Nucleon structure in lattice QCD with dynamical domain-wall fermions quarks

We report RBC and RBC/UKQCD lattice QCD numerical calculations of nucleon electroweak matrix elements with dynamical domain-wall fermions (DWF) quarks. The first, RBC, set of dynamical DWF ensembles employs two degenerate flavors of DWF quarks and the DBW2 gauge action. Three sea quark mass values of 0.04, 0.03 and 0.02 in lattice units are used with about 200 gauge configurations each. The lattice cutoff is about 1.7 GeV and the spatial volume is about (1.9 fm)^3. Despite the small volume, the ratio of the isovector vector and axial charges g_A/g_V and that of structure function moments _{u-d}/_{Delta u - Delta d} are in agreement with experiment, and show only very mild quark mass dependence. The second, RBC/UK, set of ensembles employs one strange and two degenerate (up and down) dynamical DWF quarks and Iwasaki gauge action. The strange quark mass is set at 0.04, and three up/down mass values of 0.03, 0.02 and 0.01 in lattice units are used. The lattice cutoff is about 1.6 GeV and the spatial volume is about (3.0 fm)^3. Even with preliminary statistics of 25-30 gauge configurations, the ratios g_A/g_V and _{u-d}/_{Delta u - Delta d} are consistent with experiment and show only very mild quark mass dependence. Another structure function moment, d_1, though yet to be renormalized, appears small in both sets.Comment: 7 pages, 4 figures, talk presented at Lattice 2006, Tucson, Arizona, to be published in PoS(LAT2006)118; replaced Figure 3 with the pion mass squared in GeV^2 unit and corrected a minor error in the abstract in number of gauge configuration

Matrix String Description of Cosmic Singularities in a Class of Time-dependent Solutions

A large class of time-dependent solutions with 1/2 supersymmetry were found previously. These solutions involve cosmic singularities at early time. In this paper, we study if matrix string description of the singularities in these solutions with backgrounds is possible and present several examples where the solutions can be described well in the perturbative picture.Comment: 12 pages, v2: typos corrected, a ref. adde

Charm as a domain wall fermion in quenched lattice QCD

We report a study describing the charm quark by a domain-wall fermion (DWF) in lattice quantum chromodynamics (QCD). Our study uses a quenched gauge ensemble with the DBW2 rectangle-improved gauge action at a lattice cutoff of $a^{-1} \sim 3$ GeV. We calculate masses of heavy-light (charmed) and heavy-heavy (charmonium) mesons with spin-parity $J^P = 0^\mp$ and $1^\mp$, leptonic decay constants of the charmed pseudoscalar mesons ($D$ and $D_s$), and the $D^0$-$\bar{D^0}$ mixing parameter. The charm quark mass is found to be $m^{\bar{\rm MS}}_{c}(m_{c})=1.24(1)(18)$ GeV. The mass splittings in charmed-meson parity partners $\Delta_{q,J=0}$ and $\Delta_{q, J=1}$ are degenerate within statistical errors, in accord with experiment, and they satisfy a relation $\Delta_{q=ud, J} > \Delta_{q=s, J}$, also consistent with experiment. A C-odd axial vector charmonium state, $h_c), lies 22(11) MeV above the$\chi_{c1}$meson, or$m_{h_{c}} = 3533(11)_{\rm stat.}$MeV using the experimental$\chi_{c1}) mass. However, in this regard, we emphasize significant discrepancies in the calculation of hyperfine splittings on the lattice. The leptonic decay constants of $D$ and $D_s$ mesons are found to be $f_D=232(7)_{\rm stat.}(^{+6}_{-0})_{\rm chiral}(11)_{\rm syst.}$ MeV and $f_{D_s}/f_{D} = 1.05(2)_{\rm stat.}(^{+0}_{-2})_{\rm chiral}(2)_{\rm syst.}$, where the first error is statistical, the second a systematic due to chiral extrapolation and the third error combination of other known systematics. The $D^0$-$\bar{D^0}$ mixing bag parameter, which enters the $\Delta C = 2$ transition amplitude, is found to be $B_D(2{GeV})=0.845(24)_{\rm stat.}(^{+24}_{-6})_{\rm chiral}(105)_{\rm syst.}$.Comment: 49 pages, 15 figure

Nucleon isovector structure functions in (2+1)-flavor QCD with domain wall fermions

We report on numerical lattice QCD calculations of some of the low moments of the nucleon structure functions. The calculations are carried out with gauge configurations generated by the RBC and UKQCD collaborations with (2+1)-flavors of dynamical domain wall fermions and the Iwasaki gauge action ($\beta = 2.13$). The inverse lattice spacing is $a^{-1} = 1.73$ GeV, and two spatial volumes of ((2.7{\rm fm})^3) and ((1.8 {\rm fm})^3) are used. The up and down quark masses are varied so the pion mass lies between 0.33 and 0.67 GeV while the strange mass is about 12 % heavier than the physical one. The structure function moments we present include fully non-perturbatively renormalized iso-vector quark momentum fraction, (_{u-d}), helicity fraction, (< x >_{\Delta u - \Delta d}), and transversity, (_{\delta u - \delta d}), as well as an unrenormalized twist-3 coefficient, (d_1). The ratio of the momentum to helicity fractions, (_{u-d}/_{\Delta u - \Delta d}), does not show dependence on the light quark mass and agrees well with the value obtained from experiment. Their respective absolute values, fully renormalized, show interesting trends toward their respective experimental values at the lightest quark mass. A prediction for the transversity, (0.7 _{\delta u -\delta d} < 1.1), in the (\bar{\rm MS}) scheme at 2 GeV is obtained. The twist-3 coefficient, (d_1), though yet to be renormalized, supports the perturbative Wandzura-Wilczek relation.Comment: 14 pages, 22 figures

