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In the framework of quark models, hybrid mesons are either seen as two-body $q\bar q$ systems with an excited flux tube connecting the quark to the antiquark or as three-body $q\bar q g$ systems including a constituent gluon. In this work we show that, starting from the three-body wave function of the $q\bar q g$ hybrid meson in which the gluonic degrees of freedom are averaged, the excited flux tube picture emerges as an equivalent $q\bar q$ potential. This equivalence between the excited flux tube and the constituent gluon approach is confirmed for heavy hybrid mesons but, for the first time, it is shown to hold in the light sector too, provided the contribution of the quark dynamics is correctly taken into account.

The strong decays of a meson into two mesons are studied in the framework of the 3 P 0 model. The meson wave functions are determined by means of a realistic chiral quark model constructed in the baryon sector and comparison is made with a traditional potential of “Coulomb + linear” type. Two different forms for the creation vertex are analyzed. A momentum dependent vertex is proved to be definitively superior. The chiral quark model provides an overall good description of all known transitions and gives results of roughly the same quality as those obtained from phenomenological quark–antiquark potentials.

A recent model of hadron states is extended to include meson decays. We find that the overall success of the model is quite good. Possible improvements to the model are suggested., Comment: 13 pages, RevTeX. 2 postscript figures, uses epsf

The I = 1 and 0 kaon-nucleon s-wave phase shifts have been calculated in a quark potential model using the resonating group method (RGM). The Hill-Wheeler equation has been solved numerically without any parametrization of the KN relative wave-function. The kaon and the nucleon wave-functions have been expanded as sums of several well-chosen gaussian functions, and the sensitivity of the results to the number of terms was analyzed carefully. The I = 0 phase shifts are in agreement with the experimental data. In the I = 1 channel too much repulsion is obtained, probably due to the lack of medium-range boson exchange type attraction.

Within the framework of a simple model including chromomagnetic interactions only, the energies of diquonia ${Q}^{2}({\overline{Q}}^{2})$ with orbital angular momentum $L=0$ are calculated and compared to the threshold energies. The results are given as functions of mass ratios and all possible diquonia built with $u$, $d$, $s$, $c$, $b$ quarks and spins $S=0,1,2$ are studied. A number of new systems which could be bound under strong interactions are proposed.

We analyze, within a non-relativistic quark model, the low energy part of the baryonic spectrum in the octet and decuplet flavour representations. The relevance of a strong Coulomb potential is emphasized in order to explain its general features. The addition of a three-body force allows to solve the ‘Roper puzzle’, giving a consistent explanation to its relative position in the spectrum.

In the framework of a pure chromomagnetic Hamiltonian we study all the ${q}^{6}$ systems allowed by the Pauli principle. In a first step, where we consider an exact ${\mathrm{SU}(3)}_{F}$ symmetry, the wave functions are analyzed by group-theoretical techniques. The breaking of the flavor symmetry is performed exactly by introducing a parameter $\ensuremath{\delta}$. The emphasis is put on the corresponding energies relative to the ${q}^{3}+{q}^{3}$ thresholds.

A hybrid meson is a quark-antiquark pair in which, contrary to ordinary mesons, the gluon field is in an excited state. In the framework of constituent models, the interaction potential is assumed to be the energy of an excited string. An approximate, but accurate, analytical solution of the Schr\"{o}dinger equation with such a potential is presented. When applied to hybrid charmonia and bottomonia, towers of states are predicted in which the masses are a linear function of a harmonic oscillator band number for the quark-antiquark pair. Such a formula could be a reliable guide for the experimental detection of heavy hybrid mesons., Comment: 3 figures

The three-gluon glueball states are studied with the generalization of a semirelativistic potential model giving good results for two-gluon glueballs. The Hamiltonian depends only on 3 parameters fixed on two-gluon glueball spectra: the strong coupling constant, the string tension, and a gluon size which removes singularities in the potential. The Casimir scaling determines the structure of the confinement. Our results are in good agreement with other approaches and lattice calculation for the odderon trajectory but differ strongly from lattice in the $J^{+-}$ sector. We propose a possible explanation for this problem., Comment: 1 figure

