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].

China

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

The production of heavy-quark (HQ) jets is a new area that addresses the mass effect of jet quenching in heavy-ion physics. This paper presents a theoretical study of HQ jet yield suppression in Pb+Pb collisions at the Large Hadron Collider (LHC) and focuses on the energy loss of HQ jets produced by different mechanisms. The $\textit{p+p}$ baseline is provided by the generator simulation of high-energy reactions of particles (SHERPA), and the jet-medium interactions are described by the SHELL transport model, which considers the elastic and inelastic partonic energy loss in the quark-gluon plasma (QGP). In $\textit{p+p}$ collisions, our numerical results indicate that the HQ jets from gluon splitting ( $ g \rightarrow Q $ -jet) are the dominant contribution at high $ p_T $ , displaying more dispersive structures than the HQ-initiated ( $ Q \rightarrow Q $ -jet). In nucleus-nucleus collisions, our calculations were consistent with the inclusive and b-jet $ R_{AA} $ recently measured by the ATLAS collaboration, revealing a remarkable manifestation of the mass effect of jet energy loss. As a result of the dispersive substructure, the $ g \rightarrow Q $ -jet loses more energy than the $ Q \rightarrow Q $ -jet in the QGP. Due to the significant contribution of $ g \rightarrow c $ -jet, the $ R_{AA} $ of $\textit{c}$-jet is comparable or even smaller than that of inclusive jet. To experimentally distinguish the $ g \rightarrow Q $ -jet and $ Q \rightarrow Q $ -jet, we propose event selection strategies based on their topological features and test their performances. By isolating the $ c \rightarrow c $ -jet, $ b \rightarrow b $ -jet, and the jets initiated by heavy quarks, we predicted that the order of their $ R_{AA} $ are in line with the mass hierarchy of energy loss. Future measurements on the $ R_{AA} $ of $ Q \rightarrow Q $ -jet and $ g \rightarrow Q $ -jet will provide a unique opportunity for testing the flavor/mass dependence of energy loss at the jet level.

Sa Wang

Shuang Li

Yao Li

Ben-Wei Zhang

Enke Wang

Probing the mass effect of heavy quark jets in high-energy nuclear collisions * Supported by the MajorProject of Basic and Applied Basic Research of Guangdong Province, China (2020B0301030008, 2023A1515011460), and the National Natural Science Foundation of China (11935007, 12035007, 12247127, 12375137). Sa Wang is supported by the Open Foundation of Key Laboratory of Quark and Lepton Physics (MOE) (QLPL2023P01) and the Talent Scientific Star-up Foundation of the China Three Gorges University, China (CTGU) (2024RCKJ013)

Very recently, the Belle II collaboration presented a measurement for the decays <math><msup><mi>B</mi><mo>+</mo></msup><mo>→</mo><msup><mover><mi>D</mi><mo>¯</mo></mover><mrow><mo>(</mo><mo>*</mo><mo>)</mo><mn>0</mn></mrow></msup><msup><mi>K</mi><mo>+</mo></msup><msup><mover><mi>K</mi><mo>¯</mo></mover><mn>0</mn></msup></math> and <math><msup><mi>B</mi><mn>0</mn></msup><mo>→</mo><msup><mi>D</mi><mrow><mo>(</mo><mo>*</mo><mo>)</mo><mo>−</mo></mrow></msup><msup><mi>K</mi><mo>+</mo></msup><msup><mover><mi>K</mi><mo>¯</mo></mover><mn>0</mn></msup></math>, with the bulk of observed <math><mi>m</mi><mo>(</mo><msup><mi>K</mi><mo>+</mo></msup><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><mo>)</mo></math> distributions showing low-mass structures in all four channels. In this work, we study the contributions of <math><mi>ρ</mi><mo>(</mo><mn>770</mn><mo>,</mo><mn>1450</mn><msup><mo>)</mo><mo>+</mo></msup></math>, <math><msub><mi>a</mi><mn>2</mn></msub><mo>(</mo><mn>1320</mn><msup><mo>)</mo><mo>+</mo></msup></math>, and <math><msub><mi>a</mi><mn>0</mn></msub><mo>(</mo><mn>980</mn><mo>,</mo><mn>1450</mn><msup><mo>)</mo><mo>+</mo></msup></math> resonances to these decay processes. The intermediate states <math><mi>ρ</mi><mo>(</mo><mn>770</mn><mo>,</mo><mn>1450</mn><msup><mo>)</mo><mo>+</mo></msup></math> are found to dominate the low-mass distribution of kaon pairs roughly contributing to half of the total branching fraction in each of the four decay channels. The contribution of the tensor <math><msub><mi>a</mi><mn>2</mn></msub><mo>(</mo><mn>1320</mn><msup><mo>)</mo><mo>+</mo></msup></math> meson is found to be negligible. Near the threshold of the kaon pair, the state <math><msub><mi>a</mi><mn>0</mn></msub><mo>(</mo><mn>980</mn><msup><mo>)</mo><mo>+</mo></msup></math> turns out to be much less important than expected, not being able to account for the enhancement of events in that energy region observed in the <math><msup><mi>B</mi><mo>+</mo></msup><mo>→</mo><msup><mover><mi>D</mi><mo>¯</mo></mover><mrow><mo>(</mo><mo>*</mo><mo>)</mo><mn>0</mn></mrow></msup><msup><mi>K</mi><mo>+</mo></msup><msup><mover><mi>K</mi><mo>¯</mo></mover><mn>0</mn></msup></math> decays. Further studies both from the theoretical and experimental sides are needed to elucidate the role of the nonresonant contributions governing the formation of <math><msup><mi>K</mi><mo>+</mo></msup><msup><mover><mi>K</mi><mo>¯</mo></mover><mn>0</mn></msup></math> pairs near their threshold in these decay processes.

