Two analytical constraints on the \(\eta\)-\(\eta^\prime\) mixing

• Published in: arXiv.org 2000-01
• Main Authors: Fu-Guang Cao, Signal, A I
• Format: Article
• Language: English
• Subjects: Decay; Form factors; Mathematical analysis; Momentum transfer
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.9908481

We obtained two analytical constraints on the \(\eta\)-\(\eta^\prime\) mixing parameters by considering two-photon decays of \(\eta\) and \(\eta^\prime\) [\(\eta (\eta^\prime) \ra \gamma \gamma\)], and productions of \(\eta\) and \(\eta^\prime\) in the \(e^+ e^-\) scattering at large momentum transfer (\(Q^2 \ra \infty\)). Using the data given in the PDG98 for the decay processes and recent CLEO measurements on the meson-photon transition form factors, we estimate for the \(\eta_8\)-\(\eta_1\) mixing scheme the mixing angle to be \(\theta=-14.5^\circ \pm 2.0^\circ\) and the ratio of the decay constants of singlet to octet to be \(f_1/f_8=1.17 \pm 0.08\). Applying our approach to the recently proposed \(q \qbar\)-\(s \sbar\) mixing scheme, we obtain the mixing angle to be \(\phi=39.8^\circ \pm 1.8^\circ\) and the ratio of the decay constants of \(s\sbar\) state to \(q\qbar\) state to be \(f_s/f_q=1.20 \pm 0.10\).