Quark-hadron duality and meson-meson scattering amplitudes

We investigate a special concept of quarkhadron duality in meson physics at low and intermediate energies. With a relativistic propagator for confined quarks, we calculated masses and widths of the mesons which areS- andP-wave states ofq¯q (J ^P=0^?, 1^?, 0⁺, 1^+c, 2⁺) as well as meson-meson scattering amplitudes at energies up totrs ≤ 1.3 GeV by including light pseudoscalar and vector mesons into the interaction dynamics. Our investigation shows that the influence of the light meson dynamics resutls in:

1. a contribution to the constituent quark mass of approximately 200 MeV.
2. the appearance of a new soft confinement force barrier responsible for the formation of the highly excited meson states.

     

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.     

Quark model for the production of pseudoscalar mesons in annihilation

A modification of the quark model for annihilation permits the calculation of the relative probabilities of all observed channels with pseudoscalar mesons. Agreement with the experimental data on proton-antiproton annihilations at rest into three and more mesons is obtained.     

Mass splitting of the pseudoscalar and vector mesons induced by the homogeneous vacuum gluon field

Masses of the pseudoscalar and vector mesons are calculated within the generalized Nambu-Jona-Lasinio model taking into account homogeneous vacuum gluon field. This vacuum provides an analytical quark confinement. Colorless modes are determined by the confined gluons and are described by the nonlocal quark currents with appropriate radial and angular quantum numbers. An interaction of the quark spin with the vacuum gluon field arises naturally within the model under consideration. It is shown that this spin-field interaction leads to mass splitting between vector and pseudoscalar mesons with identical quark structure (ρ-π,K-K ^* and so on). This allows to use the four-fermion coupling constant being common for both nonets.     

Gluon effects and nonet mixing in the current quark picture

The effects on the meson mass spectrum of gluon interactions, and in particular of quark annihilation diagrams, are investigated in the current quark framework. The resulting mixing scheme leads to mixing angles θp ? ?13° and θ_V ? ? 52° for the pseudoscalar and vector nonets respectively, in moderate agreement with present data on radiative decays. For virtual electromagnetic processes additional gluon diagrams play a role. In η → 3π the net effect is to almost double the current algebra prediction, while in ω → 2π the ω → ?⁰ transition amplitude is correctly predicted in both sign and magnitude. The relation between the Hamiltonian approach and the U(1) problem, as formulated in terms of axial divergences, is briefly discussed.     

Low energy antiproton-proton annihilation and meson spectroscopy

Recent results in antiproton-proton annihilation at rest from the Crystal Barrel at CERN/LEAR are reviewed. Rates for annihilation at rest into various two-body channels have been measured. In spite of the complexity of the annihilation mechanism, simple tests based on the underlying quark constituents can be applied. The annihilation process is also useful to investigate the spectrum of light quark mesons and to search for exotic (non-q¯q) mesons. Three scalar states have been found in the 1500 MeV mass region. One of them is a good candidate for the ground state glueball.     

Rates for the reactions\bar pp \to \pi \phi andγ φ

We study ¯pp annihilation at rest intoπφ andγφ. Rescattering by ¯K^*K+K^*¯K and ρ⁺ρ^? for ¯pp→πφ states is sizable, of order (0.90 to 2.6) × 10^?4 in the branching ratio, but smaller than experiment. For ¯pp→γφ the rescattering contributions are negligible, but theγφ channel is well explained by aρφ intermediate state combined with vector meson dominance.     

The inclusive proton spectrum for\bar pd \to 3\pi p at rest re-examined

We re-analyze the spectator proton distribution for ¯pd→π ⁺ π^? π^? p. For this channel previous calculations underestimated the cross section for proton momenta of 300 to 600 MeV/c by about a factor 7 while the channels with higher pion multiplicities and the ¯pd→K¯ Kmπp reactions were well explained. By using detailed experimental information on ¯pn and ¯pp annihilation, meson rescattering can in fact explain the cross section also for the 3π case. The¯ pp annihilation followed by charge exchange pion rescattering is much larger than in the 5π case. Vector meson exchange is small but not negligible at high spectator momenta.     

