<p>In this work, the soft rescattering parameters in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>±</mo></msup><mo stretchy="false">→</mo><msup><mi>π</mi><mo>±</mo></msup><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>±</mo></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mo>±</mo></msup><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> decays with the light scalar meson <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>500</mn><mo stretchy="false">)</mo></math> as the intermediate resonance are studied within the quantum chromodynamics (QCD) factorization. Considering the interference effect between <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi><mo stretchy="false">(</mo><mn>770</mn><msup><mo stretchy="false">)</mo><mn>0</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>500</mn><mo stretchy="false">)</mo></math>, we utilize the experimentally more direct event yields for fitting and get the soft rescattering parameters <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msubsup><mi>ρ</mi><mi>k</mi><mrow><mi>S</mi><mi>P</mi></mrow></msubsup><mo stretchy="false">|</mo><mo>=</mo><mn>3.29</mn><mo>±</mo><mn>1.01</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msubsup><mi>ρ</mi><mi>k</mi><mrow><mi>P</mi><mi>S</mi></mrow></msubsup><mo stretchy="false">|</mo><mo>=</mo><mn>2.33</mn><mo>±</mo><mn>0.73</mn></math> in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>P</mi><mi>S</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>S</mi><mi>P</mi></math> decays (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math> denote pseudoscalar and scalar mesons, respectively), respectively. We also study the branching ratios and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetries in the decay modes involving other scalar mesons, including <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>1450</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>1430</mn><mo stretchy="false">)</mo></math>, to test the rationality of the values of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msubsup><mi>ρ</mi><mi>k</mi><mrow><mi>S</mi><mi>P</mi></mrow></msubsup><mo stretchy="false">|</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msubsup><mi>ρ</mi><mi>k</mi><mrow><mi>P</mi><mi>S</mi></mrow></msubsup><mo stretchy="false">|</mo></math>. Meanwhile, the wealth of experimental data facilitate the examination of the forward-backward asymmetry induced <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetries (FB-CPAs), and the localized <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetries (LACPs). We investigate these asymmetries resulting from the interference between <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi><mo stretchy="false">(</mo><mn>770</mn><msup><mo stretchy="false">)</mo><mn>0</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>500</mn><mo stretchy="false">)</mo></math> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>±</mo></msup><mo stretchy="false">→</mo><msup><mi>π</mi><mo>±</mo></msup><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>±</mo></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mo>±</mo></msup><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> decays when the invariant mass of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> locates in the low-energy region <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0.445</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>&lt;</mo><msub><mi>m</mi><mrow><mi>π</mi><mi>π</mi></mrow></msub><mo>&lt;</mo><mn>0.795</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>. Our theoretical results of FB-CPAs and LACPs align with the experimental findings. We propose that the interference between <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi><mo stretchy="false">(</mo><mn>770</mn><msup><mo stretchy="false">)</mo><mn>0</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>500</mn><mo stretchy="false">)</mo></math> can be extended to other beauty and charmed mesons decays.</p>

China

Jing-Juan Qi

Zhen-Yang Wang

Zhen-Hua Zhang

Ke-Wei Wei

Xin-Heng Guo

Probing the soft rescattering parameters in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> decays involving a scalar meson with QCD factorization

The mass and decay of the \(s\bar {s}\) member of the \(1^{3}F_{4}\) meson nonet are investigated in the framework of the Regge phenomenology and the \(^{3}P_{0}\) model. We propose, based on the results, that the assignment of the \(s\bar {s}\) member of the \(1^{3}F_{4}\) meson nonet will require additional testing in the future. Our results also provide information for future studies of the \(1^{3}F_{4}\) meson nonet.

Xue-Chao Feng

Mass and Decay of the \(s\bar {s}\) Member of the 1\(^{3}F_{4}\) Meson Nonet

In this work, we investigate the mass spectrum of \(1^{1}D_{2}\) and \(1^{3}D_{2}\) meson nonets in the framework of the meson mass matrix and Regge phenomenology. The results are compared with the values from different phenomenological models and may be useful for the assignment of the \(1^{1}D_{2}\) and \(1^{3}D_{2}\) meson nonets in the future.

Jie Wu

Xue-Zhen Zhai

Shi-Zhuo Wang

Towards the Assignments for \(1^{1}D_{2}\) and \(1^{3}D_{2}\) Meson Nonets

Based on the relations from the meson–meson mass mixing matrix, the mixing angles of the isoscalar state have been re-evaluated via mass relations and the latest experimental results. The results in the present work are compared with the values from different theoretical models and the quarkonia content of the isoscalar state is presented. In order to check the validity of the analysis, some predictions on the decays of the isoscalar state are presented. These predictions may be useful for the phenomenological analysis for meson nonet in future experiments.

