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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Two-neutrino double-𝛽 decay in pionless effective field theory from a Euclidean finite-volume correlation function

Two-neutrino double-β decay of certain nuclear isotopes is one of the rarest Standard Model processes observed in nature. Its neutrinoless counterpart is an exotic lepton-number nonconserving process that is widely searched to determine if the neutrinos are Majorana fermions. In order to connect the rate of these processes to the Standard Model and beyond the Standard Model interactions, it is essential that the corresponding nuclear matrix elements are constrained reliably from theory. Lattice quantum chromodynamics (LQCD) and low-energy effective field theories (EFTs) are expected to play an essential role in constraining the matrix element of the two-nucleon subprocess, which could in turn provide the input into ab initio nuclear-structure calculations in larger isotopes. Focusing on the two-neutrino process $nn\rightarrow pp(ee\bar{v}_{e}\bar{v}_e)$, the amplitude is constructed in this work in pionless EFT at next-to-leading order, demonstrating the emergence of a renormalization-scale independent amplitude and the absence of any new low-energy constant at this order beyond those present in the single-weak process. Most importantly, it is shown how a LQCD four-point correlation function in Euclidean and finite-volume spacetime can be used to constrain the Minkowski infinite-volume amplitude in the EFT. The same formalism is provided for the related single-weak process, which is an input to the double-β decay formalism. The LQCD-EFT matching procedure outlined for the double-weak amplitude paves the road toward constraining the two-nucleon matrix element entering the neutrinoless double-β decay amplitude with a light Majorana neutrino.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Light-front puzzles

Abstract Light-front formulations of quantum field theories have many advantages for computing electroweak matrix elements of strongly interacting systems and other quantities that are used to study hadronic structure. The theory can be formulated in Hamiltonian form so non-perturbative calculations of the strongly interacting initial and final states are in principle reduced to linear algebra. These states are needed for calculating parton distribution functions and other types of distribution amplitudes that are used to understand the structure of hadrons. Light-front boosts are kinematic transformations so the strongly interacting states can be computed in any frame. This is useful for computing current matrix elements involving electroweak probes where the initial and final hadronic states are in different frames related by the momentum transferred by the probe. Finally in many calculations the vacuum is trivial so the calculations can be formulated in Fock space. The advantages of light front-field theory would not be interesting if the light-front formulation was not equivalent to the covariant or canonical formulations of quantum field theory. Many of the distinguishing properties of light-front quantum field theory are difficult to reconcile with canonical or covariant formulations of quantum field theory. This paper discusses the resolution of some of the apparent inconsistencies in canonical, covariant and light-front formulations of quantum field theory. The puzzles that will be discussed are (1) the problem of inequivalent representations (2) the problem of the trivial vacuum (3) the problem of ill-posed initial value problems (4) the problem of rotational covariance (5) the problem of zero modes and (6) the problem of spontaneously broken symmetries.

Physics↗
NASA NTRS1994

Measuring attitude with a gradiometer

This paper explores using a gravity gradiometer to measure the attitude of a satellite, given that the gravity field is accurately known. Since gradiometers actually measure a combination of the gradient and attitude rate and acceleration terms, the answer is far from obvious. The paper demonstrates that it can be done and at microradian accuracy. The technique employed is dynamic estimation, based on the momentum biased Euler equations. The satellite is assumed nominally planet pointed, and subject to control, gravity gradient, and partly radom drag torques. The attitude estimator is unusual. While the standard method of feeding back measurement residuals is used, the feedback gain matrix isn't derived from Kalman theory. instead, it's chosen to minimize a measure of the terminal covariance of the error in the estimate. This depends on the gain matrix and the power spectra of all the process and measurement noises. An integration is required over multiple solutions of Lyapunov equations.

Sonnabend, David↗
NASA NTRS1996

A Note on Multigrid Theory for Non-nested Grids and/or Quadrature

We provide a unified theory for multilevel and multigrid methods when the usual assumptions are not present. For example, we do not assume that the solution spaces or the grids are nested. Further, we do not assume that there is an algebraic relationship between the linear algebra problems on different levels. What we provide is a computationally useful theory for adaptively changing levels. Theory is provided for multilevel correction schemes, nested iteration schemes, and one way (i.e., coarse to fine grid with no correction iterations) schemes. We include examples showing the applicability of this theory: finite element examples using quadrature in the matrix assembly and finite volume examples with non-nested grids. Our theory applies directly to other discretizations as well.

