Next-to-Leading Order Unitarity Fits in the Extended Georgi-Machacek Model

Abstract

We compute one-loop corrections to all $2\to2$ bosonic scattering amplitudes in the generalized two-triplet scalar extension of the Standard Model and place next-to-leading order unitarity bounds on the scalar quartic couplings of the Georgi-Machacek (GM) and the extended Georgi-Machacek (eGM) models. Further, we derive the bounded-from-below (BFB) conditions on the scalar quartic couplings demanding the stability of the scalar potential in the field subspaces. We find that, in the GM and eGM models, the BFB conditions with all combinations of three non-zero scalar fields provide a very good approximation of the all field BFB conditions while being computationally more efficient. With these improved theoretical constraints, we present results for the GM and eGM models from global fits to the latest Higgs signal strength measurements at the $13$ TeV Large Hadron Collider. We observe that the global fit disfavors the regions where $\kappa_V > 1.05$, $\kappa_V < 0.95$, and $\kappa_f > 1.05$, $\kappa_f< 0.92$ at a $95.4\%$ probability for both models. We obtain an upper limit on the absolute values of the scalar quartic couplings to be $1.91\:(3.0)$ in the GM (eGM) model. We find that the absolute mass differences between the heavy Higgs bosons are less than $410$ GeV and $520$ GeV in the GM and eGM models, respectively, if their individual masses are restricted to be below $1.1$ TeV.