Constraints on the trilinear Higgs self coupling from precision observables

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 sin 2 θ lep eff is performed in a theory in which the scalar potential in the Standard Model Lagrangian is modified by an (in)finite tower of (Φ†Φ) n terms with Φ 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.