Measurement Of Doubly Cabibbo-suppressed Decay D~0→K~+π~-π~0 And Search For D~0→K~+π~-π~0π~0 At BESⅢ

At √s=3.773 GeV,the e⁺ e^- collides and annihilates Ψ（3770）resonant state,and then mainly decays to D（?） Meson pair.Due to D⁰（?）⁰ data samples are generated in pairs,so this feature provides us with a unique "double-tag method".In the traditional double-tag method for measuring D meson decay,some D meson hadron decay channels with simple end states,high detection efficiency and many cases are usually used to reconstruct the D meson on the tag side,such as （?）⁰→K⁺π^-,（?）⁰→K⁺π^-π,（?）⁰→K⁺π^-π^-π⁺.Then on this basis,another D meson is reconstructed from the signal channel.But,for example,（?）⁰→K⁺π^-（CF）vs.D⁰→K⁺π^-π⁰（DCS）and D⁰→K⁺π^-（DCS）vs.（?）⁰→K⁺π^-π⁰（CF）,the final state particles are completely consistent,so the traditional double-tag method cannot distinguish whether the final state particles of DCS hadron decay in D⁰（?）⁰ decay come from the signal side or the tag side.Therefore,the measurement method of this analysis is to use the semileptonic tag method different from the traditional double-tag method,and replace the traditional hadron decay with semileptonic decay on the tag side.Since only one neutrino is lost,we can obtain the number of double-tag signal yields by fitting the difference between energy and momentum distribution spectrum of neutrinos,and finally calculate the absolute branching ratio of D meson DCS decay through the branching ratio formula.By analyzing the e⁺e^- annihilation data sample of 2.93 fb^-1 collected at the center-of-mass energy of 3.773 GeV with the BESⅢ detector,we present the measurement of the branching fraction for the doubly Cabibbo-suppressed（DCS）decay of D⁰→K⁺π^-π⁰ and the first search for the DCS decay of D⁰→K⁺π^-π⁰π⁰ by using semileptonic tag.We obtain B（D⁰→K⁺π^-π⁰）=(3.13_-0.56^+0.60±0.08)×10^-4 and B（D⁰→K⁺π^-π⁰π⁰）=(1.84_-1.00^+1.19±0.06)× 10^-4.The upper limit on the product branching fraction of D⁰→K⁺π^-π⁰π⁰ at 90%confidence level is set to be B（D⁰→K⁺π^-π⁰π⁰）<3.6×10^-4.When combined with the world averages of B（D⁰→K^-π⁺π⁰）=（14.4±0.5）%and B（D⁰→K^-π⁺π⁰π⁰）=（8.86±0.23）%,the ratios of the DCS/CF branching fractions are determined to be B（D⁰→K⁺π^-π⁰）/B（D⁰→K^-π⁺π⁰）=（0.22±0.03）%and B（D⁰→K⁺π^-π⁰π⁰）/B（D⁰→K^-π⁺π⁰π⁰）=(0.21_-0.10^+0.12),which correspond to（0.75±0.10）× tan⁴ θ_C and（0.75±0.10）× tan⁴ θ_C,respectively.Our result for D⁰→K⁺π^-π⁰π⁰ and the world-average value of B（D⁰→K^-π⁺π⁺π⁰）leads to the upper limit B（D⁰→K⁺π^-π⁰π⁰）/B（D⁰→K^-π⁺π⁰π⁰）<0.40%at the 90%confidence level,corresponding to 1.37×tan⁴ θ_C,where θ_C is the Cabibbo mixing angle.