Spain

Wen-Fei Wang

Li-Fei Yang

Ai-Jun Ma

Àngels Ramos

Low-mass enhancement of kaon pairs in <math><mrow><msup><mrow><mi>B</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>→</mo><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>(</mo><mo>*</mo><mo>)</mo><mn>0</mn></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> and <math><mrow><msup><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msup><mo>→</mo><msup><mrow><mi>D</mi></mrow><mrow><mo>(</mo><mo>*</mo><mo>)</mo><mo>−</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> decays

We study the contributions for <math><mi>K</mi><msup><mi>η</mi><mo>′</mo></msup></math> pair originating from the scalar intermediate state <math><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo>(</mo><mn>1430</mn><mo>)</mo></math> in the three-body decays <math><mi>B</mi><mo>→</mo><mi>K</mi><msup><mi>η</mi><mo>′</mo></msup><mi>h</mi></math> (<math><mrow><mi>h</mi><mo>=</mo><mi>π</mi></mrow></math>, <math><mrow><mi>K</mi></mrow></math>) within the perturbative QCD approach. The contribution of <math><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo>(</mo><mn>1430</mn><mo>)</mo><mo>→</mo><mi>K</mi><msup><mi>η</mi><mo>′</mo></msup></math> is described by the Flatté formula with coupled channels <math><mi>K</mi><mi>π</mi></math>, <math><mi>K</mi><mi>η</mi></math>, and <math><mi>K</mi><msup><mi>η</mi><mo>′</mo></msup></math>. The strong coupling constants <math><msub><mi>g</mi><mrow><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mi>K</mi><msup><mi>η</mi><mrow><mo>(</mo><mo>′</mo><mo>)</mo></mrow></msup></mrow></msub></math> are extracted from <math><msub><mi>g</mi><mrow><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mi>K</mi><mi>π</mi></mrow></msub></math> within flavor SU(3) symmetry. In spite of the strong depression by phase space near the threshold of <math><mi>K</mi><msup><mi>η</mi><mo>′</mo></msup></math>, the <math><mi>C</mi><mi>P</mi></math> averaged branching fractions for the <math><mi>B</mi><mo>→</mo><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo>(</mo><mn>1430</mn><mo>)</mo><mi>h</mi><mo>→</mo><mi>K</mi><msup><mi>η</mi><mo>′</mo></msup><mi>h</mi></math> decays are predicted to be on the order of <math><msup><mn>10</mn><mrow><mo>−</mo><mn>8</mn></mrow></msup></math> to <math><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup></math>, which are non-negligible for the corresponding three-body <math><mi>B</mi></math> decays. Since the <math><mrow><mi>K</mi><mi>η</mi></mrow></math> system is almost decoupled from the even-spin strange mesons under flavor SU(3) symmetry, those quasi-two-body <math><mi>B</mi></math> decays with subprocess <math><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo>(</mo><mn>1430</mn><mo>)</mo><mo>→</mo><mi>K</mi><mi>η</mi></math> shall have quite small branching ratios and are not taken into account in this work. We also estimate that the branching fraction for <math><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo>(</mo><mn>1430</mn><mo>)</mo><mo>→</mo><mi>K</mi><msup><mi>η</mi><mo>′</mo></msup></math> is about one fifth of that for <math><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo>(</mo><mn>1430</mn><mo>)</mo><mo>→</mo><mi>K</mi><mi>π</mi></math>. The predictions for the relevant decays are expected to be tested by the LHCb and Belle-II experiments in the future.

