Flavor singlet meson mass in the continuum limit in two-flavor lattice QCD

We present results for the mass of the ${\eta }^{\prime }$ meson in the continuum limit for two-flavor lattice QCD, calculated on the CP-PACS computer, using a renormalization-group-improved gauge action, and the Sheikoleslami-Wohlert fermion action with a tadpole-improved $c_{\mathrm{sw}}.$ The correlation functions are measured at three values of the coupling β corresponding to the lattice spacing $a\approx 0.22,$ 0.16, 0.11 fm and for four values of the quark mass parameter κ corresponding to $m_{\pi }{/m}_{\rho }\approx 0.8,$ 0.75, 0.7, 0.6. For each (β, κ) pair, 400–800 gauge configurations are used. The two-loop diagrams are evaluated using a noisy source method. We calculate ${\eta }^{\prime }$ propagators using both smeared and local sources, and find that excited state contaminations are much reduced by smearing. A full analysis for the smeared propagators gives $m_{{\eta }^{\prime }}{=0.960\mathrm{}\left(87\right)\mathrm{}}_{-0.248}^{+0.036\mathrm{}}\mathrm{GeV}$ in the continuum limit, where the second error represents the systematic uncertainty coming from varying the functional form for chiral and continuum extrapolations.