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In the framework of the Standard Model effective field theory, we examine theindirect constraints on the trilinear Higgs coupling $\lambda$ that arise fromHiggs production in gluon-gluon-fusion and diphoton Higgs decays. We calculate2-loop contributions to the $gg \to h$ and $h \to \gamma \gamma$ amplitudesthat are affected by modifications of the trilinear Higgs-boson vertex. Thiscalculation involves both the computation of anomalous dimensions and finitematching corrections. Based on our new results, we analyse the sensitivity ofpresent and future measurements of the $hgg$ and $h \gamma \gamma$ couplings toshifts in $\lambda$. Under the assumption that $O_6 = - \lambda \left(H^\dagger H \right )^3$ is the only dimension-6 operator that alters thetrilinear Higgs interactions, we find that at present the considered loop-levelprobes provide stronger constraints than $pp \to 2h$. At future high-energycolliders indirect ${\cal O} (5)$ determinations of the trilinear Higgscoupling may be possible, making precision measurements of $gg \to h$ and $h\to \gamma \gamma$ a useful addition to direct extractions of $\lambda$ throughdouble-Higgs production.

Indirect probes of the trilinear Higgs coupling: $gg \to h$ and $h \to \gamma \gamma$