# Constraints on the trilinear Higgs self coupling from precision observables

## TL;DR

This paper investigates how loop effects in precision electroweak measurements constrain the Higgs trilinear self coupling, showing that these bounds are competitive with direct Higgs pair production constraints.

## Contribution

It provides a detailed two-loop calculation of the impact of an anomalous Higgs self coupling on precision observables, linking effective field theory modifications to experimental bounds.

## Key findings

- Constraints from precision observables are comparable to Higgs pair production bounds.
- Two-loop diagrams with anomalous couplings significantly affect $W$ mass and effective sine.
- The analysis connects scalar potential modifications to measurable electroweak parameters.

## 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 $m_{ \scriptscriptstyle W}$ and $\mbox{$\sin^2 \theta^{{\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 $(\Phi^\dagger \Phi)^n$ 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.