arXiv subjects

Jian-Zhong Gu

Publications and source records attributed to Jian-Zhong Gu.

13 recordsLinked to original sources

arXiv2026

Low-lying singly heavy baryon states based on the rigorous calculation with the relativized quark model

In this work, the low-lying $\mathbf{6}_{F}$ singly heavy baryon states with positive-parity are studied in detail in the framework of the relativized quark model by using the improved calculation scheme which has successfully explained the fine structure of the low-lying negative-parity singly heavy baryons. The complete mass spectra of all the singly heavy baryon families obtained in the same framework and calculation scheme are systematically analyzed. The baryon states marked with (mass)$J^{P}$ are obtained by considering the mixing effect rigorously. It is found that the mixing effect in the singly heavy baryons depends on the flavor symmetry of the two light quarks and the baryon parity. The results show that the high-precision calculation can reproduce most of the data perfectly, and the statistical error between the calculated masses and the experimental data is only 6.96 MeV. This confirms the reliability of the improved calculation scheme. The rigorous calculation achieved by the two-step GEM enables us to analyze the detailed behavior of the various strong interaction components within the baryons with a high-precision and discover the truth of the ``soft QCD''. The large amount of data obtained in this work serves as the reliable references for related experimental and theoretical researches.

hep-ph↗

arXiv2026

Spin-dependent interactions and fine structure in the negative-parity singly heavy baryons

In order to meet the high-precision measurement of the current baryon spectroscopy, for the first time, we rigorously analyze the spin-dependent interactions and the fine structure of the negative-parity singly heavy baryons in the relativized quark model, which was previously unfeasible in the three-quark system. This gains access to the exploration of the strong interactions dominated by the non-perturbative QCD, and reveals how the various forms of strong interactions in a baryon compete with each other, affect the evolution of the energy levels, cause the energy level splitting and contribute to the mixing effect responsible for the formation of the fine structures. It is shown that the rigorous calculation can perfectly reproduce the data, the averaged deviation between the calculated and experimental energy levels is less than 5 MeV for the negative-parity singly heavy baryons. Therefore, the theoretical precision has reached the experimental high precision. This confirms the reliability of the calculation and also helps make reasonable assignments for the observed negative-parity baryons. The large amount of data obtained by the rigorous calculations contains a wealth of interaction information and is helpful for both of the theoretical and experimental studies. The key to the rigorous calculation in this work is the proposal of a new method, namely the two-step Gaussian expansion method. This new method not only overcomes the long-standing unresolved problem in the relativized quark model, but also provides an effective approach for the high-precision calculation of other few-body systems such as the compact tetraquarks and pentaquarks, especially for the treatment of spin-orbit interactions and tensor interactions which actually appear ubiquitously in all of quantum many-body systems.

hep-ph↗

arXiv2025

Mass spectra of doubly heavy baryons in the relativized quark model with heavy-quark dominance

In the framework of the relativized quark model, the mass spectra of the doubly heavy baryons are rigorously calculated in the three-quark system under the heavy-quark dominance mechanism, by using the Gaussian expansion method and the infinitesimally-shifted Gaussian basis functions. With the obtained mass spectra of all doubly heavy baryon families, the contribution of each Hamiltonian term to the energy levels is analyzed. It is found that the spin splitting is mainly determined by the spin-dependent interactions associated with the light quark. Moreover, it is shown that the spin splitting evolves regularly with the mass of heavy quarks by the evolution of the spectral structure, which is consistent with the heavy quark symmetry. Meanwhile, the orbital excitation is dominated by the $ρ$-mode, which is different from that of the singly heavy baryons. At last, our analysis indicates that the $Ξ_{cc}^{+}(3520)$ state should not exist truly and the $Ξ_{cc}^{++}(3621)$ should be the true ground state with $J^{P}$ = $\frac{1}{2}^{+}$. It is recommended to design the corresponding experiments to search for the $Ξ_{cc}^{*}$ in the energy range from 3694 to 3714 MeV.

hep-ph↗

arXiv2025

Mass spectra of singly heavy baryons in the relativized quark model with heavy-quark dominance

The rigorous calculation of the spin-orbit terms in the three-quark system is realized based on the Gaussian expansion method and the infinitesimally-shifted Gaussian basis functions in the frame work of the relativized quark model, by ignoring the mixing between different excited states. Then, the complete mass spectra of the singly heavy baryons are obtained rigorously, under the mechanism of the heavy-quark dominance. On these bases, the systematical analyses are carried out for the reliability and predictive power of the model, the fine structure of the singly heavy baryon spectra, the assignments of the excited baryons, and some important topics about the heavy baryon spectroscopy such as the missing states, the `spin-orbit puzzle', the clustering effect, etc. The result confirms that under the heavy-quark dominance mechanism, the relativized quark model can describe the excitation spectra and the fine structures of the singly heavy baryons correctly and precisely.

