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We propose a new treatment for the quantum three-body problem. It is based on an expansion of the wave function on harmonic oscillator functions with different sizes in the Jacobi coordinates. The matrix elements of the Hamiltonian can be calculated without any approximation and the precision is restricted only by the dimension of the basis. This method can be applied whatever the system under consideration. In some cases, the convergence property is greatly improved in this new scheme as compared to the old traditional method. Some numerical tricks to reduce computer time are also presented.

The auxiliary field method is a technique to obtain approximate closed formulae for the solutions of both nonrelativistic and semirelativistic eigenequations in quantum mechanics. For a many-body Hamiltonian describing identical particles, it is shown that the approximate eigenvalues can be written as the sum of the kinetic operator evaluated at a mean momentum $p_0$ and of the potential energy computed at a mean distance $r_0$. The quantities $p_0$ and $r_0$ are linked by a simple relation depending on the quantum numbers of the state considered and are determined by an equation which is linked to the generalized virial theorem. The (anti)variational character of the method is discussed, as well as its connection with the perturbation theory. For a nonrelativistic kinematics, general results are obtained for the structure of critical coupling constants for potentials with a finite number of bound states., Comment: New improved presentation

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

We present a model for odd-$C$ (negative charge parity) glueballs with three constituent gluons. The model is an extension of a previous study of two-gluon glueballs. We show that, even if spin-1 gluons seem to reproduce properly the lattice QCD spectrum for $C=+$ states, the extension for $C=-$ cannot match with the lattice results. Resorting to the helicity formalism, we show how transverse gluons fit in better agreement the lattice QCD spectrum., Comment: Invited talk at 'Selected Problems of Modern Theoretical Physics', Dubna June 23-27 2008. Talk at 'Confinement 8', Mainz, September 1-6 2008

The auxiliary field method has been recently proposed as an efficient technique to compute analytical approximate solutions of eigenequations in quantum mechanics. We show that the auxiliary field method is completely equivalent to the envelope theory, which is another well-known procedure to analytically solve eigenequations, although relying on different principles \textit{a priori}. This equivalence leads to a deeper understanding of both frameworks., Comment: v2 to appear in J. Math. Phys

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

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., Comment: 4 figures

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., Comment: 3 Figures

Most of the theories involving extra dimensions assume that only the gravitational interaction can propagate in them. In such approaches, called brane world models, the effective, 4-dimensional, Newton's law is modified at short as well as at large distances. Usually, the deformation of Newton's law at large distances is parametrized by a Yukawa potential, which arises mainly from theories with compactified extra dimensions. In many other models however, the extra dimensions are infinite. These approaches lead to a large distance power-law deformation of the gravitational newtonian potential $V_N(r)$, namely $V(r)=(1+k_b/r^b)V_N(r)$, which is less studied in the literature. We investigate here the dynamics of a particle in a gravitational quantum well with such a power-law deformation. The effects of the deformation on the energy spectrum are discussed. We also compare our modified spectrum to the results obtained with the GRANIT experiment, where the effects of the Earth's gravitational field on quantum states of ultra cold neutrons moving above a mirror are studied. This comparison leads to upper bounds on $b$ and $k_b$., Comment: 11 pages, 1 figure

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. Low-lying $J^{PC}$ states are computed and compared with recent lattice calculations. A good agreement is found for $1^{--}$ and $3^{--}$ states, but our model predicts a $2^{--}$ state much higher in energy than the lattice result. The $0^{-+}$ mass is also computed., Comment: 2 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., Comment: 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., Comment: 14 pages, 1 figure, accepted for publication in Phys. Rev. D

The masses of two-gluon glueballs are studied with a semirelativistic potential model whose interaction is a scalar linear confinement supplemented by a one-gluon exchange mechanism. The gluon is massless but the leading corrections of the dominant part of the Hamiltonian are expressed in terms of a state dependent constituent gluon mass. The Hamiltonian depends only on 3 parameters: the strong coupling constant, the string tension, and a gluon size which removes all singularities in the leading corrections of the potential. Accurate numerical calculations are performed with a Lagrange mesh method. The masses predicted are in rather good agreement with lattice results and with some experimental glueball candidates., Comment: 4 figures

