arXiv subjects

Hyun-Chul Kim

Publications and source records attributed to Hyun-Chul Kim.

At least 37 records · Page 2Linked to original sources

arXiv2025

Heavy-light quark systems from the QCD instanton vacuum: $N_f=1$ light flavor case

We investigate heavy-light quark systems within the framework of the QCD instanton vacuum, focusing on the $N_f = 1$ light flavor case. We derive an effective heavy-light quark interaction from the low-energy QCD partition function and construct a heavy-meson effective Lagrangian. The physical residual mass of heavy mesons, $Λ$, is determined by employing compositeness and normalization conditions. We calculate the masses of $D$ and $B$ mesons and their weak decay constants to the leading order and next-to-leading order in the $1/m_Q$ expansion. The current results for $f_D$ and $f_B$ are in good agreement with recent lattice QCD data and PDG average values.

hep-ph↗

arXiv2025

Nucleon tensor form factors at large $N_{c}$

We investigate nucleon tensor form factors in the large-$N_{c}$ limit. In this picture, the nucleon emerges as a state of the $N_c$ valence quarks, which were bound by pion mean fields that were created by the presence of the valence quarks self-consistently. We find that the tensor charge ($g^{u-d}_{T}=0.99$) and the anomalous tensor magnetic moment ($κ^{u+d}_{T}=7.61$) are dominated by valence quarks, while the tensor quadrupole moment ($Q^{u-d}_{T}=-7.02$) shows significant sea quark effects. We examine how these quantities vary as the average size of the pion mean field is changed, showing interpolation between non-relativistic quark and Skyrme limits. We also observe that $g^{u-d}_{T}$ and $κ^{u+d}_{T}$ depend weakly on the pion mass. In contrast, $Q^{u-d}_{T}$ exhibits strong enhancement near the chiral limit. The numerical results are in good agreement with available lattice QCD data and provide predictions for unmeasured quantities.

hep-ph↗

arXiv2024

Pentaquarks and Maxim V. Polyakov

This brief review is dedicated to the memory of Maxim V. Polyakov and his pioneering contributions to pentaquark physics. We focus on his seminal 1997 work with Diakonov and Petrov that predicted the $Θ^+$ pentaquark, a breakthrough that initiated an intense period of research in hadron physics. The field faced a significant setback when the CLAS Collaboration at Jefferson Lab reported null results in 2006, leading to a dramatic decline in light pentaquark research. Nevertheless, Maxim maintained his scientific conviction, supported by continued positive signals from DIANA and LEPS collaborations. Through recent experimental findings on the $Θ^+$ and the nucleon-like resonance $N^*(1685)$, we examine how Polyakov's theoretical insights, particularly the prediction of a narrow width ($Γ\approx 0.5$-$1.0$ MeV), remain relevant to our understanding of the $Θ^+$ light pentaquark.

hep-ph↗

arXiv2024

Discrete Dictionary-based Decomposition Layer for Structured Representation Learning

Neuro-symbolic neural networks have been extensively studied to integrate symbolic operations with neural networks, thereby improving systematic generalization. Specifically, Tensor Product Representation (TPR) framework enables neural networks to perform differentiable symbolic operations by encoding the symbolic structure of data within vector spaces. However, TPR-based neural networks often struggle to decompose unseen data into structured TPR representations, undermining their symbolic operations. To address this decomposition problem, we propose a Discrete Dictionary-based Decomposition (D3) layer designed to enhance the decomposition capabilities of TPR-based models. D3 employs discrete, learnable key-value dictionaries trained to capture symbolic features essential for decomposition operations. It leverages the prior knowledge acquired during training to generate structured TPR representations by mapping input data to pre-learned symbolic features within these dictionaries. D3 is a straightforward drop-in layer that can be seamlessly integrated into any TPR-based model without modifications. Our experimental results demonstrate that D3 significantly improves the systematic generalization of various TPR-based models while requiring fewer additional parameters. Notably, D3 outperforms baseline models on the synthetic task that demands the systematic decomposition of unseen combinatorial data.

cs.LG↗

arXiv2024

Two-pole structure of the $h_1(1415)$ axial-vector meson: resolving mass discrepancy