Re-evaluation of the Isoscalar Mixing Angle within Selected Mesonic Nonets

The dynamical similarity which exists between the <math><mi>λ</mi></math>-mode excited <math><mi>b</mi><mi>b</mi><mi>q</mi></math> baryons (<math><mi>q</mi></math> refers to the <math><mi>u</mi></math>, <math><mi>d</mi></math>, and <math><mi>s</mi></math> quarks) and the <math><mover><mi>b</mi><mo>¯</mo></mover><mi>q</mi></math> mesons inspires us to carry out a combined study of their spectroscopy. In this work, the masses and strong decays of these low-lying <math><mi>b</mi><mover><mi>q</mi><mo>¯</mo></mover></math> and <math><mi>b</mi><mi>b</mi><mi>q</mi></math> states are studied by the same theoretical methods, and the dynamical similarity which is implied in their mass spectra and strong decays are also discussed. The recent discovered <math><mover><mi>b</mi><mo>¯</mo></mover><mi>q</mi></math> states, including the <math><msub><mi>B</mi><mi>J</mi></msub><mo>(</mo><mn>5840</mn><mo>)</mo></math>, <math><msub><mi>B</mi><mi>J</mi></msub><mo>(</mo><mn>5970</mn><mo>)</mo></math>, <math><msub><mi>B</mi><mrow><mi>s</mi><mi>J</mi></mrow></msub><mo>(</mo><mn>6064</mn><mo>)</mo></math>, and <math><msub><mi>B</mi><mrow><mi>s</mi><mi>J</mi></mrow></msub><mo>(</mo><mn>6114</mn><mo>)</mo></math>, are analyzed. According to our result, the <math><msub><mi>B</mi><mi>J</mi></msub><mo>(</mo><mn>5840</mn><mo>)</mo></math> could be assigned as a <math><mrow><mn>2</mn><mi>S</mi></mrow></math> state, while the <math><msub><mi>B</mi><mi>J</mi></msub><mo>(</mo><mn>5970</mn><mo>)</mo></math> could be regarded as a member of the <math><mn>1</mn><mi>D</mi><mo>(</mo><msup><mn>2</mn><mo>−</mo></msup><mo>,</mo><msup><mn>3</mn><mo>−</mo></msup><msub><mo>)</mo><mrow><msub><mi>j</mi><mi>q</mi></msub><mo>=</mo><mn>5</mn><mo>/</mo><mn>2</mn></mrow></msub></math> doublet. The <math><msub><mi>B</mi><mrow><mi>s</mi><mi>J</mi></mrow></msub><mo>(</mo><mn>6064</mn><mo>)</mo></math> and <math><msub><mi>B</mi><mrow><mi>s</mi><mi>J</mi></mrow></msub><mo>(</mo><mn>6114</mn><mo>)</mo></math> are probably the <math><mi>D</mi></math>-wave states. Especially, they could be explained as the members of the <math><mn>1</mn><mi>D</mi><mo>(</mo><msup><mn>1</mn><mo>−</mo></msup><mo>,</mo><msup><mn>2</mn><mo>−</mo></msup><msub><mo>)</mo><mrow><msub><mi>j</mi><mi>q</mi></msub><mo>=</mo><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msub></math> and <math><mn>1</mn><mi>D</mi><mo>(</mo><msup><mn>2</mn><mo>−</mo></msup><mo>,</mo><msup><mn>3</mn><mo>−</mo></msup><msub><mo>)</mo><mrow><msub><mi>j</mi><mi>q</mi></msub><mo>=</mo><mn>5</mn><mo>/</mo><mn>2</mn></mrow></msub></math> doublets, respectively. The predicted masses and decay properties of other unknown <math><mover><mi>b</mi><mo>¯</mo></mover><mi>q</mi><mo>/</mo><mi>b</mi><mi>b</mi><mi>q</mi></math> states may provide useful clues to the future experiment.

Bing Chen

Si-Qiang Luo

Xiang Liu

<math><mi>b</mi></math>-hadron spectroscopy study based on the similarity of double bottom baryon and bottom meson

It is believed that there are more fundamental gauge symmetries beyond those described by the Standard Model of particle physics. The scales of these new gauge symmetries are usually too high to be reachable by particle colliders. Considering that the phase transition (PT) relating to the spontaneous breaking of new gauge symmetries to the electroweak symmetry might be strongly first order, we propose considering the stochastic gravitational waves (GW) arising from this phase transition as an indirect way of detecting these new fundamental gauge symmetries. As an illustration, we explore the possibility of detecting the stochastic GW generated from the PT of 
					 in the space-based interferometer detectors. Our study demonstrates that the GW energy spectrum is reachable by the LISA, Tianqin, Taiji, BBO, and DECIGO experiments only for the case where the spontaneous breaking of 
					 is triggered by at least two electroweak singlet scalars.
				

