Pseudoscalars in the charmonium model

We take the recently found charmonium state at 2.976 GeV to be the η _c and show that it can be included in a charmonium model with relativistic corrections which reproduces the s-wave spectrum, the leptonic widths Γ(V→e ⁺ e^?) and the p-wave splittings. The upsilon spectrum is discussed as are the effects of radial and pseudoscalar mixing.     

Dynamical relativistic corrections to the leptonic decay width of heavy quarkonia

We calculate the dynamical relativistic corrections, originating from radiative one-gluon exchange, to the leptonic decay width of heavy quarkonia in the framework of a covariant formulation of light-front dynamics. Comparison with the non-relativistic calculations of the leptonic decay width of J = 1 charmonium and bottomonium S-ground states shows that relativistic corrections are large. Most importantly, the calculation of these dynamical relativistic corrections legitimate a perturbative expansion in , even in the charmonium sector. This is in contrast with the ongoing belief based on calculations in the non-relativistic limit. Consequences for the ability of several phenomenological potentials to describe these decays are described. Received: 6 December 2001 / Published online: 5 April 2002     

Structure of quantum-mechanical relativistic two-body interactions for spinning particles

Relativistic constraint mechanics yields consistent systems of coupled Dirac equations for pairs of spinning particles. We explicitly connect these equations to the Bethe-Salpeter equation of quantum field theory and to the interactions of classical Fokker-Tetrode dynamics (and hence to classical relativistic field theory) to obtain versions of these equations governed by systems of (possibly noncoulombic) relativistic potentials whose detailed structures contain important relativistic effects like correct Darwin interactions. We recast the defining pair of Dirac equations in a number of equivalent but important forms—“external potential,” Sazdjian, hyperbolic, and Breit— and examine their interconnection. Since the potentials in these equations are no more singular than — 1/4r² we are able to solve appropriate versions of them nonperturbatively for the qˉq system to obtain a very good fit to the entire meson spectrum and for the e ⁺ e ⁻ system to calculate the positronium spectrum of QED correct through order α ⁴ .     

Search for higher laying charmonium states and charmed hybrids in experiments using antiproton beam with momentum ranging from 1 GeV/<Emphasis Type="Italic">c</Emphasis> to 15 GeV/<Emphasis Type="Italic">c</Emphasis>

The elaborated analysis of spectrum of scalar and vector charmonium states in the mass region above D[`(D)]D\bar D — threshold is given. The combined approach based on the potential model and relativistic spherical symmetric top model for decay products has been proposed. Ten radial excited states of charmonium in the mass region above D[`(D)]D\bar D — threshold are anticipated to exist in the framework of the combined approach. The experimental data from different collaborations were analyzed. Especial attention was given to the new states with the hidden charm discovered recently. Eight of these states may be interpreted as higher laying radial excited charmonium states. But much more data on different decay modes are needed for deeper analysis. These data can be derived directly from the experiments using high quality antiproton beam with the momentum ranging from 1 GeV/c to 15 GeV/c (PANDA experiment at FAIR).     

Charmonium States in QCD-Inspired Quark Potential Model Using Gaussian Expansion Method

We investigate the mass spectrum and electromagnetic processes of charmonium system with the nonperturbative treatment for the spin-dependent potentials, comparing the pure scalar and scalar-vector mixing linear confining potentials. It is revealed that the scalar-vector mixing confinement would be important for reproducing the mass spectrum and decay widths, and therein the vector component is predicted to be around 22?%. With the state wave functions obtained via the full-potential Hamiltonian, the long-standing discrepancy in M1 radiative transitions of J/ψ and ψ′ are alleviated. This work also provides an inspection and suggestion for the possible cc? states among the copious higher charmonium-like states. Particularly, the newly observed X(4160) and X(4350) are found in the charmonium family mass spectrum as M(2¹ D ₂)?= 4164.9 MeV and M(3³ P ₂)?= 4352.4 MeV, which strongly favor the J ^PC ?=?2^?+, 2⁺⁺ assignments respectively. The corresponding radiative transitions, leptonic and two-photon decay widths have been also predicted theoretically for the further experimental search.     

