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The 't Hooft determinant resolution of the eta' puzzle

Alexander A. Osipov·Alex H. Blin·Brigitte Hiller
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Abstract

The six-quark instanton induced 't Hooft interaction, which breaks the unwanted U_A(1) symmetry of QCD, is also a sourse of semi-classical corrections to the low energy effective action. It is argued that there emerges a dimensionless expansion parameter that introduces a new mass scale, Lambda_E^2=6 GeV^2, in the 0^-, 0^+ channels. This scale plays a similar role as the large critical mass M^2_crit > 4.2-6.6 GeV^2 discovered in the framework of QCD sum rules in the 0^-, 0^+ gluonic channels. In particular, it allows to resolve the eta' puzzle. To extract Lambda_E we calculate the masses of the lightest pseudoscalar meson nonet by using the Nambu --Jona-Lasinio (NJL) type U_L(3)X U_R(3) chiral symmetric Lagrangian together with the 't Hooft determinant. The mechanism which leads to the large value of Lambda_E is scrutinized.

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Alexander A. Osipov, Alex H. Blin, Brigitte Hiller. 2004-10-11. The 't Hooft determinant resolution of the eta' puzzle. https://arxiv.org/abs/hep-ph/0410148

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