We propose a new method to obtain approximate solutions for the Schr\"{o}dinger equation with an arbitrary potential that possesses bound states. This method, relying on the auxiliary field technique, allows in many cases to find analytical solutions. It offers a convenient way to study the qualitative features of the energy spectrum of bound states in any potential. In particular, we illustrate our method by solving the case of central potentials with power-law form and with logarithmic form. For these types of potentials, we propose very accurate analytical energy formulae which improve a lot the corresponding formulae that can be found in literature., Comment: 2 figures

We analyze and compare two different descriptions of hybrid mesons, namely a two-body quark-antiquark system with an excited string linking both particles, or a three-body quark-antiquark-constituent gluon system. In particular, we prove that the constituent gluon approach is equivalent to an effective excited string in the heavy hybrid sector. The quantum numbers of the gluon are then replaced by the string excitation number. In the light hybrid sector, the equivalence between the excited string and the constituent gluon models remains valid provided the quark dynamics is properly taken into account as a dynamical contribution to the string energy.

In their textbook, Suzuki and Varga [Y. Suzuki and K. Varga, {\em Stochastic Variational Approach to Quantum-Mechanical Few-Body Problems} (Springer, Berlin, 1998)] present the stochastic variational method in a very exhaustive way. In this framework, the so-called correlated gaussian bases are often employed. General formulae for the matrix elements of various operators can be found in the textbook. However the Fourier transform of correlated gaussians and their application to the management of a relativistic kinetic energy operator are missing and cannot be found in the literature. In this paper we present these interesting formulae. We give also a derivation for new formulations concerning central potentials; the corresponding formulae are more efficient numerically than those presented in the textbook., Comment: 10 pages

An interstellar Bussard ramjet is a spaceship using the protons of the interstellar medium in a fusion engine to produce thrust. In recent papers, it was shown that the relativistic equation of motion of an ideal ramjet and of a ramjet with radiation loss are analytical. When a mass loss appears, the limit speed of the ramjet is more strongly reduced. But, the parametric equations, in terms of the ramjet's speed, for the position of the ramjet in the inertial frame of the interstellar medium, the time in this frame, and the proper time indicated by the clocks on board the spaceship, can still be obtained in an analytical form. The non-relativistic motion and the motion near the limit speed are studied., 4 figures

The masses of $uudd\bar s $, $uudd\bar d$ and $uuss\bar d$ pentaquarks are evaluated in a framework of both the Effective Hamiltonian approach to QCD and spinless Salpeter using the Jaffe--Wilczek diquark approximation and the string interaction for the diquark--diquark--antiquark system. The pentaquark masses are found to be in the region above 2 GeV. That indicates that the Goldstone boson exchange effects may play an important role in the light pentaquarks. The same calculations yield the mass of $[ud]^2\bar c$ pentaquark $\sim$ 3250 MeV and $[ud]^2\bar b$ pentaquark $\sim$ 6509 MeV., 14 pages, 2 tables, LaTeX2e. References corrected

Despite the apparent simplicity of meson spectroscopy, light scalar mesons cannot be accommodated in the usual $q\bar q$ structure. We study the description of the scalar mesons below 2 GeV in terms of the mixing of a chiral nonet of tetraquarks with conventional $q\bar q$ states. A strong diquark-antidiquark component is found for several states. The consideration of a glueball as dictated by quenched lattice QCD drives a coherent picture of the isoscalar mesons., 14 pages, 1 figure, accepted for publication in Phys. Rev. D

The masses of $uudd\bar s $, $uudd\bar d$, and $uuss\bar d$ pentaquarks are evaluated in a framework of both the Effective Hamiltonian approach to QCD and spinless Salpeter using the Jaffe-Wilczek diquark approximation and the string interaction for the diquark-diquark-antiquark system. The masses of the light pentaquarks are found to be in the region above 2 GeV. The similar calculations yield the mass of $[ud]^2\bar c$ pentaquark $\sim$ 3250 MeV and $[ud]^2\bar b$ pentaquark $\sim$ 6509 MeV., Comment: 5 pages. Based on talk by I.M.Narodetskii at BEACH 2004, 6th International Conference on Hyperons, Charm and Beauty Hadrons, Illionois Institute of Technology, Chicago, June. 27 - July 3, 2004. Typos corrected

