The Fermion Determinant in External Scalar Fields: Exact Results and Large Mass Approximation

Abstract

We present results for the fermion determinant in an external Yukawa-coupled scalar field, a quantity relevant to instanton and sphaleron transition rates as well as bubble nucleation occuring in the electroweak phase transition when the scalar field is identified with the Higgs field. We calculate the determinant exactly and find an approximation (essentialy of the gradient expansion type) that reproduces the exact results very well if the fermion mass $m_F$ becomes larger than the inverse of the size $R$ of the background field configuration. The results are given for 2, 3 and 4 Euclidean dimensions.

Dortmund University DO-TH-94/04, 16 pages, LaTeX, macros: epsfig.sty 7 figures appended as uuencoded, tar-compressed .eps files

References in corpus (1)

• One-Loop Corrections to Bubble Nucleation Rate at Finite Temperature

Cited by in corpus (6)

• Fluctuation corrections to bubble nucleation
• Fermion Fluctuation Determinant and Sphaleron Bound
• Self-consistent treatment of bubble nucleation at the electroweak phase transition
• Finite-temperature bubble nucleation with shifting scale hierarchies
• Fermionic fluctuation corrections to bubble nucleation
• What is the lightest excited state of the strongly selfcoupled Higgs field?