Strange Axial-vector Mesons In D Meson Decays

The nature of strange axial-vector mesons are not well understood and stil-l need to be investigated.The main work of this paper is that we investigate the strange axial-vector mesons in D meson decays starting from a problem which is found in an experiment.it is found that the experimental data of D⁰→K^±K₁^?（1270）（→ρK or K^*π）in the D⁰→K⁺K^-π⁺π^-mode given by CLEO collaboration,disagree with the equality relation under the narrow width approximation and CP conservation of strong decays,namely the ratio of the two corresponding cascade decays of D⁰→K⁺K₁^-（1270）equals to that of the other two corresponding cascade decays of D⁰→K^-K₁⁺（1270）.Comparing with the other data of the strong decays of K₁（1270）given by BESIII,LHCb,Belle II and ACCOMOR collaborations,it is found that the branching fraction of B(D⁰→K^-K₁⁺（1270）(→K^*0π⁺))is probably overestimated by one order of magnitude and the new possible branching fraction is predicted under equality relation.And it may be the neglect of K₁（1400）in the experiment results into the problem because K₁（1270）and K₁（1400）are all J^P=1⁺states.We calculate the branching factions of the four corresponding cascade de-cays whose resonant states are all K₁（1400）under the naive factorization ap-proach with the finite width effect of K₁（1400）and find?(D⁰→K^-K₁⁺（1400）(→K^*0π⁺))is comparable to the predicted B(D⁰→K^-K₁⁺（1270）(→K^*0π⁺))us-ing the equality relation.Besides,we suggest to measure the ratios between K₁（1270）→ρK and K^*πor to test the equality relations in other D meson decay modes.