We investigate the discovery potential of the $T_{ bc}$ states with $J^P = 0^+$ in proton-proton ($pp$) collisions at LHCb at a center-of-mass energy of $\sqrt{ s} = 13~\mathrm{ TeV}$. The study focuses on the decay channel $T_{ bc} \to B^- D^+$. A phenomenological approach is employed to construct the background model based on the associated production of $B$ and $D$ mesons, incorporating previously published LHCb results. Background processes are simulated using $\texttt{ MadGraph5\_aMC@NLO}$ and $\texttt{ Pythia8.3}$. We explore the parameter space of the $T_{ bc}$ mass, width, production cross section, and the effective double-parton-scattering cross section ($\sigma_{ \mathrm{ eff}}$) relevant for the $B D$ meson background. The integrated luminosity required for a $5\sigma$ discovery at LHCb is evaluated under various assumptions. We find that a $5\sigma$ observation is achievable for a production cross section of $103~\mathrm{ nb}$, which is expected to be within reach during Run~4. In addition, we estimate the minimum observable $\sigma(T_{ bc}) \times \mathrm{ BR}(T_{ bc} \to B^- D^+)$ for a $5\sigma$ discovery under different luminosity scenarios, providing guidance for future experimental searches at LHCb.
Categories: hep-ph hep-ex