The mass of the 1/2 + \(uudd\bar s\) pentaquark is calculated within the framework of a semirelativistic effective Hamiltonian approach to QCD with instanton-induced forces, using a diquark picture. This approximation allows a correct treatment of the confinement, assumed here to be a Y-junction. With the [ud] diquark mass fitted on the \(\Lambda\)-baryon, the ground-state pentaquark is found around 2.2 GeV.

The kaon–nucleon S, P, D, F, G waves phase shifts have been calculated using a non-relativistic quark potential model and the resonating group method (RGM). The calculation has been performed using quark–quark potential which both includes gluon, pion and sigma exchanges and reproduces as well as possible the meson spectrum. The agreement obtained with the existing experimental phase shifts is quite poor. The results are also compared with a previous calculation based only on gluon exchanges at the quark level. (Elsevier)

The kaon–nucleon S -wave phase shifts have been calculated, for both isospin channels I =0 and I =1, in the framework of a semirelativistic quark potential model which includes an instanton induced force. The agreement with experimental phase shifts is poor essentially because of a dominant attraction coming from instantons. The low-energy behaviour of S -wave phase shifts, for I =0 and I =1 channels, obtained in the kaon–nucleon system is characteristic of a potential which can produce one loosely bound state.

A form factor is introduced in the quark electromagnetic current. Its effect is analyzed on charge mean square radii and form factors in the mesonic sector. The decay of a vector meson into lepton–antilepton pair is also affected. Two different expressions for the form factors, and two different types of quark potential are tested and some relativistic kinematical corrections are proposed. In any case the introduction of a quark form factor greatly improves the agreement with experimental data. (Elsevier)

In this work we study tetraquark bound states in the framework of the constituent quark model of Ref. [2], which has been used for the description of non-strange two- and three-baryon systems and later on applied to the hadron spectra., Comment: Contribution to the MESON 2002 Workshop. Krakow 24-28 May 2002

The classical van Royen-Weisskopf formula for the decay width of a meson into a lepton-antilepton pair is modified in order to include non-zero quark momentum contributions within the meson as well as relativistic effects. Besides, a phenomenological electromagnetic density for quarks is introduced. The meson wave functions are obtained from two different models: a chiral constituent quark model and a quark potential model including instanton effects. The modified van Royen-Weisskopf formula is found to improve systematically the results for the widths, giving an overall good description of all known decays., Comment: 22 pages, 3 figures, RevTex, epsfig. To be published in Nucl. Phys. A

The I =1 and I =0 kaon–nucleon s, p, d, f, g-waves phase shifts have been calculated in a nonrelativistic quark potential model using the resonating group method (RGM). The interquark potential includes gluon exchanges with a spin–orbit interaction. This force has been determined to reproduce as well as possible the meson and baryon spectra. The same force is employed for the cluster and intercluster dynamics and the relative KN wave-function is calculated without any approximation. While some channels are correctly described, the theory is still unable to explain others. (Elsevier)

In a first step, the I =1 and I =0 kaon–nucleon s-wave phase shifts have been calculated in a quark potential model using the resonating group method (RGM) and a relativistic kinematics. The spinless Salpeter equation has been solved numerically using the Fourier grid hamiltonian method. The results have been compared to the nonrelativistic ones. For each isospin channel the phase shifts obtained are not so far from the nonrelativistic results. Then, K-nucleon p, d, f, g-waves phase shifts have been calculated using a nonrelativistic kinematics.

The I=1 and I=0 kaon-nucleon s-wave phase shifts have been calculated in a quark potential model using the resonating group method (RGM) and a relativistic kinematics. The spinless Salpeter equation has been solved numerically using the Fourier grid Hamiltonian method. The results have been compared to the non relativistic ones. For each isospin channel the phase shifts obtained are not so far from the non relativistic results.

