Polarized Vector Mesons Research Articles

DOMINANCE OF LONG DISTANCE EFFECTS IN THE KL-KS MASS DIFFERENCE

It is argued that the asymptotic behavior of the matrix elements of Hw involving on-mass-shell ground-state mesons with infinite momenta, which were instrumental in explaining the |ΔI|=1/2 rule in the K→ππ decays, actually implies [Formula: see text]. The long distance effects (contributions of PS and vector meson poles and ππ intermediate states) may reproduce the observed KL−Ks mass difference, consistent with the |ΔI|=1/2 rule. Its estimate is however sensitive to the η-η′-… mixing.

The K ∗ pole model of K → ππ decays and final-state interactions

It is shown that final-state interactions can enhance (suppress) substantially the ΔI = 1 2 (ΔI = 3 2 ) K → ππ parity-violating decay amplitude calculated from the K ∗ vector meson pole model. This enhancement (suppression) combined with short-distance QCD corrections to the effective weak interaction almost brings the K ∗ pole model into agreement with experiment.

Chiral anomalies and vector-meson dominance.

Amplitudes for \ensuremath{\eta} and \ensuremath{\eta}'\ensuremath{\rightarrow}${\ensuremath{\pi}}^{+}$${\ensuremath{\pi}}^{\mathrm{\ensuremath{-}}}$\ensuremath{\gamma}, ${K}_{e4}$, \ensuremath{\omega}\ensuremath{\rightarrow}${\ensuremath{\pi}}^{+}$${\ensuremath{\pi}}^{\mathrm{\ensuremath{-}}}$${\ensuremath{\pi}}^{0}$, and \ensuremath{\gamma}\ensuremath{\rightarrow}${\ensuremath{\pi}}^{+}$${\ensuremath{\pi}}^{\mathrm{\ensuremath{-}}}$${\ensuremath{\pi}}^{0}$ are constructed that respect the low-energy chiral-anomaly theorems but also have realistic vector-meson pole continuations to physical energies, respecting the well satisfied Kawarabayashi-Suzuki-Riazuddin-Fayyazuddin relation. The amplitudes are compared to experiment, with good results, verifying the need for the current-algebra ``contact'' term.

Nonleptonic hyperon decays-wave amplitudes and negative-parity excited baryons

The contribution of negative-parity excited baryons is calculated and found to be small relative to other contributions (i.e. the equal-time commutator and the vector-meson pole) which have been successfully employed in the recent past. While positive-parity excited baryons help to explainp-wave (B) amplitudes, 1/2− baryon poles do not spoil the existing description ofs-wave (A) amplitudes.

Deviation from the exactSU 3 symmetry in hadronic decays of ψ and contributions of electromagnetic interactions

It is assumed that hadronic two-body decays of ψ proceed via the ψ-V (V=ρ, ω, ϕ) mixing and that the strong interactions which induce the ψ→V transition are mediated by gluons. The deviations from the exactSU 3 symmetry in the decays of ψ and the contributions of the amplitudes via the ψ→V transition mediated by a photon are examined semi-phenomenologically by fitting the calculated branching ratios for these decays to the corresponding experimental data. Our results are the following. i) There are sizable deviations (0.3≲β≲0.5) from the exactSU 3 symmetry in the decays of ψ into two-boson final states. They can be understood in terms of the symmetry-breaking effects in the residues of the vector meson poles. ii) The contributions of the amplitudes via the one-photon intermediate state are neither negligibly small nor dominant (|G(u)/E(u)|≈2.8). iii) The relative phase between the amplitudes via the gluon and the one-photon intermediate states is approximately equal to π/2. By using the values of the parameters estimated in this way, the branching ratios for the decays in which the amplitudes via the one-photon intermediate state dominate (in theSU 3 symmetry limit) can be predicted. Γ(f→2γ) is also discussed by using the vector meson dominance hypothesis.

