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We present preliminary results for the masses and decay constants of the $eta$ and $eta^prime$ mesons using CLS $N_f = 2+1$ ensembles. One of the major challenges in these calculations are the large statistical fluctuations due to disconnected quark loops. We tackle these by employing a combination of noise reduction techniques which are tuned to minimize the statistical error at a fixed cost. On the analysis side we carefully assess excited states contributions by using a direct fit approach.
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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 $aapprox 0.086,$fm down to $aapprox 0.050,$fm. The pion masses vary from $M_{pi}=420,$MeV to $126,$MeV and the spatial lattice extents $L_s$ are such that $L_sM_pigtrsim 4$, 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 $F^8_eta=F^8cos theta_8$, $F^8_{eta^prime}=F^8sin theta_8$, $F^0_eta=-F^0sin theta_0$ and $F^0_{eta^prime}=F^0cos theta_0$. 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.
We investigate the masses and decay constants of eta and eta mesons using the Wilson twisted mass formulation with N_f=2+1+1 dynamical quark flavours based on gauge configurations of ETMC. We show how to efficiently subtract excited state contributions to the relevant correlation functions and estimate in particular the eta mass with improved precision. After investigating the strange quark mass dependence and the continuum and chiral extrapolations, we present our results for masses and mixing angle(s) at the physical point. Using chiral perturbation theory we also extract the decay constants f_l and f_s and use them to estimate the decay widths of eta,eta to gamma gamma and the transition form factor in the limit of large momentum transfer.
Masses of the eta and eta-prime mesons are estimated in Nf=2+1 lattice QCD with the non-perturbatively O(a) improved Wilson quark action and the Iwasaki RG-improved gluon action, using CP-PACS/JLQCD configurations on a 16^3 x 32 lattice at beta=1.83 (lattice spacing is 0.122 fm). We apply a stochastic noise estimator technique combined with smearing method to evaluate correlators among flavor SU(2) singlet pseudoscalar operators and strange pseudoscalar operators for 10 combinations of up/down and strange quark masses. The correlator matrix is then diagonalized to identify signals for mass eigenstates. Masses of the ground state and the first excited state extrapolated to the physical point are m_eta= 0.545(16) GeV and m_eta-prime= 0.871(46) GeV, being close to the experimental values of the eta and eta-prime masses.
The hadronic decays eta, eta-prime -> 3 pi and eta-prime -> eta pi pi are investigated within the framework of U(3) chiral effective field theory in combination with a relativistic coupled-channels approach. Final state interactions are included by deriving s- and p-wave interaction kernels for meson-meson scattering from the chiral effective Lagrangian and iterating them in a Bethe-Salpeter equation. Very good overall agreement with currently available data on decay widths and spectral shapes is achieved.
We report the results of the first search for the decay $B_s^0 rightarrow eta^prime eta$ using $121.4~textrm{fb}^{-1}$ of data collected at the $Upsilon(5S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider. We observe no significant signal and set a 90% confidence-level upper limit of %$7.1 times 10^{-5}$ $6.5 times 10^{-5}$ on the branching fraction of this decay.
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