Strangeness-changing Vector Currents Research Articles

K¯*0(890)decay density matrix elements and partial conservation of strangeness-changing vector current

We show that the zeros in the density matrix elements ${\ensuremath{\rho}}_{1,\ensuremath{-}1}^{t}$ and $\mathrm{Re}{\ensuremath{\rho}}_{10}^{s}$ for ${K}^{\ensuremath{-}}p\ensuremath{\rightarrow}{{\overline{K}}^{*}}^{0}n$ (${K}^{+}n\ensuremath{\rightarrow}{{K}^{*}}^{0}p$) are correlated and imply fundamental relationships among the Ball amplitudes following from partial conservation of strangeness-changing vector currents and the smoothness hypothesis.

Exact representation of meson-meson scattering amplitudes consistent with current-algebra constraints

All four-point Green functions connected to the vector and axial-vector currents by Ward identities are constructed, consistent with the constraints of an arbitrary current algebra. The structure of the four-point functions is separated into one-particle reducible and irreducible parts, without approximations. That is, no single-particle approximation is made, nor is it assumed that the strangeness-changing vector currents are conserved. The result is a representation of the meson-meson scattering amplitude that explicitly satisfies all the constraints of the current algebra. In particular, it satisfies: (i) threshold theorems, (ii) crossing symmetry and (iii) reduction to the usual tree-approximation in the single-particle approximation. Application is made to kaon-pion scattering, obtaining a representation of the scattering amplitude that is suitable for the investigation of the constraints of elastic unitarity.

Model of Spontaneous Breakdown of SU(3) ⊗ SU(3) Symmetry. II

Strong interactions of spin-zero and spin-one mesons are studied in a model in which the Lagrangian is approximately invariant under coordinate-dependent $\mathrm{SU}(3)\ensuremath{\bigotimes}\mathrm{SU}(3)$ gauge transformations. The scalar and pseudoscalar nonets are assigned to the (3,3*) \ensuremath{\bigoplus} (3*,3) representation, whereas the vector and axial-vector octets are introduced as gauge fields belonging to the (1,8) \ensuremath{\bigoplus} (8,1) representation. Spontaneous symmetry breaking to the isospin-hypercharge level is introduced by giving nonzero vacuum expectation values to some scalar fields. The effective Lagrangian obtained after considering field mixings and renormalizations is used in a phenomenological manner to study the masses and couplings of various particles. With some of the experimental meson masses as input, the predicted masses of remaining observed mesons are in reasonable agreement with experiment. Some scalar-meson masses are also predicted (${\ensuremath{\mu}}_{{S}_{K}}=527$ MeV and ${\ensuremath{\mu}}_{{S}_{\ensuremath{\pi}}}=771$ MeV). The widths for $V\ensuremath{\rightarrow}\mathrm{PP}$ and $A\ensuremath{\rightarrow}\mathrm{VP}$ decays are calculated and compare well with experiment. The axial-vector currents and the strangeness-changing vector currents satisfy partial conservation equations. Decay constants for spin-zero mesons are calculated. We get $\frac{{F}_{K}}{{F}_{\ensuremath{\pi}}}=1.17$ and $\frac{{F}_{{S}_{K}}}{{F}_{\ensuremath{\pi}}}=\ensuremath{-}0.59$. The ${K}_{l3}$ form factors are calculated, the effect of the scalar kaon being included; we get ${f}_{+}(0)=0.86$, $\ensuremath{\xi}=\ensuremath{-}0.197$, ${\ensuremath{\lambda}}_{+}=0.023$, and ${\ensuremath{\lambda}}_{\ensuremath{-}}=0.013$.

Model of Spontaneous Breakdown ofSU(3)⊗SU(3)Symmetry. I

Strong interactions of spin-zero and spin-one mesons are studied in a model in which the Lagrangian is approximately invariant under coordinate-dependent $\mathrm{SU}(3)\ensuremath{\bigotimes}\mathrm{SU}(3)$ gauge transformations. The scalar and pseudoscalar nonets are assigned to the (3,3*) \ensuremath{\bigoplus} (3*,3) representation, whereas the vector and axial-vector octets are introduced as gauge fields belonging to the (1,8) \ensuremath{\bigoplus} (8,1) representation. Spontaneous symmetry breaking to the isospin-hypercharge level is introduced by giving nonzero vacuum expectation values to some scalar fields. The effective Lagrangian obtained after considering field mixings and renormalizations is used in a phenomenological manner to study the masses and couplings of various particles. With some of the experimental meson masses as input, the predicted masses of remaining observed mesons are in reasonable agreement with experiment. Some scalar-meson masses are also predicted (${\ensuremath{\mu}}_{{S}_{K}}=527$ MeV and ${\ensuremath{\mu}}_{{S}_{\ensuremath{\pi}}}=771$ MeV). The widths for $V\ensuremath{\rightarrow}\mathrm{PP}$ and $A\ensuremath{\rightarrow}\mathrm{VP}$ decays are calculated and compare well with experiment. The axial-vector currents and the strangeness-changing vector currents satisfy partial conservation equations. Decay constants for spin-zero mesons are calculated. We get $\frac{{F}_{K}}{{F}_{\ensuremath{\pi}}}=1.17$ and $\frac{{F}_{{S}_{K}}}{{F}_{\ensuremath{\pi}}}=\ensuremath{-}0.59$. The ${K}_{l3}$ form factors are calculated, the effect of the scalar kaon being included; we get ${f}_{+}(0)=0.86$, $\ensuremath{\xi}=\ensuremath{-}0.197$, ${\ensuremath{\lambda}}_{+}=0.023$, and ${\ensuremath{\lambda}}_{\ensuremath{-}}=0.013$.

