Chiral Current Algebra Research Articles

Electromagnetic mass differences from an effective Lagrangian

An effective-Lagrangian model that gave finite lowest-order dynamical electromagnetic corrections to the masses of vector mesons is generalized to a chiral O(4) model, which includes A$sub 1$ mesons and pions. Aside from a PCAC (partial-conservation-of-axial-vector-current) ''tadpole'' term, the Lagrangian is chiral-O(4)-symmetric, but a term responsible for supplying a part of the A$sub 1$ mass is not gauge-symmetric. Both pion and A$sub 1$ mass differences contain logarithmically divergent terms, as in chiral current-algebra calculations. The soft-pion part of the pion mass difference is, however, 3.2 MeV, instead of 5.0 MeV as given by current-algebra and other effective- Lagrangian calculations. (AIP)

Veneziano Amplitude, Current Algebra, and Vertex Functions

The possibility is examined of extending the $\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ and $\ensuremath{\pi}{A}_{1}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ Veneziano amplitudes to the case of one or two mesons off the mass shell in a fashion consistent with chiral current algebra, partial conservation of axial-vector current, and conserved vector current. Soft-pion formulas for the pion-vector form factor and the $\ensuremath{\sigma}$-commutator vertex are deduced. The hard-meson analysis shows that if one wishes to maintain Veneziano form with two mesons off the mass shell, some of the $\ensuremath{\pi}{A}_{1}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ amplitudes must develop poles in one of the off-shell momenta at ${p}^{2}=0$. The soft-pion vertex function equations are seen to be a consequence of removing the leading part of this singularity at the soft-pion point ${p}^{\ensuremath{\mu}}=0$. However, the resultant amplitudes are still singular at ${p}^{2}=0$, ${p}^{\ensuremath{\mu}}\ensuremath{\ne}0$ for a continuum of $s$, $t$, and $u$. The fixed poles implied by the presence of form factors (when two mesons are off shell) are seen to occur only in those amplitudes orthogonal to the ${A}_{1}$ polarization vector and do not affect the amplitudes that make nonzero contributions for $\ensuremath{\pi}{A}_{1}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ scattering on the mass shell.

Partially conserved dilatation and special Liouville currents combined with chiral current algebras

Combining recent results from an analysis of partially broken dilatation and special Liouville (conformal) symmmetries with the concepts of chiral SU 2 × SU 2 and SU 3 × SU 3 algebras of currents yields predictions for the following quantities: The width of the σ(700), s-wave pion-pion scattering lengths, the σ-contribution to the pion-pion Adler-Weisberger sum rule, the partial widths of the η o +(1070) and - in the framework of SU 3 - the partial widths for the other members of the nonet of scalar mesons. Almost all predictions are in good agreement with available data.

Pion-Nucleon Scattering Lengths

Pion-nucleon scattering lengths have been calculated using a model in which $N$, ${N}^{*}$, $\ensuremath{\rho}$, and $\ensuremath{\epsilon}$ exchanges are assumed to dominate the low-energy pion-nucleon interaction. This simple model yields remarkably good agreement with the experimental $s$- and $p$-wave scattering lengths. We find that the coupling of the $\ensuremath{\epsilon}$ meson to the nucleon is consistent with estimates made using chiral symmetry and current algebra.

Vector and Axial Vector Mesons and Chiral Current Algebra

Vector and Axial Vector Mesons and Chiral Current Algebra