hep-ph↗

arXiv2024

Heavy-quark dominance and fine structure of excited heavy baryons $Σ_{Q}$, $Ξ'_{Q}$ and $Ω_{Q}$

In the framework of the relativized quark model, the calculation of spin-orbit interactions is improved by considering the contribution from the light quark cluster in a singly heavy baryon. It modifies the energy level splitting of the orbital excitation significantly and causes the emergence of fine structures for $Σ_{Q}$, $Ξ'_{Q}$ and $Ω_{Q}$ baryons. Based on this improvement, we systematically analyze the fine structures and retest the heavy quark dominance mechanism. This mechanism is found to be violated in the $1P$-wave states of the $Σ_{c}$, $Ξ'_{c}$ and $Ω_{c}$ baryons although it remains effective overall, which may help to understand the nature of the heavy quarks and strong interactions. With the predicted fine structures, we make the precise assignments of those observed heavy baryons which once could not be accurately explained due to their close mass values. The method used in this work is instructive and applicable for the study of more complex exotic hadrons, such as the heavy tetraquarks and pentaquarks.

hep-ph↗

arXiv2024

Heavy quark dominance in orbital excitation of singly and doubly heavy baryons

A mechanism of the heavy quark dominance in the orbital excitation is proposed in this paper which is testified to be reasonable for singly and doubly heavy baryons. In the relativistic quark model, an analysis of the Hamiltonian figures out the mechanism that the excitation mode with lower energy levels is always associated with the heavy quark(s), and the splitting of the energy levels is suppressed by the heavy quark(s). So, the heavy quarks dominate the orbital excitation of singly and doubly heavy baryons. Furthermore, a physical understanding of this mechanism is given in a semi-classical way. Accordingly, the predicted mass spectra of singly and doubly heavy baryons confirm the rationality of this mechanism. In addition, an interesting consequence of this mechanism is that a heavy-light meson is more likely to be produced in the strong decay of the high-orbital excited states, which is supported by experiments. This mechanism is rooted in the breakdown of the mass symmetry. Therefore, it may be also valid for other multi-quark systems, such as the tetraquarks Qqqq and QQqq, or the pentaquarks Qqqqq and QQqqq.

hep-ph↗

arXiv2023

Mass spectra of bottom-charm baryons

In this paper, we investigate the mass spectra of bottom-charm baryons systematically, where the relativistic quark model and the infinitesimally shifted Gaussian basis function method are employed. Our calculation shows that the $ρ$-mode appears lower in energy than the other excited modes. According to this feature, the allowed quantum states are selected and a systematic study of the mass spectra for $Ξ_{bc}^{'}$ ($Ξ_{bc}$) and $Ω_{bc}^{'}$ ($Ω_{bc}$) families is performed. The root mean square radii and quark radial probability density distributions of these baryons are analyzed as well. Next, the Regge trajectories in the $(J,M^{2})$ plane are successfully constructed based on the mass spectra. At last, we present the structures of the mass spectra, and analyze the difficulty and opportunity in searching for the ground states of bottom-charm baryons in experiment.

hep-ph↗

arXiv2023

Mass spectra of double-bottom baryons

Based on the relativistic quark model and the infinitesimally shifted Gaussian basis function method, we investigate the mass spectra of double bottom baryons systematically. In the $ρ$-mode which appears lower in energy than the other excited modes, we obtain the allowed quantum states and perform a systematic study of the mass spectra of the $Ξ_{bb}$ and $Ω_{bb}$ families. We analyze the root mean square radii and quark radial probability density distributions to deeply understand the structure of the heavy baryons. Meanwhile, the mass spectra allow us to successfully construct the Regge trajectories in the $(J,M^{2})$ plane. We also predict the masses of the ground states of double bottom baryons and discuss the differences between the structures of our spectra and those from other theoretical methods. At last, the shell structure of the double bottom baryon spectra is shown, from which one could get a bird's-eye view of the mass spectra.

