Year: 2015
Type: article
Abstract: The $\ensuremath{\eta}\ensuremath{-}{\ensuremath{\eta}}^{\ensuremath{'}}$ mixing mass term due to the derivative coupling $SU(3)\ifmmode\times\else\texttimes\fi{}SU(3)$ symmetry breaking term, produces an additional momentum-dependent pole term for processes with ${\ensuremath{\eta}}^{\ensuremath{'}}$ but is suppressed in the $\ensuremath{\eta}$ amplitude by a factor ${m}_{\ensuremath{\eta}}^{2}/{m}_{{\ensuremath{\eta}}^{\ensuremath{'}}}^{2}$. This seems to be the origin of the two-angle description of the pseudoscalar decay constants used in the literature. In this paper, by diagonalizing both the mixing mass term and the momentum-dependent mixing term, we show that the $\ensuremath{\eta}\ensuremath{-}{\ensuremath{\eta}}^{\ensuremath{'}}$ system can be described by a meson field renormalization and a new mixing angle $\ensuremath{\theta}$ which differs from the usual mixing angle ${\ensuremath{\theta}}_{P}$ by a small momentum-dependent mixing $d$ term. This new mixing scheme with exact treatment of the momentum-dependent mixing term is actually simpler than the perturbation treatment and should be used in any determination of the $\ensuremath{\eta}\ensuremath{-}{\ensuremath{\eta}}^{\ensuremath{'}}$ mixing angle and the momentum-dependent mixing term. Assuming nonet symmetry for the ${\ensuremath{\eta}}_{0}$ singlet amplitude, from the sum rules relating $\ensuremath{\theta}$ and $d$ to the measured vector meson radiative decay amplitudes, we obtain consistent solutions: $\ensuremath{\theta}=\ensuremath{-}(13.99\ifmmode\pm\else\textpm\fi{}3.1)\ifmmode^\circ\else\textdegree\fi{}$, $d=0.12\ifmmode\pm\else\textpm\fi{}0.03$ from $\ensuremath{\rho}\ensuremath{\rightarrow}\ensuremath{\eta}\ensuremath{\gamma}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\rightarrow}\ensuremath{\rho}\ensuremath{\gamma}$ decays, for $\ensuremath{\omega}$, $\ensuremath{\theta}=\ensuremath{-}(15.47\ifmmode\pm\else\textpm\fi{}3.1)\ifmmode^\circ\else\textdegree\fi{}$, $d=0.11\ifmmode\pm\else\textpm\fi{}0.03$, and for $\ensuremath{\phi}$, $\ensuremath{\theta}=\ensuremath{-}(12.66\ifmmode\pm\else\textpm\fi{}2.1)\ifmmode^\circ\else\textdegree\fi{}$, $d=0.10\ifmmode\pm\else\textpm\fi{}0.03$. It seems that vector meson radiative decays would favor a small $\ensuremath{\eta}\ensuremath{-}{\ensuremath{\eta}}^{\ensuremath{'}}$ mixing angle and a small momentum-dependent mixing term.
Author: T. N. Pham
Language: Latvian
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2165625440