Vector Meson Couplings Research Articles

Properties ofK*(890)andK*(1400)Produced inK−pInteractions at 4.1 and 5.5 GeV/c

The results presented in this paper were obtained from an analysis of ${K}^{\ensuremath{-}}p$ interactions in the 30-in. hydrogen bubble chamber at the Argonne ZGS using incident ${K}^{\ensuremath{-}}$ beams of momenta 4.1 and 5.5 GeV/c. The $\overline{K}\ensuremath{\pi}N$ final states were studied extensively; the most prominent feature of these is production of the ${K}^{*}(890)$ and ${K}^{*}(1400)$ resonances. The ${\overline{K}}^{0}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}n$ final state was used to measure the branching ratio of the decay of the ${K}^{*}(1400)$ into ${K}^{*}(890)\ensuremath{\pi}$ and $K\ensuremath{\rho}$. Evidence for quasi-two-body production of ${K}^{*}{(890)}^{\ensuremath{-}}$ and ${K}^{*}{(1400)}^{\ensuremath{-}}$ is presented both from the two-prong events in which the positive track was identified as a proton, and from events where the ${\overline{K}}^{0}$ decay was observed. For final states with a missing neutron, a study of the missing-mass distributions proved that the kinematical fits to ${K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}n$ and ${\overline{K}}^{0}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}n$ final states could be used with confidence to study ${K}^{*}{(890)}^{0}$ and ${K}^{*}{(1400)}^{0}$ production. The ${K}^{*}{(890)}^{0,\ensuremath{-}}$ production angular distribution and decay correlations are analyzed in the framework of the absorptive peripheral model. Vector exchange dominates the ${K}^{*}{(890)}^{\ensuremath{-}}$ production, whereas ${K}^{*}{(890)}^{0}$ is formed mainly via pseudoscalar exchange. An absorptive-peripheral-model calculation using the vector-meson coupling strengths to the nucleon given by relativistic $\mathrm{SU}(6)$ gives a good fit to the ${K}^{*}{(890)}^{0,\ensuremath{-}}$ density-matrix elements as a function of production angle, and gives a reasonable fit to the differential cross section. For the ${K}^{*}(1400)$ resonance, a mass and width of 1416\ifmmode\pm\else\textpm\fi{}8 and 107\ifmmode\pm\else\textpm\fi{}20 MeV are obtained. Decay branching ratios measured for this resonance of $K\ensuremath{\pi}:{K}^{*}\ensuremath{\pi}:K\ensuremath{\rho}$ of 1: (0.52\ifmmode\pm\else\textpm\fi{}0.12): (0.26\ifmmode\pm\else\textpm\fi{}0.16) are in agreement with those predicted from $\mathrm{SU}(3)$ assuming the ${K}^{*}(1400)$ is a member of a ${2}^{+}$ nonet. The absorptive peripheral model gives no reasonable fits to the ${K}^{*}(1400)$ production angular distributions. The ${K}^{*}{(1400)}^{0,\ensuremath{-}}$ production and decay angular distributions suggest that the spin parity of the ${K}^{*}(1400)$ is ${2}^{+}$, but without many more events, or a better model for the production mechanism, we cannot make a decisive determination.

A crossing-symmetric bootstrap model of a nearly degenerate vector-meson octet

The effect of pseudoscalar meson octet mass splitting and of “riving terms” on the vector-meson octet masses and coupling constants is investigated in a perturbation pattern of theSU3-symmetric problem. Using a crossing symmetric model for bootstrap, the following results were obtained which are independent of the concrete form of theSU3-symmetric unperturbated solution:a) If an octet enhancement occures then an enhancement must occur in the one- and 27-representation too.b) Omitting the “driving terms” the following relations are valid: $$\frac{{\delta M_{27}^2 }}{{M^2 }} = \frac{1}{3}\frac{{\delta m_{27}^2 }}{{m^2 }},\frac{{\delta M_8^2 }}{{M^2 }} = \frac{1}{2}\frac{{\delta m_8^2 }}{{m^2 }},\frac{{\delta M_1^2 }}{{M^2 }} = \frac{{\delta m_1^2 }}{{m^2 }},\delta g_{8_2 }^{27} = \delta g_{8_2 }^{8_1 } = \delta g_{8_2 }^1 = 0.$$ .

