Properties of the Strange Axial Mesons in the Relativized Quark Model
We studied properties of the strange axial mesons in the relativized quark model. We calculated the $K_1$ decay constant in the quark model and showed how it can be used to extract the $K_1 (^3P_1) - K_1 (^1P_1)$ mixing angle ($θ_K$) from the weak decay $τ\to K_1 ν_τ$. The ratio $BR(τ\to ν_τK_1 (1270))/BR(τ\to ν_τK_1(1400))$ is the most sensitive measurement and also the most reliable since the largest of the theoretical uncertainties factor out. However the current bounds extracted from the TPC/Two-Gamma collaboration measurements are rather weak: we typically obtain $-30^o \lesssim θ_K \lesssim 50^o$ at 68\% C.L. We also calculated the strong OZI-allowed decays in the pseudoscalar emission model and the flux-tube breaking model and extracted a $^3P_1 - ^1P_1$ mixing angle of $θ_K \simeq 45^o$. Our analysis also indicates that the heavy quark limit does not give a good description of the strange mesons.