Abstract The open N = 2 string theory is defined on the 4D space-time with the split signature (+, +, −, −). The string field theory action of the open N = 2 string theory is described by the 4D Wess–Zumino–Witten (WZW$_{4}$) model. The equation of motion of the WZW$_{4}$ model is the Yang equation, which is equivalent to the anti-self-dual Yang–Mills equation. In this paper, we study soliton-type classical solutions of the WZW$_{4}$ model in the split signature by calculating the action density of the WZW$_{4}$ model. We find that the action density of the one-soliton solutions is localized on a 3D hyperplane. This shows that there would be codimension-one-solitonic objects, or equivalently some kind of three-branes in the open N = 2 string theory. We also prove that, in the asymptotic region of the space-time, the action density of the n-soliton solutions is a “non-linear superposition” of n one-solitons. This suggests the existence of n intersecting three-branes in the N = 2 strings. Finally we make a reduction to a (1 + 2)D real space-time to calculate the energy densities of the soliton solutions. We can successfully evaluate the energy distribution for the two-soliton solutions and find that there is no singularity in the interacting region. This implies the existence of smooth intersecting codimension-one branes in the whole region. Soliton solutions in the Euclidean signature are also discussed.

Japan

Masashi Hamanaka

Shan-Chi Huang

Hiroaki Kanno

Solitons in open = 2 String Theory Kahler-Chen-Simons theory A tour through N=2 strings On soliton solutions of the anti-self-dual Yang-Mills equations from the perspective of integrable systems Soliton solutions in an integrable chiral model in 2+1 dimensions On the space-time monopole equation A review on tachyon condensation in open string field theories Soliton equations as dynamical systems on infinite dimensional Grassmann manifold

We use the spectral lag catalog of 46 short GRBs aggregated by Xiao et al. (Astrophys J Lett 924:L29, 2022), to carry out an independent search for Lorentz invariance violation (LIV). For this purpose, we use a power-law model as a function of energy for the intrinsic astrophysical induced spectral lags. The expansion history of the universe needed for constraining LIV was obtained in a non-parametric method using cosmic chronometers. We use Bayesian model comparison to determine if the aforementioned spectral lags show evidence for LIV as compared to only astrophysically induced lags. We do not find any evidence for LIV, and obtain 95% CL lower limits on the corresponding energy scale to be  $$4 \times 10^{15}$$  <math> <mrow> <mn>4</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>15</mn> </msup> </mrow> </math>   GeV and  $$6.8 \times 10^{9}$$  <math> <mrow> <mn>6.8</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>9</mn> </msup> </mrow> </math>   GeV for the linear and quadratic LIV models respectively. Our results obtained by using the flat  $$\Lambda $$  <math> <mi>Λ</mi> </math>  CDM model for characterizing the cosmic expansion history are consistent with those obtained using chronometers.

India

Shantanu Desai

Rajdeep Agrawal

Germany

Haveesh Singirikonda

Search for Lorentz invariance violation using Bayesian model comparison applied to Xiao et al. GRB spectral lag catalog