Bjorken Limit and Sum Rules for theπ0Lifetime and theρωπCoupling Constant

The Bjorken limit is applied to obtain sum rules for the lifetime of ${\ensuremath{\pi}}^{0}$ and for the vector-meson coupling constants. In particular we obtain predictions that $\frac{{{g}_{\ensuremath{\rho}\ensuremath{\omega}\ensuremath{\pi}}}^{2}}{4\ensuremath{\pi}}=0.53\ifmmode\pm\else\textpm\fi{}0.1$ and ${\ensuremath{\tau}}_{{\ensuremath{\pi}}^{0}}\ensuremath{\simeq}(0.84\ifmmode\pm\else\textpm\fi{}0.83)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$ sec. The latter is in good agreement with the experimental value (0.89\ifmmode\pm\else\textpm\fi{}0.18)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}16}$ sec. From our knowledge of the approximate value of ${g}_{\ensuremath{\rho}\ensuremath{\omega}\ensuremath{\pi}}$, we conclude that the high-energy behavior of the ${\ensuremath{\pi}}^{0}\ensuremath{\gamma}\ensuremath{\gamma}$ vertex function is not important to the pion lifetime. The results of this calculation constitute a consistency condition on the plausibility of the Bjorken limit.

Partial Conservation of Tensor Currents and Vector-Meson Couplings in Broken Unitary Symmetry

We suggest that the eight conserved vector currents generated by $\mathrm{SU}(3)$ gauge transformations, to which vector mesons are coupled, are related to the divergence of antisymmetric tensor currents. This leads to generalized Goldberger-Treiman relations. We predict $\ensuremath{\Gamma}(\ensuremath{\varphi}K\overline{K})\ensuremath{\simeq}3.3$ MeV, in agreement with experiments (3.3\ifmmode\pm\else\textpm\fi{}0.6 MeV).

Algebra of Currents and the Vector-Meson-Baryon Coupling Constants in BrokenSU(3)

Employing the method of current algebra and a hypothesis of partially conserved tensor current, we study the renormalization effects on the vector-meson---baryon coupling constants, due to the first-order $\mathrm{SU}(3)$ breaking. We find that the sum rules within the couplings of one vector meson with baryons are the same as those found in the $\mathrm{SU}(3)$ limit, and that the renormalization effects are present only when we compare the coupling of one vector meson with the couplings of different vector mesons. With the use of $\ensuremath{\omega}\ensuremath{-}\ensuremath{\varphi}$ mixing with the mixing angle $\ensuremath{\theta}=invtan(\ensuremath{\surd}\frac{1}{2})$, the $\ensuremath{\rho}$ and $\ensuremath{\omega}$ couplings have the same amount of renormalization effects.

Meson Decays in BrokenSU(3)and Current Commutation Relations

Assuming that the symmetry-breaking Hamiltonian is given by the space integral of the eighth component of the scalar-quark current density, the first-order renormalization of the vector and tensor meson couplings are calculated in the formalism of the algebra of currents. The results are compared with experimental widths and the agreement is found to be good.

Universal coupling of vector mesons revisited

It is shown that “the partial conservation of a tensor current” (PCTC) leads to a universality of vector-meson interactions, without assuming the Sakurai hypothesis on universal coupling of vector mesons to currents of symmetry generators. Meson electromagnetic decays are discussed on the grounds of PCTC and the results compared with the Sakurai universality.

