We investigate the electromagnetic polarizabilities of singly heavy mesons and doubly heavy baryons within the framework of heavy hadron chiral perturbation theory up to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mrow><mi>p</mi></mrow><mrow><mn>3</mn></mrow></msup><mo stretchy="false">)</mo></mrow></math>. We estimate the low-energy constants using the nonrelativistic constituent quark model. A striking prediction of our study is the giant electric polarizabilities of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup></math> mesons: <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>E</mi></msub><mo stretchy="false">(</mo><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mrow><mo>*</mo><mn>0</mn></mrow></msup><mo stretchy="false">)</mo><mo>≈</mo><mn>294</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup><mtext> </mtext><mtext> </mtext><msup><mrow><mi>fm</mi></mrow><mn>3</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>E</mi></msub><mo stretchy="false">(</mo><msup><mi>D</mi><mrow><mo>*</mo><mo>−</mo></mrow></msup><mo stretchy="false">)</mo><mo>≈</mo><mspace linebreak="goodbreak"></mspace><mn>1.42</mn><mi>–</mi><mn>64.5</mn><mi mathvariant="normal">i</mi><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup><mtext> </mtext><mtext> </mtext><msup><mrow><mi>fm</mi></mrow><mn>3</mn></msup></math>. These anomalously large values arise from the near-degenerate mass between <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mi>π</mi></math>, which are orders of magnitude larger than those of their bottom counterparts. This kinematic coincidence induces a pronounced cusp structure in the chiral loops, reflecting the long-range dynamics of a pion cloud. For doubly heavy baryons, polarizabilities depend strongly on heavy-flavor composition: the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi><mi>c</mi><mi>q</mi></math> system differs markedly from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>c</mi><mi>c</mi><mi>q</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi><mi>b</mi><mi>q</mi></math> due to mixing with scalar heavy-diquark states. Using heavy diquark–antiquark symmetry (HDAS), we unify the chiral dynamics of singly heavy mesons and doubly heavy baryons in the heavy-quark limit. The pion-loop contributions dominate the electromagnetic structure of heavy hadrons and provide essential benchmarks for future lattice QCD simulations.

China

Hao Dang

Liang-Zhen Wen

Yan-Ke Chen

Shi-Lin Zhu

Electromagnetic polarizabilities of the triplet hadrons in heavy hadron chiral perturbation theory

Motivated by the observation of the doubly charmed tetraquark $ T_{cc}(3875)^+ $ , we present a systematic study of doubly heavy tetraquarks ( $ T_{QQ'\bar{q}\bar{q}'} $ ) using heavy antiquark-diquark symmetry (HADS) within a constituent quark model. By calibrating model parameters to known hadron spectra and incorporating the effective mass formula, we predict the masses for 38 ground-state tetraquarks with $ cc $ , $ bb $ , and $ bc $ heavy quark pairs, including the non-strange, single-strange, and double-strange configurations with quantum numbers $ J^P = 0^+, 1^+ $ and $ 2^+ $ . Notably, we identify several stable states below the relevant meson-meson thresholds, particularly in the $ bb\bar{q}\bar{q}' $ sector. The explicit connection between the doubly heavy tetraquark and the heavy baryon spectra through HADS reduces model dependence and reveals the fundamental systematics in the heavy-quark hadron landscape.

Liu-Yu Zhang

Tian-Wei Wu

Yong-Liang Ma

Bridging doubly heavy tetraquark mass spectrum with heavy baryons utilizing heavy antiquark-diquark symmetry * The work of Tian-Wei Wu is supported by the National Natural Science Foundation of China (12405108). Yong-Liang Ma is supported in part by the National Science Foundation of China (NSFC) (12347103) and Gusu Talent Innovation Program (ZXL2024363)

The Schwinger effect, a non-perturbative mechanism for particle production in strong fields, plays a crucial role in understanding quantum vacuum decay and high-energy phenomena, including heavy-ion collisions (HIC). Although holographic quantum chromodynamics (QCD) models have been widely used to study this effect, most treatments assume isotropy or consider only a single type of anisotropy, neglecting the interplay between spatial and magnetic anisotropies that arise in realistic HIC scenarios. A unified framework accounting for both anisotropies is needed to accurately model particle production. We investigate the Schwinger effect in a twice anisotropic holographic QCD model incorporating both spatial and magnetic anisotropies. Using the anti-de Sitter/conformal field theory correspondence, we compute the total potential of a particle-antiparticle pair to quantify how these anisotropies influence pair production. Our results show that the magnetic field (parameterized by $c_B$ and $q_3$ ) enhances the Schwinger effect by lowering and narrowing the potential barrier, while increasing spatial anisotropy (controlled by $\nu$ ) suppresses the process by raising and widening the barrier. These findings demonstrate that magnetic and spatial anisotropies exert competing effects on particle production, emphasizing the necessity of treating both concurrently in holographic models. This work advances the theoretical description of the Schwinger effect in anisotropic environments, with implications for understanding non-equilibrium dynamics in HIC and other strongly coupled systems.

