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Register a new userLattice calculations of Ds to eta and eta decay form factors
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Authors
Issaku Kanamori
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We report on lattice results of the form factors for semi-leptonic decays of the D_s meson to eta and eta, with n_f=2+1 configurations. The calculation contains disconnected fermion loop diagrams, which are challenging to calculate on the lattice. Our result shows that the disconnected diagrams give significant contributions to the form factors.
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We report lattice results of $D_s$ meson semi-leptonic decay form factors to $eta$ and $eta$ mesons. This decay process contains disconnected fermion loops, which are challenging in lattice calculations. Our result shows that the disconnected loops give significant contributions to the form factors.
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 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.
We calculate the flavor-singlet contribution to the $Btoeta^{(prime)}$ transition form factors from the gluonic content of the $eta^{(prime)}$ meson in the large-recoil region using the perturbative QCD approach. The formulation for the $eta$-$eta$ mixing in the quark-flavor and singlet-octet schemes is compared, and employed to determine the chiral enhancement scales associated with the two-parton twist-3 $eta^{(prime)}$ meson distribution amplitudes. It is found that the gluonic contribution is negligible in the $Btoeta$ form factors, and reaches few percents in the $Btoeta$ ones. Its impact on the accommodation of the measured $Btoeta^{(prime)} K$ branching ratios in the perturbative QCD and QCD-improved factorization approaches is elaborated.
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.
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