In this work, we systematically study the mass spectrum of the fully heavy tetraquark in an extended chromomagnetic model, which includes both color and chromomagnetic interactions. Numerical results indicate that the energy level is mainly determined by the color interaction, which favors the color-sextet <math><mrow><mo>|</mo><mo>(</mo><mi>Q</mi><mi>Q</mi><msup><mrow><mo>)</mo></mrow><mrow><msub><mrow><mn>6</mn></mrow><mrow><mi>c</mi></mrow></msub></mrow></msup><mo>(</mo><mover><mrow><mi>Q</mi></mrow><mrow><mo>¯</mo></mrow></mover><mover><mrow><mi>Q</mi></mrow><mrow><mo>¯</mo></mrow></mover><msup><mrow><mo>)</mo></mrow><mrow><msub><mrow><mover><mrow><mn>6</mn></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>c</mi></mrow></msub></mrow></msup><mo>⟩</mo></mrow></math> configuration over the color-triplet <math><mrow><mo>|</mo><mo>(</mo><mi>Q</mi><mi>Q</mi><msup><mrow><mo>)</mo></mrow><mrow><msub><mrow><mover><mrow><mn>3</mn></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>c</mi></mrow></msub></mrow></msup><mo>(</mo><mover><mrow><mi>Q</mi></mrow><mrow><mo>¯</mo></mrow></mover><mover><mrow><mi>Q</mi></mrow><mrow><mo>¯</mo></mrow></mover><msup><mrow><mo>)</mo></mrow><mrow><msub><mrow><mn>3</mn></mrow><mrow><mi>c</mi></mrow></msub></mrow></msup><mo>⟩</mo></mrow></math> one. The chromomagnetic interaction mixes the two color configurations and gives small splitting. The ground state is always dominated by the color-sextet configuration. We find no stable state below the lowest heavy quarkonium pair thresholds. Most states may be wide since they have at least one <math><mi>S</mi></math>-wave decay channel into two <math><mi>S</mi></math>-wave mesons. One possible narrow state is the <math><mrow><msup><mrow><mn>1</mn></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> <math><mrow><mi>b</mi><mi>b</mi><mover><mrow><mi>b</mi></mrow><mrow><mo>¯</mo></mrow></mover><mover><mrow><mi>c</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> state with a mass 15719.1 MeV. It is just above the <math><msub><mi>η</mi><mi>b</mi></msub><msub><mover><mi>B</mi><mo>¯</mo></mover><mi>c</mi></msub></math> threshold. But this channel is forbidden because of the conservation of the angular momentum and parity.

China

Xin-Zhen Weng

Xiao-Lin Chen

Wei-Zhen Deng

Shi-Lin Zhu

Systematics of fully heavy tetraquarks

Employing the relativized quark model and the quark-interchange model, we investigate the decay of the charged heavy quarkonium-like states $$Z_c(3900)$$ <math><mrow><msub><mi>Z</mi><mi>c</mi></msub><mrow><mo>(</mo><mn>3900</mn><mo>)</mo></mrow></mrow></math> , $$Z_c(4020)$$ <math><mrow><msub><mi>Z</mi><mi>c</mi></msub><mrow><mo>(</mo><mn>4020</mn><mo>)</mo></mrow></mrow></math> , $$Z_c(4430)$$ <math><mrow><msub><mi>Z</mi><mi>c</mi></msub><mrow><mo>(</mo><mn>4430</mn><mo>)</mo></mrow></mrow></math> , $$Z_b(10610)$$ <math><mrow><msub><mi>Z</mi><mi>b</mi></msub><mrow><mo>(</mo><mn>10610</mn><mo>)</mo></mrow></mrow></math>  and $$Z_b(10650)$$ <math><mrow><msub><mi>Z</mi><mi>b</mi></msub><mrow><mo>(</mo><mn>10650</mn><mo>)</mo></mrow></mrow></math>  into the ground and radially excited heavy quarkonia via emitting a pion meson. The $$Z_c$$ <math><msub><mi>Z</mi><mi>c</mi></msub></math>  and $$Z_b$$ <math><msub><mi>Z</mi><mi>b</mi></msub></math>  states are assumed to be hadronic molecules composed of open-flavor heavy mesons. The calculated decay ratios can be compared with the experimental data, which are useful in judging whether the molecule state assignment for the corresponding $$Z_c$$ <math><msub><mi>Z</mi><mi>c</mi></msub></math>  or $$Z_b$$ <math><msub><mi>Z</mi><mi>b</mi></msub></math>  state is reasonable or not. The theoretical framework constructed in this work will be helpful in revealing the underlying structures of some exotic hadrons.

Guang-Juan Wang

Xiao-Hai Liu

Li Ma

Xiang Liu

The strong decay patterns of $$Z_c$$ <math><msub><mi>Z</mi><mi>c</mi></msub></math>  and $$Z_b$$ <math><msub><mi>Z</mi><mi>b</mi></msub></math>  states in the relativized quark model

