arXiv subjects

D. R. Phillips

Publications and source records attributed to D. R. Phillips.

At least 19 recordsLinked to original sources

arXiv2025

Assessing Convergence Patterns Across Modern Nucleon-Nucleon Potentials

The BUQEYE model for correlated effective field theory (EFT) truncation errors assumes a regular pattern of dimensionless coefficients extracted from order-by-order observable calculations. This enables results from lower orders to inform statistical predictions for error estimates of omitted higher orders. We test the model for multiple chiral EFT ($\chi$EFT) nucleon-nucleon (NN) potentials using a suite of six common NN scattering observables represented as functions of relative momentum and scattering angle. First, we flag irregularity in the convergence patterns of potentials with so-called "soft" regulator scales, namely that the sizes of the coefficients in the observables' expansions are mismatched between the even and odd orders. Second, we test the BUQEYE model's assumption of Gaussian process (GP) stationarity against the data and find that the GP's correlation structure as encoded in its length scale is nonstationary: The GP length scale in the angular dimension $\ell_{\theta}$ is approximately inversely proportional to the relative momentum of the scattering process. After we remediate this issue by allowing $\ell_{\theta}$ to vary with momentum, diagnostics show significant improvement, validating the application of the BUQEYE model after this modification. Third, we find that good performance of the BUQEYE model relies on properly choosing the $\chi$EFT breakdown scale $\Lambda_{b}$. With $m_{\text{eff}}$ held fixed at the physical pion mass we find $\Lambda_{b}=600$--$750$ MeV for various N$^{3}$LO interactions. Statistically consistent distributions for $\Lambda_{b}$ across orders are only found for the SMS potential at a regulator scale of 450 or 500 MeV. All our results can be reproduced using a publicly available Jupyter notebook, which can be straightforwardly modified to analyze other $\chi$EFT NN potentials.

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arXiv2025

Microscopic constraints for the equation of state and structure of neutron stars: a Bayesian model mixing framework

Bayesian model mixing (BMM) is a statistical technique that can combine constraints from different regions of an input space in a principled way. Here we extend our BMM framework for the equation of state (EOS) of strongly interacting matter from symmetric nuclear matter to asymmetric matter, specifically focusing on zero-temperature, charge-neutral, $\beta$-equilibrated matter. We use Gaussian processes (GPs) to infer constraints on the neutron star matter EOS at intermediate densities from two different microscopic theories: chiral effective field theory ($\chi$EFT) at baryon densities around nuclear saturation, $n_B \sim n_0$, and perturbative QCD at asymptotically high baryon densities, $n_B \geqslant 20 n_0$. The uncertainties of the $\chi$EFT and pQCD EOSs are obtained using the BUQEYE truncation error model. We demonstrate the flexibility of our framework through the use of two categories of GP kernels: conventional stationary kernels and a non-stationary changepoint kernel. We use the latter to explore potential constraints on the dense matter EOS by including exogenous data representing theory predictions and heavy-ion collision measurements at densities $\geqslant 2n_0$. We also use our EOSs to obtain neutron star mass-radius relations and their uncertainties. Our framework, whose implementation will be available through a GitHub repository, provides a prior distribution for the EOS that can be used in large-scale neutron-star inference frameworks.

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arXiv2025

Order-by-order uncertainties of nucleon-nucleon Wolfenstein amplitudes in chiral effective field theory

Quantum mechanical invariance principles dictate the most general operator structure that can be present in the nucleon-nucleon (NN) interaction. Five independent operators appear in the on-shell NN amplitude together with five corresponding coefficient functions. The usual choice for these coefficient functions is known as the NN Wolfenstein amplitudes. We analyze the order-by-order convergence of each of the five NN Wolfenstein amplitudes predicted by a semi-local coordinate space potential implementation of chiral effective field theory ($\chi$EFT). We do this at laboratory kinetic energies between 25 and 200 MeV for both neutron-proton and proton-proton scattering. Our analysis uses the Gaussian-Process methods developed by the BUQEYE collaboration to describe the contributions of each $\chi$EFT order, and so yields truncation uncertainties for each Wolfenstein amplitude that are correlated across scattering angles. We combine information on the size of different orders in the EFT to infer the $\chi$EFT breakdown scale for each amplitude, finding, on average, $\Lambda_b$ between 750 and 800 MeV. With this choice of $\Lambda_b$, the EFT truncation uncertainties cover both higher-order results and empirical Wolfenstein amplitudes well for all orders other than the leading order.