Vector-meson dominance and other models of parity-violatingDandFdecays

A vector-meson-dominance model is presented for nonleptonic decays of the charmed mesons $D$ and $F$ into two uncharmed pseudoscalar mesons. Generalized Cabibbo mixing as suggested by the standard six-quark model is incorporated into the vector-pseudoscalar transition junction. Explicit SU(3) mass-splitting factors give distinctive departures from the predictions based on SU(3). Comparison with the SU(3) parametrization and soft-gluon-corrected charmed-quark decay model are discussed. For Cabibbo-favored modes the latter model makes predictions which are identical to those of the SU(3) limit of our vector-meson pole model. A clear test of the pole model is the prediction that $\ensuremath{\Gamma}({D}^{+}\ensuremath{\rightarrow}{\overline{K}}^{0}{K}^{+})=\ensuremath{\Gamma}({D}^{0}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}})$. The ${D}^{0}\ensuremath{\leftrightarrow}{\overline{D}}^{0}$ mixing question is touched on briefly, and it is argued that the experimentally measured disparity between ${D}^{0}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}$ and ${D}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ branching ratios means that ${D}^{0}\ensuremath{\leftrightarrow}{\overline{D}}^{0}$ mixing will be a "normal" ${{tan}^{2}\ensuremath{\theta}}_{C}$ in amplitude---not suppressed as in the SU(3) limit. The argument is illustrated by the vector-pole-model amplitudes. To organize the decay patterns and to compare different models, we propose a mnemonic quark-graph rule. For $K$ ($D$) decays, the strange- (charmed-) quark decay graphs---called radiation graphs---are asserted to be suppressed relative to others. The $F$-meson decays will be critical in testing this rule. The extension to decays of mesons which carry $b$-quark constituent is outlined briefly.

Vector meson couplings and the obsevability of the K → Kππ decays

The K ∗ → Kππ rate is calculated using vector meson pole dominance in several recent coupling-constant models. Including the effects of the contact interaction, the various models give results ranging from 8 to 86 keV for the decay rate. Taking the ω → 3π and ø → 3π decays into accont, we believe the result of 50 keV to be more reliable upper bound. This is significantly higher than older estimates and within the realm of experimental measurement.

SU(3) symmetry for the vector meson-nucleon interaction

When comparing data on VBB coupling constants with SU(3) one usually assumes Sakurai's idea that the ϱ-meson couples universally to the isovector current. In order to use this assumption one has to continue the coupling from the vector meson pole to t=0. The implications for the coupling constants depend upon how this continuation is carried out. In this paper we present arguments to expect simple continuation properties for VNN form factors defined in analogy with the Sachs electromagnetic form factors, rather than for the vector and tensor form factors. We show that in this case experimental data are consistent with SU(3), Sakurai's universality idea and with Zweig's rule. Furthermore we find F D ratios close to the SU(6) prediction.

SU(3) trace identities and the calculation of effective couplings in a baryon-loop model of weak radiative kaon decays

A simple algorithm for the recursive reduction of the trace of a product of any number of the $f$ and $d$ matrices of SU (3) is given. SU (3) trace identities (through fourth order) are used to construct effective interaction Lagrangians in the baryon-loop model for $\mathrm{PVV}$, $\mathrm{PV}\ensuremath{\gamma}$, and weak (strangeness-changing) $\mathrm{PV}\ensuremath{\gamma}$ couplings. At the same time it is shown that the effects of baryon-mass breaking on the $\mathrm{PVV}$ coupling are negligible in the loop model. The usefulness of this formal compaction is further illustrated in the calculation of the contributions of all vector-meson poles to ${K}_{2}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\gamma}$ decay. It is found that the previous neglect of the contribution of ${K}^{*}$ poles in this case is justified.

On the need for off-diagonal terms in the hypothesis of generalized vector-meson dominance

It is argued that the diagonal ansatz in GVMD models is theoretically unjustified, and we show that off-diagonal contributions are necessary to explain recent data on the electroproduction of polarized vector mesons.

