We perform a theoretical study of the decay process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">→</mo><msup><mi>D</mi><mo>−</mo></msup><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></math> in search of the doubly heavy tetraquark states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math> with quark content <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>d</mi><mo stretchy="false">¯</mo></mover></math>. These <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math> states are assumed to be dynamically generated molecular states from the S-wave interactions between <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mi>s</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mn>0</mn></mrow></msubsup><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mo>+</mo></mrow></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mn>0</mn></mrow></msup><msubsup><mi>D</mi><mi>s</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mo>+</mo></mrow></msubsup></math> meson pairs. Based on the total angular momentum and the type of the constituent mesons (pseudoscalars <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math> or vectors <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>V</mi></math>), they are labeled as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>0</mn><mo>,</mo><mi>P</mi><mi>P</mi></mrow></msubsup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>0</mn><mo>,</mo><mi>V</mi><mi>V</mi></mrow></msubsup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>2</mn><mo>,</mo><mi>V</mi><mi>V</mi></mrow></msubsup></math>, respectively. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></math> invariant mass distribution for this decay is calculated using current algebra, incorporating contributions from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math> states arising from final-state interactions. Our results reveal a clear peak structure in the 7415–7425 MeV region, which is attributed to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>2</mn><mo>,</mo><mi>V</mi><mi>V</mi></mrow></msubsup></math> state. Additionally, a distinct dip structure appears near the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mrow><mo>*</mo><mn>0</mn></mrow></msup><msubsup><mi>D</mi><mi>s</mi><mrow><mo>*</mo><mo>+</mo></mrow></msubsup></math> threshold, characteristic of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>2</mn><mo>,</mo><mi>V</mi><mi>V</mi></mrow></msubsup></math> as a hadronic molecular state. A near-threshold enhancement associated with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>0</mn><mo>,</mo><mi>P</mi><mi>P</mi></mrow></msubsup></math> state and a dip arising from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>0</mn><mo>,</mo><mi>V</mi><mi>V</mi></mrow></msubsup></math> state are also identified, though the manifestation of these features depends sensitively on model parameter fine-tuning. Therefore, with increased experimental statistics, the decay channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">→</mo><msup><mi>D</mi><mo>−</mo></msup><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></math> offers a promising avenue for discovering and characterizing the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math> states.

China

Wen-Ying Liu

Hua-Xing Chen

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math> states in the process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">→</mo><msup><mi>D</mi><mo>−</mo></msup><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></math>

We investigate the electromagnetic properties of the axial-vector molecular states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup><mi>K</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>K</mi><mo>*</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>*</mo></msup><mi>K</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><msup><mi>K</mi><mo>*</mo></msup></math>, which are used to model the charmed states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow><mo>+</mo></msubsup><mo stretchy="false">(</mo><mn>2460</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow><mo>+</mo></msubsup><mo stretchy="false">(</mo><mn>2536</mn><mo stretchy="false">)</mo></math>, and their bottom partners with quantum numbers <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>1</mn><mo>+</mo></msup></math>. To our knowledge, this presents the first comprehensive calculation of the magnetic and quadrupole moments for these specific molecular configurations. Employing the QCD light-cone sum rule method with molecular-type interpolating currents, we compute these moments and perform a detailed flavor decomposition to reveal the internal distribution of the electromagnetic charge and spin. Our results demonstrate that the light up and down quarks dominate the electromagnetic response, with negligible contributions from the heavy quarks. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup><mi>K</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>*</mo></msup><mi>K</mi></math> states exhibit negative quadrupole moments and slightly oblate charge distributions, whereas the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>K</mi><mo>*</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><msup><mi>K</mi><mo>*</mo></msup></math> states possess positive quadrupole moments and prolate distributions, with significant contributions from the strange quark. The predicted moments provide benchmarks for lattice QCD calculations and are testable through their influence on radiative transitions and photo- and electroproduction observables at high-luminosity facilities, offering crucial insights into the internal structure and nature of these axial-vector states.

