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

The Georgi-Machacek (GM) model is a triplet scalar extension of the Standard Model (SM) that preserves custodial symmetry (CS) due to an explicit global $SU(2{)}_L\otimes SU(2{)}_R$ symmetry in the scalar potential at tree-level. However, it is also possible to construct a triplet extended scalar sector of the SM without imposing this global symmetry in the potential while still maintaining CS at tree-level. This is referred to as the extended GM (eGM) model. We compute one-loop corrections to all $2\to 2$ bosonic scattering amplitudes in both models and place next-to-leading order (NLO) unitarity bounds on the quartic couplings. Further, we derive the bounded-from-below (BFB) conditions on the quartic couplings demanding the stability of the scalar potential in the field subspaces. We show that the 3-field BFB conditions provide a very good approximation of the 13-field BFB conditions for both models and are computationally more efficient. With these theoretical constraints, we perform a global fit of both models to the latest Higgs signal strength results from 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 $95.4\mathrm{\%}$ CL for both models. The global fit results demonstrate that NLO unitarity and stability bounds play a significant role in constraining the allowed parameter space of both models. We obtain an upper limit on the absolute values of the scalar quartic couplings to be $1.91(2.51)$ in the GM (eGM) model. We find that in both models, the absolute mass differences between the heavy Higgs bosons are less than $410$ GeV if their masses are below $1.1$ TeV. The maximal mass difference among the members of each CS multiplet is less than $210$ GeV in the eGM model.