N\bar N annihilation at rest into πππ andK\bar K\pi in the3 P 0 model and selection rules on the πρ,K\bar K* and\bar KK* production

\(N\bar N\) annihilation into three pseudoscalar mesons especially πππ and \(K\bar K\pi \) are studied in the quark pair creation model or the³ P ₀ model in which two \(q\bar q\) pairs are annihilated and two \(q\bar q\) pairs are created with quantum numbers of the vacuum or³ P ₀. The correlations of two pions to form ?,f ₂ and the resonance AX(1565) which is recently found by the ASTERIX group are taken into account. A proper treatment of the symmetry among the three pions in the final state shows that the \({}^{31}S_0 p\bar p\) annihilation into ?π is suppressed in agreement with the experiment. We calculate the cosθ distribution or the distribution of the Dalitz plot as the function of the angle between the direction of emission of one decay pion in the resonance centre of mass and the line of flight of the resonance. The interferences of π⁺ρ⁺, π^?ρ⁺ and π⁰ρ⁰ in the isospin 0 channels and π^±ρ^? and π⁰ f ₂ in the isospin 1 channel reproduce the peaks. The cos θ distribution for the P-wave \(p\bar p\) annihilation into πAX depends strongly on the size of the pion since the amplitude interfers with the π^±ρ^? amplitude which is sensitive to the size of the pion. The same model qualitatively explains the \(p\bar p\) annihilation into \(K\bar K\pi \) in whichK or \(\bar K\) and π are correlated to formK* \(\bar K\) or \(\bar K\) *K final states. We can qualitatively reproduce different patterns of the cos θ distribution for theK ^*+ andK ^*0.     

Can η mesons have a magnetic moment?

The response of pseudoscalar and vector mesons to strong magnetic fields is studied within a simple constituent quark model using analogy with bound states of Positronium. Magnetic moments of charged vector mesons K*, D*, B* are predicted and it is found that η mesons have magnetic polarizability. In extremely strong magnetic fields, behaviour of J/Ψ mesons is discussed. We speculate on the existence of an induced magnetic moment of η meson.     

Effective meson lagrangian with chiral and heavy quark symmetries from quark flavor dynamics

By bosonization of an extended NJL model we derive an effective meson theory which describes the interplay between chiral symmetry and heavy quark dynamics. This effective theory is worked out in the low-energy regime using the gradient expansion. The resulting effective lagrangian describes strong and weak interactions of heavy B and D mesons with pseudoscalar Goldstone bosons and light vector and axial-vector mesons. Heavy meson weak decay constants, coupling constants and the Isgur-Wise function are predicted in terms of the model parameters partially fixed from the light quark sector. Explicit SU(3)_F symmetry breaking effects are estimated and, if possible, confronted with experiment.     

Radiative decays and transition form factors of strange mesons in the relativistic constituent quark model

Motivated by the recent lattice QCD results indicating that the topological charge contribution to the flavor singlet axial vector current can be traded off by the constituent quark masses, we investigate the radiative decays of pseudoscalar (π,K, η, η′), vector (ρ,K*, ω, ?) and axial vector (A ₁) mesons using a simple relativistic constituent quark model. For both simplicity and relativity, we take advantage of the distinguished features in the light-cone quantization method: (1) the Fock-state expansion of meson wavefunctions are not contaminated by the vacuum fluctuation, (2) the assignment of meson quantum numbers are given by the Melosh transformation. Except the well-known constituent quark masses of (u,d,s) quarks and the spin-averaged meson masses, the only parameter in the model is the gaussian parameter β which determines the broadness (or sharpness) of radial wavefunction. The computed decay widths and the transition form factors of ρ, ω → π(η)γ*,K* →Kγ* andA ₁ → πγ* at 0≤Q ²≤5 GeV² and π⁰(η) → γ*γ at 0≤Q ²≤3 GeV² are in a remarkably good agreement with the experimental data and the result forA ₁ ⁺ → π₊ γ* transition is quite consistent with the experiments of pion scattering on a nucleus using Primakoff effect. This model is potentially useful in the cocktail analyses of the dilepton productions in proton-proton, proton-nucleus and nucleus-nucleus collisions at SPS energies and a little above.     

Elementary scalar mesons and Regge poles

We show, for the annihilation amplitude of π⁺π^? → two vector mesons, that parity conservation and rotational symmetry demand the existence of a triplet of Regge singularities crossing at t = 0. In the usual scalar-vector field theory, calculations of the leading terms of this amplitude up to the eight order show that these singularities are moving Regge poles. Contrary to common belief, the elementary scalar meson lies on one of them.     

Constituent quarks,soft pions and meson masses

In the constituent quark model, a simple mass formula is given to relate the masses of the vector and pseudoscalar mesons. Good agreement is obtained for all mesons, from the lightest π, ? mesons to the heaviest. In the limit of vanishing pion mass, alower limit of 230 MeV is obtained for the constituent quark mass.     