The nucleon form factors are calculated using a non-relativistic description in terms of constituent quarks. The emphasis is put on the reliability of present numerical methods used to solve the three-body problem in order to correctly reproduce the expected asymptotic behavior of form factors. Nucleon wave functions obtained in the hyperspherical formalism or employing Faddeev equations have been considered. While a q**(-8) behavior is expected at high q for a quark-quark force behaving like 1/r at short distances, it is found that the hypercentral approximation in the hyperspherical formalism (K=0) leads to a q**(-7) behavior. An infinite set of waves is required to get the correct behavior. Solutions of the Faddeev equations lead to the q**(-8) behavior. The amplitude of the corresponding term however depends on the number of partial waves retained in the Faddeev amplitude. The convergence to the asymptotic behavior has also been studied. Sizeable departures are observed in some cases at squared momentum transfers as high as 50 (GeV/c)**2. It is not clear whether these departures are of the order 1/q or 1/q**2 log q relatively to the dominant contribution and whether the bad convergence results from truncations in the calculations. From a comparison with the most complete Faddeev results, a q**2 validity range is obtained for the calculation made in the hyperspherical formalism or in the Faddeev approach with the minimum number of amplitudes.

We present an investigation of the total decay rate of the (ground state) B_c meson within the framework of the relativistic constituent quark model formulated on the light-front (LF). The exclusive semileptonic (SL) and nonleptonic (NL) beauty and charm decays of the B_c meson are described through vector and axial hadronic form factors, which are calculated in terms of a constituent quark model LF wave functions. The latter ones are derived via the Hamiltonian LF formalism using as input the update versions of the constituent quark model. The inclusive SL and NL partial rates are calculated within a convolution approach inspired by the partonic model and involving the same B_c wave function which is used for evaluation of the exclusive modes. The framework incorporates systematically 84 exclusive and 44 inclusive partial rates corresponding to the underlying \bar{b}\to\bar{c} and c\to s quark decays. Based on our approach we find\tau_{B_c}=0.59 \pm 0.06 ps where the theoretical uncertainty is dominated by the uncertainty in the choice of LF wave functions and the threshold values for the hadron continuum. For the branching fractions of the B^+_c \to J/\psi\mu^+\nu_{\mu} and B_c^+\to J/\psi\pi^+ decays we obtain 1.6 % and 0.1 %, respectively., Comment: 10 pages, LaTeX, 1 ps figure

The kaon-nucleon s-wave phase shifts have been calculated in a quark potential model using the resonating group method (RGM). The interquark potential includes gluon, pion and sigma exchanges. The kaon and nucleon wave functions are expanded as a sum of Gaussian functions and the Hill-Wheeler (HW) equation is solved numerically. The I = 0 phase shifts present too much attraction and in the I = 1 channel too much repulsion is obtained.

We propose eight types of quark-antiquark interactions suited to describe various meson sectors. They contain QCD inspired components: the Coulomb-like interaction, the confinement potential and an instanton interaction. These forms are supplemented with a phenomenological hyperfine energy term. The size of the constituent quarks is taken into account. We consider two different kinematics: non-relativistic and semi-relativistic. The parameters are determined by a minimization procedure on representative samples of mesons. The full spectra are calculated and the form factors for the pion and the kaon are also studied. A careful analysis of the different models is performed through a comparison with experiment and between themselves.

The introduction of an adequate auxiliary space allows us to replace the problem of the treatment of coupled phonons, which is very complicated and voluminous, with the problem of the treatment of usual matrices. As applications of this approach, the formulation of a Wick{close_quote}s theorem for coupled phonons and recursion formulas which can be used to calculate the overlap matrix elements of multiphonon states built with {ital n} coupled phonons of different types and collectivities are given. {copyright} {ital 1996 The American Physical Society.}

Using several realistic interquark potentials, the ground-state energies of all the baryons containing one, two or three heavy quarks of type c or b are studied within a non-relativistic quark model. The three-body problem is rigorously solved using the Faddeev formalism. Various static properties, such as mass radii, charge radii, magnetic moments, and wave functions at the origin are calculated as well. The complete spectrum for all these baryons is computed using a harmonic-oscillator basis with states up to 8 quanta. Emphasis is put on the levels lying below the thresholds corresponding to quark-pair creation.

