Chiral Algebra Research Articles

Sum rules for the mixing angles of the baryons in SU(3) ⊗ SU(3) chiral algebra at infinite momentum

Under the assumption that axial charges couple the baryon octet only to one-particle states belonging to 1, 8, 10 SU(3) representations, sum rules for the mixing angles of the baryon wave function are derived. The results obtained from their saturation are in good agreement with the known electromagnetic properties of nucleons.

Current Algebra, Vertex Functions, and Decay Widths ofK*,Q, andφMesons

Ward identities are set up for three-point functions obeying $\mathrm{SU}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(3)$ chiral algebra. Assuming single-particle dominance and simple momentum dependence of the vertex functions, decay widths of the ${K}^{*}$, $Q$, and $\ensuremath{\varphi}$ mesons are obtained with all the mesons on the mass shell. Further, within this scheme, momentum-dependent ${K}_{l3}$-decay form factors are also obtained. Our results are in good agreement with experiments.

On chiral algebra, meson dominance, and the soft-pion evaluation of gϱ

The derivations of g ϱ 2 = 2 F π 2 m ϱ 2 by Kawarabayashi and Suzuki and others are re-examined. It is shown that when the full content of chiral algebra is exploited, the analysis reduces to an identity rather than a determination of g ϱ .

Schwinger's chiral dynamics and the pion mass difference

Schwinger's scheme of chiral dynamics is reviewed and elaborated. An explicit form of the generators of his chiral algebra is found, and with its help the relation of this work to the σ model is elucidated. The pion mass difference and the η-decay rate are calculated on the assumption that only the isospin subgroup of Schwinger's chiral group is broken by electromagnetic interactions.

Current Algebra,s-Wave Meson-Baryon Scattering Lengths, and the Ademollo-Gatto Theorem

$s$-wave meson-baryon scattering lengths to first order in symmetry breaking are investigated within the framework of the $\mathrm{SU}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(3)$ chiral algebra. We find that there are no renormalization effects in these scattering lengths to first order in symmetry breaking under the assumption of current commutation relations, the hypothesis of partially conserved axial-vector current, and the Ademollo-Gatto theorem for the vector-baryon---baryon coupling. However, if we do not assume the Ademollo---Gatto theorem, we do observe symmetry-breaking effects in the scattering-length sum rules.

Current Algebra and Three-Body Weak Radiative Decays of the Hyperons

The three-body weak radiative decays of the hyperons have been studied within the framework of the $\mathrm{SU}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(3)$ chiral algebra. Following the same procedure as used for nonleptonic hyperon decays, we have obtained sum rules for the parity-violating case and, further, taking the pole model for the weak two-body vertex, decay rates for both parity-violating and parity-conserving cases have been calculated in terms of $S$-wave nonleptonic hyperon decay parameters. The result for the ${\ensuremath{\Sigma}}^{+}\ensuremath{\rightarrow}n+{\ensuremath{\pi}}^{+}+\ensuremath{\gamma}$ decay agrees reasonably with the experimental value.

Current Algebra and Pion Production in High-Energy Neutrino-Nucleon Collisions

Using the [current, charge] equal-time commutation relations and the hypothesis of partially conserved axial-vector current, we have obtained a number of sum rules between off-mass-shell matrix elements for the high-energy neutrino-nucleon "inelastic" processes. In addition, the $\mathrm{SU}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(3)$ chiral algebra has enabled us to express the pion-production matrix element in terms of $\ensuremath{\beta}$-decay form factors in a most straightforward manner. The results obtained are in reasonable agreement with the experimental data available and the previous models.

