arXiv subjects

Xilin Zhang

Publications and source records attributed to Xilin Zhang.

At least 37 records · Page 2Linked to original sources

arXiv2021

Fast emulation of quantum three-body scattering

We develop a class of emulators for solving quantum three-body scattering problems. They are based on combining the variational method for scattering observables and the recently proposed eigenvector continuation concept. The emulators are first trained by the exact scattering solutions of the governing Hamiltonian at a small number of points in its parameter space, and then employed to make interpolations and extrapolations in that space. Through a schematic nuclear-physics model with finite-range two and three-body interactions, we demonstrate the emulators to be extremely accurate and efficient. The computing time for emulation is on the scale of milliseconds (on a laptop), with relative errors ranging from $10^{-13}$ to $10^{-4}$ depending on the case. The emulators also require little memory. We argue that these emulators can be generalized to even more challenging scattering problems. Furthermore, this general strategy may be applicable for building the same type of emulators in other fields, wherever variational methods can be developed for evaluating physical models.

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arXiv2021

Fast & accurate emulation of two-body scattering observables without wave functions

We combine Newton's variational method with ideas from eigenvector continuation to construct a fast & accurate emulator for two-body scattering observables. The emulator will facilitate the application of rigorous statistical methods for interactions that depend smoothly on a set of free parameters. Our approach begins with a trial $K$ or $T$ matrix constructed from a small number of exact solutions to the Lippmann--Schwinger equation. Subsequent emulation only requires operations on small matrices. We provide several applications to short-range potentials with and without the Coulomb interaction and partial-wave coupling. It is shown that the emulator can accurately extrapolate far from the support of the training data. When used to emulate the neutron-proton cross section with a modern chiral interaction as a function of 26 free parameters, it reproduces the exact calculation with negligible error and provides an over 300x improvement in CPU time.

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arXiv2021

Efficient emulators for scattering using eigenvector continuation

Eigenvector continuation EC has been shown to accurately and efficiently reproduce ground states for targeted sets of Hamiltonian parameters. It uses as variational basis vectors the corresponding ground-state eigensolutions from selected other sets of parameters. Here we extend the EC approach to scattering using the Kohn variational principle. We first test it using a model for S-wave nucleon-nucleon scattering and then demonstrate that it also works to give accurate predictions for non-local potentials, charged-particle scattering, complex optical potentials, and higher partial waves. These proofs-of-principle validate EC as an accurate emulator for applying Bayesian inference to parameter estimation constrained by scattering observables. The efficiency of such emulators is because the accuracy is achieved with a small number of variational basis elements and the central computations are just linear algebra calculations in the space spanned by this basis.

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arXiv2021

Can a protophobic vector boson explain the ATOMKI anomaly?

In 2016, the ATOMKI collaboration announced [PRL {\bf 116}, 042501 (2016)] observing an unexpected enhancement of the $e^+-e^-$ pair production signal in one of the $^8$Be nuclear transitions induced by an incident proton beam on a $^7$Li target. Many beyond-standard-model physics explanations have subsequently been proposed. One popular theory is that the anomaly is caused by the creation of a protophobic vector boson ($X$) with a mass around 17 MeV [e.g., PRL\ {\bf 117}, 071803 (2016)] in the nuclear transition. We study this hypothesis by deriving an isospin relation between photon and $X$ couplings to nucleons. This allows us to find simple relations between protophobic $X$-production cross sections and those for measured photon production. The net result is that $X$ production is dominated by direct transitions induced by $E1^X$ and $L1^X$ (transverse and longitudinal electric dipoles) and $C1^X$ (charge dipole) without going through any nuclear resonance (i.e. Bremsstrahlung radiation) with a smooth energy dependence that occurs for all proton beam energies above threshold. This contradicts the experimental observations and invalidates the protophobic vector boson explanation.

hep-ph↗

arXiv2020

From bound states to the continuum

This white paper reports on the discussions of the 2018 Facility for Rare Isotope Beams Theory Alliance (FRIB-TA) topical program "From bound states to the continuum: Connecting bound state calculations with scattering and reaction theory". One of the biggest and most important frontiers in nuclear theory today is to construct better and stronger bridges between bound state calculations and calculations in the continuum, especially scattering and reaction theory, as well as teasing out the influence of the continuum on states near threshold. This is particularly challenging as many-body structure calculations typically use a bound state basis, while reaction calculations more commonly utilize few-body continuum approaches. The many-body bound state and few-body continuum methods use different language and emphasize different properties. To build better foundations for these bridges, we present an overview of several bound state and continuum methods and, where possible, point to current and possible future connections.

