Conventional Quark Model Research Articles

The various configurations of pentaquark in quark models

The pentaquark with different configurations, (Jaffe–Wilczek), (Karliner–Lipkin) and also a tetrahedral structure, was studied in various quark models. In the quark models, the negative parity state is always found at a lower mass than the positive parity one. The results show that the pentaquark is very difficult to fit into quark models. The channel-coupling calculations show that the different configurations give almost the same results if the same Hamiltonian is used for conventional quark models. Only the modified quark delocalization colour screening model gives little different results for different configurations. The results depend largely on how to model the interaction among quarks in different colour structures. A possible resonance may exist in the multiquark system due to the colour structure.

Results on Charmonium-like States from Belle

We present results from the Belle experiment on various charmonium-like states: X(3872), Y(3940), X(3940), Z(3930), and Y(4260). Several of these are difficult to interpret within the conventional quark model and may represent new types of hadronic structure.

Constituent quark model study of the meson spectra

The spectrum is studied in a generalized constituent quark model constrained in the study of the NN phenomenology and the baryon spectrum. An overall good fit to the available experimental data is obtained. A detailed analysis of all sectors from the light-pseudoscalar and vector mesons to bottomonium is performed paying special attention to the existence and nature of some non well-established states. These results should serve as a complementary tool in distinguishing conventional quark model mesons from glueballs, hybrids or multiquark states.

B→f0(980)Kdecays and subleading corrections

The decay $B\to f_0(980)K is studied within the framework of QCD factorization and the two-quark scenario for $f_0(980)$. There are two distinct penguin contributions and their interference depends on the unknown mixing angle $\theta$ of strange and nonstrange quark contents of $f_0(980)$: destructive for $0<\theta<\pi/2$ and constructive for $\pi/2<\theta<\pi$. The QCD sum rule method is applied to evaluate the leading-twist light-cone distribution amplitudes and the scalar decay constant of $f_0$. We conclude that the short-distance approach is not adequate to explain the observed large rates of $f_0K^-$ and $f_0\ov K^0$. Among many possible subleading corrections, we study and estimate the contributions from the three-parton Fock states of the $f_0$ and from the intrinsic gluon inside the $B$ meson. It is found that the spectator gluon of the $B$ meson may play an eminent role for the enhancement of $f_0(980)K$. We point out that if $f_0(980)$ is a four-quark state as widely perceived, there will exist extra diagrams contributing to $B\to f_0(980)K$. However, in practice it is difficult to make quantitative predictions based on the four-quark picture for $f_0(980)$ as it involves additional nonfactorizable contributions that are difficult to estimate and the calculations of the decay constant and form factors of $f_0(980)$ are beyond the conventional quark model.

Bosonic operator methods for the quark model

Quark model matrix elements can be computed using bosonic operators and the holomorphic representation for the harmonic oscillator. The technique is illustrated for normal and exotic baryons for an arbitrary number of colors. The computations are much simpler than those using conventional quark model wave functions.

Strong decays of strange quarkonia

In this paper we evaluate strong decay amplitudes and partial widths of strange mesons (strangeonia and kaonia) in the 3P0 decay model. We give numerical results for all energetically allowed open-flavor two-body decay modes of all nsbar and ssbar strange mesons in the 1S, 2S, 3S, 1P, 2P, 1D and 1F multiplets, comprising strong decays of a total of 43 resonances into 525 two-body modes, with 891 numerically evaluated amplitudes. This set of resonances includes all strange qqbar states with allowed strong decays expected in the quark model up to ca. 2.2 GeV. We use standard nonrelativistic quark model SHO wavefunctions to evaluate these amplitudes, and quote numerical results for all amplitudes present in each decay mode. We also discuss the status of the associated experimental candidates, and note which states and decay modes would be especially interesting for future experimental study at hadronic, e+e- and photoproduction facilities. These results should also be useful in distinguishing conventional quark model mesons from exotica such as glueballs and hybrids through their strong decays.

