Constraints on a Light Singlet Scalar from Combined Exotic Higgs Decays
We investigate the phenomenology of the Standard Model extended by a real gauge-singlet scalar field, focusing on exotic Higgs decay channels. For a light scalar mass in the range \(0 < m_{\phi} < 40\) GeV, the Higgs boson can decay to both two and three scalar final states. We derive analytical expressions for these decay rates and impose a global constraint on the model parameters by requiring that their sum does not exceed the total Standard Model Higgs boson decay width. This requirement translates into a fourth-order inequality with respect to the singlet vacuum expectation value, \(v_{\phi}\). We demonstrate that satisfying this inequality imposes an upper bound of \(\cos \theta < 0.12 - 0.13\) across the entire mass range, providing a complementary constraint to existing direct search limits. Utilizing stronger independent constraints on the mixing (e.g., \(\cos \theta < 0.1\)), we then predict upper bounds on the individual exotic decay rates as a function of \(m_{\phi}\) as \(\Gamma_{h \rightarrow \phi \phi} < 0.06\) MeV and \(\Gamma_{h \rightarrow \phi \phi \phi} < 5 \times 10^{- 6}\) MeV, respectively.