Session GG02: V: Nuclear Theory

Criticality Analysis of Artifical Neural Networks in Nuclear Physics

Machine learning methods, in particular deep learning methods such as artificial neural networks (ANNs), have become extremely useful tools in nuclear physics.

However ANNs often are treated as "black boxes", where their architecture (width, depth, and weight/bias initialization) is decided empirically based on what allows them to be trained most effectively. To actually investigate the principles of neural network architecture in a non-empirical, method based way, some have turned to performing criticality arguments with renormalization group flows in terms of the hyperparameters for weight/bias initialization and the ratio of depth to width. These criticality arguments are meant to tune these hyperparameters to give an effective theory of the neural network as an expansion in the ratio of depth to width. This allows for the study of properties of neural networks so they can have a more ideal architecture chosen from the beginning, giving a methodology to improve many projects in nuclear physics utilizing ANNs.  I’ll present preliminary studies using criticality analyses geared towards nuclear physics.   

Generative modeling of nucleon-nucleon interactions

A key challenge in ab initio nuclear theory is to develop high-precision models of the nuclear force and propagate the associated uncertainties in many-body calculations of atomic nuclei and nuclear matter. Here we show that modern generative machine learning models can be used to construct novel instances of the nucleon-nucleon interaction when trained on existing potentials from the literature. Specifically, we train the generative model on nucleon-nucleon potentials from chiral effective field theory at three different choices of the resolution scale. We then show that the model can generate novel samples of the nucleon-nucleon potential over a continuous distribution of resolution scales. Finally, we show that the generated potentials are able to produce high-quality nucleon-nucleon scattering phase shifts.   

Assessing the BUQEYE Model for Effective Field Theory Correlated Truncation Errors

The BUQEYE model is a Bayesian model of correlated effective field theory (EFT) truncation errors. It hypothesizes that dimensionless coefficient functions extracted from the order-by-order corrections to observables can be treated as draws from a Gaussian process (GP). Recent work applied to nucleon-nucleon observables combines a variety of graphical and statistical diagnostics to assess when predicted observables have a chiral EFT convergence pattern consistent with the hypothesized GP statistical model. We have demonstrated the BUQEYE model's success in describing truncation errors for Reinert, Krebs, and Epelbaum's 500 MeV semi-local momentum-space potential. The analysis has yielded recommendations for model-specific parametrization choices and generated preliminary estimates for the soft scale and breakdown scale of the theory. However, the analysis has also identified issues with assumed GP stationarity. Work reported here extends to comparisons (a) within regulation schemes (potentials) across regulator scales (cutoffs), (b) across schemes, with implications for scheme choice and "hard" vs. "soft" cutoffs; and (c) using nonstationary GP kernels.   

Road to EFT for EDFs: Variational Perturbation Theory for Effective Actions

Nuclear energy density functionals (EDFs) have been used with success to describe emergent features of nuclear systems. They suffer, however, from a lack of a systematic way to improve predictive accuracy. Casting the nuclear EDF as an effective field theory (EFT) is desirable since the hallmark features of an EFT would address precisely the current weaknesses of nuclear EDFs. There are multiple avenues of exploration for formulating such an EFT; my work is centered around formulating the EDF as an effective action, focusing first on constructing an expansion of correlations in different channels for collective variables when defining the action. The traditional path towards collective variables in a quantum field theory is the Hubbard-Stratonovich transformation (HST). While formally exact, the HST picks only one channel for a collective coordinate, meaning physics from other channels may be obscured. I will present an adaptation of Variational Perturbation Theory - a method of rewriting the path integral that allows for the inclusion of multiple auxiliary parameters in an optimizable manner- as a way of introducing collective fields for all channels when constructing the Effective Action.   

Evolving optical potentials to low resolution

The Similarity Renormalization Group (SRG) evolves Hamiltonians by continuous unitary transformations, driving hard potentials to softer potentials by decoupling high- and low-momentum components. The SRG will shift high-momentum physics such as short-range correlations from the wavefunction to the operator when calculating nuclear observables such as cross sections. Previously we used a toy one-dimensional model to examine whether optical potentials behaved similarly under SRG transformations, and demonstrated much faster convergence of the optical potential expansion [1]. Extending these studies to realistic interactions faces multiple challenges. We start addressing them by constructing a folding potential suitable for d(n,d)n transfer reactions using realistic nucleon-nucleon (NN) interactions, While initially we apply a local projection of the NN forces and other approximations to enable easier computations, we can study the impact of SRG evolution on the perturbativeness of the optical potential, including the NN tensor force.   

