Bound State Mass Research Articles

Accurate solutions of quasipotential equations with orbital momentum ?=1

It is shown that the integral quasipotential Logunov-Tavkhelidze and Kadyshevskii equations with local —in Lobachevskii momentum space — quasipotentials, the transforms of which are even rational functions of r in relativistic configurational space, may be reduced to a Sturm-Liouville problem in the case of unit orbital momentum. In the critical limit, when the bound-state mass is zero, accurate wave functions are obtained.

MESONS AND DIQUARKS IN CHIRAL QCD: GENERATION OF CONSTITUENT QUARK MASSES

A new technique for analyzing mesons and diquarks as [Formula: see text] and qq states bound by gluon exchange reveals how quarks acquire constituent masses. Our method, which involves the approximate reformulation of the Bethe-Salpeter equations for chiral QCD in terms of mass functionals, is covariant, has dynamically hidden chiral symmetry and is free of all divergences. From a numerical analysis of these mass functionals, we conclude that the quarks have a preferred or 'constituent' mass, as signalled by a dramatic peaking in the meson and diquark form factors. We obtain values for the bound state and constituent quark masses and also for the ρ → ππ decay width and the ω – ρ mass splitting.

Parity doubling at the critical point in tightly bound systems

Integral equations are developed for bound states in QED. These equations are then solved numerically and the critical values, i.e. the values of the coupling constants at which the bound-state mass vanishes, are obtained. We find that at the critical values the pseudoscalar and scalar as well as the vector and pseudovector states are degenerate.

LARGE-BASIS MESON WAVEFUNCTIONS

Full O(g) meson wavefunctions are constructed in the context of Perturbative Cavity Dynamics. In addition to the valence [Formula: see text] state these wavefunctions contain [Formula: see text] (Bremsstrahlung) and [Formula: see text] (vacuum fluctuation) configurations. The divergent O(g2) self-energy contributions to the ground state energy are regulated by truncating the basis size and demanding that the bound state mass be independent of the cut-off parameter. This regularization procedure results in a nontrivial cut-off dependence of the model parameters. Parameter functions are computed for the light mesons π-ρ, K-K* and ϕ.

Solvable light-front model of a relativistic bound state in 1+1 dimensions

The bound-state equation at equal light-front time is investigated in the framework of a scalar field model in one space and one time dimension in the limit of an infinitely massive exchanged boson. Analytic expressions for the bound-state mass and form factor are obtained. In a weak-binding limit the results for mass and wave function coincide with those based on the nonrelativistic Schr\"odinger equation with \ensuremath{\delta}-type potential. For weakly bound systems the form factor reduces to the proper static limit in the whole domain of momentum transfers. In general, the quality of the static approximation is controlled by a dimensionless parameter (B\ifmmode\bar\else\textasciimacron\fi{}/m) that characterizes the strength of the binding.

Anomalous magnetic moment of a relativistic bound-state fermion

The anomalous magnetic moment of a relativistic bound-state fermion due to its compositeness is derived in the framework of the Bethe-Salpeter equation in the ladder approximation. In the limit the bound state mass is negligible compared to the compositeness mass scale, the (g - 2)/2 factor tends to zero, but the anomalous magnetic moment δμc remains finite, though it is very small compared to the Dirac magnetic moment. If the scalar functionsT andW of the bound-state wave function do not depend onS · B or S ·B’, then the anomalous magnetic moment vanishes automatically, regardless of the masses of the constituents or the binding mechanism between the constituents.

Finite-volume effects on spectrum calculations: Monte Carlo study of an exactly solvable lattice field theory

A study of finite-lattice-volume effects on Monte Carlo mass calculations is carried out for the massive Thirring/sine-Gordon model. The lattice version of the model on which the Monte Carlo simulations are carried out is provided by the Baxter eight-vertex model, an exactly solved statistical mechanics model. The particle spectrum of this theory consists of fermions and fermion-antifermion bound states. In the infinite volume limit, the mass spectrum of the model is known exactly for any value of the lattice spacing, so it is not necessary to take the lattice spacing to zero to separate finite volume from finite lattice spacing effects. With a modest amount of computer time, the Monte Carlo simulation gives mass values to an accuracy of < 3% and allows a detailed study of the functional dependence of the mass on lattice volume. The mass of the lowest-lying bound state is studied for several values of the coupling strength. We also calculate the bound state wave function and show that the lattice size for which finite-size corrections to the bound state mass become important is determined by the spread of the wave function. The results suggest that finite-size effects may be estimates by using wave-function information on a given size lattice rather than by varying the lattice size.

A nonperturbative treatment of radiative decays and the relativistic kinetic energy in heavy quarkonia

Using a “regularized potential” we solve the Schrodinger equation including all spin dependent interactions nonperturbatively and calculate the radiative decays of heavy quarkonia. The influence ofS-D mixing due to the tensor term is discussed. Applying the variational approach we investigate the influence of the relativistic kinetic energy on the bound state masses.

Which is heavier—d oru quark?

For a large class of phenomenological potential models motivated by quantum chromodynamics, we have studied the behaviour of bound state masses as the constituent mass is increased and found that the mass of a quark-antiquark bound state increases when a constituent mass is increased. It appears, for these potentials, thatd quark is heavier thanu quark.

Two-body bound-state mass in strongly coupled classical electrodynamics

The mass of a strongly coupled two-particle system is obtained from a Fokker action principle in which particles interact through their time-symmetrical electromagnetic field, considering the spin contributions in a nonperturbative calculation. We obtain a critical value for the coupling constant which is independent of the mass of the fermion, related to the problem of the true ground state. We discuss the stability of the system in the frame of aSU2 theory.