Contributions of the subprocess <math><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo>(</mo><mn>1430</mn><mo>)</mo><mo>→</mo><mi>K</mi><msup><mi>η</mi><mo>′</mo></msup></math> in the charmless three-body <math><mi>B</mi></math> meson decays

The decays   <math> <mi>B</mi> <mo>→</mo> <msup> <mover> <mi>D</mi> <mo>¯</mo> </mover> <mfenced> <mo>∗</mo> </mfenced> </msup> <mi>ωπ</mi> </math>  $$ B\to {\overline{D}}^{\left(\ast \right)}\omega \pi $$  are very important for the investigation of ρ excitations and the test of factorization hypothesis for B meson decays. The   <math> <msup> <mi>B</mi> <mo>+</mo> </msup> <mo>→</mo> <msup> <mover> <mi>D</mi> <mo>¯</mo> </mover> <mrow> <mfenced> <mo>∗</mo> </mfenced> <mn>0</mn> </mrow> </msup> <mi>ω</mi> <msup> <mi>π</mi> <mo>+</mo> </msup> </math>  $$ {B}^{+}\to {\overline{D}}^{\left(\ast \right)0}\omega {\pi}^{+} $$  and B 0 → D (*)−  ωπ + have been measured by different collaborations but without any predictions for their observables on theoretical side. In this work, we study the contributions of ρ(770, 1450) → ωπ for the cascade decays   <math> <msup> <mi>B</mi> <mo>+</mo> </msup> <mo>→</mo> <msup> <mover> <mi>D</mi> <mo>¯</mo> </mover> <mrow> <mfenced> <mo>∗</mo> </mfenced> <mn>0</mn> </mrow> </msup> <msup> <mi>ρ</mi> <mo>+</mo> </msup> <mo>→</mo> <msup> <mover> <mi>D</mi> <mo>¯</mo> </mover> <mrow> <mfenced> <mo>∗</mo> </mfenced> <mn>0</mn> </mrow> </msup> <mi>ω</mi> <msup> <mi>π</mi> <mo>+</mo> </msup> </math>  $$ {B}^{+}\to {\overline{D}}^{\left(\ast \right)0}{\rho}^{+}\to {\overline{D}}^{\left(\ast \right)0}\omega {\pi}^{+} $$ , B 0 → D (*)−  ρ + → D (*)−  ωπ + and   <math> <msubsup> <mi>B</mi> <mi>s</mi> <mn>0</mn> </msubsup> <mo>→</mo> <msubsup> <mi>D</mi> <mi>s</mi> <mrow> <mfenced> <mo>∗</mo> </mfenced> <mo>−</mo> </mrow> </msubsup> <msup> <mi>ρ</mi> <mo>+</mo> </msup> <mo>→</mo> <msup> <mi>D</mi> <mrow> <mfenced> <mo>∗</mo> </mfenced> <mo>−</mo> </mrow> </msup> <mi>ω</mi> <msup> <mi>π</mi> <mo>+</mo> </msup> </math>  $$ {B}_s^0\to {D}_s^{\left(\ast \right)-}{\rho}^{+}\to {D}^{\left(\ast \right)-}\omega {\pi}^{+} $$ . We introduce ρ(770, 1450) → ωπ subprocesses into the distribution amplitudes for ωπ system via the vector form factor F  ωπ (s) and then predict the branching fractions for the first time for concerned quasi-two-body decays with ρ(770, 1450) → ωπ, as well as the corresponding longitudinal polarization fractions Γ L  /Γ for the cases with the vector   <math> <msup> <mover> <mi>D</mi> <mo>¯</mo> </mover> <mrow> <mo>∗</mo> <mn>0</mn> </mrow> </msup> </math>  $$ {\overline{D}}^{\ast 0} $$  or   <math> <msubsup> <mi>D</mi> <mfenced> <mi>s</mi> </mfenced> <mrow> <mo>∗</mo> <mo>−</mo> </mrow> </msubsup> </math>  $$ {D}_{(s)}^{\ast -} $$  in their final states. The branching fractions of these quasi-two-body decays are predicted at the order of 10 −3, which can be detected at the LHCb and Belle-II experiments. The predictions for the decays B 0 → D *− ρ(770)+ → D *−  ωπ + and B 0 → D *−  ρ(1450)+ → D *−  ωπ + agree well with the measurements from Belle Collaboration. In order to avoid the pollution from annihilation Feynman diagrams, we recommend to take the   <math> <msubsup> <mi>B</mi> <mi>s</mi> <mn>0</mn> </msubsup> <mo>→</mo> <msubsup> <mi>D</mi> <mi>s</mi> <mrow> <mo>∗</mo> <mo>−</mo> </mrow> </msubsup> <mi>ρ</mi> <msup> <mfenced> <mn>770</mn> <mn>1450</mn> </mfenced> <mo>+</mo> </msup> </math>  $$ {B}_s^0\to {D}_s^{\ast -}\rho {\left(770,1450\right)}^{+} $$  decays, which have only emission diagrams at quark level, to test the factorization hypothesis for B decays.