Implications of a DK molecule at 2.32 GeV

We discuss the implications of a possible quasinuclear DK bound state at 2.32 GeV. Evidence for such a state was recently reported in ${D}_{s}^{+}{\ensuremath{\pi}}^{0}$ by the BaBar Collaboration. We first note that a conventional quark model $c\overline{s}$ assignment is implausible, and then consider other options involving multiquark systems. An $I=0$ $c\overline{s}n\mathrm{n\ifmmode \bar{}\else \={}\fi{}}$ baryonium assignment is one possibility. We instead favor a DK meson molecule assignment, which can account for the mass and quantum numbers of this state. The higher-mass scalar $c\overline{s}$ state expected at 2.48 GeV is predicted to have a very large DK coupling, which would encourage formation of an $I=0$ DK molecule. Isospin mixing is expected in hadron molecules, and a dominantly $I=0$ DK state with some $I=1$ admixture could explain both the narrow total width of the 2.32 GeV state as well as the observed decay to ${D}_{s}^{+}{\ensuremath{\pi}}^{0}.$ Additional measurements that can be used to test this and related scenarios are discussed.

Covariant quark model for the baryons

A family of simply solvable covariant quark models for the baryons is presented. With optimal parameter choices the models reproduce the empirical spectra of the baryons in all flavor sectors to an accuracy of a few percent. Complete spectra are obtained for all states of the strange, charm and beauty hyperons with L ⩽2. The magnetic moments and axial coupling constants of the ground state baryons correspond to those of conventional quark models. We construct current-density operators tjat are consistent with empirical nucleon form factors at low and medium momenta.

Kaon-nucleon scattering amplitudes and Z* enhancements from quark Born diagrams.

We derive closed form kaon-nucleon scattering amplitudes using the ``quark Born diagram" formalism, which describes the scattering as a single interaction (here the OGE spin-spin term) followed by quark line rearrangement. The low energy I=0 and I=1 S-wave KN phase shifts are in reasonably good agreement with experiment given conventional quark model parameters. For $k_{lab}> 0.7$ Gev however the I=1 elastic phase shift is larger than predicted by Gaussian wavefunctions, and we suggest possible reasons for this discrepancy. Equivalent low energy KN potentials for S-wave scattering are also derived. Finally we consider OGE forces in the related channels K$\Delta$, K$^*$N and K$^*\Delta$, and determine which have attractive interactions and might therefore exhibit strong threshold enhancements or ``Z$^*$-molecule" meson-baryon bound states. We find that the minimum-spin, minimum-isospin channels and two additional K$^*\Delta$ channels are most conducive to the formation of bound states. Related interesting topics for future experimental and theoretical studies of KN interactions are also discussed.

Diagrammatic approach to meson-meson scattering in the nonrelativistic quark potential model.

In this paper we use Born-order quark-exchange diagrams in a nonrelativistic potential model to describe low-energy scattering of $q\overline{q}$ mesons. A formalism for evaluating quark Born diagrams is developed, and as a first application we consider meson-meson scattering in channels in which $q\overline{q}$ annihilation is thought to be unimportant. In particular our results are relevant to $I=2 \ensuremath{\pi}\ensuremath{\pi}$ and $I=1 \mathrm{KK}$ elastic scattering. Simple rules for the Born diagrams are given, which allow the evaluation of scattering amplitudes in terms of external meson wave functions by inspection. These techniques are applied to systems having identical quarks, and ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}$, ${K}^{+}{K}^{+}$, and ${\ensuremath{\rho}}^{+}{\ensuremath{\rho}}^{+}$ elastic scattering phase shifts, cross sections, and equivalent potentials are derived as examples. The $S$-wave $I=2 \ensuremath{\pi}\ensuremath{\pi}$ phase shift for a Gaussian $q\overline{q}$ wave function with conventional quark model parameters ${\ensuremath{\alpha}}_{s}$, ${m}_{q}$, and ${\ensuremath{\beta}}_{\mathrm{SHO}}$ is found to be in good agreement with experiment and with Weinberg's PCAC (partial conservation of axial-vector current) result. At higher energies the predicted differential cross sections have the characteristic diffractive features of an exponential $t$ peak at small angles and vacuum quantum number exchange. The phase of the predicted amplitude however differs from the experimental diffractive amplitude, so these quark Born diagrams cannot be directly identified with the Pomeron of diffractive scattering phenomenology.

Electromagnetic structure of octet baryons.

