Constraints on the trilinear Higgs self coupling from precision observables

Abstract

We present the constraints on the trilinear Higgs self coupling that arise from loop effects in the $W$ boson mass and the effective sine predictions. We compute the contributions to these precision observables of two-loop diagrams featuring an anomalous trilinear Higgs self coupling. We explicitly show that the same anomalous contributions are found if the analysis of $m_W$ and $\mbox{$\sin^2 θ^{\rm lep}_{\rm eff}$}$ is performed in a theory in which the scalar potential in the Standard Model Lagrangian is modified by an (in)finite tower of $({\Phi }^{†}\Phi {)}^n$ terms with $\Phi$ the Higgs doublet. We find that the bounds on the trilinear Higgs self coupling from precision observables are competitive with those coming from Higgs pair production.

23 pages, 4 figures; V2: References added, version published on JHEP

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