William Detmold

Chiral Extrapolation of Lattice Moments of Proton Quark Distributions

We present the resolution of a long-standing discrepancy between the moments of parton distributions calculated from lattice QCD and their experimental values. We propose a simple extrapolation formula for the moments of the nonsinglet quark distribution u-d, as a function of quark mass, which embodies the general constraints imposed by the chiral symmetry of QCD. The inclusion of the leading nonanalytic behavior leads to an excellent description of both the lattice data and the experimental values of the moments.

Bethe-Salpeter equation and a nonperturbative quark gluon vertex

A Ward-Takahashi identity preserving Bethe-Salpeter kernel can always be calculated explicitly from a dressed-quark-gluon vertex whose diagrammatic content is enumerable. We illustrate that fact using a vertex obtained via the complete resummation of dressed-gluon ladders. While this vertex is planar, the vertex-consistent kernel is nonplanar and that is true for any dressed vertex. In an exemplifying model the rainbow-ladder truncation of the gap and Bethe-Salpeter equations yields many results; e.g., ensuremath{pi}- and ensuremath{rho}-meson masses, that are changed little by including higher-order corrections. Repulsion generated by nonplanar diagrams in the vertex-consistent Bethe-Salpeter kernel for quark-quark scattering is sufficient to guarantee that diquark bound states do not exist.

Present constraints on the H-dibaryon at the physical point from Lattice QCD

The current constraints from lattice QCD on the existence of the H-dibaryon are discussed. With only two significant lattice QCD calculations of the H-dibaryon binding energy at approximately the same lattice spacing, the forms of the chiral and continuum extrapolations to the physical point are not determined. In this brief report, we consider the constraints on the H-dibaryon imposed by two simple chiral extrapolations. In both instances, the extrapolation to the physical pion mass allows for a bound H-dibaryon or a near-threshold scattering state. Further lattice QCD calculations are required to clarify this situation.

Kaon Condensation with Lattice QCD

Kaon condensation may play an important role in the structure of hadronic matter at densities greater than that of nuclear matter, as exist in the interior of neutron stars. We present the results of the first lattice QCD investigation of kaon condensation obtained by studying systems containing up to 12 negatively charged kaons. Surprisingly, the properties of the condensate that we calculate are remarkably well reproduced by leading order chiral perturbation theory. In our analysis, we also determine the three-kaon interaction from the multi-kaon systems and update our results for pion condensates.

Twist-two matrix elements at finite and infinite volume

We present one-loop results for the forward twist-two matrix elements relevant to the unpolarized, helicity and transversity baryon structure functions, in partially-quenched (N{sub f}=2 and N{sub f}=2+1) heavy baryon chiral perturbation theory. The full-QCD limit can be straightforwardly obtained from these results and we also consider SU(2|2) quenched QCD. Our calculations are performed in finite volume as well as in infinite-volume. We discuss features of lattice simulations and investigate finite volume effects in detail. We find that volume effects are not negligible, typically around 5%-10% in current partially-quenched and full-QCD calculations, and are possibly larger in quenched QCD. Extensions to the off-forward matrix elements and potential difficulties that occur there are also discussed.

Multipion systems in lattice QCD and the three-pion interaction.

The ground-state energies of 2, 3, 4, and 5 pi(+)s in a spatial volume V approximately (2.5 fm)(3) are computed with lattice QCD. By eliminating the leading contribution from three-pi(+) interactions, particular combinations of these n-pi(+) ground-state energies provide precise extractions of the pi(+)pi(+) scattering length in agreement with that obtained from calculations involving only two pi(+)s. The three-pi(+) interaction can be isolated by forming other combinations of the n-pi(+) ground-state energies. We find a result that is consistent with a repulsive three-pi(+) interaction for m_(pi) less, similar352 MeV.

