Bottomonium and B results from full lattice QCD

We have developed two methods for handling b quarks in lattice QCD. One uses NRQCD (now improved to include radiative corrections) and the other uses Highly Improved Staggered Quarks (HISQ), extrapolating to the b quark from lighter masses and using multiple lattice spacings to control discretisation errors. Comparison of results for the two different methods gives confidence in estimates of lattice QCD systematic errors, since they are very different in these two cases. Here we show results for heavyonium hyperfine splittings and vector current-current correlator moments using HISQ quarks, to add to earlier results testing the heavy HISQ method with pseudoscalar mesons. We also show the form factor for B → πlv decay at zero recoil using NRQCD b quarks and u=d quarks with physical masses. This allows us to test the soft pion theorem relation ( f_B(q² _max) = f_B= f_π ) accurately and we find good agreement as M_π →0.