Observation of $D^{+}\to K^{\ast 0}{\rho }^{+}$ and $D^{+}\to K^{\ast +}{\rho }^0$ in Doubly Cabibbo-Suppressed Decay $D^{+}\to K^{+}{\pi }^{+}{\pi }^{-}{\pi }^0$

Abstract

By analyzing an $e^{+}{e}^{-}$ collision data sample with an integrated luminosity of 20.3 fb${}^{-1}$ collected with the BESIII detector at the center-of-mass energy of 3.773 GeV, we perform the first amplitude analysis on the doubly Cabibbo-suppressed decay $D^{+}\to K^{+}{\pi }^{+}{\pi }^{-}{\pi }^0$ and report the first observation of $D^{+}\to K^{\ast 0}{\rho }^{+}$ and $D^{+}\to K^{\ast +}{\rho }^0$. The corresponding branching fractions are $(5.67\pm 0.41_{\mathrm{stat}}\pm 0.17_{\mathrm{syst}})\times 10^{-4}$ and $(5.32\pm 0.57_{\mathrm{stat}}\pm 0.24_{\mathrm{syst}})\times 10^{-4}$, respectively. These two $D\to VV$ decay both have large transverse polarizations. The longitudinal polarization fractions are measured to be $0.111\pm 0.024_{\mathrm{stat}}\pm 0.008_{\mathrm{syst}}$ and $0.263\pm 0.049_{\mathrm{stat}}\pm 0.015_{\mathrm{syst}}$, respectively. The branching fraction of the decay $D^{+}\to K^{+}\omega$ is measured to be $(4.76\pm 0.84_{\mathrm{stat}}\pm 0.13_{\mathrm{syst}})\times 10^{-5}$.

12 pages, 3 figures, 4 tables