The g factors of bound particles in quantum electrodynamics

A quasipotential method is formulated for calculating relativistic and radiative corrections to the magnetic moment of a two-particle bound state in the case of particles of arbitrary spin. It is shown that expressions for the g factors of bound particles contain terms of order O(α²) that depend on the spin of particles. Numerical values of the g factor of an electron in the hydrogen and deuterium atoms are obtained.     

A relativistic quark model for mesons based on numerical solutions of the Bethe-Salpeter equation

A study is made to determine if the results of the nonrelativistic quark model can be reproduced by a fully relativistic model of deeply bound $\text{spin}\text{-}\text{1}\text{2}$ quarks. It is found that the relativistic model does not reproduce the nonrelativistic results, even when the quarks have nonrelativistic momenta. However, the model is rather successful in accounting for the known properties of mesons.Numerical solutions to the Bethe-Salpeter equation are obtained for pseudoscalar and vector bound states of equal mass quark-antiquark pairs, with either a scalar, pseudoscalar, or neutral vector exchange interaction. The interaction function corresponds to single particle exchange, with the addition of either one or two regulating terms. It is found that the second regulator allows the internal quark momentum to be nonrelativistic, but that the spinor structure of the wave function remains highly relativistic.Only the scalar interaction can account for the observed spectrum of states. The pseudoscalar interaction yields a vector state of lower mass than the pseudoscalar state, and the vector interaction leads to a vector state which lies approximately one quark mass above the pseudoscalar state. The λ quark is taken as slightly heavier than the p and n, and the perturbation treatment of the mass difference leads to a quadratic mass formula.The decay amplitudes for π, K → μν are calculated, and it is found, independent of parameters, that $\text{?}{}_{\mathrm{\pi }}\text{≈ ?}{}_{\mathrm{K}}$ for either a scalar or vector interaction, in agreement with experiment and in contrast with the nonrelativistic model. The amplitudes for ?^o, ω, φ → e⁺e^?, μ⁺μ^? are also calculated, but in this case the ratios (again parameter independent) are in minor discrepancy with experiment.The question of the additivity of quark amplitudes is examined by calculating (with significant restrictions) the magnetic moments of the vector mesons and the amplitudes for magnetic transitions such as ω → π^oγ. The magnetic moments of the vector mesons have the same (trivial) ratios to each other as in the nonrelativistic model, but they are strongly enhanced over the sum of the quark magnetic moments. The amplitude for magnetic transitions, however, is related to the quark magnetic moments in approximately the same ratio as in the nonrelativistic model.The model is also used to obtain parameter dependent predictions for the masses and decay amplitudes. These predictions are not experimentally correct, but are generally well within an order of magnitude for a wide range of the parameters.The most significant defect discovered of the model is the presence of ghost states (the daughters of the vector mesons, with J^PC = 0^+?) with masses of about 2 BeV.     

Magnetic moment of a two-particle bound state in quantum electrodynamics

A quasipotential method for calculating relativistic and radiative corrections to the magnetic moment of a two-particle bound state is formulated for particles of arbitrary spin. It is shown that the expression for the g factors of bound particles involve O(α ²) terms depending on the particle spin. Numerical values are obtained for the g factors of the electron in the hydrogen atom and in deuterium.     

Relativistic corrections to the baryon resonance photoexcitation amplitudes in the quark model

We calculate the relativistic corrections of order (quark mass)^?2 to the baryon resonance photoexcitation amplitudes in the harmonic-oscillator quark model. We find that the relativistic effects entail significant consequences and that the agreement with experiment is much improved.     

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.     

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.     

CP violation in gauge theories and the electric dipole moment of the neutron

A nonvanishing contribution to the neutron electric dipole moment in CP-violating gauge theories of the weak interactions, arising from interaction of the photon with two-quark subsystems of the three-bound-quark neutron system, is calculated. In the Kobayashi-Maskawa model the resulting value of the moment is estimated as O(10^?32) e cm; however, strong interaction corrections (gluonic radiative corrections) give quark moment contributions which may be numerically larger (possibly 10^?30±1 e cm). Either case clearly distinguishes gauge-sector CP violation from Higgs-sector CP violation which typically gives a neutron moment of order 10^?24 e cm.     