Scalar-Meson Pole Model for Weak Parity-Violating Baryon-Baryon-Meson Vertices

We apply a scalar-meson pole model to the parity-violating hyperon decays and to the parity-violating $\mathrm{NN}\ensuremath{\pi}$ vertex. In this model we obtain the usual octet-dominance results for the hyperon decay amplitudes: the $I=\frac{1}{2}$ rule, the Lee-Sugawara triangle, and a vanishing amplitude for $s$-wave ${\ensuremath{\Sigma}}^{+}\ensuremath{\rightarrow}n+{\ensuremath{\pi}}^{+}$ decay. The model is distinguished from the vector-meson pole models by the fact that it gives the current-algebra sum rule for the parity-violating $\mathrm{NN}\ensuremath{\pi}$ amplitude whereas the vector pole model predicts that this amplitude vanishes in the limit of isospin symmetry. Using the SU(3)\ifmmode\times\else\texttimes\fi{}SU(3) $\ensuremath{\sigma}$ model for the currents we compute the amplitudes without arbitrary constants and find that they are about half the observed amplitudes.

Physical and Formal Presentations of Dual Theory of Electromagnetic Currents

We propose a dynamical Lagrangian theory for the hadron with strong and electromagnetic interactions. We give a simple physical interpretation of our Lagrangian in the parton picture and show explicitly its equivalence with the formal string formulation of the hadron for both the free and interacting Lagrangians. The theory is gauge-invariant with a well-defined conserved current. (The low-energy theorem for currents holds.) The elastic and transition form factors are non-Gaussian and analytic with an infinite series of vector-meson poles. In the two-current channel the electromagnetic amplitude has fixed poles with the imaginary part satisfying rigorously the Dashen-Gell-Mann-Fubini sum rule. In the Bjorken limit our $\ensuremath{\nu}{W}_{2}$ scales and is saturated by narrow resonances. A dispersion relation for ${T}_{2}$ continues to hold in the scaling limit and the Gottfried sum rule for $\ensuremath{\nu}{W}_{2}(\ensuremath{\omega})$ is exactly satisfied with the fixed-pole contribution. The hadronic amplitude obtained from the off-shell Compton amplitude is equal to a beta function. In the crossed channel our theory generates Regge poles with quantized intercepts which are degenerate with the vector-meson poles in the off-shell photon line which phenomenologically implies the $\ensuremath{\rho}\ensuremath{-}f\ensuremath{-}{A}_{2}$ degeneracy. More generally, we project explicitly hadronic vertices out of our electromagnetic vertex through vector-meson poles and find that these vertices are dual and factorizable.

Broken SU(6) predictions for baryon production with polarized vector mesons

Quark model and SU(6) predictions for branching ratios of Λ, Σ and Y ∗(1385) production in strangeness exchange reactions disagree with experiment. New predictions for vector meson polarization density matrix elements are presented which seem to agree with experiment. A “broken SU(6)” description which includes configuration mixing in the Σ and Y ∗ wave functions is consistent with the success of the polarization predictions and the failure of the branching ratio predictions of unbroken SU(6).

Vector Currents and Current Algebra. II. AnN-Point Beta-Function Model

A simple $N$-point beta-function model (generalized Veneziano model) of the hadron bootstrap is assumed, and the properties of vector currents consistent with it are investigated. We find that this hadron bootstrap admits conserved vector currents satisfying the Gell-Mann current algebra in a first approximation which assumes single vector-meson poles in the form factors and requires factorization only at resonances on leading Regge trajectories. We believe the techniques employed in this simplified model will be useful in constructing current amplitudes in more general dual zero-width models. In addition, a model for a Pomeranchon contribution which does not fall off at large ${q}^{2}$ is proposed. Throughout we treat amplitudes for one or two vector currents and an arbitrary number $N$ of spinless hadrons.

Vector dominance and forward photoproduction of charged pions by polarized photons

Vector-dominance predicts a relation between the combined asymmetry in π + and π − photoproduction by polarized photons and the cross section for producing transversely polarized vector mesons. We predict that at high energies and t=− m π 2 this relation will be violated by the data. We explain this expected failure by a strong mass dependence of the mechanism which governs the forward amplitudes for these processes.