Recently, the LHCb Collaboration reported three <math><msub><mi>P</mi><mi>c</mi></msub></math> states in the <math><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow><mi>p</mi></math> channel. We systematically study the mass spectrum of the hidden charm pentaquark in the framework of an extended chromomagnetic model. For the <math><mi>n</mi><mi>n</mi><mi>n</mi><mi>c</mi><mover><mi>c</mi><mo>¯</mo></mover></math> pentaquark with <math><mi>I</mi><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn></math>, we find that (i) the lowest state is <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4327.0</mn><mo>,</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo>)</mo></math> [We use <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mi>m</mi><mo>,</mo><mi>I</mi><mo>,</mo><msup><mi>J</mi><mi>P</mi></msup><mo>)</mo></math> to denote the <math><mi>n</mi><mi>n</mi><mi>n</mi><mi>c</mi><mover><mi>c</mi><mo>¯</mo></mover></math> pentaquark], which corresponds to the <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4312</mn><mo>)</mo></math>. Its dominant decay mode is <math><msub><mi>Λ</mi><mi>c</mi></msub><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></math>. (ii) We find two states in the vicinity of <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4380</mn><mo>)</mo></math>. The first one is <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4367.4</mn><mo>,</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo>)</mo></math> and decays dominantly to <math><mi>N</mi><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> and <math><msub><mi>Λ</mi><mi>c</mi></msub><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></math>. The other one is <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4372.4</mn><mo>,</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo>)</mo></math>. Its dominant decay mode is <math><msub><mi>Λ</mi><mi>c</mi></msub><mover><mi>D</mi><mo>¯</mo></mover></math>, and its partial decay width of <math><mi>N</mi><msub><mi>η</mi><mi>c</mi></msub></math> channel is comparable to that of <math><mi>N</mi><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math>. (iii) In higher mass region, we find <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4476.3</mn><mo>,</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo>)</mo></math> and <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4480.9</mn><mo>,</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo>)</mo></math>, which correspond to <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4440</mn><mo>)</mo></math> and <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4457</mn><mo>)</mo></math>. In the open charm channels, both of them decay dominantly to the <math><msub><mi>Λ</mi><mi>c</mi></msub><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></math>. (iv) We predict two states above 4.5 GeV, namely <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4524.5</mn><mo>,</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo>)</mo></math> and <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4546.0</mn><mo>,</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo>)</mo></math>. The masses of the <math><mi>n</mi><mi>n</mi><mi>n</mi><mi>c</mi><mover><mi>c</mi><mo>¯</mo></mover></math> state with <math><mi>I</mi><mo>=</mo><mn>3</mn><mo>/</mo><mn>2</mn></math> are all over 4.6 GeV. Moreover, we use the model to explore the <math><mi>n</mi><mi>n</mi><mi>s</mi><mi>c</mi><mover><mi>c</mi><mo>¯</mo></mover></math>, <math><mi>s</mi><mi>s</mi><mi>n</mi><mi>c</mi><mover><mi>c</mi><mo>¯</mo></mover></math>, and <math><mi>s</mi><mi>s</mi><mi>s</mi><mi>c</mi><mover><mi>c</mi><mo>¯</mo></mover></math> pentaquark states.

Hidden-charm pentaquarks and <math><mrow><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></math> states

In the present work, we study the Okubo-Zweig-Iizuka-allowed three body open flavor decay properties of higher vector charmonium and bottomonium states with an extended quark pair creation model. For the bottomonium system, we get that (i) the <math><mi>B</mi><mi>B</mi><mi>π</mi></math> and <math><mrow><msup><mrow><mi>B</mi></mrow><mrow><mo>*</mo></mrow></msup><msup><mrow><mi>B</mi></mrow><mrow><mo>*</mo></mrow></msup><mi>π</mi></mrow></math> partial decay widths of the <math><mrow><mi>ϒ</mi><mo>(</mo><mn>10860</mn><mo>)</mo></mrow></math> state are consistent with the experiment, and the <math><mi>B</mi><msup><mi>B</mi><mo>*</mo></msup><mi>π</mi></math> partial decay width of the <math><mi>ϒ</mi><mo>(</mo><mn>10860</mn><mo>)</mo></math> state is smaller but very close to Belle’s experiment. Meanwhile, (ii) the <math><mi>B</mi><msup><mi>B</mi><mo>*</mo></msup><mi>π</mi></math> and <math><msup><mi>B</mi><mo>*</mo></msup><msup><mi>B</mi><mo>*</mo></msup><mi>π</mi></math> decay widths of <math><mi>ϒ</mi><mo>(</mo><mn>11020</mn><mo>)</mo></math> can reach 2–3 MeV. In addition, (iii) for most of the higher vector charmonium states, the partial decay widths of the <math><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup><mi>π</mi></math> and <math><msup><mi>D</mi><mo>*</mo></msup><msup><mi>D</mi><mo>*</mo></msup><mi>π</mi></math> modes can reach up to several MeV, which may be observed in future experiments.