Wen-Bin Chang

Defu Hou

Schwinger effect in a twice anisotropic holographic model * Defu Hou's research is supported in part by the National Key Research and Development Program of China (2022YFA1604900). Additionally, Defu Hou receives partial support from the National Natural Science Foundation of China (NSFC) (12435009, 12275104). Wen-Bin Chang is supported by the Ph.D. Research Startup Project at Hubei Minzu University (RZ2500000857)

We employ Heavy Baryon Chiral Perturbation Theory (HB $$\chi $$ PT), a non-relativistic effective field theory that treats baryons as heavy static sources, to calculate the electromagnetic polarizabilities of spin-3/2 baryons in two sectors: the light-flavor decuplet baryons and singly heavy sextet baryons. We derive the analytical expressions up to $$\mathcal {O}\left( p^3\right) $$ . Our results indicate that the long-range chiral corrections provide substantial contributions to the polarizabilities. In addition, magnetic dipole (M1) transitions of the baryons can significantly affect the magnetic polarizabilities and may reverse their signs. For the decuplet baryons, the $$\Delta ^+$$ and $$\Delta ^0$$ exhibit the largest electric polarizabilities. Their values, $$\alpha _E(\Delta ^+) = (17.5 \pm 9.5)\times 10^{-4} \, \textrm{fm}^3$$ and $$\alpha _E(\Delta ^0) = (17.0 \pm 9.3)\times 10^{-4} \, \textrm{fm}^3$$ , significantly exceed those typically observed for nucleons. Meanwhile, the electric polarizabilities of spin-3/2 singly heavy baryons are comparable to those of their spin-1/2 partners.

Germany

Lu Meng

Electromagnetic polarizabilities of the spin- $$\frac{3}{2}$$ baryons in heavy baryon chiral perturbation theory

This paper introduces a novel systematic construction of gapped domain walls (GDWs) within the Levin-Wen (LW) model. By gluing two LW models along their open sides in a compatible way, we achieve a complete GDW classification by subsets of bulk input data, which encompass the classifications in terms of bimodule categories. A generalized bimodule structure is introduced to capture domain-wall excitations. Furthermore, we demonstrate that folding along any GDW yields a gapped boundary (GB) described by a Frobenius algebra of the input UFC for the folded model, thus bridging our GDW classification and the GB classification in [1].

Yanyan Chen

Siyuan Wang

Yu Zhao

Yuting Hu

Yidun Wan

Classification of gapped domain walls of topological orders in 2+1 dimensions: a Levin-Wen model realization

We investigate the existence of bound states and resonances in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi><mi>N</mi><mi>N</mi><mo>,</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>N</mi><mi>N</mi><mo>,</mo><msub><mi>η</mi><mi>c</mi></msub><mi>N</mi><mi>N</mi></math> systems using HAL QCD interactions for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi><mi>N</mi><mo>,</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>N</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>c</mi></msub><mi>N</mi></math>. We employ the Gaussian expansion method to solve the complex-scaled Schrödinger equation and find no resonances or bound states in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>N</mi><mi>N</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>c</mi></msub><mi>N</mi><mi>N</mi></math> systems. We estimate the interaction between charmonium and nuclei, concluding that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>c</mi></msub></math> is likely to bind with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><mi mathvariant="normal">H</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>3</mn></mrow></mmultiscripts></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><mi>He</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>3</mn></mrow></mmultiscripts></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><mi>He</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>4</mn></mrow></mmultiscripts></mrow></math>, and heavier nuclei. For the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi><mi>N</mi><mi>N</mi></math> system, the lattice QCD <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>ϕ</mi><mi>N</mi><mo stretchy="false">(</mo><mrow><msub><mrow><mmultiscripts><mrow><mi>S</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>2</mn></mrow></mmultiscripts></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub><mo stretchy="false">)</mo></mrow></mrow></math> interaction is absent. We combine the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi><mi>p</mi></math> correlation function analysis and HAL QCD results in model A. We assume the spin-spin interactions for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>N</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi><mi>N</mi></math> systems are inversely proportional to their masses in model B. Model A predicts a stronger <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi><mi>N</mi><mo stretchy="false">(</mo><msub><mrow><mmultiscripts><mrow><mi>S</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>2</mn></mrow></mmultiscripts></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub><mo stretchy="false">)</mo></math> interaction and permits a two-body bound state, whereas model B suggests the interaction is attractive but too weak to form a bound state. Both models predict bound states for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo stretchy="false">(</mo><msup><mi>J</mi><mi>P</mi></msup><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mo stretchy="false">(</mo><msup><mn>0</mn><mo>−</mo></msup><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0</mn><mo stretchy="false">(</mo><msup><mn>1</mn><mo>−</mo></msup><mo stretchy="false">)</mo></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi><mi>N</mi><mi>N</mi></math> systems. In model A, these states are deeply bound with binding energies exceeding 15 MeV and remain existent when considering parameter uncertainties. In contrast, these states are very loosely bound in model B, with binding energies below 1 MeV and an existent probability of about 60% when parameter uncertainties are considered. In both models, there exist very loosely bound <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo stretchy="false">(</mo><msup><mi>J</mi><mi>P</mi></msup><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mo stretchy="false">(</mo><msup><mn>2</mn><mo>−</mo></msup><mo stretchy="false">)</mo></math> three-body states which resemble a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi></math>-d atom with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi></math> meson surrounding the deuteron, but their existence is sensitive to parameter uncertainties. No bound states or resonances are found in the isovector <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo stretchy="false">(</mo><msup><mi>J</mi><mi>P</mi></msup><mo stretchy="false">)</mo><mo>=</mo><mn>1</mn><mo stretchy="false">(</mo><msup><mn>1</mn><mo>−</mo></msup><mo stretchy="false">)</mo></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi><mi>N</mi><mi>N</mi></math> system.

