Coupling constants and the nonrelativistic quark model with charmonium potential

Hadronic coupling constants of the vertices including charm mesons are calculated in a nonrelativistic quark model. The wave functions of the mesons which enter the corresponding overlap integrals are obtained from the charmonium picture as quark-anti-quark bound state solutions of the Schrödinger equation. The model for the vertices takes into account in a dynamical way the SU₄ breakings through different masses of quarks and different wave functions in the overlap integrals. All hadronic vertices involving scalar, pseudoscalar, vector, pseudovector and tensor mesons are calculated up to an overall normalization constant. Regularities among the couplings of mesons and their radial excitations are observed: (i) Couplings decrease with increasing order of radial excitations; (ii) in general they change sign if a particle is replaced by its next radial excitation. The k-dependence of the vertices is studied. This has potential importance in explaining the unorthodox ratios in different decay channels (e.g. $\text{D}\text{D}\text{, D}\text{D}{}^1\text{, D}{}^1\text{D}{}^1$). Having got the hadronic couplings radiative transitions are obtained with the current coupled to mesons and their recurrences. The resulting width values are smaller than those conventionally obtained in the native quark model. The whole picture is only adequate for nonrelativistic configurations, as for the members of the charmonium- or of the γ-family and most calculations have been done for transitions among charmed states. To see how far nonrelativistic concepts can be applied, couplings of light mesons are also considered.     

Five quarks,new particles and V + A currents

We propose an SU(5) model for the new heavy mesons, with a charge $\text{?1}\text{3}$ fancy quark in addition to a charge $\text{+2}\text{3}$ charmed quark. Besides interpreting the two narrow vector mesons J/Ψ and Ψ′ as c$\text{c}$ and f$\text{f}$ bound states and accounting for present data in a natural way, the model has (i) three new fancy vector mesons in addition to the charmed ones of the SU (4) model, (ii) at most two new $\text{C = P = +}\text{mesons}\text{(}\text{c}\text{c}\text{,}{}^3\text{P}{}_{\mathrm{J}}\text{, J = 0, 1)}$ between J/Ψ and Ψ ′, with suppressed radiative decays $\text{Ψ′ →}{}^3\text{P}{}_{\mathrm{J}}\text{+ γ}$, (iii) a state near 4.6 GeV in e⁺e^?, decaying mostly to fancy mesons if it is broad or perhaps charmed mesons if it is narrow, (iv) V + A weak currents and a large anomaly in $\text{ν}$N reactions, (v) a possible heavy lepton.     

Meson decay constants and bare quark masses from duality for current two-point functions

Duality is applied in a quasi-local form to the SU(4) × SU(4) current two-point functions. Interpolating functions for some of their space-time components are assumed to be given by the free quark model. Mass intervals in the finite energy sum rules are taken to be approximately SU(3) × SU(3) invariant and a linear dependence of the hadronic mass spectrum upon the radial quantum number is assumed. The correct order of magnitude of various meson decay constants is reproduced provided the color gauge group is SU(3). The bare uncharmed quark masses are given by the formulae: $\text{m}{}_{\mathrm{<mtext>u</mtext>}}\text{≌ M}{}_{\mathrm{\pi }}\text{F}{}_{\mathrm{\pi }}\text{/F}{}_{\mathrm{\pi }}\text{√6 ≌ 40}\text{MeV}\text{, m}{}_{\mathrm{<mtext>s</mtext>}}\text{/m}{}_{\mathrm{<mtext>u</mtext>}}\text{≌ 1 = 6}$. The η-η mixing problem is discussed. Predictions are made for the masses and decay constants of the vector mesons of the first L = 2 level of SU(6) × O(3), as well as for the decay constants of the radially excited pseudoscalar mesons; estimates of corrections to PCAC in Goldberger-Treiman relations are presented. The bare charmed quark mass is found to be of the order of 1.1–1.2 GeV. Some decay constants of charmed mesons are evaluated.     

Electromagnetic mass differences of the old and the charmed mesons

We predict for M_?⁺?M_?⁰ the values -3.4 ± 0.8 MeV using the ?-ω mixing and the quark model, respectively. The extracted parameters indicate the necessity of a relativistic treatment of the old mesons. The problem of extrapolating these parameters to the charmed mesons is discussed. Under conservative assumptions, we predict 1.7 ? M_D⁰ ? 2.2 MeV and .     

