RENORMALIZATION and the EQUIVALENCE THEOREM: ON-SHELL SCHEME

Abstract

We perform an exhaustive analysis of the Equivalence Theorem both in the minimal Standard Model and in an Effective Electroweak Chiral Lagrangian up to $\mathcal{O}(p^4)$. We have considered the leading corrections to the usual prescription consisting in just replacing longitudinally polarized $W$ or $Z$ by the corresponding Goldstone bosons. The corrections appear through an overall constant multiplying the Goldstone boson amplitude as well as through additional diagrams. By including them we can extend the domain of applicability of the Equivalence Theorem, making it suitable for precision tests of the symmetry breaking sector of the Standard Model. The on-shell scheme has been used throughout. When considering the Equivalence Theorem in an Effective Chiral lagrangian we analyze its domain of applicability, as well as several side issues concerning gauge fixing, Ward identities, on-shell scheme and matching conditions in the effective theory. We have analyzed in detail the processes $W^{+}{W}^{-}\to W^{+}{W}^{-}$ and $W^{+}{W}^{+}\to W^{+}{W}^{+}$ to illustrate the points made.

37 pages, TeX, 9 figures in separate uu-file are included (also available in Postscript upon request to the Authors)

References in corpus (11)

• The Chiral Approach to the Electroweak Interactions
• The Electroweak Chiral Lagrangian and New Precision Measurements
• The Electroweak Chiral Lagrangian for the Standard Model with a Heavy Higgs
• Effective Field Theory of Anomalous Gauge-Boson Couplings at High-Energy pp Colliders
• Proof of the Equivalence Theorem in the Chiral Lagrangian Formalism
• Non-decoupling effects of the Standard Model Higgs boson to one loop
• On the Equivalence Theorem in the $\chi PT$ Description of the Symmetry Breaking Sector of the Standard Model
• The Equivalence Theorem for Chiral Lagrangians
• The Equivalence Theorem and Effective Lagrangians
• Some Remarks on the Matching Conditions
• The Equivalence Theorem for the Heavy-Higgs Standard Model and the Gauged Nonlinear Sigma-Model

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• Introducing tools to test Higgs interactions via $WW$ scattering II: the coupled channel formalism and scalar resonances