We investigate isoscalar axial-vector mesons using a coupled-channel formalism. The kernel amplitudes are constructed from meson-exchange diagrams in the $t$- and $u$-channels, which are derived from effective Lagrangians based on hidden local symmetry. We incorporate six channels: $πρ$, $ηω$, $K\bar{K}^*$, $ηϕ$, $η'ω$, and $η'ϕ$, and solve the off-shell coupled integral equations. We first discuss the dynamical generation of the $h_1(1170)$. The pole diagram for $h_1(1595)$ has a certain effect on the generation of $h_1(1170)$. We observe two poles at $(1387-i6)$ MeV and $(1452-i51)$ MeV, which exhibit a two-pole structure of the $h_1(1415)$ meson. This two-pole structure may resolve the discrepancy in the experimental data on the mass of $h_1(1415)$. The results show that the lower pole couples strongly to the $K\bar{K}^*$ channel, while the higher pole couples predominantly to the $ηϕ$ channel. This provides insights into the nature of $h_1$ mesons and explains ossible discrepancies in the mass of $h_1(1415)$.

hep-ph↗

arXiv2024

Production mechanism of the hidden charm pentaquark states $P_{c\bar{c}}$

We investigate hidden-charm pentaquark states using an off-shell coupled-channel formalism involving heavy meson and singly heavy baryon scattering. Our approach utilizes an effective Lagrangian to construct the kernel amplitudes, which respect both heavy quark symmetry and hidden local symmetry. After solving the coupled integral equations, we obtain the transition amplitudes for $J/ψN$ scattering and various heavy meson and singly heavy baryon scattering processes. We identify seven distinct peaks related to molecular states of heavy mesons $\bar{D}$ ($\bar{D}^*$) and singly heavy baryons $Σ_c$ ($Σ_c^*$). Four of these peaks can be associated with the known $P_{c\bar{c}}$ states: $P_{c\bar{c}}(4312)$, $P_{c\bar{c}}(4380)$, $P_{c\bar{c}}(4440)$, and $P_{c\bar{c}}(4457)$. We predict two additional resonances with masses around 4.5 GeV, which we interpret as $\overline{D}^* Σ_c^*$ molecular states, and identify one cusp structure. Additionally, we predict two $P$-wave pentaquark states with positive parity, which may be candidates for genuine pentaquark configurations. Notably, these pentaquark states undergo significant modifications in the $J/ψN$ elastic channel, with some even disappearing due to interference from the positive parity channel. The present investigation may provide insight into the absence of pentaquark states in $J/ψ$ photoproduction observed by the GlueX collaboration.

hep-ph↗

arXiv2024

$D_{s0}^(2317)$ and $B_{s0}^$ as molecular states

We investigate the dynamical generation of the $D_{s0}^*(2317)$ and $B_{s0}^*$ mesons using a meson-exchange model with a coupled-channelformalism. Our primary focus is on the $D_s^+π^0$ channel below the $DK$ threshold. First, we construct the invariant kernel amplitudes, incorporating effective Lagrangians based on heavy-quark symmetry, flavor SU(3) symmetry, and hidden local symmetry. Since the $D_{s0}^*(2317)$ state implies isospin symmetry breaking, we introduce $π^0-η$ isospin mixing. We subsequently solve the coupled-channel integral equations, which include four different channels, i.e., $D_s^+π^0$, $D^0 K^+$, $D^+ K^0$, and $D_s^+η$. We carefully analyze how the pole corresponding to the $D_{s0}^*(2317)$ state emerges from the coupled channels. Our findings reveal that the pole positions of the $D_{s0}^*(2317)$ meson are at $\sqrt{s_R}=(2317.9 - i 0.0593)$ MeV and the $\bar{B}_{s0}^*$ meson at $(5756.43-i0.0215)$ MeV, respectively. We also discuss their decay widths and destructive interference of the two sources. In conclusion, our current results provide a clear indication supporting the interpretation of the $D_{s0}^*(2317)$ meson as a $DK$ molecular state within the present coupled-channel formalism. In addition, we discuss a possible existence of $\bar{B}_{s0}^{*}$.

hep-ph↗

arXiv2024

Mechanical structure of the nucleon and the baryon octet: Twist-2 case

We investigate the gravitational form factors (GFFs) of the nucleon and the baryon octet, decomposed into their flavor components, utilizing a pion mean-field approach grounded in the large $N_c$ limit of Quantum Chromodynamics (QCD). Our focus is on the contributions from the twist-2 operators to the flavor-triplet and octet GFFs, and we decompose the mass, angular momentum, and $D$-term form factors of the nucleon into their respective flavors. The strange quark contributions are found to be relatively mild for the mass and angular momentum form factors, while providing significant corrections to the $D$-term form factor. In the course of examining the flavor decomposition of the GFFs, we uncover that the effects of twist-4 operators play a crucial role. While the gluonic contributions are suppressed by the packing fraction of the instanton vacuum in the twist-2 case, contributions from twist-4 operators are of order unity, necessitating its explicit consideration.

