Vector-meson Model Research Articles

Improved model of vector mesons in holographic QCD

We analyze the sector of dimension-three vector meson operators in the ``hard-wall'' model of holographic QCD, including the vector and axial currents, dual to gauge fields in the bulk, and the tensor operator $\overline{\ensuremath{\psi}}{\ensuremath{\sigma}}^{\ensuremath{\mu}\ensuremath{\nu}}\ensuremath{\psi}$, dual to a two-form field satisfying a complex self-duality condition. The model includes the effect of chiral symmetry breaking on vector mesons, that involves a coupling between the dual gauge field and the two-form field. We compute the leading logarithmic terms in the operator product expansion of two-point functions and the leading nonperturbative contribution to the tensor-vector correlator. The result is consistent with the operator product expansion of QCD. We also study the spectrum of vector mesons numerically.

Vector and axial anomaly in the Thirring–Wess model

We study the two dimensional vector meson model introduced by Thirring and Wess, that is to say the Schwinger model with massive photon and massless fermion. We prove, with a renormalization group approach, that the vector and axial Ward identities are broken by the Adler–Bell–Jackiw anomaly; and we rigorously establish three widely believed consequences: (a) the interacting meson-meson correlation equals a free boson propagator, although the mass is additively renormalized by the anomaly; (b) the anomaly is quadratic in the charge, in agreement with the Adler–Bardeen formula; (c) the fermion-fermion correlation has an anomalous long-distance decay.

Pion generalized parton distributions with covariant and light-front constituent quark models

We investigate the model dependence of no-helicity flip generalized parton distribution of the pion upon different approaches for the quark-hadron and quark-photon vertices, in the spacelike region. In order to obtain information on contributions from both the valence and the nonvalence regions, we compare results for spacelike momentum transfers obtained from (i) an analytic covariant model with a bare quark-photon vertex, (ii) a light-front approach with a quark-photon vertex dressed through a microscopic vector-meson model, and (iii) a light-front approach based on the relativistic Hamiltonian dynamics. Our comparisons lead us to infer the same dynamical mechanism, the one-gluon-exchange dominance at short distances, as a source of both the electromagnetic form factor at large momentum transfer and the parton distribution close to the end points. The expected collinear behavior of the generalized parton distributions at high-momentum transfer, i.e. a maximum for x{approx}1, is also illustrated, independently of the different approaches. Finally, a comparison with recent lattice calculations of the gravitational form factors is presented.

Baby Skyrmions stabilized by vector mesons

Recent results suggest that multi-Skyrmions stabilized by {omega} mesons have very similar properties to those stabilized by the Skyrme term. In this paper we present the results of a detailed numerical investigation of a (2+1)-dimensional analogue of this situation. Namely, we compute solitons in an O(3) {sigma} model coupled to a massive vector meson and compare the results to baby Skyrmions, which are solitons in an O(3) {sigma} model including a Skyrme term. We find that multisolitons in the vector meson model are surprisingly similar to those in the baby Skyrme model, and we explain this correspondence using a simple derivative expansion.

On the vector meson dominance in effective chiral lagrangians

We generalize a recently proposed effective chiral vector meson model to the N flavour case. That the low energy predictions involving purely pseudoscalar and electromagnetic processes should not be altered without any constraints on the parameters of the model, due to the new vector meson contributions, is confirmed in the presence of the Wess-Zumino term. At the end, we critically compare our scheme with another one recently proposed which introduces the vector mesons as composites of pions.

Quasi-renormalization of the axial vector model. A BPHZL approach

Using the regulator-free BPHZL renormalization scheme we reinvestigate the problem of anomalies in a massive axial vector meson model. The Adler-Bardeen-Bell-Jackiw anomaly introduces some impressive modifications: the nontrivial self-energy and the counterterm of the longitudinal part of the axial vector field depend on the anomaly via the anomalous Ward identity. Our investigations are based on a Fermitype gauge.

Perturbation theory for two-dimensional gauge models

Euclidean symmetric integration, previously proposed for the SU(N) Yang-Mills theory in the limit of large N, is used to study the propagators in the Schwinger model and the massive vector-meson model in two dimensions. The result of summing the perturbation series agrees with the exact solution in each case. Therefore, perturbation theory is here capable of dealing with non-analytic behaviour in the coupling constant.

