Masses and decay constants of the $\eta$ and ${\eta }^{\prime }$ mesons from lattice QCD

Abstract

We determine the masses, the singlet and octet decay constants as well as the anomalous matrix elements of the $\eta$ and ${\eta }^{\prime }$ mesons in $N_f=2+1$ QCD\@. The results are obtained using twenty-one CLS ensembles of non-perturbatively improved Wilson fermions that span four lattice spacings ranging from $a\approx 0.086$fm down to $a\approx 0.050$fm. The pion masses vary from $M_{\pi }=420$MeV to $126$MeV and the spatial lattice extents $L_s$ are such that $L_s{M}_{\pi }\gtrsim 4$, avoiding significant finite volume effects. The quark mass dependence of the data is tightly constrained by employing two trajectories in the quark mass plane, enabling a thorough investigation of U($3$) large-$N_c$ chiral perturbation theory (ChPT). The continuum limit extrapolated data turn out to be reasonably well described by the next-to-leading order ChPT parametrization and the respective low energy constants are determined. The data are shown to be consistent with the singlet axial Ward identity and, for the first time, also the matrix elements with the topological charge density are computed. We also derive the corresponding next-to-leading order large-$N_c$ ChPT formulae. We find $F^8=115.0(2.8)\text{MeV}$, ${\theta }_8=-25.8(2.3{)}^{\circ }$, ${\theta }_0=-8.1(1.8{)}^{\circ }$ and, in the $\overline{\mathrm{MS}}$ scheme for $N_f=3$, $F^0(\mu =2\mathrm{GeV})=100.1(3.0)\text{MeV}$, where the decay constants read $F_{\eta }^8=F^8\cos {\theta }_8$, $F_{{\eta }^{\prime }}^8=F^8\sin {\theta }_8$, $F_{\eta }^0=-F^0\sin {\theta }_0$ and $F_{{\eta }^{\prime }}^0=F^0\cos {\theta }_0$. For the gluonic matrix elements, we obtain $a_{\eta }(\mu =2\mathrm{GeV})=0.0170(10){\mathrm{GeV}}^3$ and $a_{{\eta }^{\prime }}(\mu =2\mathrm{GeV})=0.0381(84){\mathrm{GeV}}^3$, where statistical and all systematic errors are added in quadrature.

98 pages including appendices, 17 figures and 25 tables. v2: correction of minor typos, added references. v3: correction of minor typos, version as published

References in corpus (18)

• On the generalized eigenvalue method for energies and matrix elements in lattice field theory
• Simulation of QCD with N_f=2+1 flavors of non-perturbatively improved Wilson fermions
• Mesonic low-energy constants
• Isoscalar meson spectroscopy from lattice QCD
• The strong coupling from a nonperturbative determination of the $\Lambda$ parameter in three-flavor QCD
• Constant contribution in meson correlators at finite temperature
• The $\eta$ and ${\eta }^{\prime }$ mesons from Lattice QCD
• Pseudoscalar glueball mass from $\eta$-${\eta }^{\prime }$-$G$ mixing
• Transition form factors ${\gamma }^{\ast }\gamma \to \eta$ and ${\gamma }^{\ast }\gamma \to {\eta }^{\prime }$ in QCD
• Topological susceptibility and the sampling of field space in $N_f=2$ lattice QCD simulations
• $D_s\to \eta ,{\eta }^{\prime }$ semileptonic decay form factors with disconnected quark loop contributions
• Lattice QCD with Domain Decomposition on Intel Xeon Phi Co-Processors
• Singlet vs Nonsinglet Perturbative Renormalization of Fermion Bilinears
• Non-perturbative determination of improvement coefficients using coordinate space correlators in $N_f=2+1$ lattice QCD
• Unified study of $J/\psi \to PV$, $P{\gamma }^{(\ast )}$ and light hadron radiative processes
• eta' meson From Two Flavor Dynamical Domain Wall Fermions
• Fate of the ${\eta }^{\prime }$ in the Quark Gluon Plasma
• Renormalization of the flavor-singlet axial-vector current and its anomaly in dimensional regularization

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