Nuclear Theory·nucl-th

Tuesday·August 29, 2023

21 papers—12 primary·9 cross-listed

13
[Submitted on 23 Aug 2023] (cross-list from math-ph)
Solving the matrix exponential function for special orthogonal groups SO(n) and the exceptional G $_{2}$
Norbert Kaiser
In this work the matrix exponential function is solved analytically for the special orthogonal groups $S O (n)$ up to $n = 9$ . The number of occurring $k$ -th matrix powers gets limited to $0 \leq k \leq n - 1$ by exploiting the Cayley-Hamilton relation. The corresponding expansion coefficients can be expressed as cosine and sine functions of a vector-norm $V$ and the roots of a polynomial equation that depends on a few specific invariants. Besides the well known case of $S O (3)$ , a quadratic equation needs to be solved for $n = 4, 5$ , a cubic equation for $n = 6, 7$ , and a quartic equation for $n = 8, 9$ . As an interesting subgroup of $S O (7)$ , the exceptional Lie group $G_{2}$ of dimension $14$ is constructed via the matrix exponential function through a remarkably simple constraint on an invariant, $ξ = 1$ . The calculation of the trace of the $S O (n)$ -matrices arising from the exponential function, results in a sum of cosines of several angles, which specify the associated conjugation class as a point on a maximal torus.
Comments:
14 pages, 3 figures
Subjects:
Mathematical Physics (math-ph); math.MP (math.MP); Nuclear Theory (nucl-th)
arXiv:
2308.12123 [pdf]
0 citations
14
[Submitted on 25 Aug 2023] (cross-list from hep-ph)
Realtime dynamics of hyperon spin correlations from string fragmentation in a deformed four-flavor Schwinger model
João Barata🇺🇸 · Wenjie Gong🇺🇸 · Raju Venugopalan🇺🇸
Self-polarizing weak decays of $Λ$ -hyperons provide unique insight into the role of entanglement in the fragmentation of QCD strings through measurements of the spin correlations of $Λ Λ ˉ$ -pairs produced in collider experiments. The simplest quantum field theory representing the underlying parton dynamics is the four-flavor massive Schwinger model plus an effective spin-flip term, where the flavors are mapped to light (up/down) and heavy (strange) quarks and their spins. This construction provides a novel way to explore hyperon spin-correlations in 1+1-dimensions. We investigate the evolution of these correlations for different string configurations that are sensitive to the rich structure of the model Hamiltonian.
Comments:
9 pages, 5 figures, v2: Additional results on real time evolution. Expanded discussion of model
Subjects:
High Energy Physics — Phenomenology (hep-ph); Nuclear Theory (nucl-th); Quantum Physics (quant-ph)
arXiv:
2308.13596 [pdf]
PRD(2024)·53 citations
15
[Submitted on 25 Aug 2023] (cross-list from hep-ph)
Constraining the pion distribution amplitude using Drell-Yan reactions on a proton
H.-Y. Xing🇨🇳 · M. Ding🇩🇪 · Z.-F. Cui🇨🇳 · A. V. Pimikov🇨🇳 · C. D. Roberts🇨🇳 · S. M. Schmidt🇩🇪
Using a reaction model that incorporates pion bound state effects and continuum results for proton parton distributions and the pion distribution amplitude, $φ_{π}$ , we deliver parameter-free predictions for the $μ^{+}$ angular distributions in $π N \to μ^{+} μ^{-} X$ reactions on both unpolarised and polarised targets. The analysis indicates that such angular distributions are sensitive to the pointwise form of $φ_{π}$ and suggests that unpolarised targets are practically more favourable. The precision of extant data is insufficient for use in charting $φ_{π}$ ; hence, practical tests of this approach to charting $φ_{π}$ must await data with improved precision from new-generation experiments. The reaction model yields a nonzero single-spin azimuthal asymmetry, without reference to $T$ -odd parton distribution functions (DFs). This may necessitate additional care when attempting to extract such $T$ -odd DFs from data.
