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 lambda that arise from Higgs production in gluon-gluon-fusion and diphoton Higgs decays. We calculate 2-loop contributions to the gg -> h and h -> gamma gamma 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 h gamma gamma couplings to shifts in lambda. Under the assumption that O (6) = -lambda (H (aEuro) 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 determinations of the trilinear Higgs coupling may be possible, making precision measurements of gg -> h and h -> gamma gamma a useful addition to direct extractions of lambda through double-Higgs production.