Indirect probes of the trilinear Higgs coupling: gg → h and h → γγ

In the framework of the Standard Model effective field theory, we examine the indirect constraints on the trilinear Higgs coupling λ that arise from Higgs production in gluon-gluon-fusion and diphoton Higgs decays. We calculate 2-loop contributions to the gg → h and h → γγ amplitudes that are affected by modifications of the trilinear Higgs-boson vertex. Based on our new results, we analyse the sensitivity of present and future measurements of the hgg and hγγ couplings to shifts in λ. Under the assumption that O 6 = −λ (H † H)3 is the only dimension-6 operator that alters the trilinear Higgs interactions, we find that at present the considered loop-level probes provide stronger constraints than pp → 2h. At future high-energy colliders indirect O(5) determinations of the trilinear Higgs coupling may be possible, making precision measurements of gg → h and h → γγ a useful addition to direct extractions of λ through double-Higgs production.