Properties of Charmonium States in a Phenomenological Approach

We investigate the spectrum and decay rates of charmonium states within the framework of the non relativistic quark model by employing a Coulomb like potential from the perturbative one gluon exchange and the linear confining potential along with the potential derived from instanton vacuum to account for the hyperfine mass splitting of charmonium states in variational approach. We predict radiative E1, M1, two-photon, lepton and two-gluon decay rates of low lying charmonium states. An overall agreement is obtained with the experimental masses and decay widths.We have estimated the branching ratio of two gluons decaying into light hadrons.     

Relativistic Hamiltonian dynamics. II. Momentum-dependent interactions, confinement and quantization

The previously developed covariant classical relativistic N-particle dynamics is extended to momentum-dependent interactions and generalized to a gauge-independent constraint reduction. This reduction is made via center-of-momentum variables as well as via the more conventional individual particle variables. A canonical quantization is then carried out. The two-body problem is discussed in detail for the case of momentum-dependent interactions. It is demonstrated that such interactions can give rise to dynamical confinement both classically and quantum mechanically. The prototype interaction −β²(ξ · π)² has a harmonic oscillator type spectrum and shows a linear dependence of the binding energy on the angular momentum for small particle rest masses (m₁, m₂ β).     

Spin symmetry in Dirac negative-energy spectrum in density-dependent relativistic Hartree-Fock theory

The spin symmetry in the Dirac negative-energy spectrum and its origin are investigated for the first time within the density-dependent relativistic Hartree-Fock (DDRHF) theory. Taking the nucleus ¹⁶O as an example, the spin symmetry in the negative-energy spectrum is found to be a good approximation and the dominant components of the Dirac wave functions for the spin doublets are nearly identical. In comparison with the relativistic Hartree approximation where the origin of spin symmetry lies in the equality of the scalar and vector potentials, in DDRHF the cancellation between the Hartree and Fock terms is responsible for the better spin symmetry properties and determines the subtle spin-orbit splitting. These conclusions hold even in the case when significant deviations from the G -parity values of the meson-antinucleon couplings occur.     

Bethe-salpeter equation with instantaneous harmonic oscillator exchange

The Bethe-Salpeter equation in the form due to Cung et al. (Ann. Phys. (N.Y.)98 (1976), 516) is investigated for the special case of instantaneous harmonic oseillator exchange, An exact reduction to a pair of coupled ordinary differential equations for the radial excitations of the ³(J ± 1)_J modes is achieved. The equations in the mass zero case are brought to a form which is quite close to Whittaker's equation. This similarity to Whittaker's equation is exploited in a computer study of the level structure as a function of the quark mass. This study covers the region from a highly relativistic spectrum depending only upon J to the nonrelativistic regime where the spectrum depends only upon L. An expression for the leptonic width of a ³S₁ state in terms of the Bethe-Salpeter wave function is derived and applied to the ψ-family. The effect of relativistic corrections is to reduce the predicted value of the leptonic width compared to the value calculated by assuming nonrelativistic kinematics. It is also shown that the relativistic treatment allows a ³D₁ state to couple directly to a virtual photon.     

Spectrum and mechanism of the acceleration of protons in a solar flare

Investigations based on neutron monitor data show that two components of relativistic cosmic rays are generated by a solar flare. The so-called prompt component comes from a flare with flight times and is characterized by an exponential spectrum with a parameter of E ₀ ≈ 0.5 Gev. Numerical simulation of the conditions in the flare current sheet of the Bastille flare demonstrated that such a spectrum is formed at a magnetic reconnection velocity of ∼10⁷ cm s⁻¹. The delayed component has a power law spectrum and is apparently formed during the diffusion of protons in the plasma of the interplanetary magnetic field.     

