Integrating out the Standard Higgs Field in the Path Integral

Abstract

We integrate out the Higgs boson in the electroweak standard model at one loop and construct a low-energy effective Lagrangian assuming that the Higgs mass is much larger than the gauge-boson masses. Instead of applying diagrammatical techniques, we integrate out the Higgs boson directly in the path integral, which turns out to be much simpler. By using the background-field method and the Stueckelberg formalism, we directly find a manifestly gauge-invariant result. The heavy-Higgs effects on fermionic couplings are derived, too. At one loop the $\log\MH$-terms of the heavy-Higgs limit of the electroweak standard model coincide with the UV-divergent terms in the gauged non-linear $\sigma$-model, but vertex functions differ in addition by finite constant terms. Finally, the leading Higgs effects to some physical processes are calculated from the effective Lagrangian.

39 pages, latex, 7 figures uuencoded postscript, revised version, to appear in Nucl. Phys. B

References in corpus (12)

• Application of the Background-Field Method to the electroweak Standard Model
• Reduced Effective Lagrangians
• Gauge Invariance of Green Functions: Background-Field Method versus Pinch Technique
• The Electroweak Chiral Lagrangian for the Standard Model with a Heavy Higgs
• One-loop Effective Lagrangian for a Standard Model with a Heavy Charged Scalar Singlet
• Effective Lagrangians with Higher Order Derivatives
• A Global Analysis of the Top Quark Couplings to Gauge Bosons
• Non-decoupling effects of the Standard Model Higgs boson to one loop
• Unitary Gauge, Stueckelberg Formalism and Gauge Invariant Models for Effective Lagrangians
• Effective Field Theory of the Linear $O(N)$ Sigma Model
• Equivalence of Hamiltonian and Lagrangian Path Integral Quantization: Effective Gauge Theories
• Probing the Higgs mechanism via $\gamma \gamma \to W^{+}{W}^{-}$

Cited by in corpus (39)

• The Standard Model as an Effective Field Theory
• The Stueckelberg Field
• Integrating out heavy particles with functional methods: a simplified framework
• The Standard Model effective field theory at work
• A Proof of Concept for Matchete: An Automated Tool for Matching Effective Theories
• Covariant diagrams for one-loop matching
• Radiative Corrections to W^+W^- \to W^+W^- in the Electroweak Standard Model
• Complete One-Loop Renormalization of the Higgs-Electroweak Chiral Lagrangian
• LHC sensitivity to the resonance spectrum of a minimal strongly interacting electroweak symmetry breaking sector
• Evanescent Operators in One-Loop Matching Computations
• SuperTracer: A Calculator of Functional Supertraces for One-Loop EFT Matching
• Integrating Out New Fermions at One Loop
• Standard Model Extended by a Heavy Singlet: Linear vs. Nonlinear EFT
• Integrating out heavy fields in the path integral using the background-field method: general formalism
• Anomalous Couplings of the Third Generation in Rare B Decays
• Dyson summation without violating Ward identities and the Goldstone-boson equivalence theorem
• Precision Observables and Electroweak Theories
• Universal Scalar Leptoquark Action for Matching
• One-loop Self-energy and Counterterms in a Massive Yang-Mills Theory based on the Nonlinearly Realized Gauge Group
• The electroweak chiral Lagrangian reanalyzed
• Chiral-logarithmic Corrections to the S and T Parameters in Higgsless Models
• The Free Energy of High Temperature QED to Order $e^5$ From Effective Field Theory
• The Effective Lagrangian of the Two Higgs Doublet Model
• Constraints on the electroweak chiral Lagrangian from the precision data
• The Higgs Boson in the Standard Model - From LEP to LHC: Expectations, Searches, and Discovery of a Candidate
• The Effective Electroweak Chiral Lagrangian: The Matter Sector
• EFT matching from analyticity and unitarity
• Higgs-Electroweak Chiral Lagrangian: One-Loop Renormalization Group Equations
• Electroweak renormalization based on gauge-invariant vacuum expectation values of non-linear Higgs representations: 1. Standard Model
• The Hierarchy Principle and the Large Mass Limit of the Linear Sigma Model
• Limits on Anomalous Top Couplings from Z Pole Physics
• Electroweak renormalization based on gauge-invariant vacuum expectation values of non-linear Higgs representations: 2. extended Higgs sectors
• Renormalizable Extension of the Abelian Higgs-Kibble Model with a dimension 6 operator
• On the Observation of Bosonic Loop Corrections in Electroweak Precision Experiments
• On the Thermal Gauge Boson Masses of the Electroweak Theory in the Broken Phase
• Brane fluctuation and the electroweak chiral Lagrangian
• The renormalization of the effective Lagrangian with spontaneous symmetry breaking: the SU(2) case
• One-loop anomalous couplings and matching conditions in the nonlinear realization of the SU(2) Higgs Model
• From Models to SMEFT and Back?