hep-ph↗

arXiv2024

Spin-orbit correlations in the nucleon in the large-$N_{c}$ limit

We study the twist-3 spin-orbit correlations of quarks described by the nucleon matrix elements of the parity-odd rank-2 tensor QCD operator (the parity-odd partner of the QCD energy-momentum tensor). Our treatment is based on the effective dynamics emerging from the spontaneous breaking of chiral symmetry and the mean-field picture of the nucleon in the large-$N_c$ limit. The twist-3 QCD operators are converted to effective operators, in which the QCD interactions are replaced by spin-flavor-dependent chiral interactions of the quarks with the pion field. We compute the nucleon matrix elements of the twist-3 effective operators and discuss the role of the chiral interactions in the spin-orbit correlations. We derive the first-quantized representation in the mean-field picture and develop a quantum-mechanical interpretation. The chiral interactions give rise to new spin-orbit couplings and qualitatively change the correlations compared to the quark model picture. We also derive the twist-3 matrix elements in the topological soliton picture where the quarks are integrated out (skyrmion). The methods used here can be extended to other QCD operators describing higher-twist nucleon structure and generalized parton distributions.

hep-ph↗

arXiv2024

Flavor structure of the energy-momentum tensor form factors of the proton

The energy-momentum tensor form factors furnish information on the mechanics of the proton. It is essential to compute the generalized isovector-vector form factors to examine the flavor structure of the energy-momentum tensor form factors. The flavor-decomposed form factors reveal the internal structure of the proton. The up quark dominates over the down quark for the mass and spin of the proton, whereas the down quark takes over the up quark for the $D$-term form factor. We investigate for the first time the isovector $\bar{c}(t)$ form factor of the proton and its physical implications. The flavor-decomposed $\bar{c}(t)$ form factors of the proton unveil how the up-quark contribution is exactly canceled by the down-quark contribution inside a proton within the framework of the pion mean-field approach. While the proton $\bar{c}(t)$ form factor does not contribute to the proton mass, its flavor structure sheds light on how the strong force fields due to the $\bar{c}(t)$ form factor characterize the stability of the proton.

hep-ph↗

arXiv2023

Role of strange quarks in the $D$-term and cosmological constant term of the proton

We investigate the mechanics of the proton by examining the flavor-decomposed proton cosmological constants and generalized vector form factors. The interplay of up, down, and strange quarks within the proton is explored, shedding light on its internal structure. The contributions of strange quarks play a crucial role in the $D$-term and cosmological constants. We find that the flavor blindness of the isovector $D$-term form factor is only valid in flavor SU(3) symmetry.

hep-ph↗

arXiv2023

Two-pole structure of the $b_1$(1235) axial-vector meson

We investigate the dynamical generation of the $b_1$ meson in the $πω$ interaction, using the fully off-mass-shell coupled-channel formalism with the $πω$, $ηρ$, $πϕ$, and $K\bar{K}^*$ channels included. We first construct the Feynman amplitudes for the sixteen different kernel amplitudes, considering only the $t$ and $u$ channels. Solving the coupled integral equation, we obtain the transition amplitude for the $πω$ interaction. We select the axial-vector and isovector channels from the partial-wave expansion and single out the two poles corresponding to the $b_1$ mesons: $(1306-i70)$ MeV and $(1356-i65)$ MeV. They are located below the $K\bar{K}^*$ threshold. The first pole lies below the $ηρ$ threshold by about 10 MeV, whereas the second one emerges above it by about 40 MeV. We analyze the effects of the two poles and background contributions to the $πω$ total cross section by using a toy model.

hep-ph↗

arXiv2023

Two-dimensional charge distributions of the $Δ$ baryon: Interpolation between the nonrelativistic and ultrarelativistic limit

We investigate how the charge distributions of both the unpolarized and transversely polarized $Δ$ baryon change as the longitudinal momentum~($P_{z}$) of the $Δ$ baryon increases from $P_{z}=0$ to $P_{z}=\infty$ in a Wigner phase-space perspective. When the $Δ$ baryon is longitudinally polarized, its two-dimensional charge distribution is kept to be spherically symmetric with $P_{z}$ varied, whereas when the $Δ$ baryon is transversely polarized along the $x$-axis, the quadrupole contribution emerges at the rest frame ($P_{z}=0$). When $P_{z}$ grows, the electric dipole and octupole moments are induced. The induced dipole moment dominates over other higher multipole contributions and governs the deformation of the charge distribution of the $Δ$ baryon.

