Off-shell renormalization in Higgs effective field theories

Abstract

The off-shell one-loop renormalization of a Higgs effective field theory possessing a scalar potential $\sim {\left({\Phi }^{†}\Phi -\frac{v^2}{2}\right)}^N$ with $N$ arbitrary is presented. This is achieved by renormalizing the theory once reformulated in terms of two auxiliary fields $X_{1,2}$, which, due to the invariance under an extended Becchi-Rouet-Stora-Tyutin symmetry, are tightly constrained by functional identities. The latter allow in turn the explicit derivation of the mapping onto the original theory, through which the (divergent) multi-Higgs amplitude are generated in a purely algebraic fashion. We show that, contrary to naive expectations based on the loss of power counting renormalizability, the Higgs field undergoes a linear Standard Model like redefinition, and evaluate the renormalization of the complete set of Higgs self-coupling in the $N\to \infty$ case.

33 pages, no figures. v3: complete one-loop off-shell renormalization for a BSM potential involving arbitrary powers of $\left({\varphi }^{†}\varphi -\frac{v^2}{2}\right)$ presented; Higgs wavefunction renormalization shown to be SM like; renormalization of the complete set of Higgs self-coupling in the $N\to \infty$ case discussed. v3 matches the published one

References in corpus (4)

• A minimal set of top-Higgs anomalous couplings
• Probing the Higgs self coupling via single Higgs production at the LHC
• Relaxation from particle production
• Disguising the Oblique Parameters

Cited by in corpus (5)

• Off-shell renormalization in the presence of dimension 6 derivative operators. I. General theory
• Renormalizable Extension of the Abelian Higgs-Kibble Model with a dimension 6 operator
• Gauge-Invariant Quantum Fields
• Decoupling Limits in Effective Field Theories via Higher Dimensional Operators
• Renormalizable Extension of the Abelian Higgs-Kibble Model with a Dim.6 Derivative Operator