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

Abstract

We calculate the two-loop contributions from a modified trilinear Higgs self-interaction, ${\ensuremath{\kappa}}_{\ensuremath{\lambda}}{\ensuremath{\lambda}}_{\mathrm{SM}}v{h}^{3}$, 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 $\ensuremath{-}14.0\ensuremath{\le}{\ensuremath{\kappa}}_{\ensuremath{\lambda}}\ensuremath{\le}17.4$. The largest effects on $S$ and $T$ arise from two insertions of the modified trilinear coupling that result in $T/S\ensuremath{\simeq}\ensuremath{-}3/2$; remarkably, this is nearly parallel to the axis of the tightest experimental constraint in the $S\text{\ensuremath{-}}T$ plane. No contributions to $S$ and $T$ arise from a modified Higgs quartic coupling at two-loop order. These calculations utilized a gauge-invariant parametrization of the trilinear Higgs coupling in terms of higher-dimensional operators $({H}^{\ifmmode\dagger\else\textdagger\fi{}}H{)}^{n}$ with $n\ensuremath{\ge}3$. Interestingly, the bounds on ${\ensuremath{\kappa}}_{\ensuremath{\lambda}}$ 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.