The size of the pion from full lattice QCD with physical u, d, s and c quarks

We present the first calculation of the electromagnetic form factor of the π meson at physical light quark masses. We use configurations generated by the MILC collaboration including the effect of u, d, s and c sea quarks with the Highly Improved Staggered Quark formalism. We work at three values of the lattice spacing on large volumes and with u/d quark masses going down to the physical value. We study scalar and vector form factors for a range in space-like q2 from 0.0 to -0.13 GeV2 and from their shape we extract mean square radii. Our vector form factor agrees well with experiment and we find hr2iV = 0:403(18)(6) fm2. For the scalar form factor we include quark-line disconnected contributions which have a significant impact on the radius. We give the first results for SU(3) flavour-singlet and octet scalar mean square radii, obtaining: hr2isinglet S = 0:506(38)(53)fm2 and hr2ioctet S = 0:431(38)(46)fm2. We discuss the comparison with expectations from chiral perturbation theory

The mass of the b-quark from lattice NRQCD and lattice perturbation theory

We present a determination of the b-quark mass accurate through O(\alpha_s^2) in perturbation theory and including partial contributions at O(\alpha_s^3). Nonperturbative input comes from the calculation of the Upsilon and B_s energies in lattice QCD including the effect of u, d and s sea quarks. We use an improved NRQCD action for the b-quark. This is combined with the heavy quark energy shift in NRQCD determined using a mixed approach of high-beta simulation and automated lattice perturbation theory. Comparison with experiment enables the quark mass to be extracted: in the MS bar scheme we find m_b(m_b) = 4.166(43) GeV.Comment: v2 - corrected some typos and an error in the summary plo

Fast Fits for Lattice QCD Correlators

We illustrate a technique for fitting lattice QCD correlators to sums of exponentials that is significantly faster than traditional fitting methods --- 10--40 times faster for the realistic examples we present. Our examples are drawn from a recent analysis of the Upsilon spectrum, and another recent analysis of the D -> pi semileptonic form factor. For single correlators, we show how to simplify traditional effective-mass analyses.Comment: 5 pages, 4 figure

Spin foam models for 3D quantum geometry

Various aspects of three-dimensional spin foam models for quantum gravity are discussed. Spin foam models and graphical calculus are introduced via the Ponzano-Regge model for 3d gravity and some important properties of this model are described. The asymptotic formula for the 6j symbol found by Ponzano and Regge is generalised to include the Ponzano-Regge amplitude for triangulations of handlebodies. Some simple observables are computed in a model for fermions coupled to 3d gravity. The result is a sum over spin foam models with certain vertex amplitudes which are described. An explicit example is given and the vertex amplitudes expressed in terms of 6j symbols. Finally, a group field theory for this spin foam model is described

Υ and Υ′ leptonic widths, abμ, and mb from full lattice QCD

We determine the decay rate to leptons of the ground-state ϒ meson and its first radial excitation in lattice QCD for the first time. We use radiatively improved nonrelativistic QCD for the b quarks and include u, d, s and c quarks in the sea with u=d masses down to their physical values. We find Γðϒ → eþe−Þ ¼ 1.19ð11Þ keV and Γðϒ0 → eþe−Þ ¼ 0.69ð9Þ keV, both in good agreement with experimental results. The decay constants we obtain are included in a summary plot of meson decay constants from lattice QCD given in the Conclusions. We also test time moments of the vector current-current correlator against values determined from the b-quark contribution to σðeþe− → hadronsÞ and calculate the b-quark piece of the hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon, ab μ ¼ 0.271ð37Þ × 10−10. Finally we determine the b-quark mass, obtaining in the MS scheme, ¯ m¯ bðm¯ b; nf ¼ 5Þ ¼ 4.196ð23Þ GeV, the most accurate result from lattice QCD to date

Prediction of the bottomonium D-wave spectrum from full lattice QCD

We calculate the full spectrum of D-wave states in the Upsilon system in lattice QCD for the first time, using an improved version of NonRelativistic QCD on coarse and fine "second generation" gluon field configurations from the MILC collaboration that include the effect of up, down, strange and charm quarks in the sea. Taking the 2S-1S splitting to set the lattice spacing, we determine the ^3D_2 - 1S splitting to 2.3%, and find agreement with experiment. Our prediction of the fine structure relative to the ^3D_2 gives the ^3D_3 at 10.181(5) GeV and the ^3D_1 at 10.147(6) GeV. We also discuss the overlap of ^3D_1 operators with ^3S_1 states.Comment: 4 pages, 5 figure