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

TL;DR

This work tackles the challenge of predicting hadronic decays for a CP-even scalar φ that mixes with the SM Higgs in the GeV mass range. It combines high-order perturbative widths for φ → gg and φ → s s̄ with a novel hadronisation model that enforces conservation laws to produce exclusive hadronic final states, calibrated by dispersion-relations data at $m_φ = 2$ GeV and two free parameters, $w_s$ and $a_v$ (plus an overall normalization factor $a_Γ$). The framework then extrapolates to $2$ GeV < $m_φ$ < $2 m_τ$, predicting that two-body hadronic decays such as $φ → π^+π^-$ and $φ → K^+K^-$ can dominate over $φ → μ^+μ^-$ near threshold, with kaon final states offering promising Belle II sensitivity. This work provides a data-driven, physically constrained method to map GeV-scale Higgs-mportal scalars onto observable hadronic signatures and outlines extensions (cluster fission, baryons, off-shell effects, resonance mixing) as experimental input improves.

Abstract

We investigate the decay modes of a CP-even scalar boson $φ$ that mixes with the Standard Model Higgs boson, focusing on the mass range between 2 GeV and $2 m_τ$. Starting from a higher-order perturbative calculation of the inclusive decays $φ\to gg$ and $φ\to s\bar{s}$, 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 $m_φ= 2$ GeV, enabling extrapolation to higher masses. Our predictions show that two-particle hadronic final states like $π^+ π^-$ and $K^+ K^-$ dominate over $μ^+ μ^-$ for $m_φ$ near 2 GeV, suggesting promising targets for future experimental searches.

Figures (5)

• Figure 1: Decay width into gluons $\Gamma^{gg}$ (top) and into strange quarks $\Gamma^{s\bar{s}}$ (bottom) as a function of the scalar mass $m_\phi$ at different orders in perturbation theory.
• Figure 2: Widths for the decay of $\phi$ to pions and kaons obtained from dispersion relations in Ref. blackstoneHadronicDecaysHiggsmixed2024.
• Figure 3: Decay widths of the CP-even scalar $\phi$ as a function of mass. Below 2 GeV, the pion and kaon decay widths are obtained from dispersion relations blackstoneHadronicDecaysHiggsmixed2024 (labelled as "data"). Above 2 GeV, the decay widths into gluons and strange quarks are obtained from a perturbative calculation, while the decay widths into pions and kaons are obtained from our hadronisation model, after fitting the free parameters to agree with the result from dispersion relations at 2 GeV.
• Figure 4: Branching ratios for the most relevant final states as a function of the scalar mass. In each case, the solid line corresponds to the best-fit prediction and the band represents the uncertainties resulting from the uncertainties in the partial widths obtained from dispersion relations at $m_\phi = 2 \, \mathrm{GeV}$.
• Figure 5: Sensitivity of Belle II to a Higgs-mixed scalar with mass $m_\phi$ and mixing angle $\sin \theta$ for different final states, assuming that the expected exclusion limits from Ref. collaborationSearchLonglivedSpin02023 can be improved by a factor of 20.