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arXiv2020

Unified model of nucleon elastic form factors and implications for neutrino-oscillation experiments

Precise knowledge of the nucleon's axial-current form factors is crucial for modeling GeV-scale neutrino-nucleus interactions. Unfortunately, the axial form factor remains insufficiently constrained to meet the precision requirements of upcoming long-baseline neutrino-oscillation experiments. This work studies the nucleon's axial and vector form factors using the light-front approach to build a quark-diquark model of the nucleon with an explicit pion cloud. The light-front wave functions in both the quark and pion-baryon Fock spaces are first calibrated to existing experimental information on the nucleon's electromagnetic form factors, and then used to predict the axial form factor. The resulting squared charge radius of the axial pseudo-vector form factor is predicted to be $r_A^2\! =\! 0.29\! \pm\! 0.03\, \mathrm{fm}^2$, where the small error accounts for the model's parametric uncertainty. We use our form factor results to explore the (quasi-)elastic scattering of neutrinos by (nuclei)nucleons, with the result that the the widely-implemented dipole ansatz is an inadequate approximation of the full form factor for modeling both processes. The approximation leads to a $5\!-\!10\%$ over-estimation of the total cross section, depending on the (anti)neutrino energy. We project over-estimations of similar size in the flux-averaged cross sections for the upcoming DUNE long-baseline neutrino-oscillation experiment.

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arXiv2020

Ab initio calculations of low-energy nuclear scattering using confining potential traps

A recently modified method to enable low-energy nuclear scattering results to be extracted from the discrete energy levels of the target-projectile clusters confined by harmonic potential traps is tested. We report encouraging results for neutron--$α$ and neutron--$^{24}\mathrm{O}$ elastic scattering from analyzing the trapped levels computed using two different ab initio nuclear structure methods. The $n$--$α$ results have also been checked against a direct ab initio reaction calculation. The $n$--$^{24}\mathrm{O}$ results demonstrate the approach's applicability for a large range of systems provided their spectra in traps can be computed by ab initio methods. A key ingredient is a rigorous understanding of the errors in the calculated energy levels caused by inevitable Hilbert-space truncations in the ab initio methods.

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arXiv2020

Extracting free-space observables from trapped interacting clusters

The energy spectrum of two short-range interacting particles in a harmonic potential trap has previously been related to free-space scattering phase shifts. But the existing formula for this purpose is exact only in the limit of an infinitely shallow trap. Here we provide a systematically improved formula---describing the low-energy dynamics---that enables the use of finite traps. This paves the way for extracting nuclear scattering phase shifts from {\it ab initio} nuclear many-body structure calculations, a long-sought goal in nuclear physics. The derivation establishes effective field theory as a powerful framework for studying the connection between structure information of a trapped system (with two or more sub-clusters) and continuum physics in the fields of both nuclear and condensed-matter physics.

nucl-th↗

arXiv2019

$S$-factor and scattering-parameter extractions from ${}^{3}\mathrm{He} +{}^{4}\mathrm{He} \rightarrow {}^{7}\mathrm{Be} + γ$