Yao Ma

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi><mi>N</mi><mi>N</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>N</mi><mi>N</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>c</mi></msub><mi>N</mi><mi>N</mi></math> systems based on HAL QCD interactions

This work presents the first prediction of tetralepton resonant states containing muons, extending beyond the simplest tetralepton system, dipositronium (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>Ps</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math>). With the rapid advancements in experimental facilities, the production and study of these intriguing states may be within reach. We perform a comprehensive analysis of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave trilepton and tetralepton systems within the framework of a QED Coulomb potential. We employ the Gaussian expansion method to solve the three- or four-body Schrödinger equation and utilize the complex scaling method to identify resonant states. We uncover a series of bound and resonant states in the trilepton systems <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math>, as well as the tetralepton systems <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math>. The energies of these states range from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>30</mn><mtext> </mtext><mtext> </mtext><mi>eV</mi></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>1</mn><mtext> </mtext><mtext> </mtext><mi>eV</mi></math> below the total mass of three or four leptons, with their widths varying from less than 0.01 eV to approximately 0.07 eV. Additionally, we calculate the spin configurations and root mean square radii of these states, providing insight into their spatial structures. No bound or resonant states are found in the trilepton <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>e</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></math> systems, nor in the tetralepton <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>e</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> system. A comparison with fully heavy tetraquark systems reveals that the additional color degree of freedom in QCD results in the absence of low-energy bound and resonant states. However, this extra degree of freedom allows for a broader range of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi><mi>C</mi></mrow></msup></mrow></math> quantum numbers to produce resonant states, highlighting the rich complexity of QCD systems.

Trilepton and tetralepton bound and resonant states: The QED counterpart of multiquark states

We calculate the electromagnetic polarizabilities of the spin-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mfrac><mn>1</mn><mn>2</mn></mfrac></math> singly heavy baryons in the heavy baryon chiral perturbation theory up to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mi>p</mi><mn>3</mn></msup><mo stretchy="false">)</mo></math>. We estimate the low-energy constants using the magnetic moments of singly charmed baryons from lattice QCD simulations and the experimental decay widths of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Σ</mi><mi>c</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Σ</mi><mi>c</mi><mo>*</mo></msubsup></math>. Our results indicate that the long-range chiral corrections make significant contributions to the polarizabilities. Additionally, the magnetic dipole transitions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="script">B</mi><mn>6</mn><mo>*</mo></msubsup><mo stretchy="false">→</mo><msub><mi mathvariant="script">B</mi><mn>6</mn></msub><mo>+</mo><mi>γ</mi></math> also provide large contribution to the magnetic polarizabilities.

Electromagnetic polarizabilities of the spin-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mfrac><mn>1</mn><mn>2</mn></mfrac></math> singly heavy baryons in heavy baryon chiral perturbation theory

Levin-Wen string-net models provide a construction of (2+1)D topologically ordered phases of matter with anyonic localized excitations described by the Drinfeld center of a unitary fusion category. Anyon condensation is a mechanism for phase transitions between (2+1)D topologically ordered phases. We construct an extension of Levin-Wen models in which tuning a parameter implements anyon condensation. We also describe the classification of anyons in Levin-Wen models via representation theory of the tube algebra, and use a variant of the tube algebra to classify low-energy localized excitations in the condensed phase.

United States

Jessica Christian

David Green

Peter Huston

David Penneys

A lattice model for condensation in Levin-Wen systems

A realistic material may possess defects, which often bring the material new properties that have practical applications. The boundary defects of a two-dimensional topologically ordered system are thought of as an alternative way of realizing topological quantum computation. To facilitate the study of such boundary defects, in this paper, we construct an exactly solvable Hamiltonian model of topological orders with gapped boundary junctions, where the boundary defects reside, by placing the Levin-Wen model on a disk, whose gapped boundary is separated into multiple segments by junctions. We derive a formula of the ground state degeneracy and an explicit ground-state basis of our model. We propose the notion of mobile and immobile charges on the boundary and find that they are quantum observables and label the ground-state basis. Our model is computation friendly.