Interpretation of 95 GeV Excess within the Georgi-Machacek Model in Light of Positive Definiteness Constraints

The recent observation of a di-photon excess around 95 GeV by the CMS and ATLAS Collaborations, along with the $b\bar{b}$ excess reported by the LEP Collaboration in the same mass region, has drawn significant interest in the possibility of new physics beyond the Standard Model (SM). The Georgi-Machacek (GM) model, which extends the Higgs sector of the SM by introducing additional triplet scalars while preserving custodial symmetry at tree level, provides a compelling framework to explain both excesses simultaneously via a light custodial singlet Higgs. In this work, we investigate whether the GM model can still accommodate these excesses when taking into account newly proposed vacuum stability constraints, particularly the positive definiteness conditions. Our numerical analysis not only confirms the existence of a viable parameter space capable of explaining the 95 GeV excesses, but also demonstrates that, compared to traditional tree-level constraints at the electroweak scale, the positive definiteness conditions further expand the allowed parameter space, thereby enhancing the viability of the GM model. Furthermore, we emphasize that future collider experiments will play a crucial role in testing this interpretation by refining Higgs coupling measurements and searching for additional Higgs bosons.