Comments:
8 pages, 7 figures
Subjects:
High Energy Physics — Phenomenology (hep-ph); High Energy Physics — Experiment (hep-ex); High Energy Physics — Lattice (hep-lat); Nuclear Experiment (nucl-ex); Nuclear Theory (nucl-th)
arXiv:
2308.13695 [pdf]
PLB(2024)·7 citations
16
[Submitted on 26 Aug 2023] (cross-list from hep-th)
The Schrödinger Representation and 3d Gauge Theories
V.P. Nair🇺🇸
In this review we consider the Hamiltonian analysis of Yang-Mills theory and some variants of it in three spacetime dimensions using the Schrödinger representation. This representation, although technically more involved than the usual covariant formulation, may be better suited for some nonperturbative issues. Specifically for the Yang-Mills theory, we explain how to set up the Hamiltonian formulation in terms of manifestly gauge-invariant variables and set up an expansion scheme for solving the Schrödinger equation. We review the calculation of the string tension, the Casimir energy and the propagator mass and compare with the results from lattice simulations. The computation of the first set of corrections to the string tension, string breaking effects, extensions to the Yang-Mills-Chern-Simons theory and to the supersymmetric cases are also discussed. We also comment on how entanglement for the vacuum state can be formulated in terms of the BFK gluing formula. The review concludes with a discussion of the status and prospects of this approach.
Comments:
134 pages, 13 figures, Expanded version of lectures at Understanding Confinement: Prospects in Theoretical Physics Summer School, Institute for Advanced Study, Princeton, July 2023
Subjects:
High Energy Physics — Theory (hep-th); High Energy Physics — Lattice (hep-lat); Mathematical Physics (math-ph); math.MP (math.MP); Nuclear Theory (nucl-th)
arXiv:
2308.13926 [pdf]
Int.J.Mod.Phys.A(2023)·5 citations
17
[Submitted on 27 Aug 2023] (cross-list from hep-ph)
Production of the newly observed $T ˉ_{c s ˉ 0}$ by kaon-induced reactions on a proton/neutron target
Yin Huang🇨🇳 · Hao Hei🇨🇳 · Jing-wen Feng🇨🇳 · Xurong Chen🇨🇳 · Rong Wang🇨🇳
Recently, a new doubly charged tetraquark $T_{c s ˉ 0}^{a} (2900)^{++}$ and its neutral partner $T_{c s ˉ 0}^{a} (2900)^{0}$ at the invariant mass spectrum of $π D_{s}$ were observed by the LHCb Collaboration. According to its properties, such as the mass and decay width, the $T_{c s ˉ 0}^{a} (2900)^{++ /0}$ have been suggested to be a compact multi-quark state or a hadron molecule. In order to distinguish the various interpretations of the $T_{c s ˉ 0}^{a} (2900)^{++ /0}$ , we investigate the possibility to study the $T ˉ_{c s ˉ 0}^{a} (2900)$ [the antiparticle of $T_{c s ˉ 0}^{a} (2900)$ ] by kaon-induced reactions on a proton target in an effective Lagrangian approach. The production mechanism is characterized by the $t$ -channel $D$ meson exchange. Our theoretical approach is based on the assumption that $T ˉ_{c s ˉ 0}^{a} (2900)$ can be either a $K^{*} D^{*} - D_{s}^{*} ρ$ molecule or a compact tetraquark state. Using the coupling constants of the $T ˉ_{c s ˉ 0}^{a} (2900)$ to $K D$ channel obtained from molecule or compact tetraquark picture of the $T ˉ_{c s ˉ 0}^{a} (2900)$ , we compute the cross-sections for the process $K^{-} n \to T ˉ_{c s ˉ 0}^{a} (2900)^{--} Λ_{c}^{+}$ . The $K ˉ N$ initial state interaction mediated by Pomeron and Reggeon exchanges is also included, which reduces the production of the $T ˉ_{c s ˉ 0}^{a} (2900)$ . Our calculations show that whether $T ˉ_{c s ˉ 0}^{a} (2900)$ is a molecule or a compact tetraquark state, the cross-sections for the $K^{-} n \to T ˉ_{c s ˉ 0}^{a} (2900)^{--} Λ_{c}^{+}$ reaction are of similar magnitude, ranging from approximately 0.075 nb to 0.270 nb.