The quenched approximation in some two-dimensional field theories

We investigate the effect of suppressing closed fermion loops (the quenched approximation) in some (1 + 1)-dimensional field theories. In the Schwinger and Thirring models we find that effects of fermion loops on bound state masses can be absorbed in a rescaling of the coupling constant. In the Schwinger model an extra (decoupled) massless ghost appears and the order parameter 〈 ψψ〉 becomes infrared divergent. In an extension of the Schwinger model we compute effective lagrangians for the bound state spectrum in the quenched and unquenched case that look rather different.

Do light colored scalars exist?

The general question of the properties of light, neutral colored spin-zero particles in QCD is examined. Models with spontaneous breaking of QCD at very large distances, such as that of DeRújula, Giles, and Jaffe and the SO(3) scheme of Slansky, Goldman, and Shaw, require such light colored Higgs scalars. These scalars will form color-singlet hadronic bound states at short distances and estimates are given of bound state masses, decay widths, and production rates in processes such as ψ → γ + X within the MIT bag model. The resulting states are expected in the mass neighborhood ∼1.5 GeV and should resemble glueballs.

Extracting glueball masses from lattice QCD

A general transfer matrix approach to extracting bound-state masses from lattice field theory is presented. Applications are made to SU(2) and SU(3) pure gauge theories. Employing a source of variable strength in the Monte Carlo simulation provides an efficient technique. The lowest mass glueball is found to have a mass of 1.0 ± 0.3 GeV, consistent with other evaluations.

Comparison of three quark bound-state masses for various potentials

We test the assumption of a universal flavour-independent potential by applying several potentials which give good results for mesons to the baryon case. To calculate the mass spectrum we propose a variational method based on an expansion in terms of harmonic-oscillator wave functions. A comparison with other approximation schemes favours our method.

Deeply Bound Composite Fermion with a Dirac Magnetic Moment

Author(s): Bander, M; Chiu, TW; Shaw, GL; Silverman, D | Abstract: We formulate a model in which a light pointlike composite fermion is obtained dynamically from two heavy relativistic constituents bound by strong, short-range forces with the bound-state mass as low as one-tenth the sum of the constituent masses, while still obtaining the correct Dirac moment for this bound state (a factor of 5 greater than that of the constituents). Other static properties and details of the spectrum are investigated. © 1981 The American Physical Society.

Deeply Bound Composite Fermion with a Dirac Magnetic Moment

We formulate a model in which a light pointlike composite fermion is obtained dynamically from two heavy relativistic constituents bound by strong, short-range forces with the bound-state mass as low as one-tenth the sum of the constituent masses, while still obtaining the correct Dirac moment for this bound state (a factor of 5 greater than that of the constituents). Other static properties and details of the spectrum are investigated.

On the Structure of the Continuous Spectra in the Spinor-Spinor Bethe-Salpeter Equation

The Bethe-Salpeter equation for a bound state of a fermion-anti fermion system is analyzed in the ladder approximation of a massless vector particle exchange. For the bound state mass between zero and the threshold, all the continuous spectra of the coupling strength are obtained explicitly. The thresholds of the continuous spectra do not depend on the mass of the bound state, and exhibit the O( 4) symmetry even at the nonvanishing total four-momentum. Besides the positive continuous spectra of Goldstein type, there exist negative ones extending to minus infinity.

Instanton effects in bound-state dynamics

A systematic method is developed for computing the effects of instanton configurations on binding energies of threshold bound states. Weak coupling and the relevance of the dilute-gas approximation are assumed. The bound-state mass is extracted by studying the asymptotic behavior of the Euclidean two-point function of a current with the quantum numbers of the bound state in question. The formalism is illustrated both for the binding of scalar particles in a (1 + 1)-dimensional Higgs-Abelian model and for quark-antiquark binding in a (3 + 1)-dimensional non-Abelian gauge theory. In the latter case, interactions of exchanged quantum gluons with the background instanton fields are found to induce binding-energy shifts of the same order in the coupling $\ensuremath{\alpha}$ as direct interaction of quarks with the background fields. The static limit of the leading kernel arising from gluon-instanton interactions is found to depend linearly on the quark-antiquark separation.

Numerical solution of the spinor Bethe-Salpeter equation and the goldstein problem

The spinor Bethe-Salpeter equation describing bound states of a fermion-antifermion pair with massless-boson exchange reduces to a single (uncoupled) partial differential equation for special combinations of the fermion-boson couplings. For spinless bound states with positive or negative parity this equation is a generalization to nonvanishing bound-state masses of the equations studied by Kummer and Goldstein, respectively. In the tight-binding limit the Kummer equation has a discrete spectrum, in contrast to the Goldstein equation, while for loose binding only the generalized Goldstein equation has a nonrelativistic limit. For intermediate binding energies the equations are solved numerically. The generalized Kummer equation is shown to possess a discrete spectrum of coupling constants for all bound-state masses. For the generalized Goldstein equation a discrete spectrum of coupling constants is found only if the binding energy is smaller than a critical value.

More about the lattice Schwinger model

Massive QED for two fermion species in 1 + 1 dimensions is studied using Hamiltonian lattice techniques. The bound-state masses are obtained as strong-coupling expansions in inverse powers of the dimensionless coupling constant up to 16th order. Various Padé approximant methods for extracting the continuum limit are compared. In the non-relativistic regime (very massive fermions) our estimates are shown to converge to the correct continuum value. There is a phase transition as the fermion mass vanishes. The vacuum of the lattice theory changes from being Ising-like to being Heisenberg-like as chiral SU(2) symmetry is restored. We attempt to predict the strong-coupling behaviour by perturbing about two distinct Ising-like vacua. Our results are compared with those for the one-species (Schwinger) model.