H. B. Thacker

Hadronic coupling constants in lattice gauge theory

Abstract We describe an efficient method for calculating hadronic three-point functions in lattice gauge theory. We use the method to calculate the π-nucleon coupling constant the the coupling constants for the hadronic decays of the ρ and K ∗ mesons and the Δ, Σ ∗ , and Ξ ∗ baryons.

On the convergence of reflectionless approximations to confining potentials

The construction of reflectionless potentials supporting a prescribed spectrum of Schrodinger bound states is discussed and related to the inverse problem for confining potentials. A simple formula is derived for the Jost solution in a one-dimensional reflection-less potential with N bound states. This leads to compact expressions for the potential and the bound-state wavefunctions in terms of the bound-state energies. For symmetric potentials, N-fold product formulas are obtained for bound-state wavefunctions and their slopes at the origin. Corresponding quantities in a confining potential are given by infinite products. Comparison of the finite-product and infinite-product expressions allows a demonstration of the convergence of the reflectionless results to the confining potential results as N → ∞. Several sum rules satisfied by the reflectionless potential at the origin are applied to numerical studies of convergence.

Determining the fifth quark's charge: The role of the ϒ leptonic widths

Abstract Lower bounds on the leptonic decay widths of ϒ (9.4) and ϒ′ (10.0) are deduced from plausible general assumptions. It is shown that these may permit a distinction between the charge assignments e Q = (− 1 3 , + 2 3 ) for the new quark.

Integrability and Virasoro symmetry of the noncritical Baxter/Ising model

Abstract The properties of a noncritical c = 1 lattice Virasoro algebra for the exactly solvable Baxter eight-vertex model are studied in the decoupling limit in which the Baxter model is equivalent to a staggered pair of Ising models. The Virasoro operator L 0 is given by the first moment of the XY spin chain density which is proportional to the logarithm of the corner transfer matrix (CTM). The eigenmodes of L 0 are explicitly constructed in terms of lattice fermion operators. They are related to the eigenmodes of the XY hamiltonian by harmonic analysis on the spectral (rapidity) torus, which arises as the CTM group manifold. At the critical point, the results reduce to a momentum space formulation of space-time conformal symmetry. Two related Virasoro algebras are constructed from the fermionic eigenmode operators of L 0 . One is a generalization of the T = T c conformal algebra away from the critical point. The other represents diffeomorphisms of the real rapidity circle, which is compact due to the presence of the space-time lattice. Both are spectrum generating algebras of the corner transfer matrix. In the scaling limit, the Virasoro operators are expressed in terms of a massive, free Dirac field. For n ⩾ −1, the L n s are given by integrals of local densities. We discuss the relation between these densities and the integrals of motion and higher spectral flows that characterize the integrability of the system.

Statistical mechanics of an exactly integrable system

The equilibrium thermodynamics of the nonlinear Schrodinger model at finite temperature is calculated by means of the quantum inverse method. Working directly in an infinite volume we derive the equation of state and the integral equation which determines the excitation spectrum. This integral equation is found to be closely related to the Gelfand–Levitan expression for the charge density operator.

The ϱ−ππ coupling constant in lattice gauge theory

Abstract We present a method for studying hadronic transitions in lattice gauge theory which requires computer time comparable to that required by recent hadron spectrum calculations. This method is applied to a calculation of the decay ϱ → ππ .

Degeneracy in one‐dimensional quantum mechanics

The degeneracy of quantum‐mechanical energy levels is discussed from the novel perspective of the inverse scattering problem. The coalescence of energy levels is illustrated for a class of potentials which are completely characterized by their bound‐state spectra. Other applications of this style of analysis are suggested.

The H Particle on the Lattice

Jaffe’s doubly strange spin zero dibaryon (the H particle) is one of the few hadrons made of light quarks which could conceivably exist and yet not have been observed up to the present, making it an interesting test of the standard methods of lattice gauge theory. We have investigated this state and found that the mass of the dibaryon is above the two A threshold, making it unstable to strong decay.

Experimental and theoretical high energy physics. Progress report 1 Oct 1979 to 30 Sep 1980

Research performed in theoretical high energy physics includes: nonabelian Stokes theorem; connection between asymptotic behavior and bound states in QCD; classical solutions for gauge fields interacting with Higgs mesons; neutrino oscillations; relativistic wave equation and mass spectrum of gluonium; dynamical structures of the pion; convergence of reflectionless approximations to confining potentials; degeneracy in one-dimensional quantum mechanics; review of heavy quarks and new particles; semiclassical results on normalization of bound state wave functions; proton lifetime; quark magnetic moments and E1 radiative transitions in charmonium; lectures on quark models; inverse scattering and the upsilon family; and magnetic moments of quarks in baryons and mesons. In experimental high energy physics, the emphasis has been on strong interactions but also includes several crucial tests of the currently most important theories of elementary particle interactions. Experiments described include: electromagnetic couplings of vector mesons; direct photon production at large transverse momentum; hyperon experiments; spin effects in strong interactions; a dense detector for proton decay; and exclusive processes at large transverse momenta. (GHT)