Mixing scheme for chiral and collinear algebras

Mixing scheme for chiral and collinear algebras

Saturation of current algebra equations with higher baryonic resonances

The saturation of the commutation relations of the chiral $U(3)\ensuremath{\bigotimes}U(3)$ algebra with supermultiplets of $S{U}_{6}$ or $S{U}_{6}\ensuremath{\bigotimes}{O}_{3}$ is considered. The general helicity dependence of the matrix elements of axial charges at $\mathbf{p}=\ensuremath{\infty}$ is calculated. A continuity postulate is introduced to select the physically significant solutions from the multiplicity of solutions of the non-linear set of saturated commutator equations. A linearized approach is developed to derive criteria of "connection" between two supermultiplets with respect to the chiral algebra and to calculate the renormalizatioris (at second order) of the couplings. The possible relevance of the connection criteria and of the compatibility with data of the coupling renormalizations to discriminate among various possibilities of classification of higher resonances is pointed out. Special cases discussed are classifications of negative parity resonances according to the representations and 56 of $S{U}_{6}$ and (20, $L=\mathit{1}$) of $S{U}_{6}\ensuremath{\bigotimes}{O}_{3}$. Only the last one gives consistent predictions.

Chiral Algebra, Configuration Mixing, Magnetic Moments, and Pion Photoproduction

We develop a model for baryon states as a mixture of representations of the chiral $\mathrm{SU}(3)\ensuremath{\bigotimes}\mathrm{SU}(3)$ algebra generated by the time components of vector and axial-vector currents. Our model predicts a sum rule ${G}_{A}=1+\frac{1}{4}{G}^{*2}$, where ${G}_{A}$ is the axial-vector coupling constant of the nucleon and ${G}^{*}$ is the nucleon-(3,3)-resonance matrix element of the axial current. We show how to derive ${G}^{*}$ from experiment, and using this information get ${G}_{A}=1.25$. Using the electric dipole operator we also obtain that the magnetic moment of the nucleons is pure isovector, as is the photoproduction amplitude of the isospin-\textonehalf{} pion-nucleon resonances from nucleons. A value for the magnetic dipole transition from the nucleon to the (3,3) resonance is found which also agrees with experiment.

Consistency of chiral algebra approximate saturation with experiment

Consistency of chiral algebra approximate saturation with experiment

On the relation between chiralSU 3 ×SU 3 current algebra andSU 6

The general structure of the covariant sum rules derived on the basis of chiralSU3×SU3 algebra is investigated in the case in which they are saturated by a finite number of intermediate states. We discuss first the consistency of the saturation with states belonging to anSU6 supermultiplet. We find that consistency is ensured and that theSU6 results for the renormalization ratios are obtained if mass differences betweenSU3 multiplets are neglected. This is due to the fact that for equal masses and parities the matrix elements of the divergences of the axial currents are proportional to the matrix elements of the helicity. We then discuss the situation in which an arbitrary but limited set of states saturates all the matrix elements of the chiralSU3×SU3 algebra taken among them. It is shown that the matrix elements of the chiral algebra coincide with the matrix elements of a collinearSU3×SU3 algebra, so that the states that saturate the chiral algebra are a representation of the collinear one, on the basis of which the coupling constants can be calculated. The collinear group is not the same as the one generally considered as a subgroup of the staticSU6. It coincides with it only in the case of equal parities and masses of all the members of an irreducible representation.

Chiral Algebra, Configuration Mixing, and Magnetic Moments

Chiral Algebra, Configuration Mixing, and Magnetic Moments

Remarks on the saturation of the sum rules of the chiral algebra

Remarks on the saturation of the sum rules of the chiral algebra

Single-Particle Representations of Current Algebras

The requirement that matrix elements of current commutators are saturated by single-particle intermediate states leads to kinematical restrictions on the allowed momenta of these states. For the $\mathrm{SU}(6)$ algebra the momentum must be zero, while for the chiral $\mathrm{SU}(3)\ensuremath{\bigotimes}\mathrm{SU}(3)$ algebra it must be infinite. In this single-particle limit it is shown that the chiral algebra is equivalent to the collinear $\mathrm{SU}(3)\ensuremath{\bigotimes}\mathrm{SU}(3)$ subalgebra of $\mathrm{SU}(6)$, and so a relation between the $\mathrm{SU}(6)$ and chiral algebras is established.