A relativistic quark model for mesons based on numerical solutions of the Bethe-Salpeter equation

A study is made to determine if the results of the nonrelativistic quark model can be reproduced by a fully relativistic model of deeply bound $\text{spin}\text{-}\text{1}\text{2}$ quarks. It is found that the relativistic model does not reproduce the nonrelativistic results, even when the quarks have nonrelativistic momenta. However, the model is rather successful in accounting for the known properties of mesons.Numerical solutions to the Bethe-Salpeter equation are obtained for pseudoscalar and vector bound states of equal mass quark-antiquark pairs, with either a scalar, pseudoscalar, or neutral vector exchange interaction. The interaction function corresponds to single particle exchange, with the addition of either one or two regulating terms. It is found that the second regulator allows the internal quark momentum to be nonrelativistic, but that the spinor structure of the wave function remains highly relativistic.Only the scalar interaction can account for the observed spectrum of states. The pseudoscalar interaction yields a vector state of lower mass than the pseudoscalar state, and the vector interaction leads to a vector state which lies approximately one quark mass above the pseudoscalar state. The λ quark is taken as slightly heavier than the p and n, and the perturbation treatment of the mass difference leads to a quadratic mass formula.The decay amplitudes for π, K → μν are calculated, and it is found, independent of parameters, that $\text{?}{}_{\mathrm{\pi }}\text{≈ ?}{}_{\mathrm{K}}$ for either a scalar or vector interaction, in agreement with experiment and in contrast with the nonrelativistic model. The amplitudes for ?^o, ω, φ → e⁺e^?, μ⁺μ^? are also calculated, but in this case the ratios (again parameter independent) are in minor discrepancy with experiment.The question of the additivity of quark amplitudes is examined by calculating (with significant restrictions) the magnetic moments of the vector mesons and the amplitudes for magnetic transitions such as ω → π^oγ. The magnetic moments of the vector mesons have the same (trivial) ratios to each other as in the nonrelativistic model, but they are strongly enhanced over the sum of the quark magnetic moments. The amplitude for magnetic transitions, however, is related to the quark magnetic moments in approximately the same ratio as in the nonrelativistic model.The model is also used to obtain parameter dependent predictions for the masses and decay amplitudes. These predictions are not experimentally correct, but are generally well within an order of magnitude for a wide range of the parameters.The most significant defect discovered of the model is the presence of ghost states (the daughters of the vector mesons, with J^PC = 0^+?) with masses of about 2 BeV.     

Study of inclusive production of π± and protons in\bar p p interactions at 32 GeV/c

Results are presented on the inclusive production of π^± mesons and protons in \(\bar p\) p interactions at an incident antiproton momentum of 32 GeV/c in the MIRABELLE bubble chamber, based on a sample of 55,000 inelastic events. The spectra of π⁺(π^?) andp( \(\bar p\) ) are separated in the whole kinematically admitted region of phase space by a statistical method. The semi-inclusive and inclusive cross sections and the main average characteristics of π andp production are calculated. The invariant differential cross sections are studied as functions of the Fevnman scaling variablex, the rapidity and the transverse momentum. Thex distribution of π^± mesons in the proton fragmentation region does not show any significant contribution from quark exchange or annihilation processes. A possible contribution of hard quark scattering on mesons or baryons is observed for large transverse momenta.     

Tri-meson mixing of π–η–η′ and ρ–ω–φ in the light-cone quark model

The radiative transition form factors of the pseudoscalar mesons π, η, η′ and the vector mesons ρ, ω, φ are restudied with π–η–η′ and ρ–ω–φ in the tri-meson-mixing pattern, which is described by tri-mixing matrices in the light-cone constituent quark model. The experimental transition decay widths are better reproduced with tri-meson mixing than previous results in a two-mixing-angle scenario of only two-meson η–η′ mixing and ω–φ mixing.     

Molecular structure of exotic mesons

The 0^— exotic meson state is considered as the P-wave molecular state ρ′(1465) of η(550) mesons. The mass and decay width of the exotic 0^— meson are calculated on the basis of the N/D dispersion method.     

Proton-antiproton annihilation at rest into two mesons and the quark line rule

Proton-antiproton annihilation at rest into two mesons is analysed in a model describing annihilation by quark lines. The model allows to fit existing data with two parameters. The parameters describe the amplitudes for diagrams with and without rearrangement of quark lines.