hep-ph↗

arXiv2022

Molecular nature of the $a_1$(1260) axial-vector meson

We investigate $πρ$ scattering based on the coupled-channel formalism with the $πρ$ and $K\bar{K}^*$ ($\bar{K}K^*$) channels included. We construct the kernel amplitudes by using the meson-exchange model and compute the coupled integral equation for $πρ$ scattering. By performing the partial-wave expansion, we show explicitly that the $a_1(1260)$ meson is dynamically generated by the coupled-channel formalism. The $a_1$ meson only appears by including the $K\bar{K}^*$ ($\bar{K}K^*$) channel. We obtain the pole position of the $a_1$ meson as $\sqrt{s_R} = (1170.7 - i 173.0)$ MeV. We conclude that the $a_1$ meson can be interpreted as a kaon and vector kaon molecular state.

hep-ph↗

arXiv2022

Medium modification of singly heavy baryons in a pion-mean field approach

We investigate how the masses of singly heavy baryons undergo changes in nuclear matter. The mass spectrum of the singly heavy baryons was successfully described in a pion-mean field approach even with isospin symmetry breaking, based on which we extend the investigation to the medium modification of the singly heavy baryons. Since all dynamical parameters were determined by explaining the mass spectrum of the SU(3) light and singly heavy baryons in free space, we can directly implement the density-dependent functionals for the dynamical parameters, of which the density dependence was already fixed by reproducing the bulk properties of nuclear matter and medium modification of the SU(3) light baryons. We predict and discuss the density dependence of the masses of the singly heavy baryons.

hep-ph↗

arXiv2022

Twist-2 light-quark distribution functions in a singly heavy baryon in the large $N_c$ limit

A singly heavy baryon can be considered as a state consisting of the $N_c-1$ light valence quarks that create the pion mean field in the large $N_c$ limit. In the limit of the infinitely heavy quark mass, a heavy quark inside a singly heavy baryon is regarded as a mere static color source. It is required only to make the singly heavy baryon a color singlet. Thus, the $N_c-1$ valence quarks govern quark dynamics inside the singly heavy baryon. Within this pion mean field framework, we investigate the twist-2 unpolarized and longitudinally polarized light-quark distribution functions inside charmed and bottom baryons at a low renormalization point. We observe that the light quarks inside a heavy baryon carry less momentum than those inside a nucleon. This feature is more prominent as the heavy quark mass increases. We discuss the baryon sum rule, momentum sum rule, and the Bjorken spin sum rule for singly heavy baryons. We also discuss the inequality conditions for the quark distribution functions. In addition, we present the results for the light-quark quasi-distribution functions.

hep-ph↗

arXiv2022

Gravitational form factors of the baryon octet with flavor SU(3) symmetry breaking

We investigate the gravitational form factors of the baryon octet within the framework of the SU(3) chiral quark-soliton model, considering the effects of flavor SU(3) symmetry breaking, and the corresponding energy-momentum tensor distributions. We examine the effects of flavor SU(3) symmetry breaking to the mass, angular momentum, pressure, and shear force distributions of the baryon octet. We first find that a heavier baryon is energetically more compact than a lighter one. For the spin distributions of the baryon octet, they are properly normalized to their spins and are decomposed into the flavor-singlet axial charge and the orbital angular momentum even when the flavor SU(3) symmetry is broken. While the effects of the flavor SU(3) symmetry breaking differently contribute to the angular momentum distributions for the octet baryons, they are found to be rather small. The spin and orbital angular momentum almost equally contribute to the angular momentum distributions for the octet baryons. We also estimate the effects of the flavor SU(3) symmetry breaking to the pressure and shear force distributions. Interestingly, even if we include the effects of the SU(3) flavor symmetry breaking, the shear force distributions are kept to be positive over $r$. It indicates that the Polyakov & Schweitzer local stability condition is kept to be intact with the flavor SU(3) symmetry broken. Lastly, we discuss how much the gravitational form factors vary with the effects of flavor SU(3) symmetry breaking considered.

hep-ph↗

arXiv2022

Instanton effects on electromagnetic transitions of charmonia

We investigate the mass spectrum and electromagnetic transitions of charmonia, emphasizing the instanton effects on them. The heavy-quark potential consists of the Coulomb-like potential from one-gluon exchange and the linear confining potential. We introduce the nonperturbative heavy-quark potential derived from the instanton vacuum. We also consider the screened confining potential, which better describes the electromagnetic decays of higher excited states. Using this improved heavy-quark potential, we compute the mass spectrum and electromagnetic decays of the charmonia. Focusing on the instanton effects, we discuss the results compared with the experimental data and those from other works. The instanton effects are marginal on the electromagnetic decays of charmonia.

hep-ph↗