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DOE OSTI2020

Uncertainty quantification of an empirical shell-model interaction using principal component analysis

Recent investigations have emphasized the importance of uncertainty quantification (UQ) in nuclear theory. Here, we carry out UQ for configuration-interaction shell-model calculations in the 1$\textit{s}$–0$\textit{d}$ valence space, investigating the sensitivity of observables to perturbations in the 66 parameters (matrix elements) of a high-quality empirical interaction. The large parameter space makes computing the corresponding Hessian numerically costly, so we compare a cost-effective approximation, using the Feynman-Hellmann theorem, to the full Hessian and find it works well. Diagonalizing the Hessian yields the principal components of the interaction: linear combinations of parameters ordered by sensitivity. This approximately decoupled distribution of parameters facilitates theoretical uncertainty propagation onto structure observables: electromagnetic transitions, Gamow-Teller decays, and dark matter-nucleus scattering matrix elements.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Scattering using real-time path integrals

Background: Path integrals are a powerful tool for solving problems in quantum theory that are not amenable to a treatment by perturbation theory. Most path integral computations require an analytic continuation to imaginary time. While imaginary time treatments of scattering are possible, imaginary time is not a natural framework for treating scattering problems. More importantly, quantum algorithms for calculating path integrals require real-time evolution. Purpose: Here, we test a recently introduced method for performing direct calculations of scattering observables using real-time path integrals in order to understand the challenges facing real-time path integral calculations of scattering observables. Method: The computations are based on a new interpretation of the path integral as the expectation value of a potential functional on cylinder sets of continuous paths with respect to a complex probability distribution. The method can in principle be applied to arbitrary short-range potentials. Results: The method is applied to compute matrix elements of Møller wave operators applied to narrow wave packets. These are used to calculate half-shell sharp-momentum transition matrix elements for one-dimensional potential scattering. The calculations for half-shell transition operator matrix elements converge to the numerical solution of the Lippmann-Schwinger equation. Conclusions: This work presents a proof in principle that scattering observables can be computed using real-time Feynman path integrals. While the computational method is not efficient, it can be improved. It provides a laboratory for studying quantum computational algorithms that are applicable to scattering problems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Convergence of nuclear effective field theory with perturbative pions

The classic paper by Fleming, Mehen, and Stewart (FMS) cast doubts on the convergence of spin-triplet nucleon-nucleon partial wave scattering amplitudes when following the proposal of Kaplan, Savage, and Wise to construct nuclear effective field theory (EFT) around the unitary fermion limit with perturbative pion exchange. FMS identified the subclass of iterated one-pion exchange potential graphs as the cause of this poor convergence, which they showed persisted in the chiral limit. Theoretical tools are developed in this work to compute these Feynman graphs analytically to high order in all angular momentum channels simultaneously, examining the amplitudes computed to seven loops in the $\textit{L = J}$ channels and three loops in the coupled $\textit{L = J}$ ± 1 channels. One finds that there is nothing pathological about the perturbative expansion of a 1/$r^3$ potential in general and that the expansion converges satisfactorily in all partial waves except those with the lowest angular momentum, particularly the $^3P_0$ and the coupled $^3S_1 - ^3D_1$ channels. The results corroborate work by Birse, which suggests possible avenues to explore for improving the range of validity of the EFT expansion.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Calculation of the C 12 + C 12 sub-barrier fusion cross section in an imaginary-time-dependent mean field theory

The 12 C + 12 C sub-barrier fusion cross section is calculated within the framework of a time-dependent Hartree-Fock-based classical model using the Feynman path-integral method. The modified astrophysical S* factor is compared to direct and indirect experimental results. A good agreement with the direct data is found. In the lower-energy region where recent analyses of experimental data obtained with the Trojan horse method (THM) lead to contrasting results, the model predicts a nonresonant S* factor half-way between those results. Low-energy resonances revealed in the THM data are added to the calculation, and the relative reaction rate in the Gamow region is calculated. In particular, including 0 + resonances result in some agreement with the THM data. Here, the role of different resonances is discussed in detail, and their influence on the reaction rate at temperatures relevant to stellar evolution is investigated.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Detailed analysis of excited-state systematics in a lattice QCD calculation of 𝑔 𝐴

