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Strange Axial-vector Mesons in D Meson Decays

The nature of strange axial-vector mesons are not well understood and can be investigated in $D$ meson decays. In this work, it is found that the experimental data of $D^0\rightarrow K^\pm K^\mp_1(1270)(\to ρK \,\,\text{or}\,\,K^{*}π)$ in the $D^0\to K^+K^-π^+π^-$ mode, disagree with 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 $\mathcal{B}(D^0\rightarrow K^-K^+_1(1270)(\to K^{*0}π^+))$ is probably overestimated by one order of magnitude. We then calculate the branching fractions of the corresponding processes with $K_1(1400)$ in the factorization approach, and find $\mathcal{B}(D^0\rightarrow K^-K^+_1(1400)(\to K^{*0}π^+))$ is comparable to the predicted $\mathcal{B}(D^0\rightarrow K^-K^+_1(1270)(\to K^{*0}π^+))$ using the equality relation. Besides, we suggest to measure the ratios between $K_1(1270)\to ρK$ and $K^*π$ or to test the equality relations in other $D$ meson decay modes.