Anomalouseμevents ine+e−annihilation and heavy vector mesons

As a possible explanation of the SLAC anomalous $e\ensuremath{\mu}$ events, we computed the cross section for ${e}^{+}+{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{V}^{+}+{V}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ifmmode\pm\else\textpm\fi{}}+{e}^{\ensuremath{\mp}}+\mathrm{neutrinos}$, taking into account the spin correlations of ${V}^{\ifmmode\pm\else\textpm\fi{}}$. Analytic formulas for the experimentally measured cross sections are given. The spin-correlation effects turn out to be small when ${V}^{\ifmmode\pm\else\textpm\fi{}}$ has vanishing anomalous magnetic moment ($\ensuremath{\kappa} = 0$), but are considerable for $\ensuremath{\kappa} \ensuremath{\approx} 1$. While the choice $\ensuremath{\kappa} = 0$ gives an unacceptable fit to the data, the choice $\ensuremath{\kappa} = 1$ improves the fit quite dramatically. The overall fit is still not good. However, we believe that the vector-meson model (with $\ensuremath{\kappa} \ensuremath{\approx} 1$) is not yet ruled out by the available data.

Thermal states of the vector meson model in two dimensions

We compute the KMS states for the vector meson model in two-dimensional space-time. We also consider their limit to those of the Thirring model.

Thermal states of the vector meson model in two dimensions: Daniel A. Dubin. Faculty of Mathematics, The Open University, Walton Hall, Milton Keynes, MK7 6AA, England

Thermal states of the vector meson model in two dimensions: Daniel A. Dubin. Faculty of Mathematics, The Open University, Walton Hall, Milton Keynes, MK7 6AA, England

Electromagnetic mass difference of vector mesons

We discuss an effective Lagrangian model of vector mesons interacting with themselves and photons, which yields finite lowest-order dynamical electromagnetic corrections to the vector-meson masses. The strong-interaction part of the Lagrangian is given by a renormalizable model of 't Hooft, based on massless Yang-Mills fields which acquire mass by the Higgs-Kibble mechanism. The relationship of this vector field to the usual massive Yang-Mills field and of our electromagnetic interaction to that of Kroll, Lee, and Zumino is discussed in the light of a suggestion made by Lee and Zinn-Justin that the renormalizable vector field may be a regularized version of the usual massive vector field. The mass shifts of the charged and neutral $\ensuremath{\rho}$ mesons are found to be small and nearly equal, well within present experimental uncertainties in the $\ensuremath{\rho}$-meson masses.

Spontaneousφ−ωMixing in a Vector Nonet Model

A previous model of vector mesons is extended to study $\ensuremath{\varphi}\ensuremath{-}\ensuremath{\omega}$ mixing in a vector nonet. It is found that a phenomenon which can be interpreted as "spontaneous mixing" does occur in the model, and the well-known equations ${\ensuremath{\varphi}}^{2}+{\ensuremath{\omega}}^{2}=2{K}^{*2}$ and $4{K}^{*2}\ensuremath{-}3({cos}^{2}\ensuremath{\theta}{\ensuremath{\varphi}}^{2}+{sin}^{2}\ensuremath{\theta}{\ensuremath{\omega}}^{2})\ensuremath{-}{\ensuremath{\rho}}^{2}=0$ emerge from the calculation. The mixing angle cannot be determined in our model; but it is found that if violations to $\mathrm{SU}(3)$ become vanishingly small, we have a 50% mixing.

Octet Enhancement in a Model of Vector Mesons

A simple bootstrap model of vector mesons is constructed in which the origin of octet enhancement is examined. A parametrized-one-pole approximation is used to solve the $\frac{N}{D}$ equations. The pole parameter is determined by the bootstrap condition and the type of asymmetric solution that emerges. It is demonstrated that the emergence of the Gell-Mann-Okubo formula follows from two general dynamical requirements: the bootstrap self-consistency condition and the requirement that the "vector mesons" are real physical particles and not ghost states.

Potential model of SU(3)-symmetry breaking for mesons

This is an investigation in a simple model of dynamically produced deviations from unitary symmetry. A potential analogue of a bootstrap model of vector mesons is used: the vector meson octet is treated as bound state of two pseudoscalar meson octets, the latter being bound by a vector-meson octet exchange. An approximate bootstrap solution is first obtained for the mass of degenerate vector mesons and their SU(3)-invariant coupling to degenerate pseudoscalar mesons. The mass splitting within the pseudoscalar meson octet is then considered as an input. The effects of mass splitting within the exchanged vector-meson octet and the deviations from their SU(3)-symmetric values of the coupling constants of the exchanged vector mesons to the pseudoscalar mesons are studied. It is found that the direct effect of the splitting of the exchanged mass of the bound-state mass is small; however its sign cannot be determined by naive considerations and is model dependent. It is found also that the effects of the deviations in the coupling constants cannot be ignored. A comparison is made with the work of ref. [10].

