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The nature of strange axial-vector mesons are not well understood and can beinvestigated in $D$ meson decays. In this work, it is found that theexperimental data of $D^0\rightarrow K^\pm K^\mp_1(1270)(\to \rho K\,\,\text{or}\,\,K^{*}\pi)$ in the $D^0\to K^+K^-\pi^+\pi^-$ mode, disagreewith the equality relation under the narrow width approximation and $CP$conservation of strong decays. Considering more other results of $K_1(1270)$decays, the data of $\mathcal{B}(D^0\rightarrow K^-K^+_1(1270)(\toK^{*0}\pi^+))$ is probably overestimated by one order of magnitude. We thencalculate the branching fractions of the corresponding processes with$K_1(1400)$ in the factorization approach, and find $\mathcal{B}(D^0\rightarrowK^-K^+_1(1400)(\to K^{*0}\pi^+))$ is comparable to the predicted$\mathcal{B}(D^0\rightarrow K^-K^+_1(1270)(\to K^{*0}\pi^+))$ using theequality relation. Besides, we suggest to measure the ratios between$K_1(1270)\to \rho K$ and $K^*\pi$ or to test the equality relations in other$D$ meson decay modes.

Strange Axial-vector Mesons in D Meson Decays