Electroweak oblique parameters as a probe of the trilinear Higgs boson self-interaction

We calculate the two-loop contributions from a modified trilinear Higgs self-interaction, κλλSMvh3, to the electroweak oblique parameters S and T. Using the current bounds on S and T from electroweak measurements, we find the 95% C.L. constraint on the modified trilinear coupling to be −14.0≤κλ≤17.4. The largest effects on S and T arise from two insertions of the modified trilinear coupling that result in T/S≃−3/2; remarkably, this is nearly parallel to the axis of the tightest experimental constraint in the S-T plane. No contributions to S and T arise from a modified Higgs quartic coupling at two-loop order. These calculations utilized a gauge-invariant parameterization of the trilinear Higgs coupling in terms of higher dimensional operators (H†H)n with n≥3. Interestingly, the bounds on κλ that we obtain are comparable to constraints from di-Higgs production at the LHC as well as recent bounds from single Higgs production at the LHC.