A numerical simulation of quenched QCD on a 24\ifmmode\times\else\texttimes\fi{}12\ifmmode\times\else\texttimes\fi{}12\ifmmode\times\else\texttimes\fi{}24 lattice at $\ensuremath{\beta}=5.9$ is used to calculate the electric and magnetic form factors of the baryon octet. General forms of the baryon interpolating fields are considered. Magnetic moments, electric radii, magnetic radii, and magnetic transition moments are extracted from the form factors. The electric properties are found to be consistent with a quark-model picture involving spin-dependent forces. The lattice results for the magnetic properties show a mass and spin dependence of the effective quark moments which is not accounted for in conventional quark models. Lattice calculations underestimate the magnitude of electric radii, magnetic radii, and magnetic moments compared to experimental measurements. The finite volume of the periodic lattice may be responsible for the discrepancies. The pattern of electromagnetic radii in the lattice results are seen to be generally reproduced in the model results that are considered. The only exception is that of ${\ensuremath{\Xi}}^{\ensuremath{-}}$ which proves to be a sensitive probe of the quark dynamics. Lattice calculations indicate a positive value for the normalized square magnetic radius in ${\ensuremath{\Xi}}^{\ensuremath{-}}$ which contrasts Skyrme model results. Ratios of the magnetic moments allow a more detailed comparison with the experimental measurements. The lattice calculations are seen to better reproduce the experimental ratios than the model calculations.

QCD sum rule analysis of spin-orbit splitting in baryons

A determination of spin-orbit splitting in N and Λ using the QCD sum rule technique of Shifman, Vainshtein, and Zakharov is presented. The QCD sum rules coupling to J P = 1 2 − nucleons, first considered by Belyaev and Ioffe are shown to provide a consistent description of N 1 2 − (1535) . The QCD sum rules coupling to the low-lying Δ 1 2 + , Λ 1 2 − , and Λ 3 2 − , are presented as these sum rules have not been previously considered in the literature. The non-perturbative calculations of spin-orbit splitting and odd parity excitation energies in the low-lying states of N and Λ are in agreement with experimental data. This is in contrast to conventional quark models. The large spin-orbit splitting in Λ resonances arises without invoking coupling to the KN scattering channel. The reduction of the strange quark condensate relative to the u or d quark condensate acts to increase the spin-orbit splitting in the low-lying Λ resonances. The results do not exclude coupling of Λ(1405) to the KN channel provided any additional spin-orbit splitting arising from the coupling is of the order of 30 MeV. Finally the Δ 1 2 + sum rules cast doubt on the existence of the unconfirmed (one ∗) Δ 1 2 + (1550) resonance.

Strong coupling expansions in pure lattice gauge theory mixed actions: Carles Ayala and Marià Baig. Grup de Física Teòrica, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain

A determination of spin-orbit splitting in N and Λ using the QCD sum rule technique of Shifman, Vainshtein, and Zakharov is presented. The QCD sum rules coupling to JP = 12− nucleons, first considered by Belyaev and Ioffe are shown to provide a consistent description of N12−(1535). The QCD sum rules coupling to the low-lying Δ12+, Λ12−, and Λ32−, are presented as these sum rules have not been previously considered in the literature. The non-perturbative calculations of spin-orbit splitting and odd parity excitation energies in the low-lying states of N and Λ are in agreement with experimental data. This is in contrast to conventional quark models. The large spin-orbit splitting in Λ resonances arises without invoking coupling to the KN scattering channel. The reduction of the strange quark condensate relative to the u or d quark condensate acts to increase the spin-orbit splitting in the low-lying Λ resonances. The results do not exclude coupling of Λ(1405) to the KN channel provided any additional spin-orbit splitting arising from the coupling is of the order of 30 MeV. Finally the Δ12+ sum rules cast doubt on the existence of the unconfirmed (one ∗) Δ12+(1550) resonance.

Stepwise enhancement of bound dipoles in strongly coupled plasma: C. Deutsch. L.P.G.P., Bât. 212, Université Paris XI, 91405 Orsay, France and Department of Applied Physics, Stanford University, Stanford, California 94305; G. Naouri. L.P.G.P., Bât. 212, Université Paris XI, 91405 Orsay, France

A determination of spin-orbit splitting in N and Λ using the QCD sum rule technique of Shifman, Vainshtein, and Zakharov is presented. The QCD sum rules coupling to JP = 12− nucleons, first considered by Belyaev and Ioffe are shown to provide a consistent description of N12−(1535). The QCD sum rules coupling to the low-lying Δ12+, Λ12−, and Λ32−, are presented as these sum rules have not been previously considered in the literature. The non-perturbative calculations of spin-orbit splitting and odd parity excitation energies in the low-lying states of N and Λ are in agreement with experimental data. This is in contrast to conventional quark models. The large spin-orbit splitting in Λ resonances arises without invoking coupling to the KN scattering channel. The reduction of the strange quark condensate relative to the u or d quark condensate acts to increase the spin-orbit splitting in the low-lying Λ resonances. The results do not exclude coupling of Λ(1405) to the KN channel provided any additional spin-orbit splitting arising from the coupling is of the order of 30 MeV. Finally the Δ12+ sum rules cast doubt on the existence of the unconfirmed (one ∗) Δ12+(1550) resonance.

