We investigate the $K_1\to K\pi \pi$ strong interaction decays. Using the ${}^{3}P_0$ quark-pair-creation model (QPCM) to derive the basic parametrization, we discuss in detail how to obtain the various partial wave amplitudes into the possible quasi-two-body decay channels as well as their relative phases from the currently available experimental data. We obtain the $K_1$ mixing angle to be ${\theta }_{K_1}\simeq 60°$, in agreement with previous works. Our study can be applied to extract the information needed for the photon polarization determination of the radiative $B\to K_1\gamma$ decay.

• Received 10 January 2012

DOI:https://doi.org/10.1103/PhysRevD.85.074011