PoS - Proceedings of Science
Volume 396 - The 38th International Symposium on Lattice Field Theory (LATTICE2021) - Oral presentation
Properties of the $\eta$ and $\eta^{\prime}$ mesons: Masses, decay constants and gluonic matrix elements
G. Bali, S. Collins, J. Simeth*  on behalf of the RQCD Collaboration
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Pre-published on: May 16, 2022
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We present results for the $\eta$ and $\eta^\prime$ masses and their four independent decay constants at the physical point as well as their anomalous gluonic matrix elements $a_{\eta^{(\prime)}}$.
The chiral and continuum limit extrapolation is performed on twenty-one $N_f = 2+1$ Coordinated Lattice Simulations (CLS) ensembles with non-perturbatively
improved Wilson fermions at four different lattice spacings and along two trajectories in the quark mass plane, including one ensemble very close to physical
quark masses.
For the first time the decay constants are determined directly from the axialvector matrix elements without model assumptions. This allows us to study their QCD scale dependence and to determine all low-energy constants contributing at next-to-leading order in large-$N_c$ ChPT at a well defined QCD renormalization scale.
We also discuss higher excited states in the $1400\,\mathrm{MeV}$ region.
DOI: https://doi.org/10.22323/1.396.0286
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