Winding transitions at finite energy and temperature: An O(3) model

Journal Article · Sun Dec 01 04:00:00 EST 1996 · Physical Review, D

DOI:https://doi.org/10.1103/PhysRevD.54.7774· OSTI ID:399930

Habib, S ^[1]; Mottola, E ^[2]; Tinyakov, P ^[3]

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1. Theoretical Division, MS B288, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
2. Theoretical Division, MS B285, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
3. Institute for Nuclear Research of the Russian Academy of Sciences, 60th October Anniversary Prospect, 7a, Moscow 117312 (Russia)

Winding number transitions in the two-dimensional softly broken O(3) nonlinear {sigma} model are studied at finite energy and temperature. New periodic instanton solutions which dominate the semiclassical transition amplitudes are found analytically at low energies, and numerically for all energies up to the sphaleron scale. The Euclidean period {beta} of these finite energy instantons {ital increases} with energy, contrary to the behavior found in the Abelian Higgs model or simple one-dimensional systems. This results in a {ital sharp} {ital crossover} from instanton-dominated tunneling to sphaleron-dominated thermal activation at a certain critical temperature. Since this behavior is traceable to the soft breaking of conformal invariance by the mass term in the {sigma} model, semiclassical winding number transition amplitudes in the electroweak theory in 3+1 dimensions should exhibit a similar sharp crossover. We argue that this is indeed the case in the standard model for {ital M}{sub {ital H}}{lt}4{ital M}{sub {ital W}}. {copyright} {ital 1996 The American Physical Society.}

• OSTI ID: 399930
• Journal Information: Physical Review, D, Journal Name: Physical Review, D Journal Issue: 12 Vol. 54; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
CONFORMAL INVARIANCE
CRITICAL TEMPERATURE
ENERGY DEPENDENCE
HIGGS MODEL
INSTANTONS
NONLINEAR PROBLEMS
O GROUPS
SEMICLASSICAL APPROXIMATION
SIGMA MODEL
SYMMETRY BREAKING
TEMPERATURE DEPENDENCE
TRANSITION AMPLITUDES
TWO-DIMENSIONAL CALCULATIONS