Searching for a charged Higgs boson in top-quark decays via the $WZ$ mode

Top-quark decays are sensitive probes of light charged Higgs bosons (𝐻$^±$) due to the sizable 𝑡⁢$\overline{𝑡}$ production cross section at the LHC in conjunction with their distinct experimental signatures. While dedicated ATLAS and CMS searches considered only 𝐻$^±$ decays into 𝜏⁢𝜈, 𝑐⁢𝑠, or 𝑐⁢𝑏 for 𝑚$_{𝐻±}$ < 𝑚𝑡, the 𝑊⁢𝑍 channel remains unexplored, despite being the dominant mode in 𝑆⁢𝑈⁢(2)𝐿 triplet models. Since top-quark pair production with 𝑡 → 𝐻$^±$⁡𝑏 and 𝐻$^±$→𝑊⁢𝑍 gives rise to 𝑡⁢$\overline{𝑡}$⁢𝑍-like signatures, we recast existing 𝑡⁢$\overline{𝑡}$⁢𝑍 analyses to search for signs of charged Higgs bosons and set novel limits on the product of branching fractions Br⁡(𝑡→𝐻$^±$⁡𝑏) × Br⁡(𝐻$^±$→𝑊⁢𝑍). These constraints turn out to be at the sub-permille level, despite the observed 2⁢𝜎 preference for a nonzero value. Interpreted within the hypercharge 𝑌 = 0 Higgs triplet model, this translates into a stringent constraint on the triplet Higgs vacuum expectation value of 𝑣$_Δ$ ≲ 2 GeV, which is stronger than those from the 𝑐⁢𝑠, 𝜏⁢𝜈 modes and even surpasses electroweak precision constraints from the 𝜌 parameter. Moreover, the 2⁢𝜎 preference for a nonzero cross section further strengthens the cumulative case for a ≈152  GeV boson as suggested, in particular, by diphoton excesses.