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 ($H^\pm$) due to the sizable $t\bar t$ production cross section at the LHC in conjunction with their distinct experimental signatures. While dedicated ATLAS and CMS searches considered only $H^\pm$ decays into $\tau\nu$, $cs$, or $cb$ for $m_{H^\pm}<m_t$, the $WZ$ channel remains unexplored, despite being the dominant mode in $SU(2)_L$ triplet models. Since, top-quark pair production with $t \to H^\pm b$ and $H^\pm \to WZ$ gives rise to $t\bar{t}Z$-like signatures, we recast existing $t\bar{t}Z$ analyses to search for signs of charged Higgs bosons and set novel limits on the product of branching fractions Br$(t\to H^\pm b) \times $Br$(H^\pm\to WZ)$. These constraints turn out to be at the sub-permille level, despite the observed $2\sigma$ preference for a non-zero value. Interpreted within the hypercharge $Y=0$ Higgs triplet model, this translates into a stringent constraint on the triplet Higgs vacuum expectation value of $v_\Delta\lesssim 2$ GeV, which is stronger than those from the $cs,\tau\nu$ modes and even surpasses electroweak precision constraints from the $\rho$ parameter. Moreover, the $2\sigma$ preference for a non-zero cross section further strengthens the cumulative case for a $\approx152$ GeV boson as suggested, in particular, by di-photon excesses.