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arXiv2024

Bayesian analysis of nucleon-nucleon scattering data in pionless effective field theory

We perform Bayesian model calibration of two-nucleon ($NN$) low-energy constants (LECs) appearing in an $NN$ interaction based on pionless effective field theory (EFT). The calibration is carried out for potentials constructed using naive dimensional analysis in $NN$ relative momenta ($p$) up to next-to-leading order [NLO, $O(p^2)$] and next-to-next-to-next-to-leading order [N3LO, $O(p^4)$]. We consider two classes of pionless EFT potential: one that acts in all partial waves and another that is dominated by $s$-wave physics. The two classes produce broadly similar results for calibrations to $NN$ data up to $E_{\rm lab}=5$ MeV. Our analysis accounts for the correlated uncertainties that arise from the truncation of the pionless EFT. We simultaneously estimate both the EFT LECs and the parameters that quantify the truncation error. This permits the first quantitative estimates of the pionless EFT breakdown scale, $Λ_b$: the 95% intervals are $Λ_b \in [50.11,63.03]$ MeV at NLO and $Λ_b \in [72.27, 88.54]$ MeV at N3LO. Invoking naive dimensional analysis for the $NN$ potential, therefore, does not lead to consistent results across orders in pionless EFT. This exemplifies the possible use of Bayesian tools to identify inconsistencies in a proposed EFT power counting.

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arXiv2024

From chiral EFT to perturbative QCD: a Bayesian model mixing approach to symmetric nuclear matter

Constraining the equation of state (EOS) of strongly interacting, dense matter is the focus of intense experimental, observational, and theoretical effort. Chiral effective field theory ($\chi$EFT) can describe the EOS between the typical densities of nuclei and those in the outer cores of neutron stars while perturbative QCD (pQCD) can be applied to properties of deconfined quark matter, both with quantified theoretical uncertainties. However, describing the full range of densities in between with a single EOS that has well-quantified uncertainties is a challenging problem. Bayesian multi-model inference from $\chi$EFT and pQCD can help bridge the gap between the two theories. In this work, we introduce a correlated Bayesian model mixing framework that uses a Gaussian Process (GP) to assimilate different information into a single QCD EOS for symmetric nuclear matter. The present implementation uses a stationary GP to infer this mixed EOS solely from the EOSs of $\chi$EFT and pQCD while accounting for the truncation errors of each theory. The GP is trained on the pressure as a function of number density in the low- and high-density regions where $\chi$EFT and pQCD are, respectively, valid. We impose priors on the GP kernel hyperparameters to suppress unphysical correlations between these regimes. This, together with the assumption of stationarity, results in smooth $\chi$EFT-to-pQCD curves for both the pressure and the speed of sound. We show that using uncorrelated mixing requires uncontrolled extrapolation of at least one of $\chi$EFT or pQCD into regions where the perturbative series breaks down and leads to an acausal EOS. We also discuss extensions of this framework to non-stationary and less differentiable GP kernels, its future application to neutron-star matter, and the incorporation of additional constraints from nuclear theory, experiment, and multi-messenger astronomy.

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arXiv2024

Assessing Correlated Truncation Errors in Modern Nucleon-Nucleon Potentials

We test the BUQEYE model of correlated effective field theory (EFT) truncation errors on Reinert, Krebs, and Epelbaum's semi-local momentum-space implementation of the chiral EFT ($χ$EFT) expansion of the nucleon-nucleon (NN) potential. This Bayesian model hypothesizes that dimensionless coefficient functions extracted from the order-by-order corrections to NN observables can be treated as draws from a Gaussian process (GP). We combine a variety of graphical and statistical diagnostics to assess when predicted observables have a $χ$EFT convergence pattern consistent with the hypothesized GP statistical model. Our conclusions are: First, the BUQEYE model is generally applicable to the potential investigated here, which enables statistically principled estimates of the impact of higher EFT orders on observables. Second, parameters defining the extracted coefficients such as the expansion parameter $Q$ must be well chosen for the coefficients to exhibit a regular convergence pattern -- a property we exploit to obtain posterior distributions for such quantities. Third, the assumption of GP stationarity across lab energy and scattering angle is not generally met; this necessitates adjustments in future work. We provide a workflow and interpretive guide for our analysis framework, and show what can be inferred about probability distributions for $Q$, the EFT breakdown scale $Λ_b$, the scale associated with soft physics in the $χ$EFT potential $m_{\rm eff}$, and the GP hyperparameters. All our results can be reproduced using a publicly available Jupyter notebook, which can be straightforwardly modified to analyze other $χ$EFT NN potentials.