The ground state properties of heavy baryons (containing at least one quark of type c or b) are studied in a non-relativistic frame using a realistic interquark potential and the Faddeev formalism to solve the three-body problem. The complete spectra are computed by diagonalisation in a harmonic oscillator basis up to 8 quanta. Emphasis is put on the resonances lying below the thresholds corresponding to a quark pair creation.

The relativistic flux tube model is used to describe the spectra of all mesons, including the pseudoscalar light nonet. Quite good results are obtained, provided the flux tube is supplemented by a Coulomb-like potential, an interaction inspired from instanton effects, and a negative constant energy. Three different procedures to introduce this constant are compared, and two different Ansätze are tested to simulate the asymptotic freedom phenomenon. A matix method to solve the coupled nonlinear equations of the asymmetric flux tube is presented.

We study in detail the possibility of describing the nucleon (three-quark-system) wave function as a superposition of Gaussian functions. A Faddeev treatment including 8 amplitudes is performed and taken as reference for the exact values. Several approximations are proposed and compared carefully to the exact solutions. Three different potentials have been tested and several observables are considered.

The spectra of all [ital q][sup 2][ital [bar q]][sup 2] systems composed of [ital u], [ital d], or [ital s] quarks are investigated in the framework of the nonrelativistic quark model (NRQM) using a Hamiltonian which takes into account the one-gluon annihilation process. The shift in energy due to this effect is studied as well as the mixing of different flavor states. A systematics over all the possible total spin and total isospin is carried out, while the total angular momentum is fixed at zero and the parity is the natural one. The four-body problem is solved by the variational method in harmonic oscillator bases including all configurations up to six quanta. The problems arising from the calculation of pure relativistic mechanisms in the NRQM are discussed. The contribution of the one-gluon annihilation process to the structures of light diquonia is found quite weak but non-negligible. A possible model to include other annihilation mechanisms is proposed.

We present four new quark-quark potentials, developed in the framework of the nonrelativistic quark model (NRQM), which can reproduce quite well the spectra of mesons and baryons. They contain a central part which is of type “Coulomb+linear” or “Coulomb +2/3-power”, and a strong but smooth hyperfine term. With these four potentials and the one proposed by Bhaduri et al., we have calculated masses and decay properties of some interesting diquonia (q2q−2 mesons). We have not found appreciable difference between the results of the five potentials considered, indicating that the properties of diquonia are, to a large extent, potential-independent in the NRQM.

The shortcomings of the chromomagnetic model, as raised by Lichtenberg and Roncaglia, are analyzed and relativized. The chromomagnetic model fails to provide correct binding energies for multiquark systems and even to predict qualitatively stability of such objects. However, it is simple and physically sound so as to discriminate among the most favorable structures. As such, its use for a systematic study of a whole set of candidates is highly recommended in a first step.

Using the interquark potential due to Bhaduri et al., the properties ofq2q−2 systems are studied within a non-relativistic quark model. A systematics over the various flavorsu, d, s, c, b, over the total spinS and over the orbital angular momentumL=0, 1, 2, 3 is carried out, while the parity is taken as the natural one. Not only the spectrum, but also the decay properties of each state are evaluated and the wave functions are analyzed in term of dumbbell structure. We propose a number of new resonances which could have a very narrow width.

We study the connections existing between relativistic, semirelativistic, and nonrelativistic potential models of quarkonium using an interaction composed of an attractive Coulomb potential and a confining power-law term. We show that the spectra of these very different models become nearly similar provided specific relations exist between the dimensionless parameters peculiar to each model. As our analysis is carried out by taking advantage of scaling laws, our results are applicable for a wide range of physical parameters.