Li-Ye Xiao

Three body open flavor decays of higher charmonium and bottomonium

We have systematically investigated the decuplet (T) to octet (B) baryon ($$T\rightarrow B\gamma $$ <math><mrow><mi>T</mi><mo>→</mo><mi>B</mi><mi>γ</mi></mrow></math> ) transition magnetic moments to the next-to-next-to-leading order and electric quadruple moments to the next-to-leading order in the framework of the heavy baryon chiral perturbation theory. Our calculation includes the contributions from both the intermediate decuplet and octet baryon states in the loops. Throughout our calculation, we have adopted the small-scale scheme and have not considered the 1/M recoiling corrections directly. We count the octet and decuplet baryon mass splitting $$\delta $$ <math><mi>δ</mi></math> , the small momenta p, and the pion mass $$m_{\phi }$$ <math><msub><mi>m</mi><mi>ϕ</mi></msub></math>  as the same order small-scale parameter, which was denoted as $$\epsilon $$ <math><mi>ϵ</mi></math> . Our results for the transition magnetic moments show reasonably good convergence of the chiral expansion. The analytical expressions may be useful to the chiral extrapolation of the lattice simulations of the decuplet electromagnetic properties.

Hao-Song Li

Zhan-Wei Liu

Decuplet to octet baryon transitions in chiral perturbation theory

We extend the chromomagnetic model by further considering the effect of color interaction. The effective mass parameters between quark pairs (<math><msub><mi>m</mi><mrow><mi>q</mi><mi>q</mi></mrow></msub></math> or <math><msub><mi>m</mi><mrow><mi>q</mi><mover><mi>q</mi><mo>¯</mo></mover></mrow></msub></math>) are introduced to account for both the effective quark masses and the color interaction between the two quarks. Using the experimental masses of hadrons, the quark pair parameters are determined between the light quark pairs and the light-heavy quark pairs. Then the parameters of heavy quark pairs (<math><mi>c</mi><mi>c</mi></math>, <math><mi>c</mi><mi>b</mi></math>, <math><mi>b</mi><mi>b</mi></math>) are estimated based on simple quark model assumption. We calculate all masses of doubly and triply heavy-quark baryons. The newly discovered doubly charmed baryon <math><msub><mi>Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> fits into the model with an error of 12 MeV.

Masses of doubly heavy-quark baryons in an extended chromomagnetic model

In the present paper, the exact solutions of spherically symmetrical Einstein field equations describing wormholes supported by phantom energy that violates the null energy condition from Shan–Chen background fluid are obtained. We have considered the important case of the model parameter ψ≈1 , which corresponds to the “saturation effect”, and this regime corresponds to an effective form of “asymptotic freedom” for the fluids, but occurring at cosmological rather than subnuclear scales. Then we investigate the allowed range for the values of the model parameters g and ω when the spacetime metrics describe wormholes and discuss the possible singularities of the solutions, finding that the obtained spacetimes are geodesically complete. Furthermore, we construct two traversable wormholes through matching our obtained interior solutions to the exterior Schwarzschild solutions and analyze the traversablities of the wormholes. Finally, we consider the case of anisotropic pressure and discover that the transverse pressure also crosses the phantom divide -1 with the growth of the wormhole dimension, and it tends to be the same as the radial pressure with the growth of the wormhole radius.

Deng Wang

Xin-He Meng

Wormholes supported by phantom energy from Shan–Chen cosmological fluids

Compared with the charmed baryons, the bottom baryons are not very well known, either experimentally or theoretically. In this paper, we investigate the dipion strong decays of the P-wave and D-wave excited bottom baryons in the framework of the QPC model. We also extend the same analysis to the charmed baryons.