Hadron Structure Within the Point Form of Relativistic Quantum Mechanics

We present an outline of recent developments in the field of hadron form-factor calculations within constituent-quark models using the point form of relativistic quantum mechanics. Our method to calculate currents and form factors is exemplified by means of the weak B → D transition. We present results for weak B → D transition form factors in the space- and the time-like momentum-transfer region. We discuss how wrong cluster properties, which one has to deal with when employing relativistic quantum mechanics, affect these form factors and we estimate the role non-valence, Z-graph contributions may play for decay kinematics.     

Influence of relativistic effects on electron-loss cross sections of heavy and superheavy ions colliding with neutral atoms

The influence of relativistic effects, such as relativistic interaction and relativistic wave functions, on the electron-loss cross sections of heavy and superheavy atoms and ions (atomic number Z ? 92) colliding with neutral atoms is investigated using a newly created RICODE-M computer program. It is found that the use of relativistic wave functions changes the electron-loss cross section values by about 20–30% around the cross-section maximum compared to those calculated with nonrelativistic wave functions. At relativistic energies E ≥ 200 MeV/u, the relativistic interaction between colliding particles leads to a quasiconstant behavior of the loss cross sections σ _EL ^rel ～ const, to be compared with the Born asymptotic law σ _EL ^B ～ lnE/E.     

Formfactor effects in exclusiveD andB decays

Recent experimental results on the semileptonicD→K ^* transition seem to be in conflict with quark model expectations. Motivated by this finding we reinvestigate the predictions for exclusiveD andB decays in the relativistic quark model approach. Some of the invariant formfactors relevant for the transition matrix elementsD→K ^* andB→D ^* depend strongly on an explicit quarkmass-dependent integral over the meson wave functions. The dependence of decay rates and spectra in semi-leptonicD andB transitions on this integral is analysed and discussed in detail. Furthermore, we discuss how the predictions of the relativistic quark model for semi-leptonicD andB decays can be tested through measurements of the polarization of the produced vector mesonK ^* andD ^*, respectively. Some remarks on exclusive nonleptonic two-body decays of the heavy mesons are also presented. Finally the theoretical uncertainties for the determination of the K-M matrix element |V _ub | from exclusive semi-leptonic decays are discussed.     

Difficulties with injection of relativistic electron beams into toroidal fusion devices

It is shown that neither E × B drift nor diamagnetic beam configurations allow injection of externally generated strong relativistic electron beams into fusion devices for the purpose of plasma heating.     

B → πlΝ form factors calculated on the light-front

A consistent treatment of B → πlν decay is given on the light-front. The B to π transition form factors are calculated in the entire physical range of momentum transfer for the first time. The valence-quark contribution is obtained using relativistic light-front wave functions. Higher quark-antiquark Fock-state of the B-meson bound state is represented effectively by the ¦B*π〉 configuration, and its effect is calculated in the chiral perturbation theory. Wave function renormalization is taken into account consistently. The ¦B*π〉 contribution dominates near the zero-recoil point (q ² ? 25 GeV²), and decreases rapidly as the recoil momentum increases. The calculated form factor ?+(q ²) follows approximately a dipole q ²-dependence in the entire range of momentum transfer. We estimate that ¦V _ub¦=0.003.     

Relativistic coulomb excitation of neutron-rich 54,56,58Cr

The first excited 2⁺ states in neutron-rich ^54,56,58Cr were populated by relativistic Coulomb excitation and B (E2, 2 ₁ ⁺ → 0⁺) values were determined for ⁵⁶Cr and ⁵⁸Cr. The B(E2) values show a minimum for ⁵⁶Cr providing evidence for a subshell closure at N=32.     

On the superconvergence of meson-nucleon invariant scattering amplitudes

Using two models, i.e. perturbation theory with the usual PS-PS Hamiltonian and a “relativistic” version of the Lee model with the same type of interaction, it has been tried to clarify the question if there are superconvergent amplitudes in the (π, K) meson-nucleon forward scattering. Does the impressive validity of the well-known sum rule for theB ⁽⁺⁾ amplitude makes a serious support of the assumed superconvergence (becauseB describes the spin-flip scattering)? Indications, obtained from perturbation theory, including all Feynman diagrams up to the sixth order in the coupling constant and from the Lee model, where all allowed diagrams can be summed up, do not support the superconvergence assumption. Therefore the impressive prediction of theB ⁽⁺⁾ amplitude sum rule seems to be accidental.     

