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George T. Fleming
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Pentaquark states in lattice QCD probably lie close in energy to two particle scattering states. Correctly identifying the resonant state is a challenging, yet tractable, problem given the terascale computing facilities available today. We summarize the initial round of exploratory lattice calculations and discuss what should be accomplished in the next round.
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We study the question of whether or not QCD predicts a pentaquark state. We use the improved, fixed point lattice QCD action which has very little sensitivity to the lattice spacing and also allows us to reach light quark masses. The analysis was performed on a single volume of size $(1.8 {rm fm})^3times 3.6 {rm fm}$ with lattice spacing of $a=0.102$ fm. We use the correlation matrix method to identify the ground and excited states in the isospin 0, negative parity channel. In the quenched approximation where dynamical quark effects are omitted, we do not find any evidence for a pentaquark resonance in QCD.
We study three subjects on quark confinement in hadrons in SU(3)$_{rm c}$ lattice QCD. From the accurate lattice calculation for more than 300 different patterns of three-quark (3Q) systems, we find that the static 3Q potential is well described by Y-Ansatz, i.e., the Coulomb plus Y-type linear potential. We also study the multi-quark (4Q, 5Q) potentials in lattice QCD, and find that they are well described by the one-gluon-exchange (OGE) Coulomb plus string-theoretical linear potential, which supports the {it infrared string picture} even for the multi-quarks. The second subject is a lattice-QCD determination of the relevant gluonic momentum component for confinement. The string tension (confining force) is found to be almost unchanged even after cutting off the high-momentum gluon component above 1.5GeV in the Landau gauge. In fact, {it quark confinement originates from the low-momentum gluon below about 1.5GeV.} Finally, we consider a possible gauge of QCD for the quark potential model, by investigating instantaneous inter-quark potential in generalized Landau gauge, which describes a continuous change from the Landau gauge to the Coulomb gauge.
In this work we discuss in detail the non-perturbative determination of the momentum dependence of the form factors entering in semileptonic decays using unitarity and analyticity constraints. The method contains several new elements with respect to previous proposals and allows to extract, using suitable two-point functions computed non-perturbatively, the form factors at low momentum transfer $q^2$ from those computed explicitly on the lattice at large $q^2$, without any assumption about their $q^2$-dependence. The approach will be very useful for exclusive semileptonic $B$-meson decays, where the direct calculation of the form factors at low $q^2$ is particularly difficult due to large statistical fluctuations and discretisation effects. As a testing ground we apply our approach to the semileptonic $D to K ell u_ell$ decay, where we can compare the results of the unitarity approach to the explicit direct lattice calculation of the form factors in the full $q^2$-range. We show that the method is very effective and that it allows to compute the form factors with rather good precision.
We present results for application of block BiCGSTAB algorithm modified by the QR decomposition and the SAP preconditioner to the Wilson-Dirac equation with multiple right-hand sides in lattice QCD on a $32^3 times 64$ lattice at almost physical quark masses. The QR decomposition improves convergence behaviors in the block BiCGSTAB algorithm suppressing deviation between true residual and recursive one. The SAP preconditioner applied to the domain-decomposed lattice helps us minimize communication overhead. We find remarkable cost reduction thanks to cache tuning and reduction of number of iterations.
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.
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