Search for $C\!P$ violation and measurement of branching fractions and decay asymmetry parameters for $\Lambda_c^+\to\Lambda h^+$ and $\Lambda_c^+\to\Sigma^{0} h^+$ ($h\!=\!K,\,\pi$)
We report a study of $\Lambda_c^+\to\Lambda h^+$ and $\Lambda_c^+\to\Sigma^{0} h^+$ ($h\!=\!K,\,\pi$) decays based on a data sample of 980~${\rm fb}^{-1}$ collected with the Belle detector at the KEKB energy-asymmetric $e^+e^-$ collider. The first results of direct $C\!P$ asymmetry in two-body singly Cabibbo-suppressed (SCS) decays of charmed baryons are measured, $A_{C\!P}^{\rm{dir}}(\Lambda_c^+\to\Lambda K^+)\!=\!+0.021\pm0.026\pm0.001$ and $A_{C\!P}^{\rm{dir}}(\Lambda_c^+\to\Sigma^0K^+)\!=\!+0.025\pm0.054\pm0.004$. We also make the most precise measurement of the decay asymmetry parameters ($\alpha$) for the four modes of interest and search for $C\!P$ violation via the $\alpha$-induced $C\!P$ asymmetry ($A_{C\!P}^{\alpha}$). We measure $A_{C\!P}^{\alpha}(\Lambda_c^+\to\Lambda K^+)\!=\!{-0.023\pm0.086\pm0.071}$ and $A_{C\!P}^{\alpha}(\Lambda_c^+\to\Sigma^0K^+)\!=\!{+0.08\pm 0.35\pm 0.14}$, which are the first $A_{C\!P}^{\alpha}$ results for SCS decays of charmed baryons. We search for $\Lambda$-hyperon $C\!P$ violation in $\Lambda_c^+\to(\Lambda,\,\Sigma^0)\pi^+$ and find $A_{C\!P}^{\alpha}(\Lambda\to p\pi^{-})\!=\!{+0.013\pm0.007\pm0.011}$. This is the first time that hyperon $C\!P$ violation has been measured via Cabibbo-favored charm decays. No evidence of baryon $C\!P$ violation is found. We also obtain the most precise branching fractions for two SCS $\Lambda_c^+$ decays, $\mathcal{B}(\Lambda_c^+\to\Lambda K^+)\!=\!(6.57\pm0.17\pm0.11\pm0.35)\times10^{-4}$ and $\mathcal{B}(\Lambda_c^+\to\Sigma^0K^+)\!=\!(3.58\pm0.19\pm0.06\pm0.19)\times10^{-4}$. The first uncertainties are statistical and the second systematic, while the third uncertainties come from the uncertainties on the world average branching fractions of $\Lambda_c^+\to(\Lambda,\,\Sigma^0)\pi^+$.