Measurement of the doubly Cabibbo-suppressed decay $D^+to K^+pi^+pi^-pi^0$ with semileptonic tags

Using an $e^+e^-$ annihilation data sample corresponding to an integrated luminosity of $2.93,rm fb^{-1}$ collected at a center-of-mass energy of 3.773 GeV with the BESIII detector, the doubly Cabibbo-suppressed decay $D^+to K^+pi^+pi^-pi^0$ is studied with a semileptonic tag method. After removing the decays containing narrow intermediate resonances, $D^+to K^+eta$, $D^+to K^+omega$, and $D^+to K^+phi$, the branching fraction for the decay $D^+to K^+pi^+pi^-pi^0$ is determined to be $(1.03 pm 0.12_{rm stat} pm 0.06_{rm syst})times 10^{-3}$. The ratio of the branching fraction for $D^+to K^+pi^+pi^-pi^0$ to its Cabibbo-favored counterpart $D^+to K^-pi^+pi^+pi^0$ is measured to be $ (1.65pm0.21)%$, corresponding to $(5.73pm0.73)tan^4theta_C$, where $theta_C$ is the Cabibbo mixing angle. These results are consistent with our previous measurement with hadronic tags but are significantly larger than other doubly Cabibbo-suppressed decays in the charm sector.