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

We present the first lattice result of the near threshold $ \Lambda_c\Lambda_c $ scattering with $ I(J^P) = 0(0^+) $ . The calculation is performed on two $ N_f = 2+1 $ Wilson-Clover ensembles with pion mass $ m_\pi \sim 303 $ MeV and lattice spacing $ a = 0.07746 $ fm. Lüscher's finite volume method is utilized to extract the scattering parameters from the finite-volume spectrum. The coupled channel $ \Xi_{cc}N $ is ignored in the scattering analysis based on the observation that the energy levels computed from the $ \Lambda_c\Lambda_c $ and $ \Xi_{cc}N $ operators do not mix. The $ \Sigma_c\Sigma_c $ channel is not included either since the energy range explored in this study is well below its threshold. Our results indicate that the interaction in the $ \Lambda_c\Lambda_c $ single channel is repulsive, and the scattering length is determined to be $ a_0 = -0.21(4)(8) $ fm, where the first error is statistical and the second is systematic.

Hanyang Xing

Yiqi Geng

Chuan Liu

Liuming Liu

Peng Sun

Jiajun Wu

Zhicheng Yan

Ruilin Zhu

Lattice QCD study of Λ $\textit{c}$ Λ $\textit{c}$ scattering * Supported by NSFC (12293060, 12293061, 12293063, 12175279, 12435002, 12322503, 12175239). L. Liu also acknowledges the Strategic Priority Research Program of the Chinese Academy of Sciences with (XDB34030301) and Guangdong Major Project of Basic and Applied Basic Research (2020B0301030008). We also acknowledge the Science and Education Integration Young Faculty Project of University of Chinese Academy of Sciences (YSBR-101)

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.

Hongyu Wang

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

Three-body <math id="M3"><mi>B</mi></math> decays not only significantly broaden the study of <math id="M4"><mi>B</mi></math> meson decay mechanisms but also provide information of resonant particles. Because of complicate dynamics, it is very hard for us to study the whole phase space in a specific approach. In this review, we take <math id="M5"><mi>B</mi><mo>⟶</mo><mi>K</mi><mfenced><mrow><mi>R</mi><mo>⟶</mo></mrow></mfenced><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup></math> decays as examples and show the application of the perturbative QCD (PQCD) approach in studying the quasi-two-body <math id="M6"><mi>B</mi></math> decays, where two particles move collinearly with large energy and the bachelor one recoils back. To describe the dynamics of two collinear particles, the <math id="M7"><mi>S</mi></math>, <math id="M8"><mi>P</mi></math>, and <math id="M9"><mi>D</mi></math>-wave functions of kaon-pair with different waves are introduced. By keeping the transverse momenta, all possible diagrams including the hard spectator diagrams and annihilation ones can be calculated in PQCD approach. Most results are well consistent with the current measurements from BaBar, Belle, and LHCb experiments. Moreover, under the narrow-width approximation, we can extract the branching fractions of the two-body decays involving the resonant states and also predict the branching fractions of the corresponding quasi-two-body decays <math id="M10"><mi>B</mi><mo>⟶</mo><mi>K</mi><mfenced><mrow><mi>R</mi><mo>⟶</mo></mrow></mfenced><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup></math>. All predictions are expected to be tested in the ongoing LHCb and Belle-II experiments.

Ying Li

Wen-Feng Liu

Zhi-Tian Zou

Charmless Quasi-Two-Body Decays in Perturbative QCD Approach: Taking as Examples

This exploratory study computes two-photon decay widths of pseudo-scalar (
					) and scalar (
					) charmonium using two ensembles of 
					 twisted mass lattice QCD gauge configurations. The simulation is performed using two lattice ensembles with lattice spacings 
					 fm with size 
					 and 
					 fm with size 
					. The decay widths for the two charmonia are obtained within the expected ballpark, but are however smaller than the experimental ones. Possible reasons for these discrepancies are discussed.
				