D-mesons and charmonium states in hot isospin asymmetric strange hadronic matter

We study the properties of D and [`(D)] \bar{{D}} mesons in hot isospin asymmetric strange hadronic matter, arising due to their interactions with the hadrons in the hyperonic medium. The interactions of D and [`(D)] \bar{{D}} mesons with these light hadrons are derived by generalizing the chiral SU(3) model used for the study of hyperonic matter to SU(4). The nucleons, hyperons, the scalar isoscalar meson, σ and the scalar-isovector meson, d \delta as modified in the strange hadronic matter, modify the masses of D and [`(D)] \bar{{D}} mesons. It is found that, as compared to the [`(D)] \bar{{D}} mesons ([`(D<sup>0</sup>)] \bar{{D^0}}, D <sup>−</sup>), the properties of the D mesons (D <sup>0</sup>, D <sup>+</sup>) are more sensitive to the isospin asymmetry at high densities. On the other hand, the effects of strangeness fraction are found to be more dominant for the [`(D)] \bar{{D}} mesons as compared to the D mesons and these modifications are observed to be particularly appreciable at high densities. We also study the mass modifications of the charmonium states J/ψ, ψ(3686) and ψ(3770) in the isospin asymmetric strange hadronic matter at finite temperatures and investigate the possibility of the decay of the charmonium states into D [`(D)] \bar{{D}} pairs in the hot hadronic medium. The mass modifications of these charmonium states arise due to their interaction with the gluon condensates of QCD, simulated by a scalar dilaton field introduced to incorporate the broken scale invariance of QCD within the effective chiral model. The effects of finite quark masses are taken into account in the trace of the energy momentum tensor in QCD, while investigating the medium modification of the charmonium masses through the modification of the gluon condensate in the medium. We also compute the partial decay widths of the charmonium states to the D [`(D)] \bar{{D}} pairs in the hadronic medium. The strong dependence on density of the in-medium properties of the D, [`(D)] \bar{{D}} and the charmonium states, as well as the partial decay widths of charmonium states to D [`(D)] \bar{{D}} pairs, found in the present investigation, will be of direct relevance in observables like open charm enhancement as well as J/ψ suppression in the compressed baryonic matter (CBM) experiments at the future Facility for Antiproton and Ion Research, GSI, where the baryonic matter at high densities is planned to be produced.     

Charmonium production in fixed-target experiments with SPS and LHC beams at CERN

The possibility of measuring cross sections for the production of J/ψ mesons in fixed-target experiments with the proton and ion beams of the Large Hadron Collider (LHC) at CERN (Switzerland) is considered. At the present time, measurements of charmonium production in proton-proton collisions at an energy of 7 TeV have begun at LHC. Previously, the production of J/ψ and ψ′ mesons was studied in the NA38, NA50, and NA60 fixed-target experiments with beams of the CERN synchrotron (SPS) and in the PHENIX experiment at the Relativistic Heavy Ion Collider (RHIC, Brookhaven National Laboratory, USA). A normal nuclear absorption of J/ψ mesons in proton-nucleus collisions and an enhanced, anomalous, suppression of the production of charmonium states in central collisions of relativistic nuclei were observed. At the present time, there are no theoretical models that could describe the entire body of experimental data. Measurements over a broad interval of proton and ion energies are required. Measurements of charmonium production using LHC beams with fixed targets in the energy range between the SPS and RHIC energies-a beam of 7-TeV protons (√s = 114.6 GeV) and a beam of 2.75-TeV/nucleon lead ions (√s = 71.8 GeV)-will provide an additional possibility for studying the charmonium-production mechanism. Estimates of the geometric acceptance, luminosity, and counting rate for the production of J/ψ mesons are presented.     

Accurate analytic presentation of solution of the Schrödinger equation with arbitrary physical potential

High precision approximate analytic expressions of the ground state energies and wave functions for the arbitrary physical potentials are found by first casting the Schrödinger equation into the nonlinear Riccati form and then solving that nonlinear equation analytically in the first iteration of the quasilinearization method (QLM). In the QLM the nonlinear differential equation is treated by approximating the nonlinear terms by a sequence of linear expressions. The QLM is iterative but not perturbative and gives stable solutions to nonlinear problems without depending on the existence of a smallness parameter. The choice of zero iteration is based on general features of exact solutions near the boundaries. The approach is illustrated on the examples of the Yukawa, Woods-Saxon and funnel potentials. For the latter potential, solutions describing charmonium, bottonium and topponium are analyzed. Comparison of our approximate analytic expressions for binding energies and wave functions with the exact numerical solutions demonstrates their high accuracy in the wide range of physical parameters. The accuracy ranging between 10⁻⁴ and 10⁻⁸ for the energies and, correspondingly, 10⁻² and 10⁻⁴ for the wave functions is reached. The derived formulas enable one to make accurate analytical estimates of how variation of different interactions parameters affects correspondent physical systems.     

