Defining the mass spectrum of mesons while taking into account the relativistic character of interactions

Taking into account the relativistic and nonlocal character of interactions, the mass spectrum of mesons consisting of light-light and light-heavy quarks with orbital and radial excitations is determined. Our results show that good agreement with the experimental data for the slope and the intercept of the Regge trajectory can be obtained only by taking into account the nonperturbative and the nonlocal character of interactions. There is certainly a dependence of the constituent mass of constituent particles on the mass of a free state. When quarks are light, the difference in current and valent masses of quarks is greater than in valent masses of quarks; when quarks are heavy, the difference in theses masses is insignificant. One alternative version of the account of nonlocality is suggested for a definition of the properties of hadrons at large distances. The dependence of constituent mass on the radius of confinement is studied.     

Determination of the Glueball Mass Spectrum with the Spin-Orbit Interaction

Based on the investigation of the asymptotic behaviour of the polarization loop function for scalar charged particles in an external gauge field we determine the interaction Hamiltonian including the nonperturbative corrections of the relativistic character of motion and the large coupling constant. The mass spectrum of the bound state is analytically derived. The mechanism for arising of the constituent mass of the bound-state forming particles is explained. The change of the bound-state mass and of the constituent mass of particles is analyzed by varying the coupling constant. The mass spectrum of the two-gluon glueball is calculated taking into account spin-orbit and spin-spin interactions.     

Determination of the glueball mass with allowance for the relativistic character of interaction

Nonperturbative corrections to an interaction Hamiltonian that are associated with relativistic motion and a large coupling constant are determined on the basis of an investigation of the asymptotic behavior of the polarization loop for charged scalar particles in an external gauge field. The mass spectrum of a bound state is determined analytically. The mechanism responsible for the emergence of the constituent mass of particles that form a bound state is explained. It is shown that the contribution of the vector potential and the contribution of the potential associated with a nonperturbative character of interaction cancel each other and that the slope of the Regge trajectory is determined in terms of the string tension.     

Determination of the mass spectrum and the decay constant mesons consisting of c and b quarks

On the basis of an investigation into the asymptotic behavior of the correlation functions of the corresponding field currents with the necessary quantum numbers, an analytic method for determining the mass spectrum and decay constants of mesons consisting of c and b quarks with relativistic corrections is proposed. The dependence of the constituent mass of quarks on the current mass and on the orbital and radial quantum numbers is analytically derived. The mass and the wave function (WF) mesons are determined from the Schrodinger equation with a mass of constituent components particles. We calculate the splitting of the mass spectrum for the singlet and triplet states mesons, as well as to determine the width of the lepton and radiation decays due E1 transition for $\left( {\bar cc} \right)$ , $\left( {\bar bb} \right)$ , $\left( {\bar bc} \right)$ systems. Our results for the mass spectrum of mesons consisting of c and b quarks are in satisfactory agreement with the available experimental data.     

Determination of the glueball mass spectrum with allowance for spin-orbital interactions

The mass spectrum of a coupled state is analytically determined. The mechanism of production of a constituent mass of particles forming a coupled state is explained. The change of the coupled state and constituent particle component masses attendant to changes of the coupling constant is analyzed. The mass spectrum of a two-gluon glueball is determined with allowance for spin-orbital and spin-spin interactions.__________Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 33–41, December, 2004.     

Heavy baryons in the relativistic quark model

In the framework of the relativistic quasipotential quark model the mass spectrum of baryons with two heavy quarks is calculated. The quasipotentials for interactions of two quarks and of a quark with a scalar and axial vector diquark are evaluated. The bound state masses of baryons with are computed.     

Determination of the ground state energies of the H 2 + , D 2 + and H 2 + molecular ions taking into account relativistic corrections

On the basis of determination of the asymptotic behavior of correlation functions of the corresponding field currents with the corresponding quantum numbers an analytic method for determination of the energy spectrum of three-body Coulomb system is suggested. Our results show that the constituent masses of particles, which we have defined as masses of particles in a bound state, differ from masses of particles in a free-state. The constituent mass to the free state mass relation for the electron is greater than the same mass relation for the proton, deuteron and triton. It was also found that this constituent electron mass has different values in each systems, i.e. in H ₂ ⁺ , D ₂ ⁺ and T ₂ ⁺ hydrogen molecular ions. The contributions of exchange and self-energy diagrams were taken into account in the determination of the energy spectrum of the three-body Coulomb system. Our results show that the self-energy diagram contribution is inversely proportional to the square of the constituent mass of particles. This contribution is sufficient for the electron and is negligible for the proton, deuteron and triton. When defining the energy and the wave function (WF), it is necessary to take into account the contributions of both the exchange and self-energy diagrams.     