Previous studies of the reaction ${}^{3}\mathrm{He} +{}^{4}\mathrm{He} \rightarrow {}^{7}\mathrm{Be} + γ$ have focused on providing the best central value and error bar for the $S$ factor at solar energies. Measurements of this capture reaction, the ${}^{3}\mathrm{He}$-${}^{4}\mathrm{He}$ scattering phase shifts, as well as properties of ${}^{7}\mathrm{Be}$, have been used to constrain employed theoretical models. Here we show that much more information than was previously appreciated can be extracted from angle-integrated capture data alone. We use the next-to-leading-order (NLO) amplitude in an effective field theory (EFT) for the reaction to perform the extrapolation. At this order the EFT describes the reaction using an s-wave scattering length and effective range, the asymptotic properties of the final bound states, and short-distance contributions to the $E1$ capture amplitude. We extract the multi-dimensional posterior of all these parameters via a Bayesian analysis. We find that properties of the ${}^{7}\mathrm{Be}$ ground and excited states are well constrained. The total $S$ factor $S(0)= 0.578^{+0.015}_{-0.016}$ keV~b, while the branching ratio for excited- to ground-state capture at zero energy, $Br(0)=0.406^{+0.013}_{-0.011}$, both at 68\% degree of belief. This $S(0)$ is broadly consistent with other recent evaluations, including the previously recommended value $S(0)=0.56 \pm 0.03$ eV b, but has a smaller error bar. We also find significant constraints on the scattering parameters, and we obtain constraints on the $S(E)$'s angular dependence. The path forward seems to lie with better measurements of the scattering phase shift and $S(E)$'s angular dependence, together with better understanding of the asymptotic normalization coefficients of the ${}^7$Be bound states' wave functions. Data on these could further reduce $S(0)$'s uncertainty.

nucl-th↗

arXiv2018

$S$-factor and scattering parameters from ${}^3$He + ${}^4$He $\rightarrow {}^7$Be + $γ$ data

We use the next-to-leading-order (NLO) amplitude in an effective field theory (EFT) for ${}^3$He + ${}^4$He $\rightarrow {}^7$Be + $γ$ to perform the extrapolation of higher-energy data to solar energies. At this order the EFT describes the capture process using an s-wave scattering length and effective range, the asymptotic behavior of $^7$Be and its excited state, and short-distance contributions to the E1 capture amplitude. We use a Bayesian analysis to infer the multi-dimensional posterior of these parameters from capture data below 2 MeV. The total $S$-factor $S(0)= 0.578^{+0.015}_{-0.016}$ keV b at 68% degree of belief. We also find significant constraints on $^3$He-$^4$He scattering parameters.

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arXiv2017

Models, measurements, and effective field theory: proton capture on Beryllium-7 at next-to-leading order

We employ an effective field theory (EFT) that exploits the separation of scales in the p-wave halo nucleus $^8\mathrm{B}$ to describe the process $^7\mathrm{Be}(p,γ)^8\mathrm{B}$ up to a center-of-mass energy of 500 keV. The calculation, for which we develop the lagrangian and power counting, is carried out up to next-to-leading order (NLO) in the EFT expansion. The power counting we adopt implies that Coulomb interactions must be included to all orders in $α_{\rm em}$. We do this via EFT Feynman diagrams computed in time-ordered perturbation theory, and so recover existing quantum-mechanical technology such as the two-potential formalism for the treatment of the Coulomb-nuclear interference. Meanwhile the strong interactions and the E1 operator are dealt with via EFT expansions in powers of momenta, with a breakdown scale set by the size of the ${}^7$Be core, $Λ\approx 70$ MeV. Up to NLO the relevant physics in the different channels that enter the radiative capture reaction is encoded in ten different EFT couplings. The result is a model-independent parametrization for the reaction amplitude in the energy regime of interest. To show the connection to previous results we fix the EFT couplings using results from a number of potential model and microscopic calculations in the literature. Each of these models corresponds to a particular point in the space of EFTs. The EFT structure therefore provides a very general way to quantify the model uncertainty in calculations of $^7\mathrm{Be}(p,γ)^8\mathrm{B}$. We also demonstrate that the only N$^2$LO corrections in $^7\mathrm{Be}(p,γ)^8\mathrm{B}$ come from an inelasticity that is practically of N$^3$LO size in the energy range of interest, and so the truncation error in our calculation is effectively N$^3$LO. We also discuss the relation of our extrapolated $S(0)$ to the previous standard evaluation.