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arXiv2023

Interpolating between small- and large-$g$ expansions using Bayesian Model Mixing

Bayesian Model Mixing (BMM) is a statistical technique that can be used to combine models that are predictive in different input domains into a composite distribution that has improved predictive power over the entire input space. We explore the application of BMM to the mixing of two expansions of a function of a coupling constant $g$ that are valid at small and large values of $g$ respectively. This type of problem is quite common in nuclear physics, where physical properties are straightforwardly calculable in strong and weak interaction limits or at low and high densities or momentum transfers, but difficult to calculate in between. Interpolation between these limits is often accomplished by a suitable interpolating function, e.g., Padé approximants, but it is then unclear how to quantify the uncertainty of the interpolant. We address this problem in the simple context of the partition function of zero-dimensional $ϕ^4$ theory, for which the (asymptotic) expansion at small $g$ and the (convergent) expansion at large $g$ are both known. We consider three mixing methods: linear mixture BMM, localized bivariate BMM, and localized multivariate BMM with Gaussian processes. We find that employing a Gaussian process in the intermediate region between the two predictive models leads to the best results of the three methods. The methods and validation strategies we present here should be generalizable to other nuclear physics settings.

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arXiv2022

Elastic scattering of 3He+4He with SONIK

Measurements of the elastic scattering cross section of 3He and 4He are important in order to improve constraints on theoretical models of 4He(3He,g)7Be, a key reaction in Big Bang nucleosynthesis and solar neutrino production. The astrophysical S-factor for this reaction is a significant source of uncertainty in the standard solar-model prediction of the 7Be and 8B solar neutrino fluxes. The elastic scattering measurements reported in the literature do not extend to low energies and lack proper uncertainty quantification. A new measurement of the 4He(3He,3He)4He reaction has been made at center-of-mass energies Ec.m. = 0.38-3.13 MeV using the Scattering of Nuclei in Inverse Kinematics (SONIK) scattering chamber: a windowless, extended gas target surrounded by an array of 30 collimated silicon charged particle detectors situated at TRIUMF. This is the first elastic scattering measurement of 3He+4He made below 500 keV and it has greater angular range and better precision than previous measurements. The elastic scattering data were analyzed using both R-matrix and Halo Effective Field Theory (Halo EFT) frameworks, and values of the s-wave scattering length and effective range were extracted. The resulting improvement in knowledge of the s-wave effective-range function at low energies will reduce the overall uncertainty in S34 at solar energies.

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arXiv2022

Towards Precise and Accurate Calculations of Neutrinoless Double-Beta Decay: Project Scoping Workshop Report

We present the results of a National Science Foundation (NSF) Project Scoping Workshop, the purpose of which was to assess the current status of calculations for the nuclear matrix elements governing neutrinoless double-beta decay and determine if more work on them is required. After reviewing important recent progress in the application of effective field theory, lattice quantum chromodynamics, and ab initio nuclear-structure theory to double-beta decay, we discuss the state of the art in nuclear-physics uncertainty quantification and then construct a road map for work in all these areas to fully complement the increasingly sensitive experiments in operation and under development. The road map contains specific projects in theoretical and computational physics as well as an uncertainty-quantification plan that employs Bayesian Model Mixing and an analysis of correlations between double-beta-decay rates and other observables. The goal of this program is a set of accurate and precise matrix elements, in all nuclei of interest to experimentalists, delivered together with carefully assessed uncertainties. Such calculations will allow crisp conclusions from the observation or non-observation of neutrinoless double-beta decay, no matter what new physics is at play.

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arXiv2022

Does Bayesian Model Averaging improve polynomial extrapolations? Two toy problems as tests

We assess the accuracy of Bayesian polynomial extrapolations from small parameter values, x, to large values of x. We consider a set of polynomials of fixed order, intended as a proxy for a fixed-order effective field theory (EFT) description of data. We employ Bayesian Model Averaging (BMA) to combine results from different order polynomials (EFT orders). Our study considers two "toy problems" where the underlying function used to generate data sets is known. We use Bayesian parameter estimation to extract the polynomial coefficients that describe these data at low x. A "naturalness" prior is imposed on the coefficients, so that they are O(1). We Bayesian-Model-Average different polynomial degrees by weighting each according to its Bayesian evidence and compare the predictive performance of this Bayesian Model Average with that of the individual polynomials. The credibility intervals on the BMA forecast have the stated coverage properties more consistently than does the highest evidence polynomial, though BMA does not necessarily outperform every polynomial.

