Searcharxiv⌕ Search

arXiv subjects

Martin J. Savage

Publications and source records attributed to Martin J. Savage.

At least 91 records · Page 5Linked to original sources
arXiv2014

Two-Particle Elastic Scattering in a Finite Volume Including QED

The presence of long-range interactions violates a condition necessary to relate the energy of two particles in a finite volume to their S-matrix elements in the manner of Luscher. While in infinite volume, QED contributions to low-energy charged particle scattering must be resummed to all orders in perturbation theory (the Coulomb ladder diagrams), in a finite volume the momentum operator is gapped, allowing for a perturbative treatment. The leading QED corrections to the two-particle finite-volume energy quantization condition below the inelastic threshold, as well as approximate formulas for energy eigenvalues, are obtained. In particular, we focus on two spinless hadrons in the A1+ irreducible representation of the cubic group, and truncate the strong interactions to the s-wave. These results are necessary for the analysis of Lattice QCD+QED calculations of charged-hadron interactions, and can be straightforwardly generalized to other representations of the cubic group, to hadrons with spin, and to include higher partial waves.

hep-lat↗
arXiv2013

Two-Baryon Systems with Twisted Boundary Conditions

We explore the use of twisted boundary conditions in extracting the nucleon mass and the binding energy of two-baryon systems, such as the deuteron, from Lattice QCD calculations. Averaging the results of calculations performed with periodic and anti-periodic boundary conditions imposed upon the light-quark fields, or other pair-wise averages, improves the volume dependence of the deuteron binding energy from ~exp(-kappa*L)/L to ~exp(-sqrt(2)kappa*L)/L. However, a twist angle of pi/2 in each of the spatial directions improves the volume dependence from ~exp(-kappa*L)/L to ~exp(-2kappa*L)/L. Twist averaging the binding energy with a random sampling of twist angles improves the volume dependence from ~exp^(-kappa*L)/L to ~exp(-2kappa*L)/L, but with a standard deviation of ~exp(-kappa*L)/L, introducing a signal-to-noise issue in modest lattice volumes. Using the experimentally determined phase shifts and mixing angles, we determine the expected energies of the deuteron states over a range of cubic lattice volumes for a selection of twisted boundary conditions.

hep-lat↗
arXiv2013

Nuclear Forces from Lattice Quantum Chromodynamics

A century of coherent experimental and theoretical investigations have uncovered the laws of nature that underly nuclear physics. The standard model of strong and electroweak interactions, with its modest number of input parameters, dictates the dynamics of the quarks and gluons - the underlying building blocks of protons, neutrons, and nuclei. While the analytic techniques of quantum field theory have played a key role in understanding the dynamics of matter in high energy processes, they encounter difficulties when applied to low-energy nuclear structure and reactions, and dense systems. Expected increases in computational resources into the exa-scale during the next decade will provide the ability to numerically compute a range of important strong interaction processes directly from QCD with quantifiable uncertainties using the technique of Lattice QCD. These calculations will refine the chiral nuclear forces that are used as input into nuclear many-body calculations, including the three- and four-nucleon interactions. I discuss the state-of-the-art Lattice QCD calculations of quantities of interest in nuclear physics, progress that is expected in the near future, and the impact upon nuclear physics.

nucl-th↗
arXiv2013

Two-Nucleon Systems in a Finite Volume: (II) 3S1-3D1 Coupled Channels and the Deuteron

The energy spectra of two nucleons in a cubic volume provide access to the two phase shifts and one mixing angle that define the S-matrix in the 3S1-3D1 coupled channels containing the deuteron. With the aid of recently derived energy quantization conditions for such systems, and the known scattering parameters, these spectra are predicted for a range of volumes. It is found that extractions of the infinite-volume deuteron binding energy and leading scattering parameters, including the S-D mixing angle at the deuteron pole, are possible from Lattice QCD calculations of two-nucleon systems with boosts of |P| <= 2pi sqrt{3}/L in volumes with 10 fm <~ L <~ 14 fm. The viability of extracting the asymptotic D/S ratio of the deuteron wavefunction from Lattice QCD calculations is discussed.

hep-lat↗
arXiv2012

Constraints on the Universe as a Numerical Simulation

Observable consequences of the hypothesis that the observed universe is a numerical simulation performed on a cubic space-time lattice or grid are explored. The simulation scenario is first motivated by extrapolating current trends in computational resource requirements for lattice QCD into the future. Using the historical development of lattice gauge theory technology as a guide, we assume that our universe is an early numerical simulation with unimproved Wilson fermion discretization and investigate potentially-observable consequences. Among the observables that are considered are the muon g-2 and the current differences between determinations of alpha, but the most stringent bound on the inverse lattice spacing of the universe, b^(-1) >~ 10^(11) GeV, is derived from the high-energy cut off of the cosmic ray spectrum. The numerical simulation scenario could reveal itself in the distributions of the highest energy cosmic rays exhibiting a degree of rotational symmetry breaking that reflects the structure of the underlying lattice.

