New decay modes of $B$ meson into a baryon and invisible dark antibaryon $\mathrm{\Psi }$ are among the most distinctive signatures of the $B$-mesogenesis scenario. We concentrate on the proton mode and consider two versions of the underlying interaction of $\mathrm{\Psi }$ with quarks, the so-called models ($d$) and ($b$). To estimate the width of the $B^{+}\to p\mathrm{\Psi }$ decay, we obtain the $B^{+}\to p$ transition form factors, applying QCD light-cone sum rules with $B$-meson distribution amplitudes with an accuracy up to twist-5, while interpolating the proton with a current. This method is independent of the previously applied one, which was based on the nucleon distribution amplitudes. We estimate the partial width of the $B^{+}\to p\mathrm{\Psi }$ decay as a function of the dark antibaryon mass. Furthermore, we use the ratio of this width to the inclusive $B\to X_N\mathrm{\Psi }$ width, the latter predicted earlier using the heavy quark expansion method. This ratio, which is independent of the effective coupling, when combined with the minimal inclusive branching fraction of $O({10}^{-4})$, necessary for the feasibility of $B$-mesogenesis, yields lower limits on the $B^{+}\to p\mathrm{\Psi }$ branching fraction. We confront these limits with the most recent upper bounds obtained from BABAR and Belle/Belle II searches for the decays of the $B^{+}$ meson into a proton and missing energy. The comparison indicates that experimental upper bounds on the branching fraction of $B\to p\mathrm{\Psi }$ at the level of ${10}^{-8}–{10}^{-7}$ are needed for a decisive probe of this invisible mode of $B$ decays.

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• Nonperturbative effects in field theory
• Phenomenology
• Baryons
• Bottom quark
• Gluons
• Mesons