Theory Of Bound States Research Articles

New precise spectroscopy of the hyperfine structure in muonium with a high-intensity pulsed muon beam

A hydrogen-like atom consisting of a positive muon and an electron is known as muonium. It is a near-ideal two-body system for a precision test of bound-state theory and fundamental symmetries. The MuSEUM collaboration performed a new precision measurement of the muonium ground-state hyperfine structure at J-PARC using a high-intensity pulsed muon beam and a high-rate capable positron counter. The resonance of hyperfine transition was successfully observed at a near-zero magnetic field, and the muonium hyperfine structure interval of νHFS=4.463302(4)GHz was obtained with a relative precision of 0.9 ppm. The result was consistent with the previous ones obtained at Los Alamos National Laboratory and the current theoretical calculation. We present a demonstration of the microwave spectroscopy of muonium for future experiments to achieve the highest precision.

The generalized dynamical equation and the vacuum polarization effect in hydrogenlike atoms

Based on the generalized dynamical equation, vacuum polarization effects are studied within the scope of the bound state theory in quantum electrodynamics. We find a vacuum-polarization correction to the Lamb shift for the 1S state of the hydrogen atom on the order of (α/π)2(Zα)4 that is not considered in the standard theory of bound states in quantum electrodynamics.

Analytic Perturbation Theory for Bound States in the Transfer Matrix Spectrum of Weakly Correlated Lattice Ferromagnetic Spin Systems

We consider general d-dimensional lattice ferromagnetic spin systems with nearest neighbor interactions in the high temperature region (β≪1). Each model is characterized by a single site apriori spin distribution taken to be even. We also take the parameter α=〈s4〉−3〈s2〉2>0, i.e. in the region which we call Gaussian subjugation, where 〈sk〉 denotes the kth moment of the apriori distribution. Associated with the model is a lattice quantum field theory known to contain a particle of asymptotic mass −lnβ and a bound state below the two-particle threshold. We develop a β analytic perturbation theory for the binding energy of this bound state. As a key ingredient in obtaining our result we show that the Fourier transform of the two-point function is a meromorphic function, with a simple pole, in a suitable complex spectral parameter and the coefficients of its Laurent expansion are analytic in β.

Understanding heavy quarkonium systems in perturbative QCD

We review the recent theoretical progress in heavy quarkonium spectroscopy within the boundstate theory based on perturbative QCD. New microscopic pictures of the heavy quarkonium systems are obtained.

Improved perturbative QCD approach to the bottomonium spectrum

Recently it has been shown that the gross structure of the bottomonium spectrum is reproduced reasonably well within the nonrelativistic bound state theory based on perturbative QCD. In that calculation, however, the fine splittings and the $S--P$ level splittings are predicted to be considerably narrower than the corresponding experimental values. We investigate the bottomonium spectrum within a specific framework based on perturbative QCD, which incorporates all the corrections up to $\mathcal{O}({\ensuremath{\alpha}}_{S}^{5}{m}_{b})$ and $\mathcal{O}({\ensuremath{\alpha}}_{S}^{4}{m}_{b}),$ respectively, in the computations of the fine splittings and the $S--P$ splittings. We find that the agreement with the experimental data for the fine splittings improves drastically due to an enhancement of the wave functions close to the origin as compared to the Coulomb wave functions. The agreement of the $S--P$ splittings with the experimental data also becomes better. We find that natural scales of the fine splittings and the $S--P$ splittings are larger than those of the bound states themselves. On the other hand, the predictions of the level spacings between consecutive principal quantum numbers depend rather strongly on the scale $\ensuremath{\mu}$ of the operator $\ensuremath{\propto}{C}_{A}{/(m}_{b}{r}^{2}).$ The agreement of the whole spectrum with the experimental data is much better than the previous predictions when $\ensuremath{\mu}\ensuremath{\simeq}3--4\mathrm{GeV}$ for ${\ensuremath{\alpha}}_{S}{(M}_{Z})=0.1181.$ There seems to be a phenomenological preference for some suppression mechanism for the above operator.

Coupled singlet-triplet analysis of two-color cold-atom photoassociation spectra

We describe a method that is well suited to analysis of the bound states of the alkali-metal dimers near their dissociation limit. The method combines inverse perturbation theory, coupled-channel bound-state theory, and the accumulated phase method to treat the short-range part of the molecular potentials. We apply this method to analyze the bound-state energies measured in a two-color photoassociation experiment in an ultracold 85Rb gas. This analysis yields information on the interactions between ultracold 85Rb atoms that is important to the understanding of ultracold Rb collisions and Bose-Einstein condensation.

An attempt to model the Salam-Weinberg Higgs

It is shown that in a two scale confining substructure model for Standard Model fermions and weak bosons respectively where the two scale obey Λ′ ⪢ Λ a see-saw scale μ ≪ Λ, Λ′ ( μ = Λ· ( Λ/ Λ′)) is generated. We discuss the possible existence of a critical value μ c of μ where, due to an effect of level repulsion, the low energy part of the effective bound state theory lives at the Higgs-confinement phase boundary. Then μ c is identified with the weak scale. We present correlators to be measured at the phase boundary in a lattice definition of the model to determine the mass ratio m Higgs/ M W . We argue that by the Weinberg-Witten theorem only the Higgs phase is accessible and a light Higgs exists at the phase boundary. An argument that its effective renormalized couplings are weak is given.

