Properties of the strange axial mesons in the relativized quark model

Abstract

We study properties of the strange axial mesons in the relativized quark model. We calculate the ${\mathit{K}}_{1}$ decay constant in the quark model and show how it can be used to extract the ${\mathit{K}}_{1}$${(}^{3}$${\mathit{P}}_{1}$)-${\mathit{K}}_{1}$${(}^{1}$${\mathit{P}}_{1}$) mixing angle (${\mathrm{\ensuremath{\theta}}}_{\mathit{K}}$) from the weak decay \ensuremath{\tau}\ensuremath{\rightarrow}${\mathit{K}}_{1}$${\ensuremath{\nu}}_{\mathrm{\ensuremath{\tau}}}$. The ratio B(\ensuremath{\tau}\ensuremath{\rightarrow}${\ensuremath{\nu}}_{\mathrm{\ensuremath{\tau}}}$${\mathit{K}}_{1}$(1270))/B(\ensuremath{\tau}\ensuremath{\rightarrow}${\ensuremath{\nu}}_{\mathrm{\ensuremath{\tau}}}$${\mathit{K}}_{1}$(1400)) is the most sensitive measurement and also the most reliable since the largest of the theoretical uncertainties factor out. However, the current bounds extracted from the TPC/Two-Gamma Collaboration measurements are rather weak: we typically obtain -30\ifmmode^\circ\else\textdegree\fi{}\ensuremath{\lesssim}${\mathrm{\ensuremath{\theta}}}_{\mathit{K}}$\ensuremath{\lesssim}50\ifmmode^\circ\else\textdegree\fi{} at 68% C.L. We also calculate the strong OZI-allowed decays in the pseudoscalar emission model and the flux-tube-breaking model and extract a $^{3}$${\mathit{P}}_{1}$${\mathrm{\ensuremath{-}}}^{1}$${\mathit{P}}_{1}$ mixing angle of ${\mathrm{\ensuremath{\theta}}}_{\mathit{K}}$\ensuremath{\simeq}45\ifmmode^\circ\else\textdegree\fi{}. Our analysis also indicates that the heavy quark limit does not give a good description of the strange mesons. \textcopyright{} 1996 The American Physical Society.