Abstract
We present an improved analysis of our lattice data for the $\eta$--$\eta'$ system, including a correction of the relevant correlation functions for residual topological finite size effects and employing consistent chiral and continuum fits. From this analysis we update our physical results for the masses $M_\eta=557(11)_\mathrm{stat}(03)_{\chi\mathrm{PT}}\,\mathrm{MeV}$ and $M_{\eta'}=911(64)_\mathrm{stat}(03)_{\chi\mathrm{PT}}\,\mathrm{MeV}$, as well as the mixing angle in the quark flavor basis $\phi=38.8(2.2)_\mathrm{stat}(2.4)_{\chi\mathrm{PT}}^\circ$ in excellent agreement with other results from phenomenology. Similarly, we include an analysis for the decay constant parameters, leading to $f_l=125(5)_\mathrm{stat}(6)_{\chi\mathrm{PT}}\,\mathrm{MeV}$ and $f_s=178(4)_\mathrm{stat}(1)_{\chi\mathrm{PT}}\,\mathrm{MeV}$. The second error reflects the uncertainty related to the chiral extrapolation. The data used for this study has been generated on gauge ensembles provided by the European Twisted Mass Collaboration with $N_f=2+1+1$ dynamical flavors of Wilson twisted mass fermions. These ensembles cover a range of pion masses from $220\,\mathrm{MeV}$ to $500\,\mathrm{MeV}$ and three values of the lattice spacing. Combining our data with a prediction from chiral perturbation theory, we give an estimate for the physical $\eta,\eta' \rightarrow \gamma\gamma$ decay widths and the singly-virtual $\eta,\eta'\rightarrow\gamma\gamma^*$ transition form factors in the limit of large momentum transfer.
Highlights
The axial anomaly and the topological nature of quantum chromodynamics (QCD) are able to explain the large experimentally observed mass of the η0 meson
In contrast to the ω–φ meson mixing in the vector channel, the mixing in the pseudoscalar channel is ideal at the SU(3) symmetric point with mixing angle φ 1⁄4 54.7∘, but exhibits significantly smaller φ-values at physical quark
Since our simulations are performed at unphysical values of the quark masses and finite lattice spacing, a chiral extrapolation is required to obtain physical results
Summary
The axial anomaly and the topological nature of quantum chromodynamics (QCD) are able to explain the large experimentally observed mass of the η0 meson This understanding was possible due to perturbative arguments leading to the Witten-Veneziano [1,2] formula. In this paper we extend our previous studies [4,16,17] of properties of η and η0 mesons in two ways: first by an improved analysis: on an enlarged number of Monte Carlo ensembles we perform consistent chiral and continuum extrapolations. This leads to slightly changed results when compared to Ref. Dedicated ensembles with varied strange quark masses let us control the strange quark mass dependence
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