Calculation of the Relativistic Correction in Terms of the Oscillator Representation

A procedure is proposed for the calculation of the corrections associated with the relativistic motion and spin interaction of particles in a system of a few bodies. The relativistic corrections for the Coulomb and Cornell potentials are determined from the relativistic generalization of the Schrödinger equation. The slope of the Regge trajectory and the masses of mesons are calculated taking the relativistic correction into account.     

Determination of superfine splitting of positronium energy levels

Energies of the singlet and triplet positronium states are analytically calculated considering the annihilation and loop corrections in a functional approach. The dependences of the constituent mass of constituent particles on the initial-state masses and the corresponding quantum number are derived. The wave function at the origin of coordinates is calculated and the decay widths of ortho- and parapositronium are determined. The result corresponds satisfactorily to available experimental data.     

Weak decays of charm and quark masses

We calculate the effects of finite quark masses for the semileptonic and nonleptonic decays of charmed particles. The total lifetimes of charmed particles are not sensitive to the masses of the quarks in the final state. However the semileptonic branching ratios changes considerably. Using conventional constituent quark masses, one expect e.g. B_e(D⁺)≈ 21%. The brancing ratios and lifetimes of the charmed particles are estimated, taking into account the annihilation hypothesis.     

A variational approach to bound states in quantum field theory

We consider here in a toy model an approach to bound state problem in a nonperturbative manner using equal time algebra for the interacting field operators. The potential is replaced by offshell bosonic quanta inside the bound state of nonrelativistic particles. The bosonic dressing is determined through energy minimisation, and mass renormalisation is carried out in a nonperturbative manner. Since the interaction is through a scalar field, it does not include spin effects. The model however nicely incorporates an intuitive picture of hadronic bound states in which the gluon fields dress the quarks providing the binding between them and also simulate the gluonic content of hadrons in deep inelastic collisions.     

A dynamical theory for the off-shell continuation of the πN t-matrix: M. J. Reiner. Physics Department,Virginia Polytechnic Institute and State University,Blacksburg, Virginia 24061 and Department of Physics and Astronomy,University of Rochester,Rochester, New York 14627

First-order gluon radiative corrections to the rate of weak decay of a quark into three quarks are calculated taking full account of all the masses involved. Using dimensional regularization techniques, the infrared divergences inherent to the problem cancel out, and the finite parts in convenient analytic forms which tend to the correct zero-mass limits are obtained. The total correction to the decay rate always exceeds its (negative) zero-mass limit and changes sign as the masses increase. Thus, except for small mass values, it is positive and acts in a direction opposite to that expected when the masses vanish.     

Relativistic approaches to investigation of few-nucleon systems

Theoretical approaches used in investigation of relativistic effects in high energy lepton and hadron collisions with few-nucleon systems are analyzed. The Bethe-Salpeter formalism for describing interacting systems of two spinor particles both in the continuum and bound state is described in detail. Special attention is paid to partial expansions, taking into account the analytic properties of Bethe-Salpeter amplitudes and unitary transformations correlating different representations of partial amplitudes. Mathematical methods of numerical solution of equations are considered. Results of calculation of relativistic corrections and effects of interaction in the final state in particular reactions with participation of the deuteron, namely, in elastic pD backward scattering and in reactions of deuteron break-up with production of correlated pairs, are presented.     

A phenomenological quark matter equation of state

Both the MIT bag model and potential models are able to reproduce static properties of hadrons (e.g. their mass spectrum) with reasonable accuracy. However, while the extrapolation of the MIT bag model from hadrons to dense matter is rather straightforward, it is not the same for potential models. To deal with this problem, in this paper, the methods of relativistic quantum many-body theory are applied to the study of quark matter interacting through an instantaneous potential at zero temperature. It is shown that under some conditions, the quark plasma undergoes a first order transition from a massive state at low density to a gas of particles of decreasing mass at high density—as one expects from perturbative QCD. In addition, immediately after the transition, the quarks are in a collective bound state, which might perhaps be interpreted as the fact that they just start to leave the inside of hadrons.     

