Search for $C\text{\hspace{0.17em}⁣}P$ violation and measurement of branching fractions and decay asymmetry parameters for ${\mathrm{\Lambda }}_c^{+}\to \mathrm{\Lambda }{h}^{+}$ and ${\mathrm{\Lambda }}_c^{+}\to {\mathrm{\Sigma }}^0{h}^{+}$ ($h\text{\hspace{0.17em}⁣}=\text{\hspace{0.17em}⁣}K,\pi$)

We report a study of ${\mathrm{\Lambda }}_c^{+}\to \mathrm{\Lambda }{h}^{+}$ and ${\mathrm{\Lambda }}_c^{+}\to {\mathrm{\Sigma }}^0{h}^{+}$ ($h\text{\hspace{0.17em}⁣}=\text{\hspace{0.17em}⁣}K,\pi$) decays based on a data sample of 980~${\mathrm{f}\mathrm{b}}^{-1}$ collected with the Belle detector at the KEKB energy-asymmetric $e^{+}{e}^{-}$ collider. The first results of direct $C\text{\hspace{0.17em}⁣}P$ asymmetry in two-body singly Cabibbo-suppressed (SCS) decays of charmed baryons are measured, $A_{C\text{\hspace{0.17em}⁣}P}^{\mathrm{d}\mathrm{i}\mathrm{r}}({\mathrm{\Lambda }}_c^{+}\to \mathrm{\Lambda }{K}^{+})\text{\hspace{0.17em}⁣}=\text{\hspace{0.17em}⁣}+0.021\pm 0.026\pm 0.001$ and $A_{C\text{\hspace{0.17em}⁣}P}^{\mathrm{d}\mathrm{i}\mathrm{r}}({\mathrm{\Lambda }}_c^{+}\to {\mathrm{\Sigma }}^0{K}^{+})\text{\hspace{0.17em}⁣}=\text{\hspace{0.17em}⁣}+0.025\pm 0.054\pm 0.004$. We also make the most precise measurement of the decay asymmetry parameters ($\alpha$) for the four modes of interest and search for $C\text{\hspace{0.17em}⁣}P$ violation via the $\alpha$-induced $C\text{\hspace{0.17em}⁣}P$ asymmetry ($A_{C\text{\hspace{0.17em}⁣}P}^{\alpha }$). We measure $A_{C\text{\hspace{0.17em}⁣}P}^{\alpha }({\mathrm{\Lambda }}_c^{+}\to \mathrm{\Lambda }{K}^{+})\text{\hspace{0.17em}⁣}=\text{\hspace{0.17em}⁣}-0.023\pm 0.086\pm 0.071$ and $A_{C\text{\hspace{0.17em}⁣}P}^{\alpha }({\mathrm{\Lambda }}_c^{+}\to {\mathrm{\Sigma }}^0{K}^{+})\text{\hspace{0.17em}⁣}=\text{\hspace{0.17em}⁣}+0.08\pm 0.35\pm 0.14$, which are the first $A_{C\text{\hspace{0.17em}⁣}P}^{\alpha }$ results for SCS decays of charmed baryons. We search for $\mathrm{\Lambda }$-hyperon $C\text{\hspace{0.17em}⁣}P$ violation in ${\mathrm{\Lambda }}_c^{+}\to (\mathrm{\Lambda },{\mathrm{\Sigma }}^0){\pi }^{+}$ and find $A_{C\text{\hspace{0.17em}⁣}P}^{\alpha }(\mathrm{\Lambda }\to p{\pi }^{-})\text{\hspace{0.17em}⁣}=\text{\hspace{0.17em}⁣}+0.013\pm 0.007\pm 0.011$. This is the first time that hyperon $C\text{\hspace{0.17em}⁣}P$ violation has been measured via Cabibbo-favored charm decays. No evidence of baryon $C\text{\hspace{0.17em}⁣}P$ violation is found. We also obtain the most precise branching fractions for two SCS ${\mathrm{\Lambda }}_c^{+}$ decays, $\mathcal{B}({\mathrm{\Lambda }}_c^{+}\to \mathrm{\Lambda }{K}^{+})\text{\hspace{0.17em}⁣}=\text{\hspace{0.17em}⁣}(6.57\pm 0.17\pm 0.11\pm 0.35)\times {10}^{-4}$ and $\mathcal{B}({\mathrm{\Lambda }}_c^{+}\to {\mathrm{\Sigma }}^0{K}^{+})\text{\hspace{0.17em}⁣}=\text{\hspace{0.17em}⁣}(3.58\pm 0.19\pm 0.06\pm 0.19)\times {10}^{-4}$. The first uncertainties are statistical and the second systematic, while the third uncertainties come from the uncertainties on the world average branching fractions of ${\mathrm{\Lambda }}_c^{+}\to (\mathrm{\Lambda },{\mathrm{\Sigma }}^0){\pi }^{+}$.