hep-ph↗
arXiv2012

Restoration of Rotational Symmetry in the Continuum Limit of Lattice Field Theories

We explore how rotational invariance is systematically recovered from calculations on hyper-cubic lattices through the use of smeared lattice operators that smoothly evolve into continuum operators with definite angular momentum as the lattice-spacing is reduced. Perturbative calculations of the angular momentum violation associated with such operators at tree-level and at one-loop are presented in phi^4 theory and QCD. Contributions from these operators that violate rotational invariance occur at tree-level, with coefficients that are suppressed by O(a^2) in the continuum limit. Quantum loops do not modify this behavior in phi^4, nor in QCD if the gauge-fields are smeared over a comparable spatial region. Consequently, the use of this type of operator should, in principle, allow for Lattice QCD calculations of the higher moments of the hadron structure functions.

hep-lat↗
arXiv2011

Nuclear Physics from Lattice QCD

I review recent progress in the development of Lattice QCD into a calculational tool for nuclear physics. Lattice QCD is currently the only known way of solving QCD in the low-energy regime, and it promises to provide a solid foundation for the structure and interactions of nuclei directly from QCD.

nucl-th↗
arXiv2011

Improving the Volume Dependence of Two-Body Binding Energies Calculated with Lattice QCD

Volume modifications to the binding of two-body systems in large cubic volumes of extent L depend upon the total momentum and exponentially upon the ratio of L to the size of the boosted system. Recent work by Bour et al determined the momentum dependence of the leading volume modifications to nonrelativistic systems with periodic boundary conditions imposed on the single-particle wavefunctions, enabling them to numerically determine the scattering of such bound states using a low-energy effective field theory and Luscher's finite-volume method. The calculation of bound nuclear systems directly from QCD using Lattice QCD has begun, and it is important to reduce the systematic uncertainty introduced into such calculations by the finite spatial extent of the gauge-field configurations. We extend the work of Bour et al from nonrelativistic quantum mechanics to quantum field theory by generalizing the work of Luscher and of Gottlieb and Rummukainen to boosted two-body bound states. The volume modifications to binding energies can be exponentially reduced from ~ e^{-kappa L}/L to ~ e^{-2 kappa L}/L in nonrelativistic systems (where kappa is the binding momentum of the state) by forming particular combinations of the binding energies determined in the four lowest-lying boosted systems. Relativistic corrections to this combination, and others, that violate the exponential reduction are determined. An analysis of what can be expected from Lattice QCD calculations of the deuteron is performed, the results of which are representative of a generic loosely bound system.

hep-lat↗
arXiv2011

Extracting Scattering Phase-Shifts in Higher Partial-Waves from Lattice QCD Calculations

Lüscher's method is routinely used to determine meson-meson, meson-baryon and baryon-baryon s-wave scattering amplitudes below inelastic thresholds from Lattice QCD calculations - presently at unphysical light-quark masses. In this work we review the formalism and develop the requisite expressions to extract phase-shifts describing meson-meson scattering in partial-waves with angular-momentum l<=6 and l=9. The implications of the underlying cubic symmetry, and strategies for extracting the phase-shifts from Lattice QCD calculations, are presented, along with a discussion of the signal-to-noise problem that afflicts the higher partial-waves.

hep-lat↗
arXiv2010

Nuclear Physics from QCD : The Anticipated Impact of Exa-Scale Computing

I discuss highlights in the progress that is being made toward calculating processes of importance in nuclear physics from QCD using high performance computing. As exa-scale computing resources are expected to become available around 2017, I present current estimates of the computational resources required to accomplish central goals of nuclear physics.

nucl-th↗
arXiv2010

A method to study complex systems of mesons in Lattice QCD

Finite density systems can be explored with Lattice QCD through the calculation of multi-hadron correlation functions. Recently, systems with up to 12 $π^+$'s or $K^+$'s have been studied to determine the 3-$π^+$ and 3-$K^+$ interactions, and the corresponding chemical potentials have been determined as a function of density. We derive recursion relations between correlation functions that allow this work to be extended to systems of arbitrary numbers of mesons and to systems containing many different types of mesons, such as $π^+$'s, $K^+$'s, $\bar{D}^0$'s and $B^+$'s. These relations allow for the study of finite-density systems in arbitrary volumes, and for the study of high-density systems.

hep-lat↗
arXiv2009

High Statistics Analysis using Anisotropic Clover Lattices: (III) Baryon-Baryon Interactions