Subjects:
High Energy Physics — Phenomenology (hep-ph); Nuclear Theory (nucl-th)
arXiv:
2308.14148 [pdf]
PRD(2023)·9 citations
18
[Submitted on 28 Aug 2023] (cross-list from hep-ph)
Heavy quark diffusion and radiation at intermediate momentum
Juhee Hong🇰🇷
We discuss heavy quark diffusion and radiation in an intermediate-momentum regime where finite mass effects can be significant. Diffusion processes are described in the Fokker-Planck approximation for soft momentum transfer, while radiative ones are taken into account by nearly collinear gluon emission from a single scattering in the Boltzmann equation. We also consider radiative corrections to the transverse momentum diffusion coefficient, which are $O (g^{2})$ suppressed than the leading-order diffusion coefficient but logarithmically enhanced. Numerical results show that the heavy quark distribution function depends on the energy loss mechanism so that the momentum dependence of suppression is distinguishable. Employing the heavy quark diffusion coefficient constrained by lattice QCD data, we estimate the nuclear modification factor which exhibits a transition from diffusion at low momentum to radiation at high momentum. The significance of radiative effects at intermediate momentum depends on the diffusion coefficient and running coupling constant.
Comments:
15 pages, 6 figures
Subjects:
High Energy Physics — Phenomenology (hep-ph); Nuclear Theory (nucl-th)
arXiv:
2308.14530 [pdf]
PRC(2024)·8 citations
19
[Submitted on 28 Aug 2023] (cross-list from hep-ph)
Production of leptons from decay of heavy-flavor hadrons in high-energy nuclear collisions
Sa Wang🇨🇳 · Yao Li🇨🇳 · Shuwan Shen🇨🇳 · Ben-Wei Zhang🇨🇳 · Enke Wang🇨🇳
This paper presents a theoretical study on the production of the heavy-flavour decay lepton (HFL) in high-energy nuclear collisions at the LHC. The pp-baseline is calculated by the FONLL program, which matches the next-to-leading order pQCD calculation with the next-to-leading-log large- $p_{T}$ resummation. The in-medium propagation of heavy quarks is driven by the modified Langevin equations, which consider both the elastic and inelastic partonic interactions. We propose a method to separate the respective influence of the six factors, such as pp-spectra, the cold nuclear matter (CNM) effects, in-medium energy loss (E-loss), fragmentation functions (FFs), coalescence (Coal), and decay channels, which may contribute to the larger $R_{AA}$ of HFL $\leftarrow b$ compared to that of HFL $\leftarrow c$ in nucleus-nucleus collisions. Based on quantitative analysis, we demonstrate that both coalescence hadronization, decay channels and the mass-dependent E-loss play an essential role at $p_{T} < 5$ GeV, while the latter dominates the higher $p_{T}$ region. It is also found that the influences of the CNM effects and FFs are insignificant. At the same time, different initial pp-spectra of charm and bottom quarks have a considerable impact at $p_{T} > 5$ GeV. Furthermore, we explore the path-length dependence of jet quenching by comparing the HFL $R_{AA}$ in two different collision systems. Our investigations show smaller HFL $R_{AA}$ in Pb+Pb than in Xe+Xe within the same centrality bin, consistent with the ALICE data. The longer propagation time and more effective energy loss of heavy quarks in Pb+Pb collisions play critical roles in the stronger yield suppression of the HFL compared to that in Xe+Xe. In addition, we observe a scaling behavior of the HFL $R_{AA}$ in Xe+Xe and Pb+Pb collisions.
