Generalizing a method elaborated for three-body systems, we derive a new lower bound on four-body ground-state energies in terms of two-body binding energies in the unequal-mass case. For simple power-law potentials, this bound is compared to variational calculations and is shown to be very close to the exact result. In particular, it gives the exact answer for harmonic interactions.

We derive a set of inequalities which relate the translation invariant problem of N identical particles with pairwise interactions to an independent particle problem. These inequalities apply to attractive power law potentials V(r)=rq, 1≤q≤∞, and superpositions of such potentials; they become identities in the harmonic oscillator case q=2. We use the inequalities to derive new upper and lower bounds for the ground state energies of fermion systems, which interact through these potentials. These bounds improve all previous results in the range 1≤q≤∞; they reduce to the exact answer in the harmonic oscillator case.

We derive new lower bounds on three-body ground-state energies in terms of two-body binding energies. For three-body systems with different masses, we obtain a significant improvement as compared to previous results. In particular, the present method leads to exact results in the case of harmonic interactions, as opposed to what was found previously. It sheds light on the mechanism by which such bounds are obtained and appears to be extendable to four and more particles. The numerical results displayed show up to be very accurate estimates of the exact values, and can be used as checks in actual numerical calculations. Possible applications or generalizations are briefly outlined.

In the standard Higgs model of electroweak symmetry breaking, the Higgs boson is associated with both vector-boson and fermion mass generation. In contrast, we discuss a two-Higgs-doublet model in which these masses are associated with two different scalar bosons. We show that the Higgs boson associated with vector-boson mass generation produces a characteristic peak-dip structure in the cross section for tt→ZZ via a final-state interaction.

We derive an improved lower limit on the binding energy of a three-body system in terms of the binding energies of two-body systems with a fictitious mass. This represents a considerable improvement with respect to the previous lower limit and gives results very close to high accuracy calculations in the hyperspherical formalism for pairwise potentials rβ, 0⩽β⩽3. For β = 2, the inequality becomes an equality, and this is also true for its N-body generalization. This is clarified in an appendix by T.T. Wu. It is also possible to make model-independent predictions on the masses of the baryons by using the known dependence of the masses of the mesons on the masses of the quarks. Possible generalizations and other applications are discussed, in particular in atomic physics.

We propose a new method to obtain lower bounds on the ground-state energy of an N-body hamiltonian considered as a sum of two-body hamiltonians. When this is applied to a system of non-relativistic graviting bosons, the difference between variational upper bounds and the new lower bound never exceeds 17% or, if we accept to take a refined numerical calculation for the three-body case as input, 11%. As an illustration, the variational upper bound is used to obtain a semi-relativistic upper limit on the mass of a miniboson star.

Some technical methods used to solve two- and three-body bound-state equations in momentum space are described. These methods are, in particular, very efficient when applied to the calculation of spectra in semirelativistic confining potential Hamiltonians, which are used in hadron spectroscopy. They have a vast range of applicability.

A new, simple minded, model of hadronization is applied to charmed meson decay. By assuming a gaussian damping for the wave functions of the quarks produced, mimick an effective quark confinement coupled with asymptotic freedom within a region beyond in which hadronization occurs. The main practical consequence is the replacement of the usual Dirac delta function conservation of three-momenta of the quarks produced by a gaussian distribution. This leads, in a natural way, to non-zero contributions from W-exchange and W-annihilation (in the cases of D0 and F+ decay, respectively), in addition to the usual W-radiation mechanism which dominates D+ decay and which is the leading mechanism in conventional models of charmed mesons decay. The mathematical properties of the model are briefly analyzed and the model is applied to the study of implicit charm decay, i.e. the study of the total widths.

A model proposed recently for explaining the decay of pseudoscalar charmed mesons is applied to studying their explicit decay into two pseudoscalar mesons. The model realized quark confinement and asymptotic freedom in a simple minded way which leads in a natural way to the enhancement of the hitherto neglected W-exchange and W-annihilation decay modes. The key ingredient giving rise to this enhancement is the appearance of a new term violating the vector (as well as the axial-vector) current conservation in addition to the usual one proportional to the differences (sums) of quark masses which are negligibly small. In the valence quark approximation these new contributions are estimated and found to be in quite good agreement with all available data. Many predictions are made which could and should be experimentally checked.

We study the spectrum of a semi relativistic three-body hamiltonian. The hyperspherical method proves to be very efficient. We show that the ground states of baryons can be calculated with good accuracy. However, when using the meson potential, together with the colour assumption\(Vqq = \tfrac{1}{2}Vq\bar q\), baryon Regge slopes come out noticeably too small. We analyze this problem and show that a quarkdiquark structure for baryons cures this defect. Altogether the construction of a global unified potential model for mesons and baryons seems quite hopeful.