Quark mass effects as isospin and SU(3) violations in radiative decays of vector mesons

Radiative decays of vector mesons, V → Pγ, are discussed in terms of the QCD quark model, in the chiral limit. By taking into account isospin and SU(3) breaking by the quark mass matrix good agreement is found with the experimental data. In particular, the hitherto unexplained smallness of the K¹⁰ → K⁰γ and ?^? → π^?γ rates is justified provided $\text{m}{}_{\mathrm{<mtext>s</mtext>}}\text{m}{}_{\mathrm{<mtext>d</mtext>}}\text{≈ 20}$ and $\text{m}{}_{\mathrm{<mtext>d</mtext>}}\text{m}{}_{\mathrm{<mtext>u</mtext>}}\text{? 50}$.     

Meson decays in the non-relativistic quark model

Treating light as well as heavy pseudoscalar and vector mesons as non-relativistic quarkonia, we calculate various decay modes, including lowest QCD corrections. All decay modes studied are in good agreement with experiment, indicating that the quarkonium treatment is applicable to light mesons η, η′, π, also. Consistency of the quarkonium and current algebra treatments for the process π⁰ → 2λ leads to $\text{f}{}_{\mathrm{\pi }}\text{= (}\text{3}\text{2π}\text{)m}{}_{\mathrm{<mtext>u</mtext>}}\text{{1 ? (0.62/4π)α}{}_{\mathrm{<mtext>s</mtext>}}\text{(μ)},}\text{where}\text{m}{}_{\mathrm{<mtext>u</mtext>}}$ is the constituent u-quark mass, and $\text{f}{}_{\mathrm{\pi }}\text{? 93}\text{MeV}$.     

Neutral K1(890) and ρ0 meson production in e+e− annihilation at ;s=29GeV

The production of neutral K¹(890) and ρ⁰ mesons was studied in e⁺e^? annihilation at $\text{s}\text{=29}\text{GeV}$ using the High Resolution Spectrometer at PEP. Differential cross sections are presented as a function of the scaled energy variable z and compared to π⁰ and K⁰ production. The measured multiplicities are 0.84±0.08 ?⁰ mesons and $\text{0.57±0.09 K}{}^{10}\text{(890)}$ mesons per event for a meson momentum greater than 725 MeV/c. The ratios of vector meson to pseudoscalar meson production for (u,d), s and c quark are compared to predictions of the Lund model.     

Chiral ward identities,effective actions and meson-glueball mixing

The low-energy spectrum of 1⁺ and 0^? mesons in one-flavour QCS is investigated. It is shown that there exist two light pseudoscalar mesons, which are linear combinations of pure quark and pure glueball states. Simple relations implied by the axial anomaly for their decay constants are confirmed. The mass generation mechanism for the lightest pseudoscalar meson is identified as due to the mixing of the operators $\text{i}\text{ψ}\text{γ}{}_5\text{ψ}$ and $\text{(?}\text{g}{}^2\text{16π}{}^2\text{)}{}^1\text{F}{}_{\mathrm{\mu \nu }}{}^{\mathrm{a}}\text{F}{}^{\mathrm{a\mu \nu }}$, and the U(1) problem in this model is resolved. To establish these results, new functional methods are developed to determine the effective action for the appropriate fields in a low-energy approximation. A novel feature of our work is the introduction of a “symmetric” effective action, defined using a non-standard Legendre transform. The anomalous chiral Ward identities imply a simple invariance property for this functional, enabling it to be constructed in a particularly systematic way. Finally, the relation of our general results to the literature on effective lagrangians in the $\text{1}\text{N}$ approximation is discussed.     

