Large-time correlation functions have a pivotal role in extracting particle masses from Euclidean lattice field theory calculations, however little is known about the statistical properties of these ...quantities. In this work, the asymptotic form of the distributions of the correlation functions at vanishing momentum is determined for bosonic interacting lattice field theories with a unique gapped vacuum. It is demonstrated that the deviations from the asymptotic form at large Euclidean times can be utilized to determine the spectrum of the theory.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Numerical lattice quantum chromodynamics studies of the strong interaction are important in many aspects of particle and nuclear physics. Such studies require significant computing resources to ...undertake. A number of proposed methods promise improved efficiency of lattice calculations, and access to regions of parameter space that are currently computationally intractable, via multi-scale action-matching approaches that necessitate parametric regression of generated lattice datasets. The applicability of machine learning to this regression task is investigated, with deep neural networks found to provide an efficient solution even in cases where approaches such as principal component analysis fail. The high information content and complex symmetries inherent in lattice QCD datasets require custom neural network layers to be introduced and present opportunities for further development.
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A
bstract
X
-space schemes are gauge-invariant, regulator-independent renormalization schemes that are defined by requiring position-space correlation functions of gauge-invariant operators to be ...equal to their noninteracting values at particular kinematic points. These schemes can be used to nonperturbatively renormalize composite operators in Lattice Quantum Chromodynamics (LQCD), and by computing matching coefficients between the
X
-space scheme and
MS
¯
in the dimensionally-regulated continuum, matrix elements calculated with LQCD can be converted to
MS
¯
-renormalized matrix elements. Using
X
-space schemes for Heavy Quark Effective Theory (HQET) operators has the additional benefit that appropriate ratios of position-space correlation functions cancel the power-divergent static-quark self-energy of Lattice HQET nonperturbatively. This work presents the
O
(
α
S
) matching coefficients between
X
-space renormalized four-quark flavor-nonsinglet HQET operators relevant for the lifetimes of charm- and bottom-hadrons, and four-quark HQET operators relevant for mixing between neutral mesons containing a heavy quark, such as
B
−
B
¯
mixing.
We show that the empirical linear relation between the magnitude of the EMC effect in deep inelastic scattering on nuclei and the short-range correlation scaling factor a_{2} extracted from ...high-energy quasielastic scattering at x≥1 is a natural consequence of scale separation and derive the relationship using effective field theory. While the scaling factor a_{2} is a ratio of nuclear matrix elements that individually depend on the calculational scheme, we show that the ratio is independent of this choice. We perform Green's function Monte Carlo calculations with both chiral and Argonne-Urbana potentials to verify this and determine the scaling factors for light nuclei. The resulting values for ^{3}He and ^{4}He are in good agreement with experimental values. We also present results for ^{9}Be and ^{12}C extracted from variational Monte Carlo calculations.
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Monte Carlo studies of many quantum systems face exponentially severe signal-to-noise problems. We show that noise arising from complex phase fluctuations of observables can be reduced without ...introducing bias using path integral contour deformation techniques. A numerical study of contour deformations for correlation functions in Abelian gauge theory and complex scalar field theory demonstrates that variance can be reduced by orders of magnitude without modifying Monte Carlo sampling.
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Complete flavor decompositions of the matrix elements of the scalar, axial, and tensor currents in the proton, deuteron, diproton, and ^{3}He at SU(3)-symmetric values of the quark masses ...corresponding to a pion mass m_{π}∼806 MeV are determined using lattice quantum chromodynamics. At the physical quark masses, the scalar interactions constrain mean-field models of nuclei and the low-energy interactions of nuclei with potential dark matter candidates. The axial and tensor interactions of nuclei constrain their spin content, integrated transversity, and the quark contributions to their electric dipole moments. External fields are used to directly access the quark-line connected matrix elements of quark bilinear operators, and a combination of stochastic estimation techniques is used to determine the disconnected sea-quark contributions. The calculated matrix elements differ from, and are typically smaller than, naive single-nucleon estimates. Given the particularly large, O(10%), size of nuclear effects in the scalar matrix elements, contributions from correlated multinucleon effects should be quantified in the analysis of dark matter direct-detection experiments using nuclear targets.
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The role of gluons in the structure of the nucleon and light nuclei is investigated using lattice quantum chromodynamics (QCD) calculations. The first moment of the unpolarized gluon distribution is ...studied in nuclei up to atomic number A=3 at quark masses corresponding to pion masses of mπ∼450 and 806 MeV. Nuclear modification of this quantity defines a gluonic analogue of the EMC effect and is constrained to be less than ∼10% in these nuclei. This is consistent with expectations from phenomenological quark distributions and the momentum sum rule. In the deuteron, the combination of gluon distributions corresponding to the b1 structure function is found to have a small first moment compared with the corresponding momentum fraction. The first moment of the gluon transversity structure function is also investigated in the spin-1 deuteron, where a nonzero signal is observed at mπ∼806 MeV. This is the first indication of gluon contributions to nuclear structure that can not be associated with an individual nucleon.
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We calculate the axial couplings of mesons and baryons containing a heavy quark in the static limit using lattice QCD. These couplings determine the leading interactions in heavy hadron chiral ...perturbation theory and are central quantities in heavy quark physics, as they control strong decay widths and the light quark mass dependence of heavy hadron observables. Our analysis makes use of lattice data at six different pion masses, 227 MeV<m(π)<352 MeV, two lattice spacings, a=0.085, 0.112 fm, and a volume of (2.7 fm)(3). Our results for the axial couplings are g(1)=0.449(51), g(2)=0.84(20), and g(3)=0.71(13), where g(1) governs the interaction between heavy-light mesons and pions and g(2,3) are similar couplings between heavy-light baryons and pions. Using our lattice result for g(3), and constraining 1/m(Q) corrections in the strong decay widths with experimental data for Σ(c)(*) decays, we obtain ΓΣ(b)(*)→Λ(b)π(±)=4.2(1.0), 4.8(1.1), 7.3(1.6), 7.8(1.8) MeV for the Σ(b)(+), Σ(b)(-), Σ(b)(*+), Σ(b)(*-) initial states, respectively. We also derive upper bounds on the widths of the Ξ(b)(I(*)) baryons.
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The numerical technique of lattice quantum chromodynamics (LQCD) holds the promise of connecting the nuclear forces, nuclei, the spectrum and structure of hadrons, and the properties of matter under ...extreme conditions with the underlying theory of the strong interactions, quantum chromodynamics. A distinguishing, and thus far unique, feature of this formulation is that all of the associated uncertainties, both statistical and systematic can, in principle, be systematically reduced to any desired precision with sufficient computational and human resources. We review the sources of uncertainty inherent in LQCD calculations for nuclear physics, and discuss how each is quantified in current efforts.
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