η−η′ mixing in large- Nc chiral perturbation theory

Abstract

We present a calculation of the η-η mixing in the framework of large-N c chiral perturbation theory. A general expression for the η-η mixing at next-to-next-to-leading order (NNLO) is derived, including higher-derivative terms up to fourth order in the four momentum, kinetic and mass terms. In addition, the axial-vector decay constants of the η-η system are determined at NNLO. The numerical analysis of the results is performed successively at LO, NLO, and NNLO. We investigate the influence of one-loop corrections, OZI-rule-violating parameters, and O(N c p 6 ) contact terms.

$\eta$-$\eta\prime$ mixing in Large-Nc ChPT: discussion, phenomenology, and prospects

“…Other numerical scenarios with a detailed discussion of loop effects and different determinations of LECs can be found in Ref. [1].…”

“…After the field redefinition η BC = Z C · η B to remove the higher-derivative terms, the Lagrangian takes the form 8) where the expressions for the new kinetic matrix K and for Z C can be found in Ref. [1]. We then perform two additional transformations, Z 1/2 and R, to diagonalize the Lagrangian in Eq.…”

“…(2.8), and the full transformation for the states reads 9) where the matrices Z C , Z 1/2 , and R are given in Ref. [1]. The mass matrix M 2 in Eq.…”

“…(2.6) needs to be diagonalized (a detailed discussion of this procedure can be found in Ref. [1]). After the field redefinition η BC = Z C · η B to remove the higher-derivative terms, the Lagrangian takes the form 8) where the expressions for the new kinetic matrix K and for Z C can be found in Ref.…”

“…

A systematic study of the η-η mixing in Large-N c chiral perturbation theory is presented [1], with special emphasis on the role of the next-to-next-to-leading-order contributions in the combined momentum, quark-mass, and 1/N c expansions. At this order, loop corrections as well as OZIrule-violating pieces need to be included.

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