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arXiv2017

Can nuclear physics explain the anomaly observed in the internal pair production in the Beryllium-8 nucleus?

Recently the experimentalists in [PRL 116, 042501 (2016)] announced observing an unexpected enhancement of the electron-positron pair production signal in one of the Beryllium-8 nuclear transitions. The following studies have been focused on possible explanations based on introducing new types of particle. In this work, we improve the nuclear physics modeling of the reaction by studying the pair emission anisotropy and the interferences between different multipoles in an effective field theory inspired framework, and examine their possible relevance to the anomaly. The connection between the previously measured on-shell photon production and the pair production in the same nuclear transitions is established. These improvements, absent in the original experimental analysis, should be included in extracting new particle's properties from the experiment of this type. We then study the possibility of using the nuclear transition form factor to explain the anomaly. The reduction of the anomaly's significance by simply rescaling our predicted event count is also investigated.

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arXiv2016

A Novel Method to Study Bottom-up Visual Saliency and its Neural Mechanism

In this study, we propose a novel method to measure bottom-up saliency maps of natural images. In order to eliminate the influence of top-down signals, backward masking is used to make stimuli (natural images) subjectively invisible to subjects, however, the bottom-up saliency can still orient the subjects attention. To measure this orientation/attention effect, we adopt the cueing effect paradigm by deploying discrimination tasks at each location of an image, and measure the discrimination performance variation across the image as the attentional effect of the bottom-up saliency. Such attentional effects are combined to construct a final bottomup saliency map. Based on the proposed method, we introduce a new bottom-up saliency map dataset of natural images to benchmark computational models. We compare several state-of-the-art saliency models on the dataset. Moreover, the proposed paradigm is applied to investigate the neural basis of the bottom-up visual saliency map by analyzing psychophysical and fMRI experimental results. Our findings suggest that the bottom-up saliency maps of natural images are constructed in V1. It provides a strong scientific evidence to resolve the long standing dispute in neuroscience about where the bottom-up saliency map is constructed in human brain.

cs.CV↗

arXiv2016

Hot and dense matter beyond relativistic mean field theory

Properties of hot and dense matter are calculated in the framework of quantum hadro-dynamics by including contributions from two-loop (TL) diagrams arising from the exchange of iso-scalar and iso-vector mesons between nucleons. Our extension of mean-field theory (MFT) employs the same five density-independent coupling strengths which are calibrated using the empirical properties at the equilibrium density of iso-spin symmetric matter. Results of calculations from the MFT and TL approximations are compared for conditions of density, temperature, and proton fraction encountered in astrophysics applications involving compact objects. The TL results for the equation of state (EOS) of cold pure neutron matter at sub- and near-nuclear densities agree well with those of modern quantum Monte Carlo and effective field-theoretical approaches. Although the high-density EOS in the TL approximation for neutron-star matter is substantially softer than its MFT counterpart, it is able to support a $2M_\odot$ neutron star required by recent precise determinations. In addition, radii of $1.4M_\odot$ stars are smaller by $\sim 1$ km than obtained in MFT. In contrast to MFT, the TL results also give a better account of the single-particle or optical potentials extracted from analyses of medium-energy proton-nucleus and heavy-ion experiments. In degenerate conditions, the thermal variables are well reproduced by results of Landau's Fermi-Liquid theory in which density-dependent effective masses feature prominently. The ratio of the thermal components of pressure and energy density expressed as $Γ_{th}=1+(P_{th}/ε_{th})$, often used in astrophysical simulations, exhibits a stronger dependence on density than on proton fraction and temperature in both MFT and TL calculations. The prominent peak of $Γ_{th}$ at supra-nuclear density found in MFT is, however, suppressed in TL calculations.

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arXiv2015

How strange is pion electroproduction?