Türkiye

Ulaş Özdem

Electromagnetic properties of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow><mo>+</mo></msubsup><mo stretchy="false">(</mo><mn>2460</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow><mo>+</mo></msubsup><mo stretchy="false">(</mo><mn>2536</mn><mo stretchy="false">)</mo></math>, and their bottom partners in a molecular configuration

Under chiral effective field theory, we study the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> interactions up to second chiral order at one-loop level, which contain full contact, one-pion-exchange (OPE) and two-pion-exchange (TPE) contributions. Here, we adopt a new subtraction scheme of the two-particle-reducible contributions and attempt different regularization schemes uniquely for the TPE contributions since they are highly divergent on the momentum transfer. Under these schemes, we conclude that, in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo>=</mo><mn>0</mn></math> channel, the TPE contribution is repulsive, then the competition between this powerful repulsing TPE and the other two (contact and OPE) results in a quite weak attraction. This explains why <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> has an extremely small binding energy if treated as the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo>=</mo><mn>0</mn></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> bound state. This feature resembles that of hidden charm <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup></math> as we investigated in previous work [<a href="http://dx.doi.org/10.1103/PhysRevD.105.034013">Phys. Rev. D 105, 034013 (2022)</a>], which also interpreted the extremely near-threshold phenomenon of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo></math>. In addition, we also solve the Bethe-Salpeter equation with the chiral interactions for a consistency check.

Hao Xu

Li-Xiang Ren

Investigating the two-pion exchange of the double charm <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> chiral interactions and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math>

Conformal field theory (CFT) can be placed on disparate space-time manifolds to facilitate investigations of their properties. For (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional [<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mi mathvariant="normal">D</mi></mrow></math>] theories, one useful choice is the real projective space <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mi mathvariant="double-struck">RP</mi><mn>3</mn></msup></mrow></math> obtained by identifying antipodal points on the boundary sphere of a three-dimensional ball. One-point functions of scalar primary fields on this manifold generally do not vanish and encode the so-called crosscap coefficients. These coefficients also manifest on the sphere as the overlaps between certain crosscap states and CFT primary states. Taking the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mi mathvariant="normal">D</mi></mrow></math> Ising CFT as a concrete example, we demonstrate that crosscap coefficients can be extracted from microscopic models. We construct crosscap states in both lattice models defined on polyhedrons and continuum models in Landau levels, where the degrees of freedom at antipodal points are entangled in Bell-type states. By computing their overlaps with the eigenstates of many-body Hamiltonians, we obtain results consistent with those from conformal bootstrap. Importantly, our approach directly reveals the absolute values of crosscap overlaps, whereas bootstrap calculations typically yield only their ratios. Furthermore, we investigate the finite-size scaling of these overlaps and their evolution under perturbations away from criticality.

Jia-Ming Dong

Germany

Yueshui Zhang

Kai-Wen Huang

Hong-Hao Tu

Ying-Hai Wu

Numerical extraction of crosscap coefficients in microscopic models for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mi mathvariant="normal">D</mi></mrow></math> conformal field theory

Inspired by the abundant structure near the threshold of the $$D^{(*)}K^{(*)}/\bar{D}^{(*)}K^{(*)},$$ we estimate the strong decay properties of the $$T_{c\bar{s}1}^{f/a}$$ and $$T_{\bar{c}\bar{s}1}^{f/a}$$ with $$I(J^{P})=0/1(1^{+})$$ in $$DK^{*}$$ and $$\bar{D}K^{*}$$ molecular scenarios in the present paper. By employing the effective Lagrangian approach, the widths of the processes $$T_{c\bar{s}1}^{f}\rightarrow D^{*}K, D_{s}^{*}\eta , DK\pi ,$$ $$T_{c\bar{s}1}^{a}\rightarrow D^{*}K, D_{s}^{*}\pi , DK\pi ,$$ and $$T_{\bar{c}\bar{s}1}^{f/a}\rightarrow \bar{D}^{*}K, \bar{D}K\pi $$ are estimated. Considering the present estimations, we propose to search for $$T_{c\bar{s}1}^{f/a}$$ states in $$D^{*}K$$ and $$D_{s}^{*}\pi /D_{s}^{*}\eta $$ mass invariant spectra. Their ratios may serve as an important test of the molecular scenario.

