Probing $R$-parity violation in $B$-meson decays to a baryon and a light neutralino

We propose a search for $B$ meson decays to a baryon plus missing energy at the Belle II experiment to probe supersymmetry with a GeV-scale lightest neutralino ${\tilde{\chi}_1^0}$ and $R$-parity violation (RPV). We perform analytic computations of the signal branching fractions in the framework of effective field theory, with a single nonzero RPV operator $\lambda''_{ij3}\bar{U}_{i}^c\bar{D}_{j}^c\bar{D}_3^c$, where $i,j=1,2$. The hadronic form factors are calculated using an SU(3) phenomenological Lagrangian approach for the proton, as well as several hyperons and charmed baryons. Since the decay of the neutralino is kinematically and CKM suppressed in this theoretical scenario, it decays outside the detector and appears experimentally only as missing energy. We detail the analysis techniques at the experimental level and estimate the background in the ${B^+ \to p {\tilde{\chi}_1^0}}$ search using published results for $B^+\to K^+ \nu\bar\nu$. Our final sensitivity plots are shown for both $\lambda''_{113}$ versus the squark mass $m_{\tilde{q}}$ and $\lambda''_{113}/m^2_{\tilde{q}}$ versus the neutralino mass $m_{{\tilde{\chi}_1^0}}$. We find that the search at Belle II could probe $\lambda''_{113}/m^2_{\tilde{q}}$ down to the order of $10^{-8}$ GeV$^{-2}$ in the kinematically allowed $m_{{\tilde{\chi}_1^0}}$ range. We also obtain current limits on $\lambda''_{123}$ by recasting an existing search interpreted as ${B^0 \to \Lambda^0 {\tilde{\chi}_1^0}}$, and comment about searches for ${B^+ \to \Sigma^+ {\tilde{\chi}_1^0}}$, ${B^0 \to \Sigma^0 {\tilde{\chi}_1^0}}$, ${B^+ \to \Lambda_c^+ {\tilde{\chi}_1^0}}$, and ${B^+ \to \Xi_c^+ {\tilde{\chi}_1^0}}$. In closing, we briefly discuss potential searches at the LHCb and BESIII experiments.