We consider pion production in parity-violating electron scattering (PVES) in the presence of nucleon strangeness in the framework of partial wave analysis with unitarity. Using the experimental bounds on the strange form factors obtained in elastic PVES, we study the sensitivity of the parity-violating asymmetry to strange nucleon form factors. For forward kinematics and electron energies above 1 GeV, we observe that this sensitivity may reach about 20\% in the threshold region. With parity-violating asymmetries being as large as tens p.p.m., this study suggests that threshold pion production in PVES can be used as a promising way to better constrain strangeness contributions. Using this model for the neutral current pion production, we update the estimate for the dispersive $γZ$-box correction to the weak charge of the proton. In the kinematics of the Qweak experiment, our new prediction reads Re$\,\Box_{γZ}^V(E=1.165\,{\rm GeV}) = (5.58\pm1.41)\times10^{-3}$, an improvement over the previous uncertainty estimate of $\pm2.0\times10^{-3}$. Our new prediction in the kinematics of the upcoming MESA/P2 experiment reads Re$\,\Box_{γZ}^V(E=0.155\,{\rm GeV}) = (1.1\pm0.2) \times 10^{-3}$.

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arXiv2015

How well do we understand Beryllium-7 + proton -> Boron-8 + photon? An Effective Field Theory perspective

We have studied the 7Be(p,photon)8B reaction in the Halo effective field theory (EFT) framework. The leading order (LO) results were published in Phys.Rev.C89,051602(2014) after the isospin mirror process, 7Li(n,photon)8Li, was addressed in Phys.Rev.C89,024613(2014). In both calculations, one key step was using the final shallow bound state asymptotic normalization coefficients (ANCs) computed by ab initio methods to fix the EFT couplings. Recently we have developed the next-to-LO (NLO) formalism (to appear soon), which could reproduce other model results by no worse than 1% when the 7Be-p energy was between 0 and 0.5 MeV. In our recent report (arXiv:1507.07239), a different approach from that in Phys.Rev.C89,051602(2014) was used. We applied Bayesian analysis to constrain all the NLO-EFT parameters based on measured S-factors, and found tight constraints on the S-factor at solar energies. Our S(E=0 MeV)= 21.3 + - 0.7 eV b. The uncertainty is half of that previously recommended. In this proceeding, we provide extra details of the Bayesian analysis, including the computed EFT parameters' probability distribution functions (PDFs) and how the choice of input data impacts final results.

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arXiv2015

Halo effective field theory constrains the solar Beryllium-7 + proton -> Boron-8 + photon rate

We report an improved low-energy extrapolation of the cross section for the process Beryllium-7+proton -> Boron-8+photon, which determines the Boron-8 neutrino flux from the Sun. Our extrapolant is derived from Halo Effective Field Theory (EFT) at next-to-leading order. We apply Bayesian methods to determine the EFT parameters and the low-energy S-factor, using measured cross sections and scattering lengths as inputs. Asymptotic normalization coefficients of Boron-8 are tightly constrained by existing radiative capture data, and contributions to the cross section beyond external direct capture are detected in the data at E < 0.5 MeV. Most importantly, the S-factor at zero energy is constrained to be S(0)= 21.3 + - 0.7 eV b, which is an uncertainty smaller by a factor of two than previously recommended. That recommendation was based on the full range for S(0) obtained among a discrete set of models judged to be reasonable. In contrast, Halo EFT subsumes all models into a controlled low-energy approximant, where they are characterized by nine parameters at next-to-leading order. These are fit to data, and marginalized over via Monte Carlo integration to produce the improved prediction for S(E).

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arXiv2015

Charge-dependent azimuthal correlations from AuAu to UU collisions

We study the charge-dependent azimuthal correlations in relativistic heavy ion collisions, as motivated by the search for the Chiral Magnetic Effect (CME) and the investigation of related background contributions. In particular we aim to understand how these correlations induced by various proposed effects evolve from collisions with AuAu system to that with UU system. To do that, we quantify the generation of magnetic field in UU collisions at RHIC energy and its azimuthal correlation to the matter geometry using event-by-event simulations. Taking the experimental data for charge-dependent azimuthal correlations from AuAu collisions and extrapolating to UU with reasonable assumptions, we examine the resulting correlations to be expected in UU collisions and compare them with recent STAR measurements. Based on such analysis we discuss the viability for explaining the data with a combination of the CME-like and flow-induced contributions.

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