Improved Nonrelativistic QCD for Heavy Quark Physics

We construct an improved version of nonrelativistic QCD for use in lattice simulations of heavy quark physics, with the goal of reducing systematic errors from all sources to below 10\%. We develop power counting rules to assess the importance of the various operators in the action and compute all leading order corrections required by relativity and finite lattice spacing. We discuss radiative corrections to tree level coupling constants, presenting a procedure that effectively resums the largest such corrections to all orders in perturbation theory. Finally, we comment on the size of nonperturbative contributions to the coupling constants.Comment: 40 pages, 2 figures (not included), in LaTe

Alien Registration- Lepage, Marie L. (Lewiston, Androscoggin County)

https://digitalmaine.com/alien_docs/28625/thumbnail.jp

Perturbation theory vs. simulation for tadpole improvement factors in pure gauge theories

We calculate the mean link in Landau gauge for Wilson and improved SU(3) anisotropic gauge actions, using two loop perturbation theory and Monte Carlo simulation employing an accelerated Langevin algorithm. Twisted boundary conditions are employed, with a twist in all four lattice directions considerably improving the (Fourier accelerated) convergence to an improved lattice Landau gauge. Two loop perturbation theory is seen to predict the mean link extremely well even into the region of commonly simulated gauge couplings and so can be used remove the need for numerical tuning of self-consistent tadpole improvement factors. A three loop perturbative coefficient is inferred from the simulations and is found to be small. We show that finite size effects are small and argue likewise for (lattice) Gribov copies and double Dirac sheets.Comment: 13 pages of revtex

Inquiry-Based Learning as a Strategy to Support Student Success

In this paper, I look at inquiry-based learning within mathematics and science in the Ontario educational system while making connections to Ontario’s 21st Century Competencies foundation document. Further to this, I researched whether it might be beneficial for English Language Learners to integrate language and content through inquiry, and also review recommendations on how to best implement this approach. I endeavored to uncover what the current research says about how this pedagogical strategy might be used to support all learners in mathematics and science, and also the associated challenges with implementation of an inquiry approach. This was done through the lens of constructivist theory, with connections made to Ontario educational documents

Microstructural abnormalities in deep and superficial white matter in youths with mild traumatic brain injury

BACKGROUND: Diffusion Tensor Imaging (DTI) studies of traumatic brain injury (TBI) have focused on alterations in microstructural features of deep white matter fibers (DWM), though post-mortem studies have demonstrated that injured axons are often observed at the gray-white matter interface where superficial white matter fibers (SWM) mediate local connectivity. OBJECTIVES: To examine microstructural alterations in SWM and DWM in youths with a history of mild TBI and examine the relationship between white matter alterations and attention. METHODS: Using DTIDWM fractional anisotropy (FA) and SWM FA in youths with mild TBI (TBI, n=63) were compared to typically developing and psychopathology matched control groups (n=63 each). Following tract-based spatial statistics, SWM FA was assessed by applying a probabilistic tractography derived SWM mask, and DWM FA was captured with a white matter fiber tract mask. Voxel-wise z-score calculations were used to derive a count of voxels with abnormally high and low FA for each participant. Analyses examined DWM and SWM FA differences between TBI and control groups, the relationship between attention and DWM and SWM FA and the relative susceptibility of SWM compared to DWM FA to alterations associated with mild TBI. RESULTS: Case-based comparisons revealed more voxels with low FA and fewer voxels with high FA in SWM in youths with mild TBI compared to both control groups. Equivalent comparisons in DWM revealed a similar pattern of results, however, no group differences for low FA in DWM were found between mild TBI and the control group with matched psychopathology. Slower processing speed on the attention task was correlated with the number of voxels with low FA in SWM in youths with mild TBI. CONCLUSIONS: Within a sample of youths with a history of mild TBI, this study identified abnormalities in SWM microstructure associated with processing speed. The majority of DTI studies of TBI have focused on long-range DWM fiber tracts, often overlooking the SWM fiber type

Subtractive renormalization of the NN interaction in chiral effective theory up to next-to-next-to-leading order: S waves

We extend our subtractive-renormalization method in order to evaluate the 1S0 and 3S1-3D1 NN scattering phase shifts up to next-to-next-to-leading order (NNLO) in chiral effective theory. We show that, if energy-dependent contact terms are employed in the NN potential, the 1S0 phase shift can be obtained by carrying out two subtractions on the Lippmann-Schwinger equation. These subtractions use knowledge of the the scattering length and the 1S0 phase shift at a specific energy to eliminate the low-energy constants in the contact interaction from the scattering equation. For the J=1 coupled channel, a similar renormalization can be achieved by three subtractions that employ knowledge of the 3S1 scattering length, the 3S1 phase shift at a specific energy and the 3S1-3D1 generalized scattering length. In both channels a similar method can be applied to a potential with momentum-dependent contact terms, except that in that case one of the subtractions must be replaced by a fit to one piece of experimental data. This method allows the use of arbitrarily high cutoffs in the Lippmann-Schwinger equation. We examine the NNLO S-wave phase shifts for cutoffs as large as 5 GeV and show that the presence of linear energy dependence in the NN potential creates spurious poles in the scattering amplitude. In consequence the results are in conflict with empirical data over appreciable portions of the considered cutoff range. We also identify problems with the use of cutoffs greater than 1 GeV when momentum-dependent contact interactions are employed. These problems are ameliorated, but not eliminated, by the use of spectral-function regularization for the two-pion exchange part of the NN potentialComment: 40 pages, 21 figure

Effects of large field cutoffs in scalar and gauge models

We discuss the notion of a large field cutoff for lattice gauge models with compact groups. We propose and compare gauge invariant and gauge dependent (in the Landau gauge) criteria to sort the configurations into ``large-field'' and ``small-field'' configurations. We show that the correlations between volume average of field size indicators and the behavior of the tail of the distribution are very different in the gauge and scalar cases. We show that the effect of discarding the large field configurations on the plaquette average is very different above, below and near beta=5.6 for a pure SU(3) LGT.Comment: Lattice2004(theory

QCD factorization for the pion diffractive dissociation to two jets

We calculate the cross section of a pion diffraction dissociation in two jets with large transverse momenta originating from a hard gluon exchange between the pion constituents. To the leading logarithmic accuracy (in energy), the contribution coming from small transverse separations between the quark and the antiquark in the pion acquires the expected factorized form, the longitudinal momentum distribution of the jets being proportional to the pion distribution amplitude. The hard gluon exchange can in this case be considered as a part of the unintegrated gluon distribution. Beyond the leading logarithms (in energy) this proportionality does not hold. Moreover, the collinear factorization appears to be broken by the end-point singularities. Remarkably enough, the longitudinal momentum distribution of the jets for the non-factorizable contribution is calculable, and turns out to be the same as for the factorizable contribution with the asymptotic pion distribution amplitude.Comment: Original version from 9 April restore

Nucleon-nucleon scattering within a multiple subtractive renormalization approach

A methodology to renormalize the nucleon-nucleon interaction, using a recursive multiple subtraction approach to construct the kernel of the scattering equation, is presented. We solve the subtracted scattering equation with the next-leading-order (NLO) and next-to-next-leading-order (NNLO) interactions. The results are presented for all partial waves up to $j=2$, fitted to low-energy experimental data. In our renormalizaton group invariant method, when introducing the NLO and NNLO interactions, the subtraction energy emerges as a renormalization scale and the momentum associated with it comes to be about the QCD scale ($\Lambda_{QCD}$), irrespectively to the partial wave.Comment: Final versio