Nucleon structure with two flavors of dynamical domain-wall fermions

We present a numerical lattice quantum chromodynamics calculation of isovector form factors and the first few moments of the isovector structure functions of the nucleon. The calculation employs two degenerate dynamical flavors of domain-wall fermions, resulting in good control of chiral symmetry breaking. Non-perturbative renormalization of the relevant quark currents is performed where necessary. The inverse lattice spacing, $a^{-1}$, is about 1.7 GeV. We use degenerate up and down dynamical quark masses around 1, 3/4 and 1/2 the strange quark mass. The physical volume of the lattice is about $(1.9{fm})^3$. The ratio of the isovector vector to axial charges, $g_A/g_V$, trends a bit lower than the experimental value as the quark mass is reduced toward the physical point. We calculate the momentum-transfer dependences of the isovector vector, axial, induced tensor and induced pseudoscalar form factors. The Goldberger-Treiman relation holds at low momentum transfer and yields a pion-nucleon coupling, $g_{\pi NN} = 15.5(1.4)$, where the quoted error is only statistical. We find that the flavor non-singlet quark momentum fraction $_{u-d}$ and quark helicity fraction $_{\Delta u-\Delta d}$ overshoot their experimental values after linear chiral extrapolation. We obtain the transversity, $_{\delta u-\delta d} = 0.93(6)$ in $\bar{\rm MS}$ at 2 GeV and a twist-3 polarized moment, $d_1$, appears small, suggesting that the Wandzura-Wilczek relation holds approximately. We discuss the systematic errors in the calculation, with particular attention paid to finite-volume effects, excited-state contamination, and chiral extrapolations.Comment: 28 pages in two columns; 37 figures, 12 table

Nucleon structure from 2+1-flavor dynamical DWF lattice QCD at nearly physical pion mass

Domain-wall fermions (DWF) is a lattice discretization for Dirac fields that preserves continuum-like chiral and flavor symmetries that are essential in hadron physics. RIKEN-BNL-Columbia (RBC) and UKQCD Collaborations have been generating sets of realistic 2+1-flavor dynamical lattice quantum chromodynamics (QCD) numerical ensembles with DWF quarks with strange mass set almost exactly at its physical value via reweighing and degenerate up and down mass set as light as practical. In this report the current status of the nucleon-structure calculations using these ensembles are summarized.Comment: 7 pages, 5 figures, talk presented at Erice School "From Quarks and Gluons to Hadrons and Nuclei,'' September 16-24, 2011, Erice, Sicil

Initial nucleon structure results with chiral quarks at the physical point

We report initial nucleon structure results computed on lattices with 2+1 dynamical M\"obius domain wall fermions at the physical point generated by the RBC and UKQCD collaborations. At this stage, we evaluate only connected quark contributions. In particular, we discuss the nucleon vector and axial-vector form factors, nucleon axial charge and the isovector quark momentum fraction. From currently available statistics, we estimate the stochastic accuracy of the determination of $g_A$ and $_{u-d}$ to be around 10%, and we expect to reduce that to 5% within the next year. To reduce the computational cost of our calculations, we extensively use acceleration techniques such as low-eigenmode deflation and all-mode-averaging (AMA). We present a method for choosing optimal AMA parameters.Comment: 7 pages, 11 figures; talk presented at the 32nd International Symposium on Lattice Field Theory, 23-28 June, 2014, Columbia University, New York, US

Warm Saturns: On the Nature of Rings around Extrasolar Planets that Reside Inside the Ice Line

We discuss the nature of rings that may exist around extrasolar planets. Taking the general properties of rings around the gas giants in the Solar System, we infer the likely properties of rings around exoplanets that reside inside the ice line. Due to their proximity to their host star, rings around such exoplanets must primarily consist of rocky materials. However, we find that despite the higher densities of rock compared to ice, most of the observed extrasolar planets with reliable radii measurements have sufficiently large Roche radii to support rings. For the currently known transiting extrasolar planets, Poynting-Robertson drag is not effective in significantly altering the dynamics of individual ring particles over a time span of $10^8$ years provided that they exceed about 1 m in size. In addition, we show that significantly smaller ring particles can exist in optically thick rings, for which we find typical ring lifetimes ranging from a few times $10^6$ to a few times $10^9$ years. Most interestingly, we find that many of the rings could have nontrivial Laplacian planes due to the increased effects of the orbital quadrupole caused by the exoplanets' proximity to their host star, allowing a constraint on the $J_2$ of extrasolar planets from ring observations. This is particular exciting, since a planet's $J_2$ reveals information about its interior structure. Furthermore, measurements of an exoplanet's oblateness and of its $J_2$, from warped rings, would together place limits on its spin period. Based on the constraints that we have derived for extrasolar rings, we anticipate that the best candidates for ring detections will come from transit observations by the Kepler spacecraft of extrasolar planets with semi-major axes $\sim 0.1$ AU and larger.Comment: Accepted for publication in Ap

Time-Dependent Supersymmetric Solutions in M-Theory and the Compactification-Decompactification Transition

We show that the diagonal light-like solution with 16 supersymmetries in eleven-dimensional supergravity derived in our previous paper (hep-th/0509173) can be generalised to non-diagonal solutions preserving the same number of supersymmetries. This class of solutions contains a subclass equivalent to the class of solutions found by Bin Chen that are dependent on the spatial-coordinates. Utilising these solutions, we construct toroidally compactified solutions that smoothly connect a static compactified region with a dynamically decompactifying region along a null hypersurface.Comment: 28 pages, 3 figures; the published versio