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arXiv2022

Analyzing rotational bands in odd-mass nuclei using Effective Field Theory and Bayesian methods

We recently developed an Effective Field Theory (EFT) for rotational bands in odd-mass nuclei. Here we use EFT expressions to perform a Bayesian analysis of data on the rotational energy levels of $^{99}$Tc, ${}^{155,157}$Gd, ${}^{159}$Dy, ${}^{167, 169}$Er, ${}^{167, 169}$Tm, ${}^{183}$W, ${}^{235}$U and ${}^{239}$Pu. The error model in our Bayesian analysis includes both experimental and EFT truncation uncertainties. It also accounts for the fact that low-energy constants (LECs) at even and odd orders are expected to have different sizes. We use Markov Chain Monte Carlo (MCMC) sampling to explore the joint posterior of the EFT and error-model parameters and show both the LECs and the expansion parameter, $Q$, can be reliably determined. We extract the LECs up to fourth order in the EFT and find that, provided we correctly account for EFT truncation errors in our likelihood, results for lower-order LECs are stable as we go to higher orders. LEC results are also stable with respect to the addition of higher-energy data. We extract the expansion parameter for all the nuclei listed above and find a clear correlation between the extracted and the expected $Q$ based on the single-particle and vibrational energy scales. However, the $Q$ that actually determines the convergence of the EFT expansion is markedly smaller than would be naively expected based on those scales.

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arXiv2022

Rigorous constraints on three-nucleon forces in chiral effective field theory from fast and accurate calculations of few-body observables

We explore the constraints on the three-nucleon force (3NF) of chiral effective field theory ($χ$EFT) that are provided by bound-state observables in the $A=3$ and $A=4$ sectors. Our statistically rigorous analysis incorporates experimental error, computational method uncertainty, and the uncertainty due to truncation of the $χ$EFT expansion at next-to-next-to-leading order. A consistent solution for the ${}^3$H binding energy, the ${}^4$He binding energy and radius, and the ${}^3$H $β$-decay rate can only be obtained if $χ$EFT truncation errors are included in the analysis. All of these except the $β$-decay rate give essentially degenerate constraints on the 3NF low-energy constants, so it is crucial for estimating these parameters. We use eigenvector continuation for fast and accurate emulation of No-Core Shell Model calculations of the considered few-nucleon observables. This facilitates sampling of the posterior probability distribution, allowing us to also determine the distributions of the hyperparameters that quantify the truncation error. We find a $χ$EFT expansion parameter of $Q=0.33 \pm 0.06$ for these observables.

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arXiv2021

Simulating core excitation in breakup reactions of halo nuclei using an effective three-body force

We extend our previous calculation of the breakup of 11Be using Halo Effective Field Theory and the Dynamical Eikonal Approximation to include an effective 10Be-n-target force. The force is constructed to account for the virtual excitation of 10Be to its low-lying 2+ excited state. In the case of breakup on a 12C target this improves the description of the neutron-energy and angular spectra, especially in the vicinity of the 11Be 5/2+ state. By fine-tuning the range parameters of the three-body force, a reasonable description of data in the region of the 3/2+ 11Be state can also be obtained. This sensitivity to the three-body force's range results from the structure of the overlap integral that governs the 11Be s-to-d-state transitions induced by the three-body force.

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arXiv2021

Dissecting reaction calculations using Halo EFT and ab initio input

We present a description of the break-up of halo nuclei in peripheral nuclear reactions by coupling a model of the projectile motivated by Halo Effective Field Theory with a fully dynamical treatment of the reaction using the Dynamical Eikonal Approximation. Our description of the halo system reproduces its long-range properties, i.e., binding energy and asymptotic normalization coefficients of bound states and phase shifts of continuum states. As an application we consider the break-up of 11Be in collisions on Pb and C targets. Taking the input for our Halo-EFT-inspired description of 11Be from a recent ab initio calculation of that system yields a good description of the Coulomb-dominated breakup on Pb at energies up to about 2 MeV, with the result essentially independent of the short-distance part of the halo wave function. However, the nuclear dominated break-up on C is more sensitive to short-range physics. The role of spectroscopic factors and possible extensions of our approach to include additional short-range mechanisms are also discussed.

