG A(x) from single-π+ electroproduction

We analyse recent threshold π+ electroproduction data by combining the current algebra and PCAC approach with a simple model-independent parametrization of the ratio σ L /σ T . Adopting the traditional dipole fit for the nucleon axial-vector form factorG A(x), we findM A=(0.96±0.19) GeV, in agreement with neutrino results.

Octet dominance in nonleptonic decays

The question of octet enhancement for the nonleptonic decays is studied within the framework of a current-algebra approach. By writing an unsubtracted dispersion relation for the matrix elements 〈 B k | H w | B j 〉 and 〈 M k | H w | M j 〉 ( B denoting a 1 2 + baryon and M a 0 − meson) in the momentum transfer squared variable t and using the assumption of threshold dominance, namely that two pseudoscalar meson states dominate the absorptive parts of the above matrix elements and that in the chiral limit the meson-baryon and meson-meson scattering amplitudes which enter in the absorptive parts are exactly given by current algebra low energy theorems, it is shown that the above matrix elements are octet enhanced without assuming the octet transformation property for H w . Further it is shown that the d′ f′ ratio for the octet enhanced matrix elements 〈 B k | H w | B j 〉 satisfies the relation ( d′ f′ ) = ( 3 10 )[( 3( f d ) A 2 −1) ( f d ) A] , where ( f d ) A denotes the f d ratio of the axial vector current baryon couplings. The implications of this result for the s- and p-wave hyperon non-leptonic decays are discussed.

Current-Algebra Approach to Landau's Quantized Hydrodynamics

Landau's quantized hydrodynamics is derived from the microscopic Hamiltonian, which is written in terms of the density and velocity operators. In Euler's equation for the velocity operator, the force per unit mass has a form different from Landau's and is given explicitly in terms of the two-body potential. A quantum pressure term, which does not occur in Landau's theory, also appears. New realizations of the density and velocity operators are given which satisfy the commutation relations, but must act in a Hilbert space larger than Fock space. It is shown that the formalism is without meaning in Fock space owing to the nonexistence of certain operators.

Kl3 form factors from current algebra

Including some straightforward consequences of analyticity and unitarity in the hard-meson current algebra approach, predictions are made for Kl3 decays with a minimal set of assumptions. Consequences of a possible disagreement between theory and experiment are discussed. Making additional assumptions about the convergence properties of certain spectral functions, we derive the relationFπ2=FK2 without PCAC, pole dominance of spectral functions or a specific type ofSU3×SU3 symmetry breaking.

Nonleptonic Hyperon Decays in a Current-Current Quark Model

The symmetric quark model is used to provide an explanation of the $S$- and $P$-wave non-leptonic hyperon decays. The current-algebra approach, applied to the current-current weak Hamiltonian constructed of Bose-type quark fields, leads to a remarkable agreement with experiment.

Theory ofΩ−Decay

The ${\ensuremath{\Omega}}^{\ensuremath{-}}$ nonleptonic decays are investigated in the framework of a chiral Lagrangian model. In this way, ambiguities of extension of meson momenta to zero which are present in the current-algebra approach are made explicit. We find that these decays may possess a rather complicated structure and a discussion of approximation schemes is given which may help to explain the present experimental data. The approximation of the $\ensuremath{\Xi}2\ensuremath{\pi}$ decay mode by ${\ensuremath{\Xi}}^{*}\ensuremath{\pi}$ is also discussed.

Chiral-symmetry breaking from pion-nucleus low-energy scattering

The study, via current algebra sum rules, of the systematic dependence of π−-nucleus elastic-scattering lengths on both mass number and isobaric spin can offer a way to discard, on an experimental basis, a (1, 8)⊕(8, 1) behaviour of theSU3⊗SU3 symmetry-breaking Hamiltonian, together with a further check of the validity of the current algebra approach to low-energy meson processes.

Phase space, fibre bundles and current algebras

The purpose of this paper is to extend into phase space the cellular description introduced by Bohmet al. (1970) and to show how this may help to give an understanding of the current algebra approach to elementary particle phenomena. We investigate this cellular structure in phase space in some detail and show how certain features of the structure may be described in terms of the mathematics of fibre bundle theory. The frame bundle is discussed and compared with the Yang-Mills theory. As a result of this discussion we are able to introduce generalised currents which are related to the duals of the curvature forms, and these are shown to span the Lie algebra of a sub-group of the structure group of the frame bundle. We then discuss the implications of these results in terms of our cell structure. By assuming that the de Rahm cohomology, defined by the curvature forms and their duals, reflect a cohomology on the integers defined on the original cell structure, we show that the currents and ‘curvature’ can be given a meaning in terms of a discrete structure. In this case the currents only span a Lie algebra in some suitable limit, implying that a description using Lie algebras is only an approximation.

Consistency condition for the A 1ϱπ system from unitarized current algebra

Using recent attempts to incorporate unitarity into the current-algebra approach additional information on the A 1 ϱπ system is obtained. When the resulting consistency condition is applied to the original hard-pion model of Schnitzer and Weinberg, the parameter δ, which is related to the magnetic moment of the A 1 meson, can be determined. The result turns out to depend crucially on the exact value of gϱ, the coupling constant of the isovector current to the ϱ-meson.

Mass quantization conditions from infinite superconvergence and chiral symmetry

The single-particle approximation implies the vanishing of all moments of scattering amplitudes which are exotic in thet-channel. These conditions are shown to be consistent with a class of amplitudes which do not identically vanish. A special class of such amplitudes is that of Veneziano. When supplemented by the Adler condition in the presence of a soft pion, such amplitudes do vanish periodically int and give rise to mass quantization conditions. Contact is made with the current-algebraic approach used in a previous work.

Hard-kaon and -pion calculations of the decays K A → K ϱ and [formula omitted

The strong decays K A → K ϱ, K ∗π are discussed in a current algebra approach by writing unsubtracted dispersion relations for the matrix elements of appropriate retarded commutators of currents or current divergences between single-particle states and vacuum, at (arbitrary) fixed linear combination of the two momentum transfers. This enables us to retain the pole contributions from both the variables. Moreover, the various form factors appearing in the calculation are allowed to satisfy at most once-subtracted dispersion relations and are treated on equal footing. The current algebra method is used to set up sum rules among the coupling constants and the subtraction constants without using the hypothesis of partial conservation of axial current. Their solution allows us to calculate the partial-decay widths as well as the Weinberg sum rules are rederived as self consistency conditions.

Theory ofΩ−Decay

The ${\ensuremath{\Omega}}^{\ensuremath{-}}$ nonleptonic decays are investigated in the framework of a chiral Lagrangian model. In this way, ambiguities of extension of meson momenta to zero which are present in the current-algebra approach are made explicit. We find that these decays may possess a rather complicated structure and a discussion of approximation schemes is given which may help to explain the present experimental data. The approximation of the $\ensuremath{\Xi}2\ensuremath{\pi}$ decay mode by ${\ensuremath{\Xi}}^{*}\ensuremath{\pi}$ is also discussed.