The flavor SU(3) multiplets of T-diquonia (q2q2) are classified, their masses estimated, and their decay widths into baryon-antibaryon pairs are evaluated. Using the same formalism, but with broken SU(2), the contributions of such states to some exclusive pp scattering cross sections are estimated, in an attempt to understand the experimental sparsity of diquonia candidates. It is found that if the meson-meson decay widths of these states are of the order of 50 MeV, they are difficult to detect experimentally. It is noted that, in general, except for the elastic scattering channel, the assumption of scattering via diquonia intermediates gives a reasonable description of physical reality.

The behavior of the low-transfer vertex for baryon--baryon-meson interaction and threshold effects plays an important role for the spin-orbit interaction in baryons. If treated correctly they are capable of explaining, at least schematically, the order and importance of spin-orbit splittings in {ital L}=1 baryons as well as partial and total widths.

Overlaps and matrix elements of one- and two-body operators are calculated in a space spanned by multiphonons of different types taking the Pauli principle properly into account. Two methods are developed: a generalized Wick's theorem dealing with new contractions and recursion formulas well suited for numerical applications.NUCLEAR STRUCTURE Multiphonon theory. Generalized Wick's theorem. Recursion formulas for calculation of overlaps and matrix elements of one- and two-body operators. Illustrative examples.

The validity of the instantaneous approximation for the Bethe-Salpeter equation is questioned within the framework of the simple scalar-scalar model of Cutkosky. Detailed numerous results for various approximations are compared to the exact ones. WKB quantization is applied to these relativistic approximations. An unexpected question arises: is the currently used Bethe-Salpeter equation (i.e., the ladder approximation) well suited to describe two interacting relativistic particles?

In the framework of a pure chromomagnetic Hamiltonian, we study all the states of {ital {bar Q}q}{sup 4} systems allowed by the Pauli principle. The wave functions are analyzed by group-theoretical techniques in a first step where the antiquark has an infinite mass and the quarks belong to an SU(3){sub {ital F}} multiplet. The breaking of these symmetries is performed exactly through two parameters {eta} and {delta}. The emphasis is put on the corresponding energies relative to the physical thresholds in {ital {bar Q}q}+{ital q}{sup 3}. We propose a number of new multiquarks which could be stable under strong interactions.

A formalism has been developed to treat the two nucleon behaviour with the incorporation of three-quark dynamics from Faddeev equations. This formalism in which a six-quark hamiltonian is decomposed in terms of nucleons, internal hamiltonians and the internucleon q-q interaction permits us to treat the nucleon internal dynamics properly. The short distance N-N behaviour has been described very well.

In the framework of the nonrelativistic quark model, we examine to what extent baryons consist of a quark bound to a localized cluster of two quarks simulating a diquark. We consider ground states and orbital excitations for various flavor combinations. A striking clustering shows up sometimes especially for the leading Regge trajectory of the nucleon and single-flavored baryons or for the ground state of baryons bearing two heavy flavors. This is, however, far from being a general pattern and there are clear differences between the three-quark description of baryons and the quark-diquark model.

We use the non-relativistic constituent quark model and the bag model to study the stability of the dilambda H = (uuddss) and pentaquark states P = ( Q uuds ), ( Q ddus ) and ( Q ssud ) . While they are stable in the limit of exact SU(3)F flavour symmetry between u, d, and s quarks, the H and the P become unbound when a realistic breaking of SU(3)F is introduced.

Some microscopic treatments of nuclear vibrational spectra are analyzed in terms of a model allowing an exact solution for a many-body nucleon system interacting via the pairing-plus-quadrupole force. The multiphonon approach — exact diagonalization in the restricted space of 1, 2, 3, … collective phonons — appears satisfactory for the few lowest-lying vibration Kπ = 0+ states in deformed nuclei. The non-conservation of the number of particles and coupling between collective and non-collective states seem to be the main sources of the discrepancies that occur for the higher states. On the other hand, the lowest-order contributions suggested by nuclear field theory lead to serious disagreement as compared with the exact solutions.

Analysis of real and complex boson expansions of the Kishimoto-Tamura type is performed in a deformed basis in order to allow a further study of the anharmonicities of vibrations in deformed nuclei. It is shown that complex solutions cannot be found in the cases where no real one exits.