Yu-Shan Ren

The ρ(770, 1450) → ωπ contributions for three-body decays   <math> <mi>B</mi> <mo>→</mo> <msup> <mover> <mi>D</mi> <mo>¯</mo> </mover> <mfenced> <mo>∗</mo> </mfenced> </msup> <mi>ωπ</mi> </math>  $$ B\to {\overline{D}}^{\left(\ast \right)}\omega \pi $$

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

We study the  $$J/\psi \rightarrow \phi K \bar{K}$$  <math> <mrow> <mi>J</mi> <mo>/</mo> <mi>ψ</mi> <mo>→</mo> <mi>ϕ</mi> <mi>K</mi> <mover> <mrow> <mi>K</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math>   decay, looking for differences in the production rates of  $$K^+ K^-$$  <math> <mrow> <msup> <mi>K</mi> <mo>+</mo> </msup> <msup> <mi>K</mi> <mo>-</mo> </msup> </mrow> </math>   or  $$K^0 \bar{K}^0$$  <math> <mrow> <msup> <mi>K</mi> <mn>0</mn> </msup> <msup> <mrow> <mover> <mrow> <mi>K</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mn>0</mn> </msup> </mrow> </math>   in the region of 1700–1800 MeV, where two resonances appear dynamically generated from the vector-vector interaction. Two resonances are known experimentally in that region, the  $$f_0(1710)$$  <math> <mrow> <msub> <mi>f</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>1710</mn> <mo>)</mo> </mrow> </mrow> </math>   and a new resonance reported by the BABAR and BESIII collaborations. The  $$K \bar{K}$$  <math> <mrow> <mi>K</mi> <mover> <mrow> <mi>K</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math>   should be produced with  $$I=0$$  <math> <mrow> <mi>I</mi> <mo>=</mo> <mn>0</mn> </mrow> </math>   in that reaction, but due to the different  $$K^{*0}$$  <math> <msup> <mi>K</mi> <mrow> <mrow></mrow> <mo>∗</mo> <mn>0</mn> </mrow> </msup> </math>   and  $$K^{*+}$$  <math> <msup> <mi>K</mi> <mrow> <mrow></mrow> <mo>∗</mo> <mo>+</mo> </mrow> </msup> </math>   masses some isospin violation appears. Yet, due to the large width of the  $$K^*$$  <math> <msup> <mi>K</mi> <mo>∗</mo> </msup> </math>  , the violation obtained is very small and the rates of  $$K^+ K^-$$  <math> <mrow> <msup> <mi>K</mi> <mo>+</mo> </msup> <msup> <mi>K</mi> <mo>-</mo> </msup> </mrow> </math>   or  $$K^0 \bar{K}^0$$  <math> <mrow> <msup> <mi>K</mi> <mn>0</mn> </msup> <msup> <mrow> <mover> <mrow> <mi>K</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mn>0</mn> </msup> </mrow> </math>   production are equal within  $$5\%$$  <math> <mrow> <mn>5</mn> <mo>%</mo> </mrow> </math>  . However, we also find that due to the step needed to convert two vectors into  $$K \bar{K}$$  <math> <mrow> <mi>K</mi> <mover> <mrow> <mi>K</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math>  , a shape can appear in the  $$K \bar{K}$$  <math> <mrow> <mi>K</mi> <mover> <mrow> <mi>K</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math>   mass distribution that can mimic the  $$a_0$$  <math> <msub> <mi>a</mi> <mn>0</mn> </msub> </math>   production around the  $$K^* \bar{K}^*$$  <math> <mrow> <msup> <mi>K</mi> <mo>∗</mo> </msup> <msup> <mrow> <mover> <mrow> <mi>K</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>∗</mo> </msup> </mrow> </math>   threshold, and is simply a threshold effect.