Dual parton model and the photoproduction of pseudoscalar and vector mesons in the high energy region

On the basis of the dynamical dual model of strong interactions followed from the parton model of hadrons as discussed in an earlier paper, we study here the photo-production of pseudoscalar and vector mesons in the high energy region. To incorporate the concept of duality, it is taken that any two spin $\text{1}\text{2}$ pointlike constituents (partons) can form a π-meson cluster in the structure of a nucleon and the basic interaction involved in MB scattering is the interaction of the incident meson with the π meson in the structure of the nucleon. In this scheme, the amplitudes for the photoproduction of mesons such as γN → Nπ, γN → N?, and γN → Nω in the high energy region can be related with the amplitudes for the process γπ → ππ, γπ → π?, and γπ → πω, respectively. To calculate the amplitudes for the relevant process we also consider a factor corresponding to the structural rearrangement of partons involved in duality diagrams. To obtain the cross sections, we take into account the photon-vector meson analogy, though the naive form of the vector dominance model (VDM) has not been considered here. From a knowledge of the coupling constants $\text{γ?}{}^2\text{4π}$, $\text{γω}{}^2\text{?π}$, , and we obtain the differential cross sections which are in excellent agreement with experimental results. Also we obtain a good fit for the scattering process γN → Nπ at backward angles. For the vector meson production processes, we have contributions from the diffraction mechanism also apart from the amplitudes considered here. In the region where the contribution from the diffraction part is negligible, we obtain the relation

which is in nice agreement with experiments. Finally, it is shown that, though the vector meson dominance is not considered here, the universality of the vector meson coupling with hadrons follows directly from the present model.     

Electro- and chromomagnetism in the charm meson spectrum

We discuss how the D and F meson spectrum is influenced by the chromomagnetic and electromagnetic hyperfine interaction. In particular a relation between the hyperfine splitting of charmed mesons and the magnetic moments of the baryons is derived. We find $\text{M(}\text{F}{}_{\mathrm{+}}{}^1\text{) ? M(}\text{F}{}_{\mathrm{+}}\text{) ≈ 100 ± 8}\text{MeV}$.     

Vector-axial vector interference terms in inelastic neutrino reactions extrapolated from single-pion photoproduction

By use of the generalized scaling sum rules the vector-axial vector interference terms in the scaling limit of the inelastic neutrino reactions are calculated from the absorptive parts of the single-pion photoproduction amplitudes at zero momentum transfer. The photoproduction amplitudes are evaluated by use of the results of multipole analysis. With the optimum values for the two parameters of the generalized scaling as determined in previous works, we have obtained F₃^νN(ω) which leads to good agreement with experiment in the ration of $\text{σ}{}^{\mathrm{<mtext>\nu </mtext><mtext>N</mtext>}}\text{/σ}{}^{\mathrm{<mtext>\nu </mtext><mtext>N</mtext>}}$. However, the zeroth moment in $\text{x( = 1/ω), ∫}{}_0{}^1\text{d}\text{x(F}{}_3{}^{\mathrm{<mtext>\nu </mtext><mtext>p</mtext>}}\text{+ F}{}_3{}^{\mathrm{<mtext>\nu </mtext><mtext>p</mtext>}}\text{)}$ turns out to be smaller than half of the value predicted in the fractionally charged quark model.     

Transition magnetic moments of hadrons and sidewise dispersion relations

Systems of linear relations for the magnetic moments of the nucleon and transition moments μ_ωπγ, μ_?πγ and ${}^{\mathrm{\mu }}\text{N}{}^1{}_{1470}\text{N}\text{γ}$ are obtained on the basis of sidewise dispersion relations in the one-pion approximation. In such an approach the magnetic moments of the transition ω(?)→ πγ and $\text{N}{}^1{}_{1470}\text{→Nγ}$ are expressed in terms of the anomalous magnetic moments of the nucleon and the strong interaction coupling constants.     

The mixing and decays of isoscalar mesons

The predictions of a linear mass mixing model for pseudoscalar and vector mesons, which incorporates the effects of radial excitations, are examined. Several analyses are made fitting in each case to a different experimental value of $\text{Γ(ψ →η'γ)}\text{Γ(ψ→ηγ)}$ upon which the η-η′ mixing pattern is very sensitive. Predictions for radiative transitions among the mesons and for the ratio of production amplitudes $\text{σ}\text{(π}{}^{\mathrm{?}}\text{p→η′n)}\text{σ}\text{(π}{}^{\mathrm{?}}\text{p→ηn)}$ are compared with experiments. Results indicate a preferred value of 3.1 for $\text{Γ(ψ→η′γ)}\text{Γ(ψ→ηγ)}$.     