The relativistic interquark potential

A method for the calculation of interaction potentials in a momentum space is proposed which is based on exact calculations of the Lorentz structures of the corresponding interaction amplitudes. With this method the kernel of the QCD-motivated potential of a quark-antiquark relativistic system is obtained for different masses and an arbitrary angular momentum J. The calculation is performed taking into account the anomalous chromodynamic moments of the quarks. The case of the singlet state of a relativistic quark system is considered. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 87–94, November, 2006.     

Effective field theories for the heavy quarkonium

We briefly review how nonrelativistic effective field theories give us a definition of the QCD potentials and a coherent field-theory-derived quantum-mechanical scheme to calculate the properties of bound states made by two or more heavy quarks. In this framework heavy quarkonium properties depend only on the QCD parameters (quark masses and α _s ) and nonpotential corrections are systematically accounted for. The relation between the form of the nonperturbative potentials and the low-energy QCD dynamics is also discussed.     

Translation invariant calculation of nonperturbative quarkonium mass shifts

The mass shifts of $\text{q}\text{q}$ bound states in the nonperturbative QCD vacuum are calculated by applying field theoretic perturbation theory as derived within the formalism of the Bethe-Salpeter equation. We obtain corrections to heavy quarkonium masses of the order of, but somewhat smaller than those of previous authors, who employed ordinary perturbation theory of nonrelativistic quantum mechanics.     

Rest Frame Properties of the Proton

The proton is modeled as three quarks of smallcurrent quark mass. The threebody Dirac equation issolved with spin-independent central diagonal linearconfining potentials with an attractive Coulombic term in a relativistic threequark model.Hyperspherical coordinates are used, and the bound stateis found analytically. After integrating over thehyperangles, the Hamiltonian is an 8 by 8 matrix ofcoupled first-order differential equations in onevariable, the hyperradius. These are analytically solvedin hypercentral approximation. For the(1/2⁺)³ ground-state configurationin the nonrelativistic large-quark-mass limit, there are no nodes in the wave function.However, in the extreme relativistic limit of smallcurrent quark masses of a few MeV, the expectation valueof the number of nodes is about 1.30 when the potential parameters are chosen to reproducethe proton rms charge radius. The quarks are assumed topossess a Pauli anomalous magnetic moment, like that ofthe electron and muon of (/2)(e/m). Assuming all three quarks have equal mass, one can fitthe rest energy, magnetic moment, rms charge radius, andaxial charge of the proton with this relativisticthree-body Dirac equation model. The solution found shows the necessity of including all componentsof the composite three-quark wave function, as the uppercomponent contributes only 0.585 to the norm.     

Triply heavy baryons in the constituent quark model

The constituent quark model is used to compute the ground and excited state masses of QQQ baryons containing either c or b quarks.The quark model parameters previously used to describe the properties of charmonium and bottomonium states were used in this analysis.The non-relativistic three-body bound state problem is solved by means of the Gaussian expansion method which provides sufficient accuracy and simplifies the subsequent evaluation of the matrix elements.Several low-lying states with quantum numbers J^P=1/2^±,3/2^±,5/2^±and 7/2^+are reported.We compare the results with those obtained by the other theoretical formalisms.There is a general agreement for the mass of the ground state in each sector of triply heavy baryons.However,the situation is more puzzling for the excited states,and appropriate comments about the most relevant features of our comparison are given.     

Octet-decuplet baryon mass splittings from self-consistent one-loop perturbation theory

The bag model of confined relativistic quarks in chiral-invariant interaction with scalar, pseudoscalar, vector, and pseudovector mesons, as well as gluons, is used to calculate the masses and wave functions of the spin-1/2 baryon octet and spin-3/2 decuplet, using selfconsistent Brillouin-Wigner bound state perturbation theory. Chiral symmetry breaking is invoked with the sigma model. SU (6) and SU (3) symmetries are broken by the experimental meson spectrum, and a strange quark mass. Mass corrections are calculated to one loop order, limited to the baryons of the octet and decuplet and the lowest lying mesons. Encouraging results are obtained, especially for theΔ — N and theΣ — Λ splittings. Convergence and stability have not been demonstrated, but are evidently improved by the self-consistency requirement. An initial parameter tuning gives a fit to all the octet and decuplet masses within ≦0.02 GeV, at the price of choosing the bag radius, the non-strange baryon input bag mass, and the strange quark mass. Even these small discrepancies can be dramatically reduced by fine-tuning the vector meson coupling and including an instanton contribution peculiar to theΛ.