Properties of the Strange Axial Mesons in the Relativized Quark Model

Abstract

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 $K_1{(}^3{P}_1)-K_1{(}^1{P}_1)$ mixing angle (${\theta }_K$) from the weak decay $\tau \to K_1{\nu }_{\tau }$. The ratio $BR(\tau \to {\nu }_{\tau }{K}_1(1270))/BR(\tau \to {\nu }_{\tau }{K}_1(1400))$ 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 $-30^o\lesssim {\theta }_K\lesssim 50^o$ 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 ${}^3{P}_1{-}^1{P}_1$ mixing angle of ${\theta }_K\simeq 45^o$. Our analysis also indicates that the heavy quark limit does not give a good description of the strange mesons.

Comments: Revised version to be published in Phys. Rev. D. Minor changes. Latex file uses revtex version 3 and epsfig, 4 postcript figures are attached. The full postcript version with embedded figures is available at ftp://ftp.physics.carleton.ca/pub/theory/godfrey/ocipc9512.ps.Z