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Register a new userComputing the eta and eta Mesons in Lattice QCD
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It has been known for a long time that the large experimental singlet-octet mass gap in the pseudoscalar meson mass spectrum originates from the anomaly of the axial vector current, i.e. from nonperturbative effects and the nontrivial topological structure of the QCD vacuum. In the N_colour -> infinity limit of the theory, this connection elucidates in the famous Witten-Veneziano relation between the eta-mass and the topological susceptibility of the quenched QCD vacuum.While lattice QCD has by now produced impressive high precision results on the flavour nonsinglet hadron spectrum, the determination of the pseudoscalar singlet mesons from direct correlator studies is markedly lagging behind, due to the computational complexity in handling observables that include OZI-rule violating diagrams, like the eta propagator. In this article, we report on some recent progress in dealing with the numerical bottleneck problem.
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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 present a lattice QCD computation of $eta$ and $eta^prime$ masses and mixing angles, for the first time controlling continuum and quark mass extrapolations. The results for the eta mass 551(8)(6) MeV (first error statistical, second systematic) and the eta mass 1006(54)(38)(+61) MeV (third error from our method) are in excellent agreement with experiment. Our data show that the mixing in the quark flavour basis can be described by a single mixing angle of 46(1)(3) degree indicating that the eta is mainly a flavour singlet state.
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.
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.
We report on a first, comprehensive partially quenched study of the eta-eta problem, based on SESAM configurations on a 16^3x32 lattice at beta=5.6 QCD with two (mass degenerate) active sea quark flavours. By means of the spectral approximation of the two-loop (hairpin) diagrams, we find clear plateau formation in the effective masses which enables us both to determine the eta-eta mass matrix and the alpha-parameter in the effective chiral Lagrangian for the flavour singlet sector, alpha=0.028 +- 0.013.
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