Hadronic Charmed Meson Decays Involving Axial Vector Mesons

Cabibbo-allowed charmed meson decays into a pseudoscalar meson and an axial-vector meson are studied. The charm to axial-vector meson transition form factors are evaluated in the Isgur-Scora-Grinstein-Wise quark model. The dipole momentum dependence of the $D\to K$ transition form factor and the presence of a sizable long-distance $W$-exchange are the two key ingredients for understanding the data of $D\to \bar{K}{a}_1$. The $K_{1A}-K_{1B}$ mixing angle of the strange axial-vector mesons is found to be $\approx \pm {37}^{\circ }$ or $\pm {58}^{\circ }$ from $\tau \to K_1{\nu }_{\tau }$ decays. The study of $D\to K_1(1270)\pi, K_1(1400)\pi$ decays excludes the positive mixing-angle solutions. It is pointed out that an observation of the decay $D^0\to K_1^-(1400)\pi^+$atthelevelof$5\times 10^{-4}$willruleout$\theta\approx -37^\circ$andfavorthesolution$\theta\approx -58^\circ$. Though the decays $D^0\to {\bar{K}}_1^0{\pi }^0$ are color suppressed, they are comparable to and even larger than the color-allowed counterparts: $\bar K_1^0(1270)\pi^0\sim K_1^-(1270)\pi^+$and$\bar K_1^0(1400)\pi^0> K_1^-(1400)\pi^+$. The finite width effect of the axial-vector resonance is examined. It becomes important for $a_1(1260)$ in particular when its width is near 600 MeV.