Estimation of CP violating EDMs from known mechanisms in the Standard Model

The baryon asymmetry in the universe needs new sources of CP violation, beyond those already known in the standard model (SM). The measurement of a non-zero permanent electric dipole moment (EDM) in fundamental particles such as electrons, neutrons, or nuclei provides insights into sources of CP violation, both within the SM and beyond. In the SM, two mechanisms, the CKM matrix in the weak sector or the QCD θ parameter in the strong sector, can generate CP-violating EDMs. Our goal is to estimate the maximum EDMs for leptons, baryons, and select atoms and molecules within this framework. This approach assumes that the EDM wholly originates from either of the two SM mechanisms independently and takes into account the current experimental upper limits on EDMs of the electron and the neutron. We use an updated value of the electron EDM to recalculate the EDM of leptons. The EDM estimates are now calculated using a more precise value of  θ < 9.5 x 10^-11 and theoretical calculations of the semi-leptonic scalar and tensor electron-nuclear interaction parameters C_S and C_T. In light of these improvements, we also updated our calculations, and will present the EDMs of an expanded list of atoms, molecules, and baryons.

Theory of Double Charge Exchange Reaction as Probes for Double Beta Decay

Single charge exchange reactions and single beta decay have established an interesting and
fruitful relationship serving for the advantage of both fields. I'll address the question whether there exists a
similar connection between nuclear double charge exchange (DCE) reactions and nuclear double beta decay (DBD). After early, disappointing attempts, DCE reactions with nuclear beams were neglected. However, recent experiments have changed the situation
by indicating the possible dominance of mesonic DCE processes. A DCE reaction
theory focused on mesonic processes is presented. Leaving aside the higher order mean-field multi-particle
transfer contributions, the competition of two interfering reaction mechanisms is essential for understanding a DCE reaction. They given by second
order sequential Double Single Charge Exchange (DSCE) and Meson-Nucleon Majorana DCE (MDCE), formally a
first order process by virtual two–meson exchange.
The DSCE mechanism is a conventional distorted wave (DW) two-step reaction. The DSCE
reaction amplitude is transformed by suitable recoupling techniques into a form corresponding in structure to the
nuclear matrix elements (NME) of 2ν2β decay, albeit with a transition operator defined by meson exchange. The second order DSCE response functions are described by higher rank polarization tensors, in practice conveniently constructed
in Quasiparticle Random Phase Approximation (QRPA).
The MDCE mode is formally a one—step DW reaction but monitored by the coherent exchange of pairs of charged
mesons between projectile and target. Each of these mesons undergoes a single charge exchange reaction, thereby
initiating short—range correlations through the intranuclear exchange of neutral mesons. The MDCE reaction corre-
sponds to a combination of an off-shell (π+, π−) reaction in one of the ions and a complementary (π−, π+) reaction
in the other ion. Altogether, the MDCE process proceeds by a dynamically generated effective rank-2 isotensor
interaction.
The elementary MDCE vertices differ significantly from the conventional SCE and DSCE charge exchange vertices.
While the latter are given by NN isovector interactions, e.g. by the exchange of virtual charged pions, described ba
a ladder diagram [3-5]. The MDCE process, however, is driven by the (off-shell) isovector pion-nucleon T-matrix,
governed by excitations of nucleon resonances as e.g. ∆33(1232) [3,6]. The MDCE interaction is a dynamically
generated rank–2 isotensor interaction described by box diagrams, extending over the two colliding nuclei. From
a nuclear structure point of view, the MDCE operator induces two–particle-two–hole DCE
transitions in the one and the other nucleus.
The DCE formalism will be introduced with main focus on the MDCE theory. In closure approximation nuclear
matrix elements are obtained which are of a striking similarity to the NMEs of 0ν2β DBD, where the neutral pions
replace the Majorana neutrinos. Physics aspects of DSCE and MDCE processes will be illustrated on examples of
QRPA response functions and cross sections and compared to data.   

Neutron star matter based on a parity doublet model including the a0(980) meson

We study the effect of the isovector-scalar meson a₀(980) on the properties of nuclear matter and the neutron star (NS) matter by constructing a parity doublet model with including the a₀ meson based on the chiral SU(2)_L×SU(2)_R symmetry. We also include the ω−ρ mixing contribution to adjust the slope parameter at the saturation. We find that, when the chiral invariant mass of nucleon m₀ is smaller than about 800 MeV, the existence of a₀(980) enlarges the symmetry energy by strengthening the repulsive ρ meson coupling. On the other hand, for large m₀ where the Yukawa coupling of a₀(980) to nucleon is small, the symmetry energy is reduced by the effect of ω−ρ mixing. We then construct the equation of state (EoS) of a neutron star matter to obtain the mass-radius relation of NS. We find that, in most choices of m₀, the existence of a₀(980) stiffens the EoS and makes the radius of NS larger. We then constrain the chiral invariant mass of nucleon from the observational data of NS, and find that 580MeV≲m₀≲860MeV for L₀=57.7 MeV.