Ionization of ytterbium atoms from an excited state

The cross sections of the photoionization and the electron impact-induced ionization of Yb atoms from the excited 6s6p(³ P ₁) state are numerically calculated. Matrix elements are computed in multielectron relativistic and nonrelativistic approximations with allowance for the superposition of configurations and a relaxation effect. The radial part of the electron wavefunction in a continuous spectrum is calculated using the solutions to one-configuration Hartree-Fock and Dirac-Fock equations. The cross sections calculated by a relativistic method are compared to those for a nonrelativistic approximation. The ratios of the radiation reduced matrix elements and the phase shifts of the wavefunctions of a continuous spectrum calculated for the 6p ɛs and 6p → ɛd transitions are compared to the values obtained by approximating the experimental dependences of the angular distribution of photoelectrons for the photoionization by ultraviolet radiation from an oriented excited state.     

Double S- and P-wave charmonium production in e+e? annihilation

On the basis of perturbative QCD and the relativistic quark model we calculate relativistic and bound state corrections in the production processes of a pair of S-wave and P-wave charmonium states. Relativistic factors in the production amplitude connected with the relative motion of heavy quarks and the transformation law of the bound state wave function to the reference frame of the moving S- and Pwave mesons are taken into account. For the gluon and quark propagators entering the production vertex function we use a truncated expansion in the ratio of the relative quark momenta to the center-of-mass energy $ \sqrt s $ \sqrt s up to the second order. Relativistic corrections to the quark bound state wave functions in the rest frame are considered by means of the Breit-like potential. It turns out that the examined effects change essentially the nonrelativistic results of the cross section for the considered reactions at the center-of-mass energy $ \sqrt s $ \sqrt s = 10.6 GeV.     

A theorem on the order of levels in confining potentials

We prove that in a two-body, non-relativistic system interacting via a potential V = ?g²/r + V_c(r), where V_c is a confining potential non-singular at the origin, the 2S level is above the 2P level if V_c satisfies the following sufficient condition: This covers the well-known cases of linear potentials or harmonic oscillator potentials, which were considered in charmonium models, but also more generally, for instance, V_c(r) = r^α, α >0.     

Asymptotic Stability of the Relativistic Boltzmann Equation for the Soft Potentials

In this paper it is shown that unique solutions to the relativistic Boltzmann equation exist for all time and decay with any polynomial rate towards their steady state relativistic Maxwellian provided that the initial data starts out sufficiently close in L^￥_l{L^\infty_\ell}. If the initial data are continuous then so is the corresponding solution. We work in the case of a spatially periodic box. Conditions on the collision kernel are generic in the sense of Dudyński and Ekiel-Jeżewska (Commun Math Phys 115(4):607–629, 1985); this resolves the open question of global existence for the soft potentials.     

Charmonium suppression by gluon bremsstrahlung in p-A and A-B collisions

Prompt gluons are an additional source for charmonium suppression in nuclear collisions, in particular for nucleus-nucleus collisions. These gluons are radiated as bremsstrahlung in N-N collisions and interact inelastically with the charmonium states while the nuclei still overlap. The spectra and mean number <n _g> of the prompt gluons are calculated perturbatively and the inelastic cross section σ_abs ^Ψg is estimated. The integrated cross sections σ(A B →J/ψX) for p-A and A-B collisions and the dependence on transverse energy for S-U and Pb-Pb can be described quantitatively with some adjustment of one parameter <n _g>σ_abs ^Ψg. Received: 20 August 1999