Partial wave analysis of the charmed baryon hadronic decay $\Lambda_c^+\to\Lambda\pi^+\pi^0$

Based on $e^+e^-$ collision samples corresponding to an integrated luminosity of 4.4 $\mbox{fb$^{-1}$}$ collected with the BESIII detector at center-of-mass energies between $4.6\,\,\mathrm{GeV}$ and $4.7\,\,\mathrm{GeV}$, a partial wave analysis of the charmed baryon hadronic decay $\Lambda_c^+\to\Lambda\pi^+\pi^0$ is performed, and the decays $\Lambda_c^+\to\Lambda\rho(770)^{+}$ and $\Lambda_c^+\to\Sigma(1385)\pi$ are studied for the first time. Making use of the world-average branching fraction $\mathcal{B}(\Lambda_c^+\to\Lambda\pi^+\pi^0)$, their branching fractions are determined to be \begin{eqnarray*} \begin{aligned} \mathcal{B}(\Lambda_c^+\to\Lambda\rho(770)^+)=&(4.06\pm0.30\pm0.35\pm0.23)\times10^{-2},\\ \mathcal{B}(\Lambda_c^+\to\Sigma(1385)^+\pi^0)=&(5.86\pm0.49\pm0.52\pm0.35)\times10^{-3},\\ \mathcal{B}(\Lambda_c^+\to\Sigma(1385)^0\pi^+)=&(6.47\pm0.59\pm0.66\pm0.38)\times10^{-3},\\ \end{aligned} \end{eqnarray*} where the first uncertainties are statistical, the second are systematic, and the third are from the uncertainties of the branching fractions $\mathcal{B}(\Lambda_c^+\to\Lambda\pi^+\pi^0)$ and $\mathcal{B}(\Sigma(1385)\to\Lambda\pi)$. In addition, %according to amplitudes determined from the partial wave analysis, the decay asymmetry parameters are measured to be $\alpha_{\Lambda\rho(770)^+}=-0.763\pm0.053\pm0.045$, $\alpha_{\Sigma(1385)^{+}\pi^0}=-0.917\pm0.069\pm0.056$, and $\alpha_{\Sigma(1385)^{0}\pi^+}=-0.789\pm0.098\pm0.056$.