Wei Chao

Wen-Feng Cui

Huai-Ke Guo

Jing Shu

Gravitational wave imprint of new symmetry breaking JS is Supported by the National Natural Science Foundation of China (11647601, 11690022, 11675243) and also Supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB23030100). Wei Chao is Supported by the National Natural Science Foundation of China (11775025)

Selecting the newly observed <math><msub><mi>Ξ</mi><mi>b</mi></msub><mo>(</mo><mn>6227</mn><msup><mo>)</mo><mo>−</mo></msup></math> by LHCb as a study example, we decode its inner structure by giving the mass spectrum analysis and the investigation of its two-body strong decay behaviors. Our result indicates that the <math><msub><mi>Ξ</mi><mi>b</mi></msub><mo>(</mo><mn>6227</mn><msup><mo>)</mo><mo>−</mo></msup></math> is a good candidate of the <math><mi>P</mi></math>-wave <math><msubsup><mi>Ξ</mi><mi>b</mi><mo>′</mo></msubsup></math> state with <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> or <math><mn>5</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math>. In addition, we further provide the information of the properties of the partners of the <math><msub><mi>Ξ</mi><mi>b</mi></msub><mo>(</mo><mn>6227</mn><msup><mo>)</mo><mo>−</mo></msup></math>. These predicted states include three <math><mn>2</mn><mi>S</mi></math> states and the remaining <math><mn>1</mn><mi>P</mi></math> states in the bottom-strange baryon family. The calculated sizable Okubo-Zweig-Iizuka–allowed decay widths of these partners show that the experimental search for them becomes possible via LHCb. We have a reason to believe that the present study can be treated as a start point for constructing the highly excited bottom baryon spectroscopy.

Ailin Zhang

Role of newly discovered <math><mrow><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>(</mo><mn>6227</mn><msup><mrow><mo>)</mo></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> for constructing excited bottom baryon family

Up to now, the excited charmed and bottom baryon states have still not been well studied experimentally or theoretically. In this paper, we predict the mass of , the only L = 0 baryon state which has not been observed, to be 6069.2 MeV. The spectra of charmed and bottom baryons with the orbital angular momentum L = 1 are studied in two popular constituent quark models, the Goldstone boson exchange (GBE) model and the one gluon exchange (OGE) hyperfine interaction model. Inserting the latest experimental data from the “Review of Particle Physics", we find that in the GBE model, there exist some multiplets (Σc(b), and Ωc(b)) in which the total spin of the three quarks in their lowest energy states is 3/2, but in the OGE model there is no such phenomenon. This is the most important difference between the GBE and OGE models. These results can be tested in the near future. We suggest more efforts to study the excited charmed and bottom baryons both theoretically and experimentally, not only for the abundance of baryon spectra, but also for determining which hyperfine interaction model best describes nature.

Spectra of charmed and bottom baryons with hyperfine interactionSupported by National Natural Science Foundation of China (11175020, 11575023, U1204115)

In this work, we systematically study the mass spectra and strong decays of 1 P and 2 S charmed and charmed-strange baryons in the framework of non-relativistic constituent quark models. With the light quark cluster–heavy quark picture, the masses are simply calculated by a potential model. The strong decays are studied by the Eichten–Hill–Quigg decay formula. Masses and decay properties of the well-established 1 S and 1 P states can be reproduced by our method. Σc(2800)0,+,++ can be assigned as a Σc2(3/2-) or Σc2(5/2-) state. We prefer to interpret the signal Σc(2850)0 as a 2S(1/2+) state although at present we cannot thoroughly exclude the possibility that this is the same state as Σc(2800)0 . Λc(2765)+ or Σc(2765)+ could be explained as the Λc+(2S) state or Σc1+(1/2-) state, respectively. We propose to measure the branching ratio of B(Σc(2455)π)/B(Σc(2520)π) in the future, which may disentangle the puzzle of this state. Our results support Ξc(2980)0,+ as the first radial excited state of Ξc(2470)0,+ with JP=1/2+ . The assignment of Ξc(2930)0 is analogous to Σc(2800)0,+,++ , i.e., a Ξc2′(3/2-) or Ξc2′(5/2-) state. In addition, we predict some typical ratios among partial decay widths, which are valuable for experimental search for these missing charmed and charmed-strange baryons.

Japan

Takayuki Matsuki

Low-lying charmed and charmed-strange baryon states

The spin is an important property of a particle. Although it is unlikely, there is still a possibility that two particles with different spins share similar masses. In this paper, we propose a method to probe this kind of mass degeneracy of particles with different spins. We use the cascade decay B+→X(3872)K+, X(3872)→D+D− to illustrate our method. It can be seen that the possible mass degeneracy of X(3872) can lead to interesting behavior in the corresponding cascade decay.

Gang Lü

Probing the mass degeneracy of particles with different spinsSupported by National Natural Science Foundation of China (11347124, 11147003, U1204115), Doctoral Scientific Research Foundation of USC, and Innovation Team of Nuclear and Particle Physics of USC