Branching Ratios of $H_{1,2,3} \rightarrow μ^{+}μ^{-}$ in the Broken-Phase N2HDM

Recent evidence from the ATLAS Collaboration for the rare decay $H \rightarrow μ^{+}μ^{-}$ provides a unique window into the Higgs boson's coupling to second-generation fermions. In this work, we investigate how this signal can probe physics beyond the Standard Model by computing the branching ratios $B(H_{i} \rightarrow μ^{+}μ^{-})$ for the three CP-even Higgs bosons $H_{1,2,3}$ in the broken-phase Next-to-Two-Higgs-Doublet Model (N2HDM). We incorporate one-loop radiative corrections and analyze deviations from the Standard Model prediction due to modified Yukawa couplings, scalar mixing, and singlet--doublet interactions. By confronting our results with the ATLAS signal strength $μ= 1.4 \pm 0.4$, we identify viable regions of the N2HDM parameter space, characterized by tan$β$, the singlet vacuum expectation value, and scalar masses, and assess the model's capacity to explain potential enhancements in the dimuon channel. Our study demonstrates that precision measurements of $H \rightarrow μ^{+}μ^{-}$ serve as a powerful tool to test extended Higgs sectors and uncover new physics at current and future colliders.