Electroweak matrix elements in the two nucleon sector from lattice QCD

Abstract We demonstrate how to make rigorous predictions for electroweak matrix elements in nuclear systems directly from QCD. More precisely, we show how to determine the short-distance contributions to low-momentum transfer electroweak matrix elements in the two-nucleon sector from lattice QCD. In potential model descriptions of multi-nucleon systems, this is equivalent to uniquely determining the meson-exchange currents, while in the context of nuclear effective field theory, this translates into determining the coefficients of local, gauge-invariant, multi-nucleon-electroweak current operators. The energies of the lowest-lying states of two nucleons on a finite volume lattice with periodic boundary conditions in the presence of a background magnetic field are sufficient to determine the local four-nucleon operators that contribute to the deuteron magnetic moment and to the threshold cross section of n p → d γ . Similarly, the energy-levels of two nucleons immersed in a background isovector axial weak field can be used to determine the coefficient of the leading local four-nucleon operator contributing to the neutral- and charged-current break-up of the deuteron. This is required for the extraction of solar neutrino fluxes at SNO and future neutrino experiments.

A New Slant on Hadron Structure

Rather than regarding the restriction of current lattice QCD simulations to quark masses that are 5–10 times larger than those observed as a problem, we note that this presents a wonderful opportunity to deepen our understanding of QCD. Just as it has been possible to learn a great deal about QCD by treating Nc as a variable, so the study of hadron properties as a function of quark mass is leading us to a deeper appreciation of hadron structure. As examples we cite progress in using the chiral properties of QCD to connect hadron masses, magnetic moments, charge radii and structure functions calculated at large quark masses within lattice QCD with the values observed physically.

High statistics analysis using anisotropic clover lattices: Single hadron correlation functions

We present the results of high-statistics calculations of correlation functions generated with single-baryon interpolating operators on an ensemble of dynamical anisotropic gauge-field configurations generated by the Hadron Spectrum Collaboration using a tadpole-improved clover fermion action and Symanzik-improved gauge action. A total of 292, 500 sets of measurements are made using 1194 gauge configurations of size 20{sup 3}x128 with an anisotropy parameter {xi}=b{sub s}/b{sub t}=3.5, a spatial lattice spacing of b{sub s}=0.1227{+-}0.0008 fm, and pion mass of M{sub {pi}}{approx}390 MeV. Ground state baryon masses are extracted with fully quantified uncertainties that are at or below the {approx}0.2%-level in lattice units. The lowest-lying negative-parity states are also extracted albeit with a somewhat lower level of precision. In the case of the nucleon, this negative-parity state is above the N{pi} threshold and, therefore, the isospin-(1/2) {pi}N s-wave scattering phase-shift can be extracted using Lueschers method. The disconnected contributions to this process are included indirectly in the gauge-field configurations and do not require additional calculations. The signal-to-noise ratio in the various correlation functions is explored and is found to degrade exponentially faster than naive expectations on many time slices. This is due to backward propagating states arising from the antiperiodic boundary conditions imposed onmorexa0» the quark propagators in the time direction. We explore how best to distribute computational resources between configuration generation and propagator measurements in order to optimize the extraction of single baryon observables.«xa0less

BB potentials in quenched lattice QCD

The potentials between two B mesons are computed in the heavy-quark limit using quenched lattice QCD at m{sub {pi}}{approx}400 MeV. Nonzero central potentials are clearly evident in all four spin-isospin channels (I,s{sub l})=(0,0), (0, 1), (1, 0), (1, 1), where s{sub l} is the total spin of the light degrees of freedom. At short distance, we find repulsion in the I{ne}s{sub l} channels and attraction in the I=s{sub l} channels. Linear combinations of these potentials that have well-defined spin and isospin in the t-channel are found, in three of the four cases, to have substantially smaller uncertainties than the potentials defined with the s-channel (I,s{sub l}), and allow quenching artifacts from single hairpin exchange to be isolated. The BB*{pi} coupling extracted from the long-distance behavior of the finite-volume t-channel potential is found to be consistent with quenched calculations of the matrix element of the isovector axial-current. The tensor potentials in both of the s{sub l}=1 channels are found to be consistent with zero within calculational uncertainties.