We present the results of a lattice QCD calculation of the pseudoscalar meson decay constants f_K, f_D and f_Ds, performed with N_f=2 dynamical fermions. The simulation is carried out with the tree-level improved Symanzik gauge action and with the twisted mass fermionic action at maximal twist. With respect to our previous study (0709.4574 [hep-lat]), here we have analysed data at three values of the lattice spacing (a=0.10 fm, 0.09 fm, 0.07 fm) and performed the continuum limit, and we have included at a=0.09 fm data with a lighter quark mass (m_pi = 260 MeV) and a larger volume (L = 2.7 fm), thus having at each lattice spacing L>= 2.4 fm and m_pi*L>= 3.6. Our result for the kaon decay constant is f_K=(157.5 +- 0.8|_{stat.} +- 3.3|_{syst.}) MeV and for the ratio f_K/f_pi=1.205 +- 0.006|_{stat.} +- 0.025|_{syst.}, in good agreement with the other N_f=2 and N_f=2+1 lattice calculations. For the D and D_s meson decay constants we obtain f_D=(205 +- 7|_{stat.} +- 7|_{syst.}) MeV, in good agreement with the CLEO-c experimental measurement and with other recent N_f=2 and N_f=2+1 lattice calculations, and f_{Ds}=(248 +- 3|_{stat.} +- 8|_{syst.}) MeV that, instead, is 2.3 sigma below the CLEO-c/BABAR experimental average, confirming the present tension between lattice calculations and experimental measurements.
Abstract In Ref. [H. Neuberger, hep-lat/03030090 ] Neuberger studied a vortex fermion model with two continuum extra-dimensions, and pointed out that there are no k ≠ 0 zero modes, which is in disagreement with our paper. Since this discrepancy is due to an error in our paper, we give relevant corrections. The main result of our paper that a normalizable zero mode solution appears at the core of the vortex does not change.
As has been confirmed meanwhile by lattice-QCD calculations (see e.g. hep-lat/0702023), the confinement spectrum of non-exotic quark-antiquark systems has its ground state for scalar mesons well above 1 GeV in the Resonance Spectrum Expansion (RSE). For instance, in the S-wave Kaon-pion RSE amplitude, a broad resonance was predicted slightly above 1.4 GeV [hep-ex/0106077], which is confirmed by experiment as the K*0(1430). However, a complete nonet of light scalar mesons was predicted (Zeit.Phys.C30,615 [this http URL]) as well, when a model strongly related to the RSE and initially developed to describe the heavy quarkonia resonance spectra (Phys.Rev.D21,772 [this http URL]) was applied in the light-quark sector. Thus, it was found that the light scalar-meson nonet constitutes part of the ordinary meson spectrum, albeit represented by "extraordinary" [hep-ph/0701038] poles [hep-ex/0106077]. Similar resonances and bound states appear in the charmed sector [hep-ph/0305035], and are predicted in the B-meson spectrum [hep-ph/0312078, hep-ph/0406242]. A recent work [hep-ph/0703286] confirmed the presence of light scalar-meson poles in the RSE amplitude for S-wave and P-wave pion-pion and Kaon-pion contributions to three-body decay processes measured by the BES, E791 and FOCUS collaborations.