Comments:
13 pages, 9 figures. Version published in Phys. Rev. C
Subjects:
High Energy Physics — Phenomenology (hep-ph); High Energy Physics — Experiment (hep-ex); Nuclear Theory (nucl-th)
arXiv:
2308.14538 [pdf]
PRC(2025)·5 citations
20
[Submitted on 28 Aug 2023] (cross-list from physics.chem-ph)
Seniority and Hierarchy Configuration Interaction for Radicals and Excited States
Fábris Kossoski · Pierre-François Loos
Hierarchy configuration interaction (hCI) has been recently introduced as an alternative configuration interaction (CI) route combining excitation degree and seniority number, which showed to efficiently recover both dynamic and static correlations for closed-shell molecular systems [\href{https://doi.org/10.1021/acs.jpclett.2c00730}{\textit{J.~Phys.~Chem.~Lett.}~\textbf{2022}, \textit{13}, 4342}]. Here, we generalize hCI for an arbitrary reference determinant, allowing calculations for radicals and for excited states in a state-specific way. We gauge this route against excitation-based CI (eCI) and seniority-based CI (sCI) by evaluating how different ground-state properties of radicals converge to the full CI limit. We find that hCI outperforms or matches eCI, whereas sCI is far less accurate, in line with previous observations for closed-shell molecules. Employing the second-order Epstein-Nesbet (EN2) perturbation theory as a correction significantly accelerates the convergence of hCI and eCI. We further explore various hCI and sCI models to calculate excitation energies of closed- and open-shell systems. Our results underline that both the choice of the reference determinant and the set of orbitals drive the fine balance between correlation of ground and excited states. State-specific hCI2 and higher order models perform similarly to their eCI counterparts, whereas lower orders of hCI deliver poor results, unless supplemented by the EN2 correction, which substantially improves their accuracy. In turn, sCI1 produces decent excitation energies for radicals, encouraging the development of related seniority-based coupled-cluster methods.
Comments:
18 pages, 5 figures
Subjects:
physics.chem-ph (physics.chem-ph); cond-mat.mtrl-sci (cond-mat.mtrl-sci); Nuclear Theory (nucl-th); Computational Physics (physics.comp-ph)
arXiv:
2308.14618 [pdf]
J.Chem.Theor.Comput.(2023)·3 citations
21
[Submitted on 28 Aug 2023] (cross-list from hep-ph)
Azimuthal Anisotropy at high transverse momentum in $p$ - $p$ and $p$ - $A$ collisions
Ismail Soudi🇺🇸 · Abhijit Majumder🇺🇸
We explore the possibility that the initial transverse momentum distribution of unpolarized and polarized partons within unpolarized nucleons, both with and without the anisotropy of unpolarized hadrons produced in the fragmentation of outgoing partons, could lead to the observed azimuthal anisotropy of high transverse momentum (high- $p_{T}$ ) hadrons produced in high energy proton-proton ( $p$ - $p$ ) or proton-ion ( $p$ - $A$ ) collisions. Including simple Gaussian forms for transverse momentum dependent parton distribution functions (PDF) and fragmentation functions, and assuming an $A^{1/3}$ enhancement of a PDF in $p$ - $P b$ collisions, we show that the observed anisotropy, with \emph{no modification} to the angle integrated spectra ( $R_{p A} = 1$ ) for 5~GeV~ $≲ p_{T} ≲ 50$ ~GeV, can be straightforwardly understood as arising from a few processes dominated by gluon-gluon to gluon-gluon scattering.
Comments:
11 pages, 10 figures
Subjects:
High Energy Physics — Phenomenology (hep-ph); High Energy Physics — Experiment (hep-ex); Nuclear Theory (nucl-th)
arXiv:
2308.14702 [pdf]
PLB(2024)·15 citations

Affiliations

first authorsco-authorsvia INSPIRE