Douglas, C. C.↗
DOE OSTI2021

Coupled-Cluster Calculations of Neutrinoless Double- β Decay in Ca 48

We use coupled-cluster theory and nuclear interactions from chiral effective field theory to compute the nuclear matrix element for the neutrinoless double-$\beta$ decay of $^{48}$Ca. Benchmarks with the no-core shell model in several light nuclei inform us about the accuracy of our approach. For $^{48}$Ca we find a relatively small matrix element. We also compute the nuclear matrix element for the two-neutrino double-$\beta$ decay of $^{48}$Ca with a quenching factor deduced from two-body currents in recent ab initio calculation of the Ikeda sum rule in $^{48}$Ca [Gysbers et al., Nat. Phys. 15, 428 (2019)].

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Extracting Inelastic Scattering Cross Sections for Finite and Aperiodic Materials from Electronic Dynamics Simulations

Explicit time-dependent electronic structure theory methods are increasingly prevalent in the areas of condensed matter physics and quantum chemistry, with the broad-band optical absorptivity of molecular and small condensed-phase systems nowadays routinely studied with such approaches. Here, in this paper, it is demonstrated that electronic dynamics simulations can similarly be employed to study cross sections for the scattering-induced electronic excitations probed in nonresonant inelastic X-ray scattering and momentum-resolved electron energy loss spectroscopies. A method is put forth for evaluating the electronic dynamic structure factor, which involves the application of a momentum boost-type perturbation and transformation of the resulting reciprocal space density fluctuations into the frequency domain. Good agreement is first demonstrated between the dynamic structure factor extracted from these electronic dynamics simulations and the corresponding transition matrix elements from linear response theory. The method is then applied to some extended (quasi)one-dimensional systems, for which the wave vector becomes a good quantum number in the thermodynamic limit. Finally, the dispersion of many-body excitations in a series of hydrogen-terminated graphene flakes (and twisted bilayers thereof) is investigated to highlight the utility of the presented approach for capturing morphology-dependent effects in the inelastic scattering cross sections of nanostructured and/or noncrystalline materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Aligned yet large dipoles: a SMEFT study

We study a non-universal flavor scenario at the level of the Standard Model Effective Field Theory, according to which the matrix of Wilson coefficients cuW of an up-type electroweak quark dipole operator is aligned with the up-type Yukawa coupling. Such an alignment usually follows from the assumption of Minimal Flavor Violation (MFV), away from which we step by allowing the entries of cuW to be sizable along the first quark generations. A particular example, which we refer to as “inverse hierarchy MFV”, features Wilson coefficients inversely proportional to quark masses, and arises from BSM models respecting MFV and containing heavy fields that replicate the mass hierarchy of SM quarks. We then analyze the phenomenology driven by cuW at colliders and at lower-energy flavor experiments. We show that precision measurements of the process pp → Wh → γγℓν at FCC-hh could set an upper bound on |cuW| ≲ O (10 -2 )(Λ/TeV) 2 , with Λ the cutoff of the effective field theory. This bound is an order of magnitude stronger than the existing LHC bounds. Moreover, we estimate that Wh → b$\overline{b}$ℓν at HL-LHC could also give competitive bounds. In the low-energy regime, we consider bounds arising from rare kaon decays, which turn out to be loose, |c$_{uW}^{11}$ | < O (1)(Λ/TeV) 2 . We finally demonstrate that our flavor and operator assumptions can be derived from a weakly-coupled UV model, which we choose to simultaneously illustrate the UV origin of inverse hierarchy MFV.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Emergent area laws from entangled matrices

We consider a wavefunction of large N matrices supported close to an emergent classical fuzzy sphere geometry. The SU( N ) Gauss law of the theory enforces correlations between the matrix degrees of freedom associated to a geometric subregion and their complement. We call this ‘Gauss law entanglement’. We show that the subregion degrees of freedom transform under a single dominant, low rank representation of SU( N ). The corresponding Gauss law entanglement entropy is given by the logarithm of the dimension of this dominant representation. It is found that, after coarse-graining in momentum space, the SU( N ) Gauss law entanglement entropy is proportional to the geometric area bounding the subregion. The constant of proportionality goes like the inverse of an emergent Maxwell coupling constant, reminiscent of gravitational entropy.