A study of the K s0K s0 system in the reaction K −p→K s0K s0Λ at 11 GeV/ c

A 4.1 event/nb sample of 11 GeV/ c K −p interactions in the LASS spectrometer at SLAC has been used in an analysis of the exclusive K s 0K s 0Λ final state. The K s 0K s 0 mass distribution exhibits a small cluster of events near threshold, but the mass spectrum is dominated by the f 2 ′(1525), which an amplitude analysis shows to be produced by both natural and unnatural parity exchange. This analysis also provides evidence for an S-wave state in the f 2 ′(1525) region, while production of the f 2(1720) is not observed. However, there is structure at ∼ 2.2 GeV/ c 2 which is similar in shape to that observed in the region of the X(2220) in radiative J/ ψ decay; an analysis of the angular distribution indicates a spin of at least 2 in this region. This, together with results from other analyses, indicates that the X(2220) may be the 2 ++ or 4 ++, mainly s s , state expected near this mass in the conventional quark model.

Spin-orbit splitting in theN-Δ spectra and the deformed baryon model

The absence of appreciable spin-orbit splitting in the low-lying even and odd parity states of the nucleon and delta is puzzling in conventional quark models. A constitutent quark model, in which the quarks interact through gluon as well as pion exchange, and the baryon is allowed to deform in the excited states, may provide a solution to the problem.

Charmed baryon magnetic moments in the covariant oscillator quark model with isospin symmetry breaking

The magnetic moments of charmed baryons are studied in the covariant oscillator quark model including isospin symmetry breaking effect. In the uncharmed sector, the results differ from those obtained using conventional non-relativistic quark model (nrqm). But in the charmed sector the present values are much nearer to thenrqm results than those calculated using models with hadron mass dependence.

Representation mixing and the ideal description of mesons

Representation mixing of meson states is considered with particular reference to the 1 ←→ 15 mixing in SU(4). The 16 meson states are assigned to the representation (4*, 4) of a non-chiral group SU(4) ⊗ SU(4), whose factors are related by charge-conjugation. Mass formula, mixing angles and electromagnetic mass shifts are rigorously derived. Connection of the present formalism with conventional quark model is pointed out and generalisations to higher groups SU(n) ⊗ SU(n) as well as to higher representations, are indicated.

Quark model of pion photoproduction from protons by polarized photons in the resonance region

Measurements on the photoproduction of pions from protons by polarized photons are compared with predictions of the conventional quark model in the photon energy range 0.8-1.6 GeV. The experimental data, from an MIT-SLAC collaboration, are for the 90\ifmmode^\circ\else\textdegree\fi{} (in the center-of-mass system) production cross section of positive and neutral pions, both along and normal to the direction of polarization of the incident photons. The computations include $s$-channel excitation of all observed resonances of mass up to 2 GeV, but neglect nonresonant background effects. Resonances are assigned to the 56-plet (even parity) and 70-plet (odd parity) representations of SU(6) \ifmmode\times\else\texttimes\fi{} O(3), assuming all baryonic states to be appropriate combinations of three quarks, interacting in an harmonic-oscillator potential. Good qualitative agreement is achieved by appropriate choice of the parameter corresponding to the strength of the potential. A greatly improved fit results from the assignment of the ${S}_{M}(1535)$ level to the spin-$\frac{3}{2}$ octet of the 70-plet, first excited baryon supermultiplet. However, attempts at mixing between corresponding levels of the spin-1/2 and spin-$\frac{3}{2}$ states of this supermultiplet fail to improve the fit. We interpret this as indicating appreciable mixing of the levels concerned with corresponding states of higher supermultiplets of SU(6).

A relativistic quark model for mesons

A relativistic quark model which is closely related to the non relativistic harmonic oscillator model is presented for mesons with spin 1/2 quarks. The conventional quark model spectrum is reproduced, with particles lying on straight line trajectories although for PC=1 states large masses are predicted. The relativistic approach used throughout gives rise naturally to spin-orbit terms. These terms are analogous to those which arise in the Melosh approach. The comparisons of the model predictions with data is encouraging and the results include meson decay widths for emission of a pseudoscalar meson or a photon.