Session FM: Nuclear Theory II

Unitarity for Two Nucleons with Pions

One can understand nuclei at the physical point by an expansion about the unitarity limit of infinite scattering length, with all other effective-range parameters zero. The $NN$ S-wave binding energies are then zero, and there is no scale at leading order. Nuclear Physics resides in a sweet spot: bound weakly enough to be insensitive to the details of the nuclear force; but dense enough that the $NN$ scattering lengths are perturbatively close to the unitarity limit. In this contribution, we study how new scales, namely the pion mass and decay constant change the picture in the $NN$ system. We find that when one imposes unitarity at zero energy, phase shifts do not significantly stray from unitarity at low energies in the $^3$S$_1$-$^3$D$_1$ and in the $^1$S$_0$ waves. Wigner's SU$(4)$ symmetry of combined spin and isospin transformations emerges then quite naturally. At a ``magic'' effective range $r_\chi\approx1.4\;$fm, the effects of these new scales are minimal in both channels. We observe that the physical values are close to it, provide further insight into unitarity with pions, and motivate a converging, perturbative expansion around the unitarity limit, with controlled corrections in the inverse scattering lengths, pion-nucleon interaction, ranges and isospin breaking.   

An anomalous structure in S=−1 meson-baryon scattering in the resonance region

We present a simultaneous analysis of s- and p-waves of the S = −1 meson-baryon scattering amplitude using low-energy experimental data. For the first time differential cross section data are included for chiral unitary coupled-channel models. From this model s- and p-wave amplitudes are extracted and we observe both well-known I(J P ) = 0(1/2 −) s-wave states as well as a new I(J P ) = 1(1/2 +) state absent in quark models and lattice QCD results. Multiple statistical and phenomenological tests suggest that, while the data clearly require an I = 1 p-wave resonance, the new state accounts for the absence of the decuplet Σ(1385)3/2 + in the model.   

Bridging phenomenology & lattice QCD in the 3-body sector

The interacting three-particle states are populated via an interacting two-particle sub-system (resonant or non-resonant), and a spectator. Using this formulation, we derive the relativistic isobar-spectator amplitude such that the three-body Unitarity is ensured exactly (Eur.Phys.J. A53 (2017) no.9, 177). Unitarity constrains the imaginary parts of such an amplitude in infinite volume. In the finite volume this determines the leading power-law finite-volume effects allowing for a derivation of a highly desired 3-body quantization condition. Short derivation of the latter in the present formalism (Eur.Phys.J. A53 (2017) no.12, 240) as well as a subsequent application to the physical system for which Lattice results exist (Phys.Rev.Lett. 122 (2019) no.6, 062503) will be presented in this talk.   

Renormalization in the Three-Body Sector with Singular Potentials

Despite the success of chiral effective field theory (EFT) in describing the nuclear interaction, there remains a significant debate over the power-counting scheme used to systematize the contributions. One-pion exchange (OPE) is part of the leading-order chiral EFT nucleon-nucleon potential, so we study the case of the attractive, inverse-cube potential, whose wave functions should have the same short-distance behavior. In principle, the renormalization at large cutoffs of two- and three-body observables found with this potential should mimic the cutoff dependence of those same observables calculated with OPE. I will present results that demonstrate the sufficiency of a two-body contact term to renormalize three-body binding energies and scattering observables. I will also discuss a rigorous analysis of the higher-order corrections that finds two-body corrections subleading to three-body corrections, suggesting that a three-body counterterm may be required at next-to-leading order.   

Fitting Nuclear Potentials with TensorFlow \& Gaussian Processes

A nuclear potential with quantified uncertainties is crucial for meaningful predictions across the nuclear chart. I will discuss how statistics and algorithms can help us find better potentials more easily. A Bayesian model discrepancy term is shown to both incorporate uncertainty from higher order terms in chiral effective field theory and also regularize the fitting procedure. Information about model correlations can be rigorously incorporated for the first time using Gaussian processes. Combined with TensorFlow, new codes can more effectively sample the posteriors of low-energy constants for full uncertainty quantification. Potential applications are discussed.   

Exploring the Magnus expansion and the similarity renormalization group

We test the Magnus expansion implementation of the similarity renormalization group (SRG) on chiral NN potentials at high cutoffs. At leading order and high cutoffs, chiral potentials feature spurious bound states in spin triplet channels. We explore how bound states decouple with two band-diagonal transformations. Furthermore, we study operator evolution and calculate consistently evolved observables.   

Applications of Nonequilibrium Green’s Function Approach to Nuclear Systems in One Dimension

While semiclassical transport theories and time-dependent Hartree-Fock method have been extensively applied to describe many-body systems, they fail to take into account the effects of quantum correlations, which can be crucial for strongly interacting quantum systems. The nonequilibrium Green’s function approach allows for a systematic way to incorporate correlations. For the time being, we consider only short-ranged two-body correlations. In this talk, I will discuss applications in the description of nuclear systems in 1D, such as the spectral function for the ground state, the isoscalar monopole mode and the isovector dipole mode, and the collision of slabs in 1D. Calculations will be compared with and without correlations.   

The iS3D particlization module for heavy-ion collision simulations

The iS3D particlization module simulates the emission of hadrons from heavy-ion collisions via Monte-Carlo sampling. The code package includes multiple choices for the non-equilibrium correction to the hadronic distribution function in the Cooper-Frye formula: the 14-moment approximation, Chapman-Enskog expansion, and two types of modified equilibrium distributions. This makes it possible to explore, using Bayesian analysis, whether heavy-ion experimental data prefers one of these models for $\delta f_n$, the main source of theoretical uncertainty in the particlization stage. We validate our particle sampler with a high degree of precision by generating several million hadron emission events from a longitudinally boost-invariant hypersurface and comparing the event-averaged particle spectra and spacetime distributions to the Cooper-Frye formula.