Branching ratios for Higgs-mixed scalars at the GeV scale from hadronisation models with conservation laws

We investigate the decay modes of a CP-even scalar boson $\phi$ that mixes with the Standard Model Higgs boson, focusing on the mass range between 2 GeV and $2 m_\tau$. Starting from a higher-order perturbative calculation of the inclusive decays $\phi \to gg$ and $\phi \to s\bar{s}$, we employ a hadronisation model to obtain predictions for individual hadronic final states. Our hadronisation model is based on the Herwig cluster model, but incorporates various conservation laws to determine the allowed final states and their respective weights. The model includes two tunable parameters, which we determine using dispersion relation results at $m_\phi = 2$ GeV, enabling extrapolation to higher masses. Our predictions show that two-particle hadronic final states like $\pi^+ \pi^-$ and $K^+ K^-$ dominate over $\mu^+ \mu^-$ for $m_\phi$ near 2 GeV, suggesting promising targets for future experimental searches.