Current Algebra Approach Research Articles

Review of current algebra results in the weak decays of the metastable hadrons

Without claiming completeness the main achievements in the applications of the current algebraic approach to weak decays are surveyed.

Four-body semileptonic decays of hyperons

The rates of four-body semileptonic hyperon decays are calculated, using Cabibbo theory and current-algebra techniques. Observation of such decays cannot be expected until the number of observed hyperons has increased by a factor 10–100. The corrections to the pure current-algebra approach are found to be considerable.

Current Algebra and Photoproduction of Pions

A low-energy theorem from current-algebra techniques is employed to derive an expression for the pion photoproduction amplitude which is shown to be gauge invariant. The low-energy predictions for the differential cross sections and the multipole amplitudes are analyzed extensively and compared with the experimental data. The predictions for the production of charged pions are in as good agreement with experimental data as those of dispersion theory are. However, the current-algebra predictions for $\ensuremath{\gamma}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}p$ characteristically differ from other theoretical models, especially at threshold. Accurate low-energy experimental data for this process should therefore provide a test of the validity of the current-algebra approach.

K ℓ3 decay form factors and current algebra

The form factors in K ℓ3 decay are discussed in a current algebra approach by writing unsubtracted dispersion relations for the matrix elements of suitable retarded commutators between single particle states and vacuum, at (arbitrary) fixed linear combination of the two momentum transfers. This allows us to include the contributions of all the relevant poles and a consistent solution of the current algebra equations is then possible.

Superconvergent Dispersion Relations and Pion-Nucleon Sum Rules

Both the Adler-Weisberger sum rule and the spin-flip sum rule for pion-nucleon scattering have been derived from superconvergent dispersion relations for weak amplitudes. Our basic assumption is that the weak axial-vector-nucleon scattering amplitude ${{T}_{\ensuremath{\mu}\ensuremath{\nu}}}^{A}$ approaches the weak vector-nucleon scattering amplitude ${{T}_{\ensuremath{\mu}\ensuremath{\nu}}}^{V}$ at high energies. This allows us to write down superconvergent dispersion relations for certain invariant amplitudes in the decomposition of ${T}_{\ensuremath{\mu}\ensuremath{\nu}}={{T}_{\ensuremath{\mu}\ensuremath{\nu}}}^{A}\ensuremath{-}{{T}_{\ensuremath{\mu}\ensuremath{\nu}}}^{V}$. We then use the hypotheses of partially conserved axial-vector current and of conserved vector current to obtain pion-nucleon scattering sum rules while avoiding the ambiguities of the $q\ensuremath{\rightarrow}0$ limit which is usually used in the current-algebra approach. We also discuss sum rules for ${G}_{A}({q}^{2})$ away from ${q}^{2}=0$.

Photopion production from nucleons

We study the low energy behavior of the S- and P-wave multipoles corresponding to the isoscalar and symmetric isovector amplitudes for the process γ + N → N + π using certain current algebraic techniques developed in an earlier paper. All terms up to and including those which are quadratic in the pion momentum are evaluated for the real parts of the multipoles. A comparison of our techniques with those of Chew, Goldberger, Low, and Nambu is carried out and some general conjectures regarding the current algebra approach to low-energy phenomena are presented. The difficulties encountered in extending this approach to the antisymmetric, isovector photoproduction amplitude are indicated.

Low-Energy Constraints on Pion Production Amplitudes inπNScattering

Using the hypothesis of the partially conserved axial-vector currents, and specific assumptions on the equal-time commutators of these currents, a calculation of the pion production amplitude near threshold of the $\ensuremath{\pi}N$ system has been attempted. The resulting matrix elements are contrasted with those obtained previously by other means, and a comparison with existing data on the total reaction cross section is made. Agreement is favorable for the energy range considered. Unlike previous studies of the production amplitudes where direct $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ interactions are thought to play a substantial role, the present calculation ignores all possibilities of strong $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ effects, and incorporates only those $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ scattering effects required by the consistency of the current-algebra approach. The evaluation of these contributions requires some assumptions on the equal-time commutators of pseudoscalar and scalar densities. Finally, suggestions are made on extensions of the present approach based on resonance models.

Final-State Interaction Effects in the Algebra-of-Currents Approach to the Three-Pion Decay Modes ofηandKMesons

The current-algebra approach to $K\ensuremath{\rightarrow}3\ensuremath{\pi}$ and $\ensuremath{\eta}\ensuremath{\rightarrow}3\ensuremath{\pi}$ decays is simply modified to take account of final-state $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ interactions. Expressions are obtained for the relevant branching ratios in terms of certain assumed analytic forms for the $I=0$ $S$-wave $\ensuremath{\pi}\ensuremath{\pi}$ scattering phase shift. It is shown how this mechanism may help to explain the anomalously low $\frac{(\ensuremath{\eta}\ensuremath{\rightarrow}3{\ensuremath{\pi}}_{0})}{(\ensuremath{\eta}\ensuremath{\rightarrow}{\ensuremath{\pi}}_{+}{\ensuremath{\pi}}_{\ensuremath{-}}{\ensuremath{\pi}}_{0})}$ branching ratio without disturbing the "good" current-algebra results.

A limitation on the use of current algebra techniques for meson decays

It is shown that for decays involving only 1− particles and an odd number of 0− particles, the current algebra approach is not useful.

Vector-Meson Dominance and Current Algebra in the Parity-Violating Nonleptonic Decays ofKMesons and Hyperons

As far as the parity-violating nonleptonic decays of $K$ mesons and hyperons are concerned, many of the results obtained from the algebra of currents can be understood in a completely trivial manner using vector-meson dominance without recourse to the current commutation relations. In particular, we show that the current-algebraic approach applied to an octet Hamiltonian supplemented by the hypothesis of the universal spurion coupling leads to exactly the same physical consequences as the ${K}^{*}$-dominance model of Lee and Swift. We also indicate how a vector-meson-dominance model of nonleptonic decays may emerge out of a current-current interaction involving neutral as well as charged currents.

On the production of isobars in a current algebra approach

Relations between off-mass-shell amplitudes for reactions of the type: γ (real or virtual) + proton → baryon resonance + vector meson are derived on the basis of the partial conserved tensor current hypothesis. An off-mass-shell gauge condition for the amplitudes of these processes is established.

Strong interaction dynamics with vertices invariant under the collinear group

The consistency of a dynamical theory, fulfilling analiticity and unitary, with vertices invariant under the collinear subgroup of SU 6 is demonstrated for low energy pion processes. The relation is pointed out to the current algebra approach. The question of the correct definition of the unstable particle couplings is clarified.