On Weinberg's model of CP violation in gauge theories

The consequences of the Weinberg model of CP violation in gauge theories (ref. [1]) are discussed in detail. It is shown (using the valence quark hypothesis) that the contribution of the induced superweak interaction to the experimentally measured quantities η+? and η₀₀ are ≈m_K²/m_π² times larger than that of the direct milliweak decay K₂⁰→2π. The correction to the relation |η+?|/|η₀₀|=1 is also calculated in the model. We estimate the neutron dipole moment $\text{(D}{}_{\mathrm{<mtext>n</mtext>}}\text{??2.8·10}{}^{\mathrm{?25}}\text{e.cm.}\text{)}$ and note that the dipole moments of particles with strange quark constituents should be about three orders of magnitude larger $\text{(}\text{e.g.}\text{D}{}_{\mathrm{\Lambda }}\text{??1.15·10}{}^{\mathrm{?22}}\text{e·}\text{cm}$. The CP violating vertex d?s + gluon is also discussed.All physical quantities appear to depend crucially on the values of quark masses, so that CP violating effects in the models of the type considered may elucidate the nature of quark masses. We argue that the bare (or “mechanical”) values should be used in the calculations and this leads to a considerable difference in the estimates of various effects as compared to those of ref. [1].     

Does the enhancement mechanism work in non-leptonic decays of heavy pseudoscalar mesons with new flavors (b and t)?

We show that the enhancement mechanism proposed for non-leptonic decays of charmed mesons (D⁰, F⁺) is still important for decays of pseudoscalar mesons with b flavor, while its effect is small for mesons with t flavor. For the semi-leptonic branching ratios of B^? (b$\text{u}$), B⁰(b$\text{d}$) and B_S⁰(b$\text{s}$) we predict BR (B^? → evX ～' 9%, BR(B⁰ → evX) ～' BR(B_s⁰ → evX) ～' 5%. We can also derive the enhancement of the branching ratios of uncharmed final states in B decays, i.e. $\text{BR}\text{(}\text{B}{}^{\mathrm{?}}\text{→}\text{X}{}_{\mathrm{<mtext>s</mtext><mtext>u</mtext>}}\text{)}$ ～' 20 %, $\text{BR}\text{(}\text{B}{}^0\text{→}\text{X}{}_{\mathrm{<mtext>s</mtext><mtext>d</mtext>}}\text{)}$ ≈ 10%, where $\text{X}{}_{\mathrm{<mtext>s</mtext><mtext>u</mtext><mtext>(</mtext><mtext>s</mtext><mtext>d</mtext><mtext>)</mtext>}}$ = $\text{K}$π + ... + $\text{K}$K$\text{K}$ + ... .     

Asymptotic energy scale factors for pseudoscalar meson scattering and charmed meson couplings

Energy scale factors ν₀ for PP → PP scattering amplitudes are related via the absence of exotic resonances to ratios of tensor to vector coupling strengths. These same ratios are extracted from FESR's for non-exotic reactions. The scale factors obtained are all of the order of 1.0 GeV²or less, independent of quantum numbers. This contradicts the expectations of dual amplitudes in which ν₀ = 1/α′, and trajectory slopes are smaller for charmed mesons. Decay widths for tensor mesons are predicted. An observed SU(3) violation for the ratio $\text{A}{}_2\text{→}\text{K}\text{K}\text{/}\text{K}{}^7\text{→}\text{K}\text{π}$ is shown to be consistent with the FESR results. Charmed meson decays are predicted to be factors of 2–3 larger than those predicted by SU(4).     

The properties of charmed baryon (Λc+) and the proton revisited

A statistical model for baryons was suggested leading to an analytical expression for the square modulus ∥ψ(r)∥² of baryon wavefunctions, which is not only free of constituent quark masses but also devoid of the interaction parameters of the effective linear potential in which a quark moves. Using ∥ψ(r)∥² as an input the lifetimes of the newly established charmed baryon ($\text{Λ}{}_{\mathrm{c}}{}^{\mathrm{+}}$) and the proton were studied and compared with other existing theoretical estimates.