Excited state contamination remains one of the most challenging sources of systematic uncertainty to control in lattice QCD calculations of nucleon matrix elements and form factors: early time separations are contaminated by excited states and late times suffer from an exponentially bad signal-to-noise problem. High-statistics calculations at large time separations ≳ 1 fm are commonly used to combat these issues. In this work, focusing on g A , we explore the alternative strategy of utilizing a large number of relatively low-statistics calculations at short to medium time separations (0.2–1 fm), combined with a multistate analysis. On an ensemble with a pion mass of approximately 310 MeV and a lattice spacing of approximately 0.09 fm, we find this provides a more robust and economical method of quantifying and controlling the excited state systematic uncertainty. A quantitative separation of various types of excited states enables the identification of the transition matrix elements as the dominant contamination. The excited state contamination of the Feynman-Hellmann correlation function is found to reduce to the 1% level at approximately 1 fm while, for the more standard three-point functions, this does not occur until after 2 fm. Critical to our findings is the use of a global minimization, rather than fixing the spectrum from the two-point functions and using them as input to the three-point analysis. We find that the ground state parameters determined in such a global analysis are stable against variations in the excited state model, the number of excited states, and the truncation of early-time or late-time numerical data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Gravitational Contact Interactions and the Physical Equivalence of Weyl Transformations in Effective Field Theory

Theories of scalars and gravity, with non-minimal interactions, $\sim (M_P^2 +F(\phi) )R +L(\phi)$, have graviton exchange induced contact terms. These terms arise in single particle reducible diagrams with vertices $\propto q^2$ that cancel the Feynman propagator denominator $1/q^2$ and are familiar in various other physical contexts. In gravity these lead to additional terms in the action such as $\sim F(\phi) T_\mu^\mu(\phi)/M_P^2$ and $F(\phi)\partial^2 F(\phi)/M_P^2$. The contact terms are equivalent to induced operators obtained by a Weyl transformation that removes the non-minimal interactions, leaving a minimal Einstein-Hilbert gravitational action. This demonstrates explicitly the equivalence of different representations of the action under Weyl transformations, both classically and quantum mechanically. To avoid such "hidden contact terms" one is compelled to go to the minimal Einstein-Hilbert representation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Comparison of transverse single-spin asymmetries for forward π 0 production in polarized pp , p Al and p Au collisions at nucleon pair c.m. energy √sNN=200 GeV

The STAR collaboration reports a measurement of the transverse single-spin asymmetries, A N , for neutral pions produced in polarized proton collisions with protons ( p p ), with aluminum nuclei ( p Al ) and with gold nuclei ( p Au ) at a nucleon-nucleon center-of-mass energy of 200 GeV. Neutral pions are observed in the forward direction relative to the transversely polarized proton beam, in the pseudorapidity region 2.7 < η < 3.8 . Results are presented for π 0 s observed in the STAR forward meson spectrometer electromagnetic calorimeter in narrow Feynman x ( x F ) and transverse momentum ( p T ) bins, spanning the range 0.17 < x F < 0.81 and 1.7 < p T < 6.0 GeV / c . For fixed x F < 0.47 , the asymmetries are found to rise with increasing transverse momentum. For larger x F , the asymmetry flattens or falls as p T increases. Parametrizing the ratio r ( A ) ≡ A N ( p A ) / A N ( p p ) = A P over the kinematic range, the ratio r ( A ) is found to depend only weakly on A , with ( P ) = - 0.027 ± 0.005 . No significant difference in P is observed between the low- p T region, p T < 2.5 GeV / c , where gluon saturation effects may play a role, and the high- p T region, p T > 2.5 GeV / c . It is further observed that the value of A N is significantly larger for events with a large- p T isolated π 0 than for events with a nonisolated π 0 accompanied by additional jetlike fragments. The nuclear dependence r ( A ) is similar for isolated and nonisolated π 0 events.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Generalized Hall currents in topological insulators and superconductors