We study the qualitative and quantitative properties of the spectrum of a two-body hamiltonian with relativistic kinematics. We show that this kinematics leads in a natural way to the observed features of light flavour (u, d, s) spectroscopy. After having established the basic properties of the operator (p2+m2)1/2+V(r) in the cases of linear or logarithmic potentials, we show that, to first approximation, all\(q_1 \bar q_2\) meson states can be reproduced with a very simple universal flavour-independent potential whose parameters are directly related to basic physical quantities: the Regge slopes of light flavours and the quasi-logarithmic coupling strength of heavy quarks. We can derive equivalent effective non-relativistic hamiltonians which justify the successes of N.R. approaches. The main difficulties encountered, in particular in incorporating spin effects, appear to be due to the fact that, in phenomenological potential models, chiral symmetry and the ensuing Goldstone nature of the pion cannot be implemented in a natural way. Hence, such an approach can take its full predictive power only if it is based on a deeper field-theoretic level.

We study the qualitative and quantitative properties of the spectrum of a two-body hamiltonian with relativistic kinematics. We show that this kinematics leads in a natural way to the observed features of light flavour (u, d, s) spectroscopy. After having established the basic properties of the operator √ p2 + m2 + V(r) in the cases of linear or logarithmic potentials, we show that, to first approximation, all q1 q2 meson states can be reproduced with a very simple universal flavour-independent potential whose parameters are directly related to basic physical quantities : the Regge slopes of light flavours and the quasi-logarithmic coupling strength of heavy quarks. We can derive equivalent effective non-relativistic hamiltonians which justify the successes of NR approaches. The main difficulties encountered, in particular in incorporating spin effects, appear to be due to the fact that, in phenomenological potential models, chiral symmetry and the ensuing Goldstone nature of the pion cannot be implemented in a natural way. Hence, such an approach can take its full predictive power only if it is based on a deeper field-theoretic level.

We have applied anisotropic chromodynamics (ACD) to a calculation of the first approximation of the meson (\(q\bar q\) spectrum. We show that ACD affords a consistent and remarkably successful description of this spectrum in terms of 5 parameters only: 4 quark masses and the « string tension » µ. We can clearly delineate which higher-order effects should act, and how, in order to produce a systematic and accurate account of the parameters of all known mesons including their decay properties.

An explicit model is constructed for the scattering of unstable particles such as $\ensuremath{\rho}\ensuremath{\pi}\ensuremath{\rightarrow}\ensuremath{\rho}\ensuremath{\pi}$, ${K}^{*}\ensuremath{\pi}\ensuremath{\rightarrow}{K}^{*}\ensuremath{\pi}$, and $\ensuremath{\rho}K\ensuremath{\rightarrow}\ensuremath{\rho}K$. It has correct analyticity properties and satisfies quasi-two-body unitarity. The essential ingredient of the approach is a Chew-Mandelstam function for unstable particles in which the particle-resonance branch cuts are located in second Riemann sheets of the three-particle complex energy plane. The model shall be applied in future studies of final states such as $\ensuremath{\rho}\ensuremath{\pi}$, ${K}^{*}\ensuremath{\pi}$, and $\ensuremath{\rho}K$.

We show that the observation of the A1 resonance in τ decay agrees with diffractive A1 production and that it confirms our previous analysis of the diffractive data.Received 12 January 1978DOI:https://doi.org/10.1103/PhysRevLett.40.994©1978 American Physical Society

Employing unitary coupled-channel ${J}^{\mathrm{PC}}={1}^{++}$ partial-wave amplitudes for the $\ensuremath{\rho}\ensuremath{\pi}$ and ${K}^{*}\overline{K}$ systems, we show that the mass dependence and phase variations of the diffractive data on $\ensuremath{\pi}p\ensuremath{\rightarrow}(\ensuremath{\rho}\ensuremath{\pi})p$ are indicative of the presence of an ${A}_{1}$ resonance whose mass and width we determine to be roughly 1.3\ifmmode\pm\else\textpm\fi{}0.15 GeV and 400\ifmmode\pm\else\textpm\fi{}100 MeV, respectively. Our unitary amplitudes incorporate the Deck backgrounds explicitly. The fits to the data are excellent. We point out some interesting quantities to be measured in the future in order to resolve remaining uncertainties.

A unitary Deck model with coupled K*..pi.. and Krho channels, including only one resonance in the Q region is constructed. Adjusting the resonance parameters, one achieves a satisfactory description of the experimental phase variations and structure in the mass spectra. The resonance is determined to belong to the J/sup PC/ = 1/sup + -/ SU(3) octet, and is thus the Q/sub B/. The relative coupling strength K*..pi../Krho is approximately 2/3.