Brazil

Luciano Abreu

Eulogio Oset

Traces of the new  $$a_0(1780)$$  <math> <mrow> <msub> <mi>a</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>1780</mn> <mo>)</mo> </mrow> </mrow> </math>   resonance in the  $$J/\psi \rightarrow \phi K^+K^-(K^0\bar{K}^0)$$  <math> <mrow> <mi>J</mi> <mo>/</mo> <mi>ψ</mi> <mo>→</mo> <mi>ϕ</mi> <msup> <mi>K</mi> <mo>+</mo> </msup> <msup> <mi>K</mi> <mo>-</mo> </msup> <mrow> <mo>(</mo> <msup> <mi>K</mi> <mn>0</mn> </msup> <msup> <mrow> <mover> <mrow> <mi>K</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mn>0</mn> </msup> <mo>)</mo> </mrow> </mrow> </math>   reaction

We have a look at the <math><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow></msub></math> states generated from the interaction of <math><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>(</mo><mo>⁎</mo><mo>)</mo></mrow></msup><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>(</mo><mo>′</mo><mo>⁎</mo><mo>)</mo></mrow></msubsup></math> coupled channels. We consider the blocks of pseudoscalar-baryon <math><mo>(</mo><msup><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mrow><mo>+</mo></mrow></msup><mo>,</mo><msup><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mrow><mo>+</mo></mrow></msup><mo>)</mo></math> and vector-baryon <math><mo>(</mo><msup><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mrow><mo>+</mo></mrow></msup><mo>,</mo><msup><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mrow><mo>+</mo></mrow></msup><mo>)</mo></math>, and find 10 resonant states coupling mostly to <math><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>,</mo><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>⁎</mo></mrow></msup><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>,</mo><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>′</mo></mrow></msubsup><mo>,</mo><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>⁎</mo></mrow></msup><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>′</mo></mrow></msubsup><mo>,</mo><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup></math> and <math><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>⁎</mo></mrow></msup><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup></math>. A novel aspect of the work is the realization that the <math><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>,</mo><msub><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>s</mi></mrow></msub><msub><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow></msub></math> or <math><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>⁎</mo></mrow></msup><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>,</mo><msubsup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>s</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup><msub><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow></msub></math> channels, with a strong transition potential, collaborate to produce a larger attraction than the corresponding states <math><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover><msub><mrow><mi>Σ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>,</mo><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover><msub><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow></msub></math> or <math><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>⁎</mo></mrow></msup><msub><mrow><mi>Σ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>,</mo><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>⁎</mo></mrow></msup><msub><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow></msub></math> appearing in the generation of the strangenessless <math><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi></mrow></msub></math> states, since in the latter case the transition potential between those channels is zero. The extra attraction obtained in the <math><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>,</mo><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>⁎</mo></mrow></msup><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow></msub></math> pairs preclude the association of these channels to the <math><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo>(</mo><mn>4338</mn><mo>)</mo></math> and <math><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo>(</mo><mn>4459</mn><mo>)</mo></math> states respectively. Then we find a natural association of the <math><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo>(</mo><mn>4338</mn><mo>)</mo></math> state coupling mostly to <math><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>⁎</mo></mrow></msup><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow></msub></math> while the <math><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo>(</mo><mn>4459</mn><mo>)</mo></math> is associated to the state found that couples mostly to <math><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>′</mo></mrow></msubsup></math>. Four more states appear, like in other molecular pictures, and some of the states are degenerate in spin. Counting different spin states we find 10 states, which we hope can be observed in the near future.

Albert Feijoo

Chu-Wen Xiao

Jia-Jun Wu

Juan Nieves

Bing-Song Zou

A new look at the States From a Molecular Perspective

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.

Hongyu Wang

Extend the Levin-Wen model to two-dimensional topological orders with gapped boundary junctions

The contributions for the kaon pair from the intermediate states   $ \rho(1450)^+ $   and   $ \rho(1450)^+ $   in the decays   $ \rho(1450)^+ $  ,   $ \rho(1450)^+ $  , and   $ \rho(1450)^+ $   are analyzed within the perturbative QCD factorization approach. The decay amplitudes for all concerned decays in this work are dominated by the factorizable Feynman diagrams with the emission of the kaon pair, and the charged ρ mesons should be of great importance in the   $ \rho(1450)^+ $   channel of the related three-body B decays. Moreover, these quasi-two-body decays are CKM-favored, and the relevant branching ratios are predicted to be in the order of   $ \rho(1450)^+ $  , which have the potential to be measured by experiments. It is also shown that the contributions of the subprocesses   $ \rho(1450)^+ $   for the three-body B meson decays are considerable according to the total three-body branching fractions presented by Belle. Therefore, the decays   $ \rho(1450)^+ $  ,   $ \rho(1450)^+ $  , and   $ \rho(1450)^+ $   can be employed to study the properties of   $ \rho(1450)^+ $   and   $ \rho(1450)^+ $   in the LHCb and Belle-II experiments.

Resonances (1450) And (1700) In → Decays  