Indirect search for light charged Higgs bosons through the dominant semileptonic decays of top quark t → b(→B/D + X)+H⁺(→τ⁺ν_τ)

In this work we introduce a new channel to indirect search for the light charged Higgs bosons, which are predicted in several extensions of the standard model (SM) such as the two-Higgs-doublet models (2HDMs). We calculate the $O\left({\alpha }_s\right)$ QCD radiative corrections to the energy distribution of bottom- and charmed-flavored hadrons ($B/D$) produced in the dominant decays of the polarized top quark in the 2HDM, i.e. $t(\uparrow )⟶b(\to B/D+\text{jet})+H^{+}(\to {\tau }^{+}{\nu }_{\tau })$. Generally, the energy distribution of hadrons is governed by the unpolarized rate and the polar and the azimuthal correlation functions which are related to the density matrix elements of the decay $t(\uparrow )\to b{H}^{+}$. In our proposed channel, any deviation of the $B/D$-meson energy spectrum from its corresponding SM predictions can be considered as a signal for the existence of charged Higgs at the LHC. We also calculate, for the first time, the azimuthal correlation rate ${\Gamma }_{\varphi }$ at next-to-leading order which vanishes at the Born level.