We present a new lattice QCD analysis of heavy-quark pseudoscalar-pseudoscalar correlators, using gluon configurations from the MILC collaboration that include vacuum polarization from u, d, s and c quarks (n f = 4). We extract new values for the QCD coupling and for the c quark's MS mass: α MS (MZ , n f = 5) = 0.11822(74) and mc(3 GeV, n f = 4) = 0.9851(63) GeV. These agree well with our earlier simulations using n f = 3 sea quarks, vindicating the perturbative treatment of c quarks in that analysis. We also obtain a new nonperturbative result for the ratio of c and s quark masses: mc/ms = 11.652(65). This ratio implies ms(2 GeV, n f = 3) = 93.6(8) MeV when it is combined with our new c mass. Combining mc/ms with our earlier m b /mc gives m b /ms = 52.55(55), which is several standard deviations (but only 4%) away from the Georgi-Jarlskop prediction from certain GUTs. Finally we obtain an n f = 4 estimate for m b /mc = 4.528(54) which agrees well with our earlier n f = 3 result. The new ratio implies m b (m b , n f = 5) = 4.162(48) GeV.
We describe a new technique to determine the contribution to the anomalous magnetic moment of the muon coming from the hadronic vacuum polarization using lattice QCD. Our method reconstructs the Adler function, using Padé approximants, from its derivatives at q 2 = 0 obtained simply and accurately from time-moments of the vector current-current correlator at zero spatial momentum. We test the method using strange quark correlators on large-volume gluon field configurations that include the effect of up and down (at physical masses), strange and charm quarks in the sea at multiple values of the lattice spacing and multiple volumes and show that 1% accuracy is achievable. For the charm quark contributions we use our previously determined moments with up, down and strange quarks in the sea on very fine lattices. We find the (connected) contribution to the anomalous moment from the strange quark vacuum polarization to be a s µ = 53.41(59) × 10 −10 , and from charm to be a c µ = 14.42(39) × 10 −10 . These are in good agreement with flavour-separated results from non-lattice methods, given caveats about the comparison. The extension of our method to the light quark contribution and to that from the quark-line disconnected diagram is straightforward.
Working with a pion mass mπ ≈ 150 MeV, we study ππ and Kπ scattering using two flavours of non-perturbatively improved Wilson fermions at a lattice spacing a ≈ 0.071 fm. Employing two lattice volumes with linear spatial extents of Ns = 48 and Ns = 64 points and moving frames, we extract the phase shifts for p-wave ππ and Kπ scattering near the ρ and K * resonances. Comparing our results to those of previous lattice studies, that used pion masses ranging from about 200 MeV up to 470 MeV, we find that the coupling gρππ appears to be remarkably constant as a function of mπ.
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