hep-ph↗

arXiv2023

Systematic analysis of strange single heavy baryons $Ξ_{c}$ and $Ξ_{b}$

Motivated by the experimental progress in the study of heavy baryons, we investigate the mass spectra of strange single heavy baryons in the $λ$-mode, where the relativistic quark model and the infinitesimally shifted Gaussian basis function method are employed. It is shown that the experimental data can be well reproduced by the predicted masses. The root mean square radii and radial probability density distributions of the wave functions are analyzed in detail. Meanwhile, the mass spectra allow us to successfully construct the Regge trajectories in the $(J,M^{2})$ plane. We also preliminarily assign quantum numbers to the recently observed baryons, including $Ξ_{c}(3055)$, $Ξ_{c}(3080)$, $Ξ_{c}(2930)$, $Ξ_{c}(2923)$, $Ξ_{c}(2939)$, $Ξ_{c}(2965)$, $Ξ_{c}(2970)$, $Ξ_{c}(3123)$, $Ξ_{b}(6100)$, $Ξ_{b}(6227)$, $Ξ_{b}(6327)$ and $Ξ_{b}(6333)$. At last, the spectral structure of the strange single heavy baryons is shown. Accordingly, we predict several new baryons that might be observed in forthcoming experiments.

hep-ph↗

arXiv2015

Statistical properties and error threshold of quasispecies on single-peak Gaussian-distributed fitness landscapes

The stochastic Eigen model proposed by Feng et al. (Journal of theoretical biology, 246 (2007) 28) showed that error threshold is no longer a phase transition point but a crossover region whose width depends on the strength of the random fluctuation in an environment. The underlying cause of this phenomenon has not yet been well examined. In this article, we adopt a single peak Gaussian distributed fitness landscape instead of a constant one to investigate and analyze the change of the error threshold and the statistical property of the quasi-species population. We find a roughly linear relation between the width of the error threshold and the fitness fluctuation strength. For a given quasi-species, the fluctuation of the relative concentration has a minimum with a normal distribution of the relative concentration at the maximum of the averaged relative concentration, it has however a largest value with a bimodal distribution of the relative concentration near the error threshold. The above results deepen our understanding of the quasispecies and error threshold and are heuristic for exploring practicable antiviral strategies.

q-bio.PE↗

arXiv2015

Error Threshold of Fully Random Eigen Model

Species evolution is essentially a random process of interaction between biological populations and their environments. As a result, some physical parameters in evolution models are subject to statistical fluctuations. In this paper, two important parameters in the Eigen model, the fitness and mutation rate, are treated as Gaussian distributed random variables simultaneously to examine the property of the error threshold. Numerical simulation results show that the error threshold in the fully random model appears as a crossover region instead of a phase transition point, and as the fluctuation strength increases the crossover region becomes smoother and smoother. Furthermore, it is shown that the randomization of the mutation rate plays a dominant role in changing the error threshold in the fully random model, which is consistent with the existing experimental data. The implication of the threshold change due to the randomization for antiviral strategies is discussed.

q-bio.PE↗

arXiv2012

Correlations between the nuclear breathing mode energy and properties of asymmetric nuclear matter

Based on microscopic Hartree-Fock + random phase approximation calculations with Skyrme interactions, we study the correlations between the nuclear breathing mode energy $E_{ISGMR}$ and properties of asymmetric nuclear matter with a recently developed analysis method. Our results indicate that the $E_{ISGMR}$ of $^{208}$Pb exhibits moderate correlations with the density slope $L$ of the symmetry energy and the isoscalar nucleon effective mass $m_{s,0}^{\ast}$ besides a strong dependence on the incompressibility $K_{0}$ of symmetric nuclear matter. Using the present empirical values of $L=60\pm 30$ MeV and $m_{s,0}^{\ast}=(0.8\pm 0.1)m$, we obtain a theoretical uncertainty of about $\pm 16$ MeV for the extraction of $K_{0}$ from the $E_{ISGMR}$ of $^{208}$Pb. Furthermore, we find the $E_{ISGMR}$ difference between $^{100}$Sn and $^{132}$Sn strongly correlates with $L$ and thus provides a potentially useful probe of the symmetry energy.

nucl-th↗

arXiv2007

Isospin dependence of incompressibility in relativistic and non-relativistic mean field calculations

The isospin dependence of incompressibility is investigated in the Skyrme Hartree-Fock (SHF) and relativistic mean field (RMF) models. The correlations between the nuclear matter incompressibility and the isospin dependent term of the finite nucleus incompressibility is elucidated by using the Thomas-Fermi approximation. The Coulomb term is also studied by using various different Skyrme Hamiltonians and RMF Lagrangians. The symmetry energy coefficient of incompressibility is extracted to be K_τ=-(500\pm50) MeV from the recent experimental data of isoscalar giant monopole resonances (ISGMR) in Sn isotopes. Microscopic HF+random phase approximation (RPA) calculations are also performed with Skyrme interactions for ^{208}Pb and Sn isotopes to study the strength distributions of ISGMR. .

nucl-th↗