First-order relativistic corrections to the theory of Coulomb excitation

It is suggested that relativistic effects may be significant in high-precision Coulomb-excitation experiments. First-order corrections to the non-relativistic theory of Coulomb excitation are determined with the restriction that all of the states involved in the excitation have the same parity and that the scattering angle is 180°. The results of some numerical calculations are presented to give an indication of the magnitude of the correction. A recent experiment to determine the B(E2;0⁺ → 2⁺) and excited-state quadrupole moment of ¹⁹⁸Hg is reanalyzed and the relativistic correction to the B(E2) is found to be several times the experimental uncertainty. Sizeable effects are also found in multiple Coulomb excitation.     

On the nonrelativistic limit of the Dirac theory

The relation between a “nonrelativistic” Hamiltonian of the formH ^∞=(A+B)²+C and a corresponding family of “Dirac-Hamiltonians”H(c) in the limitc → ∞ is investigated. It is shown that the resolvent (z ?H(c))^?1 and the relativistic perturbation of isolated eigenvalues ofH ^∞ are analytic in 1/c for sufficiently large |c|.     

Decay constants of heavy mesons from a QCD relativistic potential model

We compute masses and leptonic decay constants of charmed and beauty pseudoscalar and vector mesons by using a QCD-inspired relativistic potential model. We obtain results in agreement with the available experimental data; as for the pseudoscalar meson decay constants, we predict f_D=1.38f_π,f_Ds=1.51f_π,f_B=1.75f_π,f_Bs=1.86f _π.     

Singularity structure of massless QCD at finite temperature

A complete relativistic calculation to first order in the strong coupling constantα _s is presented for deep inelastic scattering of leptons off a heat bath of quarks and gluons. The singularity structure is studied and the cancellation of all collinear and infrared divergences is proven. It is shown that it is necessary to include all processes of a given order (i.e. not only the gluon emission and absorption as usually stated). We show that for non-equilibriumn _F andn _B distributions the collinear singularities do not cancel.     

Spin substructure of space-time

In a spin space, with noncommutative spinorial coordinatesC ^A which satisfyx ^AB =1/2{C ^A ,C ^*B }, we investigatex-dependent spin coordinate transformations which correspond to a local fermi-bose symmetry. A concept of a spin vector corresponding to these local transformations is established, and spin space is provided with a spinorial vierbein field which determines non-nil-potent line and volume elements which are direct generalizations of the conventional relativistic ones.     

A simple expression for the entropy of a fireball from experimental strange particle ratios

We derive an expression for the specific entropyS/N _B in a non-interacting, non-relativistic Boltzmann gas mixture in terms of strange particle ratios like \(N_{\bar \Lambda } /N_\Lambda ,N_{\bar K} /N_K \) ,N _K /N _Λ andN _Λ /N _N . Then we investigate the influence of relativistic and quantum statistical effects and the role of hadronic interactions on reconstructing the specific entropy from the particle ratios. Since neglection of the relativistic effects causes the largest corrections, we include them in an improved expression. The resulting formula gives the specific entropy from the observed particle ratios with less than 20% error.     

Effective-potential model for the self-interacting gluon gas

The thermodynamic behaviour of a pure gluon-plasma is investigated within the context of an effective-interaction model and the relativistic Landau theory of quantum liquids. Agreement is sought withSU (2) andSU (3) lattice computer simulations and asymptotic perturbation theory. For bothSU (2) andSU (3) the available data are fitted rather well by a logarithmically screened Coulomb potential. The difference in critical behaviour ofSU (2) andSU (3) can also be modelled. Contact is made with the Bare Bones bag model, yielding a bag pressure ofB ^1/4≈200 MeV.     

A hydrogen atom in a superstrong magnetic field and the Zeldovich effect

We consider the problem of a hydrogen atom in a superstrong magnetic field, B? B _a =2.35×10⁹ G. The analytical formulas that describe the energy spectrum of this atom are derived for states with various quantum numbers n_ρ and m. A comparison with available calculations shows their high accuracy for B?B _a . We note that the derived formulas point to a manifestation of the Zeldovich effect, i.e., a rearrangement of the atomic spectrum under the influence of strong short-range Coulomb potential distortion. We discuss the relativistic corrections to level energies, which increase in importance with magnetic field and become significant for B?10¹⁴ G. We suggest the parameters in terms of which the Zeldovich effect has the simplest form. Analysis of our precision numerical calculations of the energy spectrum for a hydrogen atom in a constant magnetic field indicates that the Zeldovich effect is observed in the spectrum of atomic levels for superstrong fields, B?5×10¹¹ G. Magnetic fields of such strength exist in neutron stars and, possibly, in magnetic white dwarfs. We set lower limits for the fields B_min required for the manifestation of this effect. We discuss some of the properties of atomic states in a superstrong magnetic field, including their mean radii and quadrupole moments. We calculated the probabilities of electric dipole transitions between odd atomic levels and a deep ground level.     