Structure of Three-Point Functions fromSU(3)⊗SU(3)Algebra

We construct three-point functions of vector and axial-vector currents consistent with the constraints of chiral $\mathrm{SU}(3)\ensuremath{\bigotimes}\mathrm{SU}(3)$ algebra. We make no single-particle approximations, nor do we assume that the strangeness-changing vector currents are conserved. We do, however, assume that the effects of symmetry breaking may be represented by a set of scalar and pseudoscalar fields transforming as a representation of the algebra. The results are presented in a form in which any approximations will be guaranteed to maintain the constraints of current algebra.

Behavior of Current Divergences underSU3×SU3

We investigate the behavior under SU3×SU3 of the hadron energy density and the closely related question of how the divergences of the axial-vector currents and the strangeness-changing vector currents transform under SU3×SU3. We assume that two terms in the energy density break SU3×SU3 symmetry; under SU3 one transforms as a singlet, the other as the member of an octet. The simplest possible behavior of these terms under chiral transformations is proposed: They are assigned to a single (3,3*)+(3*,3) representation of SU3×SU3 and parity together with the current divergences. The commutators of charges and current divergences are derived in terms of a single constant c that describes the strength of the SU3-breaking term relative to the chiral symmetry-breaking term. The constant c is found not to be small, as suggested earlier, but instead close to the value (-sqrt[2]) corresponding to an SU2×SU2 symmetry, realized mainly by massless pions rather than parity doubling. Some applications of the proposed commutation relations are given, mainly to the pseudoscalar mesons, and other applications are indicated.

On the lifetime of the kappa meson

The lifetime of a hypotheticalκ meson with low mass, introduced byGlashow andWeinberg in a model for simultaneous breaking ofSU(3) and chiral symmetry, is calculated. The coupling constant of theκ toKπ is obtained by assuming that the divergence of the strangeness changing vector current is dominated by theκ pole.

Algebra of Currents, Divergence of Strangeness-Changing Vector Currents, Unsubtracted Dispersion Relations, and theKl3form Factors

Algebra of Currents, Divergence of Strangeness-Changing Vector Currents, Unsubtracted Dispersion Relations, and the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>l</mml:mi><mml:mn>3</mml:mn><mml:mn /></mml:mrow></mml:msub></mml:mrow></mml:math>form Factors

K-Leptonic Decay and Partially Conserved Currents

An operational definition for the partial conservation of the strangeness-changing vector current is given and applied to leptonic ${K}^{+}$ and ${{K}_{2}}^{0}$ decay. The ${K}^{*}$ resonance is explicitly included in the calculation and quantitative agreement with experiment is obtained. A detailed comparison with the ${K}^{+}$ data of Brown et al. and Dobbs et al. is given. Because of rapid variations of a form factor, it is found that the data of these two groups are not in contradiction. From the ${{K}_{2}}^{0}$ experiment of Luers et al., $I=\frac{1}{2} \mathrm{and} \frac{3}{2}$ currents are seen to exist. $\ensuremath{\Lambda}\ensuremath{\beta}$ decay is briefly considered. It is found that an explanation for the slowness of $K$ leptonic decay and the vector part of $\ensuremath{\Lambda}\ensuremath{\beta}$ decay may be connected with the partial conservation of the strangeness-changing vector current.

Symmetries of Baryons and Mesons

The system of strongly interacting particles is discussed, with electromagnetism, weak interactions, and gravitation considered as perturbations. The electric current jα, the weak current Jα, and the gravitational tensor θαβ are all well-defined operators, with finite matrix elements obeying dispersion relations. To the extent that the dispersion relations for matrix elements of these operators between the vacuum and other states are highly convergent and dominated by contributions from intermediate one-meson states, we have relations like the Goldberger-Treiman formula and universality principles like that of Sakurai according to which the ρ meson is coupled approximately to the isotopic spin. Homogeneous linear dispersion relations, even without subtractions, do not suffice to fix the scale of these matrix elements; in particular, for the nonconserved currents, the renormalization factors cannot be calculated, and the universality of strength of the weak interactions is undefined. More information than just the dispersion relations must be supplied, for example, by field-theoretic models; we consider, in fact, the equal-time commutation relations of the various parts of j4 and J4. These nonlinear relations define an algebraic system (or a group) that underlies the structure of baryons and mesons. It is suggested that the group is in fact U(3)×U(3), exemplified by the symmetrical Sakata model. The Hamiltonian density θ44 is not completely invariant under the group; the noninvariant part transforms according to a particular representation of the group; it is possible that this information also is given correctly by the symmetrical Sakata model. Various exact relations among form factors follow from the algebraic structure. In addition, it may be worthwhile to consider the approximate situation in which the strangeness-changing vector currents are conserved and the Hamiltonian is invariant under U(3); we refer to this limiting case as In the limit, the baryons and mesons form degenerate supermultiplets, which break up into isotopic multiplets when the symmetry-breaking term in the Hamiltonian is turned on. The mesons are expected to form unitary singlets and octets; each octet breaks up into a triplet, a singlet, and a pair of strange doublets. The known pseudoscalar and vector mesons fit this pattern if there exists also an isotopic singlet pseudoscalar meson χ0. If we consider unitary symmetry in the abstract rather than in connection with a field theory, then we find, as an attractive alternative to the Sakata model, the scheme of Ne'eman and Gell-Mann, which we call the eightfold way; the baryons N, Λ, Σ, and Ξ form an octet, like the vector and pseudoscalar meson octets, in the limit of unitary symmetry. Although the violations of unitary symmetry must be quite large, there is some hope of relating certain violations to others. As an example of the methods advocated, we present a rough calculation of the rate of K+→μ++ν in terms of that of π+→μ++ν.