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arXiv2021

Get on the BAND Wagon: A Bayesian Framework for Quantifying Model Uncertainties in Nuclear Dynamics

We describe the Bayesian Analysis of Nuclear Dynamics (BAND) framework, a cyberinfrastructure that we are developing which will unify the treatment of nuclear models, experimental data, and associated uncertainties. We overview the statistical principles and nuclear-physics contexts underlying the BAND toolset, with an emphasis on Bayesian methodology's ability to leverage insight from multiple models. In order to facilitate understanding of these tools we provide a simple and accessible example of the BAND framework's application. Four case studies are presented to highlight how elements of the framework will enable progress on complex, far-ranging problems in nuclear physics. By collecting notation and terminology, providing illustrative examples, and giving an overview of the associated techniques, this paper aims to open paths through which the nuclear physics and statistics communities can contribute to and build upon the BAND framework.

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arXiv2021

Designing Optimal Experiments: An Application to Proton Compton Scattering

Interpreting measurements requires a physical theory, but the theory's accuracy may vary across the experimental domain. To optimize experimental design, and so to ensure that the substantial resources necessary for modern experiments are focused on acquiring the most valuable data, both the theory uncertainty and the expected pattern of experimental errors must be considered. We develop a Bayesian approach to this problem, and apply it to the example of proton Compton scattering. Chiral Effective Field Theory ($χ$EFT) predicts the functional form of the scattering amplitude for this reaction, so that the electromagnetic polarizabilities of the nucleon can be inferred from data. With increasing photon energy, both experimental rates and sensitivities to polarizabilities increase, but the accuracy of $χ$EFT decreases. Our physics-based model of $χ$EFT truncation errors is combined with present knowledge of the polarizabilities and reasonable assumptions about experimental capabilities at HI$γ$S and MAMI to assess the information gain from measuring specific observables at specific kinematics, \emph{i.e.}, to determine the relative amount by which new data are apt to shrink uncertainties. The strongest gains would likely come from new data on the spin observables $Σ_{2x}$ and $Σ_{2x^\prime}$ at $ω\simeq140$ to $200$ MeV and $40^\circ$ to $120^\circ$. These would tightly constrain $γ_{E1E1}-γ_{E1M2}$. New data on the differential cross section between $100$ and $200$\,MeV and over a wide angle range will substantially improve constraints on $α_{E1}-β_{M1}$, $γ_π$ and $γ_{M1M1}-γ_{M1E2}$. Good signals also exist around $160$ MeV for $Σ_3$ and $Σ_{2z^\prime}$. Such data will be pivotal in the continuing quest to pin down the scalar polarizabilities and refine understanding of the spin polarizabilities.

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arXiv2021

Quantifying uncertainties and correlations in the nuclear-matter equation of state

We perform statistically rigorous uncertainty quantification (UQ) for chiral effective field theory ($χ$EFT) applied to infinite nuclear matter up to twice nuclear saturation density. The equation of state (EOS) is based on high-order many-body perturbation theory calculations with nucleon-nucleon and three-nucleon interactions up to fourth order in the $χ$EFT expansion. From these calculations our newly developed Bayesian machine-learning approach extracts the size and smoothness properties of the correlated EFT truncation error. We then propose a novel extension that uses multitask machine learning to reveal correlations between the EOS at different proton fractions. The inferred in-medium $χ$EFT breakdown scale in pure neutron matter and symmetric nuclear matter is consistent with that from free-space nucleon-nucleon scattering. These significant advances allow us to provide posterior distributions for the nuclear saturation point and propagate theoretical uncertainties to derived quantities: the pressure and incompressibility of symmetric nuclear matter, the nuclear symmetry energy, and its derivative. Our results, which are validated by statistical diagnostics, demonstrate that an understanding of truncation-error correlations between different densities and different observables is crucial for reliable UQ. The methods developed here are publicly available as annotated Jupyter notebooks.

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arXiv2021

How well do we know the neutron-matter equation of state at the densities inside neutron stars? A Bayesian approach with correlated uncertainties

We introduce a new framework for quantifying correlated uncertainties of the infinite-matter equation of state derived from chiral effective field theory ($χ$EFT). Bayesian machine learning via Gaussian processes with physics-based hyperparameters allows us to efficiently quantify and propagate theoretical uncertainties of the equation of state, such as $χ$EFT truncation errors, to derived quantities. We apply this framework to state-of-the-art many-body perturbation theory calculations with nucleon-nucleon and three-nucleon interactions up to fourth order in the $χ$EFT expansion. This produces the first statistically robust uncertainty estimates for key quantities of neutron stars. We give results up to twice nuclear saturation density for the energy per particle, pressure, and speed of sound of neutron matter, as well as for the nuclear symmetry energy and its derivative. At nuclear saturation density the predicted symmetry energy and its slope are consistent with experimental constraints.

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