Nonleptonic Decays ofKMesons in Chiral Dynamics and the Proof of the ΔI=1/2 Rule

We construct weak interactions from the nonlinear chiral invariant Lagrangian, and dis­ cuss the nonleptonic decays of K mesons in the chiral vector meson model. Correction to this model due to the current-current interact jon and the K*- and KA-poles violates the AI=1/2 rule, but the violation is quite small and consistent with experiment. Moreover we assume the intermediate boson mass to be 12 Be V in the model to explain the K 1°-'>2rr: decay rate. 1 ) has derived an effective Lagrangian for soft-pion interac­ tion, which reproduces the results of current algebra in a simple way. On the basis of the (J model, he has employed an SU(2) chiral transformation. Schwinger2) has also derived an effective Lagrangian, and has introduced the vector and axial-vector mesons as gauge fields. The concept of chiral invariance plays ail important role in understanding the low energy phenomena. The purpose of this paper is to show that chiral invariance is also useful for the problem in weak interactions. Moreover we discuss the nonleptonic decays of K mesons, and prove the validity of the LJI = 1/2 rule on the basis of the chiral invariant Lagrangian. In§ 2 a generalization of the SU (2) chiral dynamics to SU (3) is formulated ll1 the quark model. S ) The vector and axial-vector mesons are introduced as gauge fields. The Lagrangian written by actual fields is invariant under the nonlinear chiral transformation. In § 3 the Lagrangian for the weak interaction is constructed from the Lagrangian for the strong interaction obtained in § 2. In § 4 the nonleptonic decays of K mesons and the LJI = 1/2 rule are discussed. It can be shown that the LJI = 1/2 rule holds, though at first sight the weak Lagrangian (17) seems to violate the 111=1/2 rule. In a previous paper 4 ) we considered the K-72n decay and proved the 111=1/2 rule for this process on the basis of the quark model. In this paper we consider the K1D decay by the self­ energy type diagram due to the vector mesons, the axial-vector mesons and the intermediate boson without introduction of quark. We find that this model (chiral vector meson model) also explains the 111=1/2 rule, and that the result of this model is the same as current algebra with a slight difference in coefficient. The contributions of the current-current interaction and the K* -pole and KA-pole;· 1402

Bootstrap Model with Hadrons of Both Parities

A bootstrap condition, used commonly to study internal symmetries, is generalized so that it may be applied to states of different spins and parities. A bootstrap model of vector mesons and spin-\textonehalf{} baryons, developed by Cutkosky and Polkinghorne, is generalized to $\mathrm{SU}{(6)}_{W}$ symmetry and to include mesons and baryons of both parities. A solution is found involving odd- and even-parity mesons and even- and odd-parity baryons that correspond to the $\mathrm{SU}{(6)}_{W}$ representations 35, 35 \ensuremath{\bigoplus} 1, 56, and 70, respectively. The existence of the solution depends on certain exact properties of the 35\ensuremath{\bigotimes}56 and 35\ensuremath{\bigotimes}35 crossing matrices of $\mathrm{SU}(6)$. The physical interpretation of the solution is discussed; the odd-parity baryon multiplet corresponds physically to the $\mathrm{SU}(6)\ensuremath{\bigotimes}O(3)$ representation (70, 3).

Interactions of massless spinors in two dimensions

The interaction of massless spinors with massive vector mesons ( m 0 > 0) in two dimensions is investigated. (We call this model the vector meson model.) Two definitions of the current are considered, and operator solutions employing auxiliary free fields are constructed. However, the presentation is heuristic in part, and the problem of positive definiteness of the theory is left open. The limit m 0 → ∞ is easily obtained; it yields the Thirring model. (This fact was expected on the basis of unpublished thesis of Wraith.) Some complications are indicated in connection with the limit m 0 → 0, to the Schwinger model.

Equation of Stars of Matter at Supernuclear Density.

Vector meson model state equation to describe matter at supernuclear density - gravitational collapse

A model requiring lie group symmetries

Cutkosky's model of vector mesons in mutual interaction is rediscussed and extended by the introduction of further particles. The dynamical picture used is one based on the generation of Regge poles in scattering amplitudes in perturbation theory. It is found that particles of spin less than one must belong to representations of the Lie group of which the vector mesons form the adjoint representation. It is also found that the strength of the interaction of the lower spin particles is determined by the strength of the mutual interaction of the vector mesons, at least in the approximation discussed.

Polarization Effects of Vector-Mesons

Adopting a vector-meson model for the $\ensuremath{\pi}$-meson we study (I) the polarization of $\ensuremath{\pi}$-mesons produced in nucleon-nucleon-collisions; (II) the angular distribution of $\ensuremath{\mu}$-mesons resulting from $\ensuremath{\pi}\ensuremath{-}\ensuremath{\mu}$-disintegrations, as depending on the polarization of the $\ensuremath{\pi}$-mesons; (III) the effect of electromagnetic fields on this polarization, in particular; (IV) the depolarization caused by the electric fields in matter. The theoretical results are encouraging for an experimental investigation.