Ying Chen

Ming Gong

Ning Li

Yu-Bin Liu

Zhaofeng Liu

Jian-Ping Ma

Yu Meng

Chao Xiong

Ke-Long Zhang

Lattice study of two-photon decay widths for scalar and pseudo-scalar charmonium This work is supported in part by the National Science Foundation of China (NSFC) (11335001, 11275169, 11405178, 11935017, 11575196, 11875169, 11775229). It is also supported in part by the DFG and the NSFC (11261130311) through funds provided to the Sino-Germen CRC 110 symmetries and the Emergence of Structure in QCD. This work is also funded in part by National Basic Research Program of China (973 Program) (2015CB856700). M. Gong and Z. Liu are partially supported by the Youth Innovation Promotion Association of CAS (2013013). This work is also supported by the Scientific Research Program Funded by Shaanxi Provincial Education Department (19JK0391) andNatural Science Basic Research Plan in Shaanxi Province of China (2019JM-001)

Recently, it has been shown that in gauge theories amplitudes to any perturbation order can be obtained by gluing together simple three-point on-shell amplitudes. These three-point amplitudes, in turn, are fixed by locality and Lorentz invariance. This factorization into three-point on-shell amplitudes follows from the Britto-Cachazo-Feng-Witten recursion relations and the Feynman-tree theorem. In an explicit example, that is, the four-gluon amplitude with all plus helicities, we illustrate the method. In a conventional calculation, this amplitude corresponds to one-loop box diagrams.

Chile

M. Maniatis

Application of Britto-Cachazo-Feng-Witten recursion relations and the Feynman-tree theorem to the four-gluon amplitude with all plus helicities

The honeycomb lattice Kitaev model <math><msub><mrow><mi>H</mi></mrow><mrow><mi>K</mi></mrow></msub></math> with two kinds of Wen–Toric-code four-body interactions <math><msub><mrow><mi>H</mi></mrow><mrow><mi>W</mi><mi>T</mi></mrow></msub></math> is investigated exactly using a new fermionization method, and the ground state phase diagram is obtained. Six kinds of three-body interactions are also considered. A Hamiltonian equivalent to the honeycomb lattice Kitaev model is also introduced. The fermionization method is generalized to two-dimensional systems, and the two-dimensional Jordan–Wigner transformation is obtained as a special case of this formula. The model <math><msub><mrow><mi>H</mi></mrow><mrow><mi>K</mi></mrow></msub><mo>+</mo><msub><mrow><mi>H</mi></mrow><mrow><mi>W</mi><mi>T</mi></mrow></msub></math> is symmetric in four-dimensional space of coupling constants, and the anyon type excitations appear in each phase.

Japan

Kazuhiko Minami

Honeycomb lattice Kitaev model with Wen–Toric-code interactions, and anyon excitations

Using the one-boson-exchange model, we investigate the , , , , , and interactions by considering the one-eta-exchange and/or one-pion-exchange contributions. We further predict the existence of hidden-charm molecular pentaquarks. Promising candidates for hidden-charm molecular pentaquarks include a state with and the states with and . Experimental searches for these predicted hidden-charm molecular pentaquarks are an interesting future research topic for experiments like LHCb.

Rui Chen

Jun He

Xiang Liu

Possible strange hidden-charm pentaquarks from and interactionsSupported by National Natural Science Foundation of China (11222547, 11175073, 11675228), Major State Basic Research Development Program in China (2014CB845405) and Fundamental Research Funds for the Central Universities. Xiang Liu is also supported by the National Program for Support of Top-notch Young Professionals

None Supervisory Editors of Nuclear Physics B

Editorial note on “Lepton-flavor violation and (g−2)μ in the μν SSM” by Hai-Bin Zhang, Tai-Fu Feng, Shu-Min Zhao and Tie-Jun Gao [Nucl. Phys. B 873 (2) (2013) 300–324]