We generalize the idea of the quantized Hall current to count gapless edge states in topological materials, applying equally well to theories in different dimensions, with or without continuous symmetries in the bulk or chiral anomalies on the boundaries. This current is related to the index of the Euclidean fermion operator and can be calculated via one-loop Feynman diagrams. Quantization of the current is shown to be governed by topology in phase space, and the procedure can be applied to topological classes governed by either Z or Z 2 invariants. We analyze several explicit examples of free fermions in relativistic field theories. We speculate that it may be possible to extend the technique to interacting theories as well, such as the interesting cases where interactions gap the edge states.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Krylov spaces for truncated spectrum methodologies

We propose herein an extension of truncated spectrum methodologies, a nonperturbative numerical approach able to elucidate the low energy properties of quantum field theories. TSMs, in their various flavors, involve a division of a computational Hilbert space, H , into two parts, one part, H 1 that is “kept” for the numerical computations, and one part, H 2 , that is discarded or “truncated.” Even though H 2 is discarded, truncated spectrum methodologies will often try to incorporate the effects of H 2 in some effective way. In these terms, we propose to keep the dimension of H 1 small. We pair this choice of H 1 with a Krylov subspace iterative approach able to take into account the effects of H 2 . This iterative approach can be taken to arbitrarily high order and so offers the ability to compute quantities to arbitrary precision. In many cases it also offers the advantage of not needing an explicit UV cutoff. To compute the matrix elements that arise in the Krylov iterations, we employ a Feynman diagrammatic representation that is then evaluated with Monte Carlo techniques. Each order of the Krylov iteration is variational and is guaranteed to improve upon the previous iteration. The first Krylov iteration is akin to the next-to-leading order approach of Elias-Miró [NLO renormalization in the Hamiltonian truncation, ]. To demonstrate this approach, we focus on the ( 1 + 1 d )-dimensional ϕ 4 model and compute the bulk energy and mass gaps in both the Z 2 -broken and unbroken sectors. We estimate the critical ϕ 4 coupling in the broken phase to be g c = 0.2645 ± 0.002 . Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Testing quantum gravity using pulsed optomechanical systems

An interesting idea, dating back to Feynman [Report from Chapel Hill Conference, edited by C. M. DeWitt and D. Rickles (1957)], argues that quantum mechanics may break down for large masses if one entertains the possibility that gravity can be “classical,” thereby leading to predictions different from conventional low-energy quantum gravity. Despite the technical difficulty in testing such deviations, a large number of experimental proposals have been put forward due to the high level of fundamental interest. Here, we consider the Schrödinger-Newton (SN) theory and the correlated worldline (CWL) theory, and show that they can be distinguished from conventional quantum mechanics, as well as each other, by performing pulsed optomechanics experiments. For CWL specifically we develop a framework resembling the commonly used “Heisenberg-picture” treatment of coupled oscillators, allowing one to perform simple calculations for such systems without delving into the deeper path-integral formalism. We find that discriminating between the theories will be very difficult until experimental control over low frequency quantum optomechanical systems is pushed much further. Furthermore, the predicted departures of SN and CWL from quantum mechanics occur at the same scale, so both alternative models could in principle be probed by a single experiment.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Renormalons and power corrections in pseudo- and quasi-GPDs

High-order behavior of the perturbative expansion for short-distance observables in QCD is intimately related to the contributions of small momenta in the corresponding Feynman diagrams and this correspondence provides one with a useful tool to investigate power-suppressed nonperturbative corrections. We use this technique to study the structure of power corrections to parton quasi- and pseudo-GPDs which are used in lattice calculations of generalized parton distributions. As the main result, we predict the functional dependence of the leading power corrections to quasi(pseudo)-GPDs on x variable for nonzero skewedness parameter ξ . The kinematic point x = ± ξ turns out to be special. We find that the nonperturbative corrections to quasi-GPDs at this point are suppressed by the first power of the hard scale only. These contributions come from soft momenta and have nothing to do with the known UV renormalon in the Wilson line. We also show that power corrections can be strongly suppressed by the normalization procedure. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Applications of flow models to the generation of correlated lattice QCD ensembles

