Nuclear Theory·nucl-th

Wednesday·November 8, 2023

10 papers—6 primary·4 cross-listed

07
The Weakly Bound States in Gaussian Wells: From the Binding Energy of Deuteron to the Electronic Structure of Quantum Dots
G. Rodriguez-Espejo · J. Segura-Landa · J. Ortiz-Monfil · D. J. Nader
Gaussian potentials serve as a valuable tool for the comprehensive modeling of short-range interactions, spanning applications from nuclear physics to the artificial confinement of electrons within quantum dots. This study focuses on examining the lowest states within Gaussian wells, with particular emphasis on the weakly bound regime. The analysis delves into the asymptotic behavior of the exact wave function at both small and large distances, motivating the development of a few-parametric Ansatz which is locally accurate and yields to a fast convergent basis set. To validate its efficacy, we assess its convergence rate using a toy model of Nuclear Physics, specifically for Deuteron. Furthermore, we employ the expansion of the energy close to the threshold to derive an analytical formula for the binding energy of the deuteron whose accuracy improves as the effective parameter approaches the critical. In concluding our investigation, we evaluate the performance of our Ansatz as an orbital in the exploration of the electronic structure of a two-electron quantum dot.
↳ quant-phnucl-thInt.J.Quant.Chem.(2024)·0 citations
08
Universal features of $2 \to N$ scattering in QCD and gravity from shockwave collisions
Himanshu Raj🇫🇷 · Raju Venugopalan🇺🇸
A remarkable double copy relation of Einstein gravity to QCD in Regge asymptotics is $Γ^{μν} = \frac{1}{2} C^{μ} C^{ν} - \frac{1}{2} N^{μ} N^{ν}$ , where $Γ^{μν}$ is the gravitational Lipatov vertex in the $2 \to 3$ graviton scattering amplitude, $C^{μ}$ its Yang-Mills counterpart, and $N^{μ}$ the QED bremssstrahlung vertex. In QCD, the Lipatov vertex is a fundamental building block of the BFKL equation describing $2 \to N$ scattering of gluons at high energies. Likewise, the gravitational Lipatov vertex is a key ingredient in a 2-D effective field theory framework describing trans-Planckian $2 \to N$ graviton scattering. We construct a quantitative correspondence between a semi-classical Yang-Mills framework for radiation in gluon shockwave collisions and its counterpart in general relativity. In particular, we demonstrate the Lipatov double copy in a dilute-dilute approximation corresponding to $R_{S, L}$ , $R_{S, H}$ $≪ b$ , with $R_{S, L}$ , $R_{S, H}$ the respective emergent Schwarzchild radii generated in shockwave collisions and $b$ is the impact parameter. We outline extensions of the correspondence developed here to the dilute-dense computation of gravitational wave radiation in close vicinity of one of the black holes, the construction of graviton propagators in the shockwave background, and a renormalization group approach to compute $2 \to N$ amplitudes that incorporates graviton reggeization and coherent graviton multiple scattering.
↳ hep-thgr-qchep-phnucl-thPRD(2024)·14 citations
09
Chiral Soliton Lattice turns into 3D crystal
Geraint W. Evans🇹🇼 · Andreas Schmitt🇬🇧
Chiral perturbation theory predicts the chiral anomaly to induce a so-called Chiral Soliton Lattice at sufficiently large magnetic fields and baryon chemical potentials. This state breaks translational invariance in the direction of the magnetic field and was shown to be unstable with respect to charged pion condensation. Improving on previous work by considering a realistic pion mass, we employ methods from type-II superconductivity and construct a three-dimensional pion (and baryon) crystal perturbatively, close to the instability curve of the Chiral Soliton Lattice. We find an analogue of the usual type-I/type-II transition in superconductivity: Along the instability curve for magnetic fields $e B > 0.12 GeV^{2}$ and chemical potentials $μ < 910 MeV$ , this crystal can continuously supersede the Chiral Soliton Lattice. For smaller magnetic fields the instability curve must be preceded by a discontinuous transition.
↳ hep-thhep-phnucl-thJHEP(2024)·24 citations
10
Elastic and resonance structures of the nucleon from hadronic tensor in lattice QCD: implications for neutrino-nucleon scattering and hadron physics
Jian Liang🇨🇳 · Raza Sabbir Sufian🇺🇸 · Bigeng Wang🇺🇸 · Terrence Draper🇺🇸 · Tanjib Khan🇧🇩 · Keh-Fei Liu🇺🇸 · Yi-Bo Yang🇨🇳 · Christian Zimmermann🇺🇸
We compute the Euclidean hadronic tensor from charge density operators and extract elastic and resonance structures by employing exponential fits to the four-point correlator, as well as a Bayesian reconstruction inverse algorithm to obtain the corresponding spectral density for qualitative comparison. We present the determination of the nucleon's Sachs electric form factor using the hadronic tensor formalism and verify that it is consistent with that from the conventional three-point function calculation. Beyond the elastic peak, we observe a structure located approximately $0.5 - 0.7$ GeV above the nucleon mass in the Bayesian reconstruction. The structure is interpreted as a mixture of the Roper resonance $(N (1440))$ , and states with both positive and negative parities in this mass region, as well as multi-hadron states. Assuming the observed structure is dominated by $J^{P} = 1/ 2^{\pm}$ states, we extract the transition electric form factor $G_{E}^{*} (Q^{2})$ and the corresponding longitudinal helicity amplitude $S_{1/2} (Q^{2})$ , and compare them with those determined from the CLAS experimental data of nucleon-to-Roper transition. Although fitting to the four-point correlation function or using the inverse algorithm does not resolve individual resonances, it nevertheless enables the determination of total inclusive lepton-nucleon scattering cross sections in appropriate energy bins. This lattice QCD calculation presents the first major step toward studying the inclusive $N \to X$ contributions with the hadronic tensor formalism.
↳ hep-lathep-phnucl-thPRD(2026)·7 citations

Affiliations

first authorsco-authorsvia INSPIRE

The Weakly Bound States in Gaussian Wells: From the Binding Energy of Deuteron to the Electronic Structure of Quantum Dots

Universal features of 2→N scattering in QCD and gravity from shockwave collisions

Chiral Soliton Lattice turns into 3D crystal

Elastic and resonance structures of the nucleon from hadronic tensor in lattice QCD: implications for neutrino-nucleon scattering and hadron physics

Affiliations

Universal features of $2 \to N$ scattering in QCD and gravity from shockwave collisions