DECAY RATE OF A POSITRONIUM: REVIEW OF THEORY AND EXPERIMENT

The present status of theoretical and experimental investigations of the decay rate of a positronium is considered. The increasing interest to this problem has been caused by the disagreement of the calculated value of Γ3 (o−Ps) and the recent series of precise experiments. The necessity of new calculations on the basis of the quantum field methods in bound state theory, taking into account the dependence of the interaction kernel on relative energies, is pointed out.

Generalized Schwinger duality in bound state theory

It is shown that an exactly solvable bound state problem is the generator of a nonterminable sequence of partially exactly solvable problems. The reversible passage from exact to partial solvability is realized through a class of admissible nonlinear coordinate transformations of which the parabolic Schwinger transformation that relates the Coulomb and oscillator problems is a particular case. Interesting spectral features of a novel set of partially solvable problems that emerge through the present considerations are also pointed out.

Calculation of the pion decay constant in the framework of the Bethe-Salpeter equation.

We elaborate on the calculation of the pion decay constant ${f}_{\ensuremath{\pi}}$ in the context of QCD and in the limit of purely spontaneous chiral-symmetry breaking. We use the expressions given by relativistic boundstate theory which require the simultaneous solution of the Schwinger-Dyson equation and of the Bethe-Salpeter equation developed to first order in the pion momentum. The equations are solved by numerical iteration in the Landau gauge and in the ladder approximation, but without any further approximations. We use a model for the gluon propagator with ultraviolet behavior determined by renormalization-group considerations and discuss its influence on the determination of ${f}_{\ensuremath{\pi}}$. We analyze approximations that have been used in the literature for the calculation of ${f}_{\ensuremath{\pi}}$ and discuss their limitations.

Can the squashed seven-sphere predict the standard model?

We argue that in Kaluza-Klein supergravity the breaking of the elementary SO(8) [ N=8] symmetry of the round S 7 down to the SO(5)×SO(3) symmetry of the squashed S 7 [ N=1 or N=0] corresponds to a breaking of a composite SU(8) down to either SU(4)×SU(2) [ N=1] or SU(5)×SU(3)×U(1) [ N=0]. We suggest that for N=0 the SO(5)×SO(3) acts as a confining force yielding bound states of SU(5)×SU(3)×U(1). By demanding that the effective bound state theory be both anomaly free and asymptotically free (in the SU(8) sense), we find with the standard SU(5) embedding a fermion spectrum with 4 generations of ( 5 ∗+10 ) together with a realistic Higgs sector.

A note on semiclassical bound states and correspondence principles

Semiclassical bound state theory is considered from the viewpoint of the phase space representations of quantum mechanics. In the small h/ limit, within a representation defined by the ordering chosen for the noncommuting position and momentum operators, we obtain: (1) equations of motion, which need not be classical and (2) correspondence principles in action-angle variables, regarded as those initial conditions on the equations of motion which dominate in the small h/ limit. The Weyl ordering is seen to generate the classical equations of motion and the normal correspondence result. Possible evaluation of semiclassical bound state energies is discussed by means of the eigenvalue approach to classical mechanics used by Prigogine and co-workers.

Changes of the lattice parameter in [formula omitted] 3d alloys due to the virtual bound state

The measurements of the lattice parameter of Al Sc alloys indicate that the change in the lattice parameters of Al 3 d alloys is influenced both by the density of states and the atomic volume effects. Using an interpolation method we subtract from our experimental data the effect of the atomic volume and compare the remaining change in the lattice parameter, with the virtual bound state theory. Good agreement between the theory and experiment is found.

Theory of Bound States in a Random Potential

A systematic procedure is proposed for calculation of the energy-level density of low-lying bound states in a random potential. The procedure is based on a function-space formulation of the problem; and certain features of the method may be useful in solving more general problems in functional integration. The method works in one, two, or three dimensions. In the one-dimensional case, the result checks exactly with the known solution.

Integral Equations for the Schrödinger Wave Function

For many problems in quantum mechanics it proves to be useful to write the Schrödinger equation as an integral equation rather than as a differential equation. In this paper we describe how the transformation of the Schrödinger equation from differential form to integral form may be accomplished. Two methods are described, one appropriate to bound-state theory and one appropriate to scattering theory. It is shown that the bound-state wave function is also a solution of the integral equation (Lippman-Schwinger equation) appropriate to scattering theory.

Covariant integral equations for Heisenberg operators

ABSTRACTSets of rules are obtained for writing down directly the exact integral equations which are satisfied by certain functions of Heisenberg operators in quantum field theory. Three kinds of function are considered: the direct product, the chronological product and the M-product. The matrix elements of the M-product are equal to the Feynman amplitudes studied by Matthews & Salam (1) and the corresponding integral equation is called here the Matthews-Salam (M.-S.) equation. These authors have given a symbolic form of the M.-S. equation and a method of repeated differentiation and integration which can be used to obtain the explicit form of the integral equation in any particular example. In practice their method involves an immense amount of calculation even in quite simple examples. The rules obtained in the present paper make it possible to write down directly the M.-S. equation without any of the tedious calculations implied by the M.-S. method.So long as the exact theory is used, the three sets of equations (for direct, chronological and M-products) are completely equivalent. When bound state theory is considered by an approximation based on a power series in the coupling constant different results are obtained. The approximation is inapplicable to the direct product equations, and leads to different approximate equations for the amplitudes obtained from the chronological and the M-products even when these amplitudes are identical. This paradox is explained and it is shown that the equation coming from the M-product corresponds to the Bethe-Salpeter equation.