Measurements of the branching fractions of ${\mathrm{\Lambda }}_c^{+}\to \mathrm{\Lambda }{K}^{+}{\pi }^0$ and ${\mathrm{\Lambda }}_c^{+}\to \mathrm{\Lambda }{K}^{+}\eta$ decays at Belle and Belle II

We present a study of the three-body, singly Cabibbo-suppressed decays ${\mathrm{\Lambda }}_c^{+}\to \mathrm{\Lambda }{K}^{+}{\pi }^0$ and ${\mathrm{\Lambda }}_c^{+}\to \mathrm{\Lambda }{K}^{+}\eta$ using data recorded with the Belle and Belle II detectors at the KEKB and SuperKEKB $e^{+}{e}^{-}$ colliders. The data samples correspond to integrated luminosities of 980${\mathrm{f}\mathrm{b}}^{-1}$ and 570${\mathrm{f}\mathrm{b}}^{-1}$, respectively. We measure their branching-fraction ratios relative to the Cabibbo-favored decay ${\mathrm{\Lambda }}_c^{+}\to \mathrm{\Lambda }{\pi }^{+}{\pi }^0$ as $\mathcal{B}({\mathrm{\Lambda }}_c^{+}\to \mathrm{\Lambda }{K}^{+}{\pi }^0)\mathrm{/}\mathcal{B}({\mathrm{\Lambda }}_c^{+}\to \mathrm{\Lambda }{\pi }^{+}{\pi }^0)=(1.82\pm 0.07\pm 0.07)\mathrm{\%}$, with significantly improved precision compared to the previous measurement, and $\mathcal{B}({\mathrm{\Lambda }}_c^{+}\to \mathrm{\Lambda }{K}^{+}\eta )\mathrm{/}\mathcal{B}({\mathrm{\Lambda }}_c^{+}\to \mathrm{\Lambda }{\pi }^{+}{\pi }^0)=(8.73\pm 0.35\pm 0.43)\times {10}^{-3}$, corresponding to the first observation of the ${\mathrm{\Lambda }}_c^{+}\to \mathrm{\Lambda }{K}^{+}\eta$ decay with a statistical significance exceeding 10 standard deviations. The first and second uncertainties are statistical and systematic, respectively. Using the world-average value of the branching fraction for ${\mathrm{\Lambda }}_c^{+}\to \mathrm{\Lambda }{\pi }^{+}{\pi }^0$, we obtain the branching fractions $\mathcal{B}({\mathrm{\Lambda }}_c^{+}\to \mathrm{\Lambda }{K}^{+}{\pi }^0)=(1.29\pm 0.05\pm 0.05\pm 0.06)\times {10}^{-3}$ and $\mathcal{B}({\mathrm{\Lambda }}_c^{+}\to \mathrm{\Lambda }{K}^{+}\eta )=(6.20\pm 0.25\pm 0.31\pm 0.30)\times {10}^{-4}$, where the third uncertainty arises from the uncertainty in the world-average value of $\mathcal{B}({\mathrm{\Lambda }}_c^{+}\to \mathrm{\Lambda }{\pi }^{+}{\pi }^0)$. The measured $\mathcal{B}({\mathrm{\Lambda }}_c^{+}\to \mathrm{\Lambda }{K}^{+}\eta )$ is significantly larger than predictions based on $SU(3)$ flavor symmetry.