1/N Expansion↗
NASA NTRS1988

Thermal properties of heterogeneous grains

Cometary dust is not spherical nor homogeneous, yet these are the assumptions used to model its thermal, optical, and dynamical properties. To better understand the effects of heterogeneity on the thermal and optical properties of dust grains, the effective dielectric constant for an admixture of magnetite and a silicate were calculated using two different effective medium theories: the Maxwell-Garnett theory and the Bruggeman theory. In concept, the MG theory describes the effective dielectric constant of a matrix material into which is embedded a large number of very small inclusions of a second material. The Bruggeman theory describes the dielectric constant of a well mixed aggregate of two or more types of materials. Both theories assume that the individual particles are much smaller than the wavelength of the incident radiation. The refractivity for a heterogeneous grain using the MG theory is very similar to the refractivity of the matrix material, even for large volume fractions of the inclusion. The equilibrium grain temperature for spherical particles sized from .001 to 100 microns in radius at 1 astronomical unit from the sun was calculated. Further explanation is given.

Lien, David J.↗
DOE OSTI2021

Activated penetrant dynamics in glass forming liquids: size effects, decoupling, slaving, collective elasticity and correlation with matrix compressibility

In this work, we employ the microscopic self-consistent cooperative hopping theory of penetrant activated dynamics in glass forming viscous liquids and colloidal suspensions to address new questions over a wide range of high matrix packing fractions and penetrant-to-matrix particle size ratios. The focus is on the mean activated relaxation time of smaller tracers in a hard sphere fluid of larger particle matrices. This quantity also determines the penetrant diffusion constant and connects directly with the structural relaxation time probed in an incoherent dynamic structure factor measurement. The timescale of the non-activated fast dissipative process is also studied and is predicted to follow power laws with the contact value of the penetrant–matrix pair correlation function and the penetrant–matrix size ratio. For long time penetrant relaxation, in the relatively lower packing fraction metastable regime the local cage barriers are dominant and matrix collective elasticity effects unimportant. As packing fraction and/or penetrant size grows, much higher barriers emerge and the collective elasticity associated with the correlated matrix dynamic displacement that facilitates penetrant hopping becomes important. This results in a non-monotonic variation with packing fraction of the degree of decoupling between the matrix and penetrant alpha relaxation times. The conditions required for penetrant hopping to become slaved to the matrix alpha process are determined, which depend mainly on the penetrant to matrix particle size ratio. By analyzing the absolute and relative importance of the cage and elastic barriers we establish a mechanistic understanding of the origin of the predicted exponential growth of the penetrant hopping time with size ratio predicted at very high packing fractions. A dynamics-thermodynamics power law connection between the penetrant activation barrier and the matrix dimensionless compressibility is established as a prediction of theory, with different scaling exponents depending on whether matrix collective elasticity effects are important. Quantitative comparisons with simulations of the penetrant relaxation time, diffusion constant, and transient localization length of tracers in dense colloidal suspensions and cold viscous liquids reveal good agreements. Multiple new predictions are made that are testable via future experiments and simulations. Extension of the theoretical approach to more complex systems of high experimental interest (nonspherical molecules, semiflexible polymers, crosslinked networks) interacting via variable hard or soft repulsions and/or short range attractions is possible, including under external deformation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Origin and resummation of threshold logarithms in the lattice QCD calculations of PDFs

Many present lattice QCD approaches to calculate the parton distribution functions (PDFs) rely on a factorization formula or effective theory expansion of certain Euclidean matrix elements in boosted hadron states. In the quasi- and pseudo-PDF methods, the matching coefficient in the factorization or expansion formula includes large logarithms near the threshold, which arise from the subtle interplay of collinear and soft divergences of an underlying 3D momentum distribution. We use the standard prescription to resum such logarithms in the Mellin-moment space at next-to-leading logarithmic accuracy, which also accounts for the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution, and we show that it can suppress the PDF at large x . Unlike the deep inelastic scattering and Drell-Yan cross sections, the resummation formula is away from the Landau pole. We then apply our formulation to reanalyze the recent lattice results for the pion valence PDF, and find that within the current data sensitivity, the effect of threshold resummation is marginal for the accessible moments and the PDF at large x.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Is the Matrix Completion of Reduced Density Matrices Unique?

