The decay $B\to K+\nu +\bar{\nu }$ at Belle II and a massless bino in R-parity-violating supersymmetry

Recently, $\mathtt{\text{Belle}}\mathtt{\text{II}}$ announced evidence for the decay $B^{+}\to K^{+}+\nu +\bar{\nu }$ at the $3.5\sigma$ significance, and measured the corresponding decay branching ratio to be $2.7\sigma$ above the Standard Model prediction. Here, we provide a theoretical explanation based on a massless bino in R-parity-violating (RPV) supersymmetry. With a single non-vanishing RPV coupling ${\lambda }_{i23\mathrm{/}i32}^{\mathrm{\prime }}$, ${\lambda }_{i13\mathrm{/}i33}^{\mathrm{\prime }}$, or ${\lambda }_{i12\mathrm{/}i22}^{\mathrm{\prime }}$, where $i=1,2,3$, the decay $B^{+}\to K^{+}++{\tilde{\chi }}_1^0$ can be induced, which would lead to the same signature as $B^{+}\to K^{+}+\nu +\bar{\nu }$. Taking into account both theoretical and experimental uncertainties, we derive the regions of the parameter space spanned by the RPV couplings and sfermion masses that could accommodate the new measurement at various significance levels and obey the existing bounds simultaneously.