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$\eta-\eta^{\prime}$ mixing · Around

2015

$\eta-\eta^{\prime}$ mixing

Pham, T. N.

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The $\eta -\eta^{\prime}$ mixing mass term due to the derivative coupling $SU(3)\times SU(3)$ symmetry breaking term, produces an additional momentum-dependent pole term for processes with $\eta^{\prime}$, but is suppressed in the $\eta$ amplitude by a factor $m_{\eta}^{2}/m_{\eta^{\prime}}^{2}$.

This seems to be the origin of the two-angle description of the pseudo-scalar 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 $\eta -\eta^{\prime}$ system could be described by a meson field renormalization and a new mixing angle $\theta$ which differs from the usual mixing angle $\theta_{P}$ 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 $\eta -\eta^{\prime}$ mixing angle and the momentum-dependent mixing term.

Built on

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