SU(6)W-Symmetric Meson Bootstrap Model

A bootstrap model of the pseudoscalar-meson octet and singlet and the vector-meson octet and singlet is constructed. The mesons ($M$) are assumed to be $\mathrm{MM}$ bound states, produced by one-$M$-exchange forces. The input $\mathrm{MMM}$ interaction is assumed $\mathrm{SU}{(6)}_{W}$-symmetric, and the forces in all $P$-wave $\mathrm{MM}$ states are examined. The forces are most attractive in 36 states of the quantum numbers of the mesons; identification of these states with the $M$ leads to output $\mathrm{MMM}$ interactions consistent with those assumed originally. However, the $\mathrm{SU}{(6)}_{W}$ symmetry requires that the total coupling of the singlet vector meson should be only $\frac{2}{3}$ that of the other mesons. The method of calculation involves continuing the interaction off the mass shell in an $\mathrm{SU}{(6)}_{W}$-symmetric fashion, and comparing the $P$-wave amplitudes at threshold in Born approximation. The technique can also be used to predict heavier resonances that do not correspond to $\mathrm{SU}(6)$ representations. This fact is encouraging, since it appears that only the lighter observed hadrons form complete representations of $\mathrm{SU}(6)$.

Vector-Meson Couplings to the Baryons

We present some arguments by which the couplings of the vector mesons to the baryons are fixed. These arguments amount to an extension of the nonet scheme which has already been successfully applied by Okubo and by Glashow and Socolow to the ${1}^{\ensuremath{-}}$ and ${2}^{+}$ mass formulas and decays. We find that, using the vector-meson couplings obtained and the physical vector masses, we can largely account for the following experimental observations: (1) the proportionality of the electric and magnetic nucleon form factors to each other and to the $p\ensuremath{-}{({{N}_{33}}^{*})}^{+}$ magnetic-dipole transition form factor; (2) the suppression of backward $\ensuremath{\varphi}$ production in ${K}^{\ensuremath{-}}\ensuremath{-}p$ experiments; (3) the over-all suppression of $\ensuremath{\varphi}$ production in $\ensuremath{\pi}\ensuremath{-}p$ experiments; and (4) the isospin independence of the hard core in nucleon-nucleon scattering. We also estimate the relative leptonic decay rates of the $\ensuremath{\rho}$, $\ensuremath{\omega}$, and $\ensuremath{\varphi}$ and predict that there will be suppressions in ${f}^{\ensuremath{'}}(1500)$ production corresponding to those observed in $\ensuremath{\varphi}$ production.

ωϕ mass-splitting, collinear U(6) symmetry; and electromagnetic form factors

In the limit of collinear U(6) symmetry, the electromagnetic form factors of baryons do not depend upon the separate singlet vector meson coupling which is characteristic for this symmetry. Introducing ωϕ mass-splitting in the pole terms of the form factors, one can relate this coupling directly to the electric form factor of the neutron. It is shown that the experimental information about the electromagnetic form factors does not require a special supression of the separate single coupling.

Peripheral Production and Decay of Resonances in High-Energy Meson-Nucleon Collisions