Machine-learned normalizing flows can be used in the context of lattice quantum field theory to generate statistically correlated ensembles of lattice gauge fields at different action parameters. This work demonstrates how these correlations can be exploited for variance reduction in the computation of observables. Three different proof-of-concept applications are demonstrated using a novel residual flow architecture: continuum limits of gauge theories, the mass dependence of QCD observables, and hadronic matrix elements based on the Feynman–Hellmann approach. In all three cases, it is shown that statistical uncertainties are significantly reduced when machine-learned flows are incorporated as compared with the same calculations performed with uncorrelated ensembles or direct reweighting. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Collinear limit of the four-point energy correlator in N = 4 supersymmetric Yang-Mills theory

We present a compact formula, expressed in terms of classical polylogarithms up to weight three, for the leading order four-point energy correlator in maximally supersymmetric Yang-Mills theory, in the limit where the four detectors are collinear. This formula is derived by combining a simplified, manifestly dual conformal invariant form of the 1 → 4 splitting function obtained from the square of the tree-level five-particle form factor of stress-tensor multiplet operators, with a novel integration-by-parts algorithm operating directly on Feynman parameter integrals. Our results provide valuable data for exploring the structure of physical observables in perturbation theory, and for calculations of jet substructure observables in quantum chromodynamics. Published by the American Physical Society 2024

Chicherin, Dmitry (ORCID:000000028985084X)↗

DOE OSTI2025

What is the geometry of effective field theories?

We elaborate on a recently proposed geometric framework for scalar effective field theories. Starting from the action, a metric can be identified that enables the construction of geometric quantities on the associated functional manifold. These objects transform covariantly under general field redefinitions that relate different operator bases, including those involving derivatives. We present a novel geometric formula for the amplitudes of the theory, where the vertices in Feynman diagrams are replaced by their geometrized counterparts. This makes the on-shell covariance of amplitudes manifest, providing the link between functional geometry and effective field theories.

effective field theory↗

DOE OSTI2025

Antipodal self-duality of square fishnet graphs

In strongly deformed planar 𝒩 = 4 super-Yang-Mills theory, or fishnet theory, a point-split single-trace correlation function of four dimension-𝑚 scalar operators is given by a single Feynman integral, which involves integrating over locations of a 𝑚 × 𝑚 grid of points. We show that for any integer 𝑚 this square fishnet graph is invariant under the combined action of a kinematic map and the antipode map of the Hopf algebra on multiple polylogarithms; i.e. it possesses an antipodal self-duality.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Nonrenormalization and Operator Mixing via On-Shell Methods

Using on-shell methods, we present a new perturbative nonrenormalization theorem for operator mixing in massless four-dimensional quantum field theories. By examining how unitarity cuts of form factors encode anomalous dimensions, we show that longer operators are often restricted from renormalizing shorter operators at the first order where Feynman diagrams exist. The theorem applies quite generally and depends only on the field content of the operators involved. We apply our theorem to operators of dimension five through seven in the standard model effective field theory, including examples of nontrivial zeros in the anomalous-dimension matrix at one through four loops. The zeros at two and higher loops go beyond those previously explained using helicity selection rules. We also include explicit sample calculations at two loops.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Index Theorems, Generalized Hall Currents, and Topology for Gapless Defect Fermions

In this work, we show how the index of the fermion operator from the Euclidean action can be used to uncover the existence of gapless modes living on defects (such as edges and vortices) in topological insulators and superconductors. The 1-loop Feynman diagram that computes the index reveals an analog of the quantum Hall current flowing on and off the defect—even in systems without conserved currents or chiral anomalies—and makes explicit the interplay between topology in momentum and coordinate space. We provide several explicit examples.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Unified Approach to Polarons and Phonon-Induced Band Structure Renormalization

Ab initio calculations of the phonon-induced band structure renormalization are currently based on the perturbative Allen-Heine theory and its many-body generalizations. These approaches are unsuitable to describe materials where electrons form localized polarons. Here, we develop a self-consistent, many-body Green’s function theory of band structure renormalization that incorporates localization and self-trapping. Here, we show that the present approach reduces to the Allen-Heine theory in the weak-coupling limit, and to total energy calculations of self-trapped polarons in the strong-coupling limit. To demonstrate this methodology, we reproduce the path-integral results of Feynman and diagrammatic Monte Carlo calculations for the Fröhlich model at all couplings, and we calculate the zero point renormalization of the band gap of an ionic insulator including polaronic effects.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