The dominantly orbital state description is applied to the study of light mesons. The effective Hamiltonian is characterized by a relativistic kinematics supplemented by the usual funnel potential with a mixed scalar and vector confinement. The influence of two different finite quark masses and potential parameters on Regge and vibrational trajectories is discussed., Comment: 1 figure

Except the vibrational excitations of $K$ and $K^*$ mesons, the main features of spectra of mesons composed of quarks $u$, $d$, and $s$ can be quite well described by a semirelativistic potential model including instanton induced forces. The spectra of baryons composed of the same quarks is studied using the same model. The results and the limitations of this approach are described. Some possible improvements are suggested., Comment: 5 figures

We study the spectra of mesons and baryons, composed of light quarks, in the framework of a semirelativistic potential model including instanton induced forces. We show how a simple modification of the instanton interaction in the baryon sector allows a good description of the meson and the baryon spectra using an interaction characterized by a unique set of parameters., Comment: 7 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 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 masses of pentaquarks $uudd\bar s$ are calculated within the framework of a semirelativistic effective QCD Hamiltonian, using a diquark picture. This approximation allows a correct treatment of the confinement, assumed here to be similar to a Y-junction. With only color antitriplet diquarks, the mass of the pentaquark candidate $\Theta$ with positive parity is found around 2.2 GeV. It is shown that, if a color sextet diquark is present, the lowest $uudd\bar s$ pentaquark is characterized by a much smaller mass with a negative parity. A mass below 1.7 GeV is computed, if the masses of the color antitriplet and color sextet diquarks are taken similar.

We analyze the possibility of heavy-light tetraquark bound states by means of a chiral constituent quark model. The study is done in a variational approach. Special attention is paid to the contribution given by the different terms of the interacting potential and also to the role played by the different color channels. We find a stable state for both $qq\bar{c}\bar{c}$ and $qq\bar{b}\bar{b}$ configurations. Possible decay modes of these structures are analyzed., Comment: 13 pages, no figures. Accepted for publication in European Journal of Physics A

Electromagnetic splittings for mesons and baryons are calculated in a formalism where the constituent quarks are considered as dressed quasiparticles. The electromagnetic interaction, which contains coulomb, contact, and hyperfine terms, is folded with the quark electrical density. Two different types of strong potentials are considered. Numerical treatment is done very carefully and several approximations are discussed in detail. Our model contains only one free parameter and the agreement with experimental data is reasonable although it seems very difficult to obtain a perfect description in any case., Comment: 14 pages, Revised published version

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

In the framework of the non relativistic quark model, an exhaustive study of radiative transitions in mesons is performed. The emphasis is put on several points. Some traditional approximations (long wave length limit, non relativistic phase space, dipole approximation for E1 transitions, gaussian wave functions) are analyzed in detail and their effects commented. A complete treatment using three different types of realistic quark-antiquark potential is made. The overall agreement with experimental data is quite good, but some improvements are suggested., Comment: 42 pages, 2 figures

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., Comment: LaTeX, 56 pages, 11 figures, submitted for publication

We discuss the isospin-breaking mass differences among baryons, with particular attention in the charm sector to the $\Sigma_c^{+}-\Sigma_c^0$, $\Sigma_c^{++}-\Sigma_c^0$, and $\Xi_c^+-\Xi_c^0$ splittings. Simple potential models cannot accommodate the trend of the available data on charm baryons. More precise measurements would offer the possibility of testing how well potential models describe the non-perturbative limit of QCD., Comment: 4 pages, aipproc.sty, Proceeding of Hadron 97

We study electromagnetic mass splittings of charmed baryons. We point out discrepancies among theoretical predictions in non-relativistic potential models. None of them seems supported by experimental data. A new calculation is presented., Comment: 4 pages, Proc. of ISS97 Tashkent 6-13 Oct. 97

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