Data on quasi-two-body reactions initiated by high-energy meson-nucleon collisions are analyzed from the viewpoint of the peripheral model. The basic interaction mechanism is assumed to be pseudoscalar and/or vector exchange, and absorptive effects arising from coupling between different channels are taken into account. Excellent agreement is found between the one-pion-exchange model and the production and decay data for the processes ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}p\ensuremath{\rightarrow}{\ensuremath{\rho}}^{\ifmmode\pm\else\textpm\fi{}}p$ for incident momenta from \ensuremath{\sim}2 to 8 GeV/c. A unified analysis of the reactions ${K}^{\ifmmode\pm\else\textpm\fi{}}p\ensuremath{\rightarrow}{K}^{*\ifmmode\pm\else\textpm\fi{}}p$ at 3 GeV/c, and ${K}^{+}n\ensuremath{\rightarrow}{K}^{0}p$ at 2.3 GeV/c, is presented; a single pair of vector coupling constants is able to account for the various angular distributions of production. The theory predicts, and preliminary data confirm, appreciable momentum-transfer dependence of the ${K}^{*}$ spin-density matrix. Equally satisfactory fits to the data are found for ${K}^{+}p\ensuremath{\rightarrow}{K}^{0}{N}^{*++}$ at 3 GeV/c, ${K}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{Y}^{*}$ (1385) at 2.24 GeV/c, and ${\ensuremath{\pi}}^{+}n\ensuremath{\rightarrow}\ensuremath{\omega}p$ at 3.25 GeV/c. In the latter reaction the absorption model reproduces the large departure of the $\ensuremath{\omega}$-decay correlations from those characteristic of $\ensuremath{\rho}$ exchange in the absence of absorption. The model cannot explain why the differential cross section for ${\ensuremath{\pi}}^{+}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{N}^{*}$ is considerably narrower than for ${K}^{+}p\ensuremath{\rightarrow}{K}^{0}{N}^{*}$. The theoretical momentum-transfer distributions and decay correlations for double resonance production ($\ensuremath{\pi}p\ensuremath{\rightarrow}\ensuremath{\rho}{N}^{*}$, $\mathrm{Kp}\ensuremath{\rightarrow}{K}^{*}{N}^{*}$) are in general agreement with the data, as are the results on combined decay correlations of $\ensuremath{\rho}$ and ${N}^{*}$ in ${\ensuremath{\pi}}^{+}p\ensuremath{\rightarrow}{\ensuremath{\rho}}^{0}{N}^{*}$. But the calculated absolute cross sections are considerably larger than observed, probably because the model fails to include the requirements of unitarity, important when the couplings are large. The determination of vector-meson coupling constants is discussed. Because of fundamental difficulties associated with vector-meson exchange amplitudes at high energies, it is concluded that important refinements of the model are necessary if such coupling constants are to be inferred from the data.

Coupling constants in broken unitary symmetry

A set of Yukawa coupling constants needed in analytic calculations of pseudoscalar meson-baryon amplitudes (including exchange of resonances, vector mesons and baryons) is presented. Since, in such calculations, the existence of poles is very sensitive to the values of the crossed-channel couplings, one needs to improve on exact unitary symmetry predictions, which, as is well known, give inaccurate ratios for a number of already known parameters (e.g.\(g_{K \cdot K\pi } /g_{\rho \pi \pi } ,g_{Y_1^ \cdot \pi \Sigma } \) and\(g_{\Xi \cdot \pi \Xi } /g\)N*Nπ). The coupling constants are here calculated by taking into account first-orderSU3 violations, as already suggested by Muraskin and Glashow. The universality conditions of Sakurai are imposed on vector-meson couplings, which drastically reduces the number of parameters. The results are compared with the scanty experimental data, which, however, can provide tests of the first-order violation hypothesis.

Erratum to: Minimal electromagnetic coupling of vector mesons

Erratum to: Minimal electromagnetic coupling of vector mesons

Unitary Symmetry and the Transformationη→π0

The transformation $\ensuremath{\eta}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}$, which is thought to play a dominant role in the decay mode $\ensuremath{\eta}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}$, is examined in the light of unitary symmetry and several different models for $\ensuremath{\eta}$ decay. Beside the models of Gell-Mann, Sharp, and Wagner (GSW), and of Barrett and Barton (BB), these include the strong coupling of pseudoscalar and vector meson octets with the unitary singlet vector meson $\ensuremath{\phi}$, and the electromagnetic coupling of pseudoscalar and vector mesons. Group-theoretical methods are used to confirm that the contributions of all but one of the lowest order diagrams on the GSW model cancel one another. The same methods show that the cancellations in lowest order are not as serious for the BB model, and are nonexistent for models involving the $\ensuremath{\phi}$ meson.

A model of the universal fermi interaction

It follows from the Feynman-Geil-Man theory that the Fermi interaction can be regarded as due to an exchange of charged vector mesons between fermions. An alternative model is possible the weak couplings among fermions may be due to an exchange at charged and partial vector mesons. An extra condition of conservation of the correct which errates the neutral field is imposed to forbid unobserved reactions. The model esters from the Feynman-Gell-Mann picture in that it leads to anintrinsic electron-neutron interaction, the effective potential being of the order of 4 eV. If the coupling of this hypothetical vector meson with fermions has the same strength as the electric charge, the particle will have about 50 proton masses and will decay very fast into pairs of hyporates.