Benjamin W. Lee

Phase transition in the nonlinearσmodel in a (2+ε)-dimensional continuum

We study the phase transition in the nonlinear O(N) σ model in 2+e dimensions. Our analysis is of the continuum theory and does not rely upon the artifice of a lattice. This phase transition occurs at a critical value of the coupling constant λc, which is an ultraviolet-stable fixed point of the renormalization group. In the low temperature phase the O(N) symmetry is realized nonlinearly with N−1 massless pions. By solving the theory in the large-N limit, to leading order in 1N, we show that in the high temperature phase the pions gain mass and there appears a new particle, σ, which is a bound state of the πs and is degenerate with them. Furthermore, by a general steepest-descent approximation to the generating functional and by explicit calculations it is shown that this upper phase is fully O(N) symmetric and can be described by a linear σ-model Lagrangian. The unitarity of the theory is demonstrated and analogies with quark confinement in quantum chromodynamics are discussed. We prove the renormalizability of the theory, taking special care to separate infrared and ultraviolet divergences.

Charmed-baryon interpretation ofΛ¯π−π−π+andΛ¯π−π−π+π±peaks

The Lambda-bar3..pi.. (2250) and Lambda-bar4..pi.. (2500) peaks recently discovered in photoproduction are interpreted as charmed antibaryons. Specifically it is suggested that the Lambda-bar3..pi.. (2250) is the charmed analog of ..lambda.. (1115) and decays weakly. Quantum-number and spin-parity assignments are discussed briefly. We give isospin relations and predictions for the mean multiplicity of nonleptonic decay products, with special attention to channels detectable in existing experiments. A strategy for studying the dynamics of multibody nonleptonic decays is outlined and an interesting soft-pion theorem is recalled. Semileptonic decays are mentioned in passing. The Lambda-bar4..pi.. (2500) is interpreted as an amalgam of the charmed analogs of ..sigma.. (1192) and Y/sub 1/* (1385); the shape of its two-peak structure is deduced. Prospects for the observation of additional charmed baryons are considered. (AIP)

Phase Transition in the Nonlinear Sigma Model in Two + Epsilon Dimensional Continuum

We study the phase transition in the nonlinear O(N) σ model in 2+e dimensions. Our analysis is of the continuum theory and does not rely upon the artifice of a lattice. This phase transition occurs at a critical value of the coupling constant λc, which is an ultraviolet-stable fixed point of the renormalization group. In the low temperature phase the O(N) symmetry is realized nonlinearly with N−1 massless pions. By solving the theory in the large-N limit, to leading order in 1N, we show that in the high temperature phase the pions gain mass and there appears a new particle, σ, which is a bound state of the πs and is degenerate with them. Furthermore, by a general steepest-descent approximation to the generating functional and by explicit calculations it is shown that this upper phase is fully O(N) symmetric and can be described by a linear σ-model Lagrangian. The unitarity of the theory is demonstrated and analogies with quark confinement in quantum chromodynamics are discussed. We prove the renormalizability of the theory, taking special care to separate infrared and ultraviolet divergences.

Phase Transition in the Nonlinear

We study the phase transition in the nonlinear O(N) σ model in 2+e dimensions. Our analysis is of the continuum theory and does not rely upon the artifice of a lattice. This phase transition occurs at a critical value of the coupling constant λc, which is an ultraviolet-stable fixed point of the renormalization group. In the low temperature phase the O(N) symmetry is realized nonlinearly with N−1 massless pions. By solving the theory in the large-N limit, to leading order in 1N, we show that in the high temperature phase the pions gain mass and there appears a new particle, σ, which is a bound state of the πs and is degenerate with them. Furthermore, by a general steepest-descent approximation to the generating functional and by explicit calculations it is shown that this upper phase is fully O(N) symmetric and can be described by a linear σ-model Lagrangian. The unitarity of the theory is demonstrated and analogies with quark confinement in quantum chromodynamics are discussed. We prove the renormalizability of the theory, taking special care to separate infrared and ultraviolet divergences.

\sigma

The Lambda-bar3..pi.. (2250) and Lambda-bar4..pi.. (2500) peaks recently discovered in photoproduction are interpreted as charmed antibaryons. Specifically it is suggested that the Lambda-bar3..pi.. (2250) is the charmed analog of ..lambda.. (1115) and decays weakly. Quantum-number and spin-parity assignments are discussed briefly. We give isospin relations and predictions for the mean multiplicity of nonleptonic decay products, with special attention to channels detectable in existing experiments. A strategy for studying the dynamics of multibody nonleptonic decays is outlined and an interesting soft-pion theorem is recalled. Semileptonic decays are mentioned in passing. The Lambda-bar4..pi.. (2500) is interpreted as an amalgam of the charmed analogs of ..sigma.. (1192) and Y/sub 1/* (1385); the shape of its two-peak structure is deduced. Prospects for the observation of additional charmed baryons are considered. (AIP)