Low-energy baryon-baryon interactions are calculated in a high-statistics lattice QCD study on a single ensemble of anisotropic clover gauge-field configurations at a pion mass of m_π~ 390 MeV, a spatial volume of L^3 ~ (2.5 fm)^3, and a spatial lattice spacing of b~0.123 fm. Lüscher's method is used to extract nucleon-nucleon, hyperon-nucleon and hyperon-hyperon scattering phase shifts at one momentum from the one- and two-baryon ground-state energies in the lattice volume. The isospin-3/2 NΣinteractions are found to be highly spin-dependent, and the interaction in the ^3S_1 channel is found to be strong. In contrast, the NΛinteractions are found to be spin-independent, within the uncertainties of the calculation, consistent with the absence of one-pion-exchange. The only channel for which a negative energy-shift is found is ΛΛ, indicating that the ΛΛinteraction is attractive, as anticipated from model-dependent discussions regarding the H-dibaryon. The NN scattering lengths are found to be small, clearly indicating the absence of any fine-tuning in the NN-sector at this pion mass. This is consistent with our previous Lattice QCD calculation of NN interactions. The behavior of the signal-to-noise ratio in the baryon-baryon correlation functions, and in the ratio of correlation functions that yields the ground-state energy splitting is explored. In particular, focus is placed on the window of time slices for which the signal-to-noise ratio does not degrade exponentially, as this provides the opportunity to extract quantitative information about multi-baryon systems.

hep-lat↗
arXiv2009

Meson-Baryon Scattering Lengths from Mixed-Action Lattice QCD

The $π^+Σ^+$, $π^+Ξ^0$, $K^+p$, $K^+n$, and $\overline{K}{}^0 Ξ^0$ scattering lengths are calculated in mixed-action Lattice QCD with domain-wall valence quarks on the asqtad-improved coarse MILC configurations at four light-quark masses, and at two light-quark masses on the fine MILC configurations. Heavy Baryon Chiral Perturbation Theory with two and three flavors of light quarks is used to perform the chiral extrapolations. To the order we work in the three-flavor chiral expansion, the kaon-baryon processes that we investigate show no signs of convergence. Using the two-flavor chiral expansion for extrapolation, the pion-hyperon scattering lengths are found to be $a_{π^+Σ^+}=-0.197\pm0.017$ fm, and $a_{π^+Ξ^0}=-0.098\pm0.017$ fm, where the comprehensive error includes statistical and systematic uncertainties.

hep-lat↗
arXiv2009

High Statistics Analysis using Anisotropic Clover Lattices: (II) Three-Baryon Systems

We present the results of an exploratory Lattice QCD calculation of three-baryon systems through a high-statistics study of one ensemble of anisotropic clover gauge-field configurations with a pion mass of m_π~ 390 MeV. Because of the computational cost of the necessary contractions, we focus on correlation functions generated by interpolating-operators with the quantum numbers of the $Ξ^0Ξ^0 n$ system, one of the least demanding three baryon systems in terms of the number of contractions. We find that the ground state of this system has an energy of E_{Ξ^0Ξ^0n}= 3877.9\pm 6.9\pm 9.2\pm3.3 MeV corresponding to an energy-shift due to interactions of δE_{Ξ^0Ξ^0n}=E_{Ξ^0Ξ^0n}-2M_{Ξ^0} -M_n=4.6\pm 5.0\pm 7.9\pm 4.2 MeV. There are a significant number of time-slices in the three-baryon correlation function for which the signal-to-noise ratio is only slowly degrading with time. This is in contrast to the exponential degradation of the signal-to-noise ratio that is observed at larger times, and is due to the suppressed overlap of the source and sink interpolating-operators that are associated with the variance of the three-baryon correlation function onto the lightest eigenstates in the lattice volume (mesonic systems). As one of the motivations for this area of exploration is the calculation of the structure and reactions of light nuclei, we also present initial results for a system with the quantum numbers of the triton (pnn). This present work establishes a path to multi-baryon systems, and shows that Lattice QCD calculations of the properties and interactions of systems containing four and five baryons are now within sight.

hep-lat↗
arXiv2009

High Statistics Analysis using Anisotropic Clover Lattices: (I) 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 20^3 x 128 with an anisotropy parameter ξ= b_s/b_t = 3.5, a spatial lattice spacing of b_s=0.1227\pm 0.0008 fm, and pion mass of m_π~ 390 MeV. Ground state baryon masses are extracted with fully quantified uncertainties that are at or below the ~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 Nπthreshold and, therefore, the isospin-1/2 πN s-wave scattering phase-shift can be extracted using Luescher's 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 anti-periodic boundary conditions imposed on 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.

hep-lat↗
arXiv2008

pi+ pi+, K+ K+ and B B Interactions

The most recent calculations of pi+ pi+ and K+ K+ scattering by the NPLQCD collaboration using domain-wall valence quarks on staggered MILC configurations are presented. In addition, a quenched calculation of the potentials between two B-mesons is discussed.

hep-lat↗
arXiv2008

Color Screening by Pions

Lattice QCD is used to calculate the potential between a static quark and anti-quark in the presence of a finite density of pi^+'s. Correlation functions of multiple pi^+'s are used in conjunction with Wilson-loop correlators to determine the difference between the Q\overline{Q}-potential in free-space and in the presence of a pion condensate. The modifications to the potential are found to have significant dependence on the Q\overline{Q} separation over the range r < 1 fm explored in this work. Our results are consistent with the pion-condensate behaving as a (nonlinear) chromo-dielectric.

hep-lat↗