Displacement Operator Formalism for Renormalization and Gauge Dependence to All Orders

Abstract

We present a new method for determining the renormalization of Green functions to all orders in perturbation theory, which we call the displacement operator formalism, or the D-formalism, in short. This formalism exploits the fact that the renormalized Green functions may be calculated by displacing by an infinite amount the renormalized fields and parameters of the theory with respect to the unrenormalized ones. With the help of this formalism, we are able to obtain the precise form of the deformations induced to the Nielsen identities after renormalization, and thus derive the exact dependence of the renormalized Green functions on the renormalized gauge-fixing parameter to all orders. As a particular non-trivial example, we calculate the gauge-dependence of $\tan \beta$ at two loops in the framework of an Abelian Higgs model, using a gauge-fixing scheme that preserves the Higgs-boson low-energy theorem for off-shell Green functions. Various possible applications and future directions are briefly discussed.

41 pages, 8 figures

References in corpus (24)

• JaxoDraw: A graphical user interface for drawing Feynman diagrams
• Renormalons
• Complete On-Shell Renormalization Scheme for the Minimal Supersymmetric Higgs Sector
• The Nielsen Identities of the SM and the definition of mass
• Power Corrections and Renormalons in Deep Inelastic Structure Functions
• The Pinch Technique to All Orders
• Gauge Invariance and Unstable Particles
• Practical Algebraic Renormalization
• Gauge dependence and renormalization of $\tan \beta$ in the MSSM
• Cancellation of Renormalon Ambiguities in the Heavy Quark Effective Theory
• A Gauge-Independent Approach to Resonant Transition Amplitudes
• Gauge-Invariant Resummation Formalism for Two-Point Correlation Functions
• The Renormalization of the Electroweak Standard Model to All Orders
• Pinch technique self-energies and vertices to all orders in perturbation theory
• Gauge- and Renormalization-Group- Invariant Formulation of the Higgs-Boson Resonance
• On the connection between the pinch technique and the background field method
• Effective Charge of the Higgs Boson
• Electroweak pinch technique to all orders
• Gauge Independence of the Effective Potential Revisited
• Gauge parameter dependence and gauge invariance in the Abelian Higgs model
• A New Gauge for Computing Effective Potentials in Spontaneously Broken Gauge Theories
• Two-loop renormalization of tan beta and its gauge dependence
• Higgs-Boson Low-Energy Theorem and Compatible Gauge-Fixing Conditions
• Probing the Nielsen identities

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• The cosmological Higgstory of the vacuum instability
• Scale Invariant Instantons and the Complete Lifetime of the Standard Model
• Consistent Use of Effective Potentials
• B-Meson Observables in the Maximally CP-Violating MSSM with Minimal Flavour Violation
• Convexity, gauge-dependence and tunneling rates
• Radiative Yukawa Couplings for Supersymmetric Higgs Singlets at Large tan(beta)
• Yang-Mills propagators in linear covariant gauges from Nielsen identities
• The One-Loop Effective Potential in Non-Linear Gauges
• Gauge fixing and renormalisation scale independence of tunneling rate in abelian Higgs model and in the Standard Model
• Pinch Technique for Schwinger-Dyson equations
• Radiative Lifting of Flat Directions of the MSSM in de Sitter Background
• Two-loop RGE of a general renormalizable Yang-Mills theory in a renormalization scheme with an explicit UV cutoff
• Tan(beta) enhanced Yukawa couplings for supersymmetric Higgs singlets at one loop