Wave functions and decay constants of <Emphasis Type="Italic">B</Emphasis> and <Emphasis Type="Italic">D</Emphasis> mesons in the relativistic potential model

With the decay constants of D and D _s mesons measured in experiment recently, we revisit the study of the bound states of quark and antiquark in B and D mesons in the relativistic potential model. The relativistic bound state wave equation is solved numerically. The masses, decay constants and wave functions of B and D mesons are obtained. Both the masses and decay constants obtained here can be seen as consistent with the experimental data. The wave functions can be used in the study of B and D meson decays.     

Propagation regimes of intense circularly polarized laser beam in magnetoactive plasma

This paper presents an analytical and numerical investigation of an intense circularly polarized wave propagating along the static magnetic field parallel to oscillating magnetic field in magnetoactive plasma. In the relativistic regime such a magnetic field is created by pulse itself. The authors have studied different regimes of propagation with relativistic electron mass effect for magnetized plasma. An appropriate expression for dielectric tensor in relativistic magnetoactive plasma has been evaluated under paraxial theory. Two modes of propagation as extraordinary and ordinary exist; because of the relativistic effect, ultra-strong magnetic fields are generated which significantly influence the propagation of laser beam in plasma. The nature of propagation is characterized through the critical-divider curves in the normalized beam width with power plane For given values of normalized density (ω_p/ω) and magnetic field (ω_c/ω) the regions are namely steady divergence (SD), oscillatory divergence (OD) and self-focusing (SF). Numerical computations are performed for typical parameters of relativistic laser-plasma interaction: magnetic field B = 10-100 MG; intensity I = 10¹⁶ to 10²⁰ W/cm²; laser frequency ω = 1.1 × 10¹⁵ s⁻¹; cyclotron frequency ω_c = 1.7 × 10¹³ s⁻¹; electron density n_e = 2.18 × 10²⁰ cm⁻³. From the calculations, we confirm that a circularly polarized wave can propagate in different regimes for both the modes, and explicitly indicating enhancement in wave propagation, beam focusing/self-guiding and penetration of E-mode in presence of magnetic field.     

Propagation of a TE surface mode in a relativistic electron beam-quantum plasma system

The dispersion properties of a transverse electric (TE) surface waves propagating along the interface between a magneto-quantum plasma-relativistic beam system and vacuum are studied by using the quantum hydrodynamic model. The general dispersion relations are derived and analyzed in some special cases of interest. Moreover, the effects of density gradients for the beam and plasma on the dispersion properties of surface waves are investigated. The kind of dispersion relations depends strongly on the ambient magnetic field Bo via the gyro-frequency ωc, the quantum parameters, and the width of the plasma layer as well as the relativistic factor for the electron beam. It is found that the quantum effects play a crucial role to facilitate the propagation of TE surface waves.     

New method to constrain the relativistic free-streaming gas in the Universe

We discuss a method to constrain the fraction density f of the relativistic gas in the radiation-dominant stage, by their impacts on a relic gravitational waves and the cosmic microwave background (CMB) B-polarization power spectrum. We find that the uncertainty of f   strongly depends on the noise power spectra of the CMB experiments and the amplitude of the gravitational waves. Taking into account of the CMBPol instrumental noises, an uncertainty Δf=0.046$\mathrm{\Delta }f=0.046$ is obtained for the model with tensor-to-scalar ratio r=0.1$r=0.1$. For an ideal experiment with only the reduced cosmic lensing as the contamination of B  -polarization, Δf=0.008$\mathrm{\Delta }f=0.008$ is obtained for the model with r=0.1$r=0.1$. So the precise observation of the CMB B-polarization provides a great opportunity to study the relativistic components in the early Universe.     

Application of commutator theorems to the integration of representations of Lie algebras and commutation relations

Sufficient conditions on unbounded, symmetric operatorsA andB which imply that $$\exp (itA)\exp (isB)\exp ( - itA)$$ satisfies the well known “multiple commutator” formula are derived. This formula is then applied to prove new necessary and sufficient conditions for the integrability of representations of Lie algebras and canonical commutation relations and the commutativity of the spectral projections of two commuting, unbounded, self-adjoint operators. A classic theorem of Nelson's is obtained as a corollary. Our results are useful in relativistic quantum field theory.