Double P-wave charmonium production in e + e − annihilation

On the basis of perturbative QCD and relativistic quark model we calculate relativistic and bound state corrections in the production processes of a pair of \(\mathcal{P}\) -wave charmonium states. Relativistic factors in the production amplitude are taken into account 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 \(\mathcal{P}\) -wave mesons. 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 nonrelativistic results of the cross section for the reaction e ⁺ + e ^? → h _c + χ _c J at the center-of-mass energy √s = 10.6 GeV.     

Heavy Quark Potential and Quarkonium Spectrum in Nonperturbative pNRQCD

The charmonium and bottomonium mass spectra are investigated systematically in potential nonrelativistic QCD with the heavy quark potential computed by lattice QCD simulations nonperturbatively. The potential consists of a static potential and relativistic corrections classified in powers of the inverse of heavy quark mass m, and the effects of the O(1/m) correction, the O(1/m ²) spin–orbit and spin–tensor corrections on the mass spectra are examined systematically. The pattern of the mass spectra is found to be in fairly good agreement with the experimental data, in which the O(1/m) correction gives an important contribution.     

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.     

Rigorous QCD-potential for thet\bar t-system at threshold

Recent evidence for the top mass in the region of 160 GeV for the first time provides an opportunity to use the full power of relativistic quantum field theoretical methods, available also for weakly bound systems. Because of the large decay width Γ of the top quark individual energy-levels in “toponium” will be unobservable. However, the potential for the $t\bar t$ system, based on a systematic expansion in powers of the strong coupling constant α _s can be rigorously derived from QCD and plays a central role in the threshold region. It is essential that the neglect of nonperturbative (confining) effects is fully justified here for the first time to a large accuracy, also justbecause of the large Γ. The different contributions to that potential are computed from real level corrections near the bound state poles of the $t\bar t$ -system which for Γ≠0 move into the unphysical sheet of the complex energy plane. Thus, in order to obtain the different contributions to that potential we may use the level corrections at that (complex) pole. Within the relevant level shifts we especially emphasize the corrections of orderO(α _s ⁴ m _t ) and numerically comparable ones to that order also from electroweak interactions which may become important as well.     

Properties of doubly heavy baryons in the relativistic quark model

Mass spectra and semileptonic decay rates of baryons consisting of two heavy (b or c) and one light quark are calculated in the framework of the relativistic quark model. The doubly heavy baryons are treated in the quark-diquark approximation. The ground and excited states of both the diquark and quark-diquark bound systems are considered. The quark-diquark potential is constructed. The light quark is treated completely relativistically, while the expansion in the inverse heavy-quark mass is used. The weak transition amplitudes of heavy diquarks bb and bc going, respectively, to bc and cc are explicitly expressed through the overlap integrals of the diquark wave functions in the whole accessible kinematic range. The relativistic baryon wave functions of the quark-diquark bound system are used for the calculation of the decay matrix elements, the Isgur-Wise function, and decay rates in the heavy-quark limit.     

Quark-diquark approximation of the three-quark structure of baryons in the quark confinement model

Octet (1/2⁺) and decuplet (3/2⁺) baryons as relativistic three-quark states are investigated using the quark confinement model (QCM), the relativistic quark model, based on some assumptions about hadronization and quark confinement. The quark-diquark approximation of the three-quark, structure of baryons is proposed. In the framework of this approach, the main low-energy characteristics of baryons, such as magnetic moments, electromagnetic radii and form factors, the ratio of axial and vector constants in semileptonic baryon decays, strong form factors and decay widths, are described. The obtained results agree with experimental data.     

Is there a tachyon in the Nambu-Goto string with massive ends?

The dependence of Casimir energy on quark mass is investigated in the model of relativistic strings with massive quarks attached to the ends. The quark dynamics are treated in the nonrelativistic approximation, and the equations of motion and boundary conditions are linearized. The Casimir energyE as a function of quark massm is found by two methods (numerically and analytically). Different subtraction procedures for both approaches result in different functional dependences ofE onm. But both cases have values ofm for which the Casimir energy is definitely positive. The sign of this energy is known to coincide with the sign of the squared mass of the ground state in the string spectrum. Hence, the obtained result indicates that it is possible at least in principle to solve the tachyon problem in the model of relativistic strings with massive ends.     

Spectral functions of currents in a relativistic confining potential model

The meson dominance calculation of current spectral functions is carried out in a relativistic potential model with confining potential and their dependence on energy and the quark mass is explicitly obtained in the WKB approximation. The resulting spectral function is independent of the potential parameters, and coincides with the quark-parton model from threshold to q² = ∞ under a certain condition.