Two-Pole Model for theη3πDecays

$\ensuremath{\eta}\ensuremath{\rightarrow}3\ensuremath{\pi}$ decays are described by a model in which the amplitudes are assumed to be dominated by two meson poles. The model is characterized by scalar, vector, and axial-vector meson poles. The strong-coupling constants in the model are obtained from the experimental decay widths. Adopting the tadpole model, the effective electromagnetic coupling is given in terms of the electromagnetic mass difference of kanos. If the $D\ensuremath{-}E$ mixing and $\ensuremath{\eta}\ensuremath{-}{\ensuremath{\eta}}^{\ensuremath{'}}$ mixing are included, then the branching ratio, the slope, and the decay rate for the $\ensuremath{\eta}\ensuremath{\rightarrow}3{\ensuremath{\pi}}^{0}$ are found to be in good agreement with experiment.

Vector and Axial-Vector Meson Dominance in theK3πDecays

A model for $K\ensuremath{\rightarrow}3\ensuremath{\pi}$ decays is proposed in which the amplitudes are assumed to be dominated by vector and axial-vector meson poles. $S$-wave and $P$-wave amplitudes are treated on the same footing in this scheme. The strong-coupling constants appearing in the model can be determined from strong decays. The $K\ensuremath{\rightarrow}3\ensuremath{\pi}$ slopes and average amplitude ratios are then determined in terms of one parameter characterizing the $\ensuremath{\Delta}I=\frac{1}{2}$ part of the weak Hamiltonian. Estimates are made of the effects of a $\ensuremath{\Delta}I=\frac{3}{2}$ contribution to the weak interaction.

Sum Rules for Photoproduction with Boson-Fermion Commutation Relations

Sum rules applicable to the photoproduction of $\ensuremath{\pi}$ and $\ensuremath{\eta}$ mesons on nucleons are written down using the commutation relation for electromagnetic current density with the field of the proton. These rules relate scattering channels obtained by interchanging a boson with a fermion line, e.g., $\ensuremath{\gamma}+N\ensuremath{\rightarrow}\ensuremath{\pi}+N$ and $N+\overline{N}\ensuremath{\rightarrow}\ensuremath{\gamma}+\ensuremath{\pi}$ channels. When saturated with nucleon, ${N}^{*}$, ${S}_{11}$, and vector-meson poles, these rules relate photonic vertices of the vector meson to the vertices of fermions. Such relations between all boson vertices and fermion vertices are consequences of the boson-fermion commutation relations. The estimate for $\ensuremath{\pi}\ensuremath{\omega}\ensuremath{\gamma}$ coupling is in agreement with the values obtained from the partial decay width for $\ensuremath{\omega}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\gamma}$. The estimate for $\ensuremath{\eta}\ensuremath{\rho}\ensuremath{\gamma}$ coupling leads via the $\ensuremath{\rho}$-dominance model to a value of total decay width for the $\ensuremath{\eta}$ meson in agreement with other such estimates.

Modified Analysis of Nucleon Electromagnetic Form-Factor Data

We suggest that the usual procedure for analyzing nucleon electromagnetic form-factor data be modified by retaining in a suitable manner the dispersion-integral contributions present even after removal of known vector-meson contributions. This allows a more general analysis consistent with all known restrictions on the form factors. The form factors are parametrized and the parameters determined by comparison with experimental data. It is possible to obtain reasonable fits to all of the data with a total of two parameters. The resulting form factors are suitable for the extraction of useful numbers, including the residues at the known vector-meson poles. In addition, analytic continuation to the annihilation region is well-defined and allows meaningful comparison with data there. It is not necessary to make statements about the existence of vector mesons other than $\ensuremath{\rho}$, $\ensuremath{\omega}$, $\ensuremath{\phi}$. We use our results to discuss the $\ensuremath{\rho}$ dominance of the isovector form factor and to estimate the vector-meson-nucleon coupling constants.

Connection between current algebras and vector-meson pole model

Following the procedure by Kawarabayashi and Suzuki in the frame of chiralU3 ⊗U3 current algebra and PCAC, we relate the amplitude for emission of two soft pions in ap-wave to the electromagnetic vertex. The result is shown to be in agreement with the vectormeson pole model. We also obtain the vector current amplitudes of the vector mesons in terms of the constant of the PCAC and we compare this result with that of higher symmetries.