Reduced density matrices are central to describing observables in many-body quantum systems. In electronic structure theory, the two-particle reduced density matrix (2-RDM) suffices to determine the energy and other key properties. Recent work has used matrix completion, leveraging the low-rank structure of RDMs and approximate theoretical models, to reconstruct the 2-RDM from partial data and thus reduce the computational cost. However, matrix completion is, in general, an under-determined problem. Revisiting Rosina’s theorem (Rosina, M. Queen’s Papers on Pure and Applied Mathematics , 1968, No. 11, 369), we here show that the matrix completion is unique under certain conditions, identifying the subset of 2-RDM elements that enables its exact reconstruction from incomplete information. Building on this, we introduce a hybrid quantum–stochastic algorithm that achieves exact matrix completion, demonstrated through applications to the Fermi–Hubbard model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Constructing tensor network influence functionals for general quantum dynamics

Here, we describe an iterative formalism to compute influence functionals that describe the general quantum dynamics of a subsystem beyond the assumption of linear coupling to a quadratic bath. We use a space-time tensor network representation of the influence functional and investigate its approximability in terms of its bond dimension and time-like entanglement in the tensor network description. We study two numerical models, the spin-boson model and a model of interacting hard-core bosons in a 1D harmonic trap. We find that the influence functional and the intermediates involved in its construction can be efficiently approximated by low bond dimension tensor networks in certain dynamical regimes, which allows the quantum dynamics to be accurately computed for longer times than with direct time evolution methods. However, as one iteratively integrates out the bath, the correlations in the influence functional can first increase before decreasing, indicating that the final compressibility of the influence functional is achieved via non-trivial cancellation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1992

Semiclassical matrix elements from periodic orbits

An extension of Gutzwiller's (1967, 1969, 1970, 1971, 1990) semiclassical theory for chaotic systems that allows a determination of matrix elements in terms of classical periodic orbits. Associated zeta functions are derived. The semiclassical predictions are found to be in good agreement with Fourier transforms of quantum spectra of hydrogen in a magnetic field. Expressions for off-diagonal matrix elements are derived that are extensions of the Bohr correspondence relations for integrable systems.

Eckhardt, B.↗
DOE OSTI2025

2-loop scattering on superstring and supermembrane in flat space

We consider the S-matrix of transverse scalar excitations on an infinite D = 10 GS superstring and D = 11 supermembrane in flat target space. We compute the 4-particle scattering amplitude in the 2-loop approximation and demonstrate that, like in the Nambu string case, the D = 10 GS string S-matrix does not contain non-trivial 2d UV divergences (UV pole not accompanied by terms with logarithms of momenta is an artifact of dimensional regularization). This is consistent with underlying integrability of this model which is maintaining by adding appropriate local counterterms. In the supermembrane case there are no 1-loop divergences but we find a genuine 2-loop UV pole. This demonstrates non-finiteness of the world-volume S-matrix of the M2 brane theory.

AdS-CFT Correspondence↗
DOE OSTI2022

Localized Phonon Densities of States at Grain Boundaries in Silicon

Since it is now possible to record vibrational spectra at nanometer scales in the electron microscope, it is of interest to explore whether extended defects in crystals such as dislocations or grain boundaries will result in measurable changes of the phonon densities of states (dos) that are reflected in the spectra. Phonon densities of states were calculated for a set of high angle grain boundaries in silicon. The boundaries are modeled by supercells with up to 160 atoms, and the vibrational densities of states were calculated by taking the Fourier transform of the velocity–velocity autocorrelation function from molecular dynamics simulations with larger supercells doubled in all three directions. In selected cases, the results were checked on the original supercells by comparison with the densities of states obtained by diagonalizing the dynamical matrix calculated using density functional theory. Near the core of the grain boundary, the height of the optic phonon peak in the dos at 60 meV was suppressed relative to features due to acoustic phonons that are largely unchanged relative to their bulk values. This can be attributed to the variation in the strength of bonds in grain boundary core regions where there is a range of bond lengths.

Materials Science↗