Italy

Zi-Li Yue

Cheng-Jian Xiao

Mexico

H. García-Tecocoatzi

Dian-Yong Chen

Elena Santopinto

Strong decays of the $$DK^*$$ and $$\bar{D}K^{*}$$ molecular states

Based on a sample of $2.7\times10^{9}$ $\psi(3686)$ events collected by the BESIII detector operating at the BEPCII collider, the decay $\psi(3686)\to\gamma\chi_{cJ}, \chi_{cJ}\to\eta\eta\eta^{\prime}$ is analyzed. The decay modes $\chi_{c1}$ and $\chi_{c2}\to\eta\eta\eta^{\prime}$ are observed for the first time, and their corresponding branching fractions are determined to be ${\cal{B}}(\chi_{c1}\to\eta\eta\eta^{\prime}) = $ $ (1.40\, \pm 0.13\, (\text{stat.}) \pm 0.09\, (\text{sys.})) \times 10^{-4}$ and ${\cal{B}}(\chi_{c2}\to\eta\eta\eta^{\prime}) = (4.18\, \pm 0.84\, (\text{stat.}) \pm 0.48\, (\text{sys.})) \times 10^{-5}$ . An upper limit on the branching fraction of $\chi_{c0}\to\eta\eta\eta^{\prime}$ is set as $2.59 \times 10^{-5}$ at a 90% confidence level (CL). A partial wave analysis (PWA) of the decay $\chi_{c1}\to\eta\eta\eta^{\prime}$ is performed to search for the $1^{-+}$ exotic state $\eta_1(1855)$ . The PWA result indicates that the structure in the $\eta\eta^{\prime}$ mass spectrum is attributed to $f_0(1500)$ , while in the $\eta\eta$ mass spectrum, it is attributed to the $0^{++}$ phase space. The upper limit of ${\cal{B}}(\chi_{c1}\to\eta_{1}(1855)\eta) \cdot {\cal{B}}(\eta_{1}(1855)\to\eta\eta^{\prime}) \lt $ $ 9.79 \times 10^{-5}$ is set based on the PWA at 90% CL.

M. Ablikim

Russia

M.N. Achasov

Sweden

P. Adlarson

X.C. Ai

R. Aliberti

A. Amoroso

Q. An

Y. Bai

O. Bakina

Y. Ban

H.R. Bao

Poland

V. Batozskaya

Mongolia

K. Begzsuren

N. Berger

M. Berlowski

M. Bertani

D. Bettoni

F. Bianchi

E. Bianco

A. Bortone

I. Boyko

United States

R.A. Briere

A. Brueggemann

H. Cai

M.H. Cai

X. Cai

A. Calcaterra

G.F. Cao

N. Cao

S.A. Cetin

X.Y. Chai

J.F. Chang

G.R. Che

Y.Z. Che

C.H. Chen

Chao Chen

G. Chen

H.S. Chen

H.Y. Chen

M.L. Chen

S.J. Chen

S.L. Chen

S.M. Chen

T. Chen

X.R. Chen

X.T. Chen

X.Y. Chen

Y.B. Chen

Y.Q. Chen

Z. Chen

Z.J. Chen

Z.K. Chen

S.K. Choi

X. Chu

G. Cibinetto

F. Cossio

United Kingdom

J. Cottee-Meldrum

J.J. Cui

H.L. Dai

J.P. Dai

A. Dbeyssi

R.E. de Boer

D. Dedovich

C.Q. Deng

Z.Y. Deng

A. Denig

I. Denysenko

M. Destefanis

F. De Mori

B. Ding

X.X. Ding

Y. Ding

Y.X. Ding

J. Dong

L.Y. Dong

M.Y. Dong

X. Dong

M.C. Du

S.X. Du

Y.Y. Duan

P. Egorov

G.F. Fan

J.J. Fan

Y.H. Fan

J. Fang

S.S. Fang

W.X. Fang

Y.Q. Fang

R. Farinelli

L. Fava

F. Feldbauer

G. Felici

C.Q. Feng

J.H. Feng

L. Feng

Q.X. Feng

Search for $\textit{η}$ $_{1}$(1855) in $\textit{χ}$ $\textit{cJ}$ → $\textit{ηηη}$′ decays * Supported in part by National Key R&D Program of China (2023YFA1606000, 2023YFA1606704); National Natural Science Foundation of China (NSFC) (11635010, 11935015, 11935016, 11935018, 12025502, 12035009, 12035013, 12061131003, 12192260, 12192261, 12192262, 12192263, 12192264, 12192265, 12221005, 12225509, 12235017, 12361141819); the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; CAS (YSBR-101); 100 Talents Program of CAS; The Institute of Nuclear and Particle Physics (INPAC) and Shanghai Key Laboratory for Particle Physics and Cosmology; Agencia Nacional de Investigación y Desarrollo de Chile (ANID), Chile (ANID PIA/APOYO AFB230003); German Research Foundation DFG (FOR5327); Istituto Nazionale di Fisica Nucleare, Italy; Knut and Alice Wallenberg Foundation (2021.0174, 2021.0299); Ministry of Development of Turkey (DPT2006K-120470); National Research Foundation of Korea ( NRF-2022R1A2C1092335); National Science and Technology fund of Mongolia; National Science Research and Innovation Fund (NSRF) via the Program Management Unit for Human Resources Institutional Development, Research and Innovation of Thailand ( B50G670107); Polish National Science Centre (2024/53/B/ST2/00975); Swedish Research Council (2019.04595); U. S. Department of Energy (DE-FG02-05ER41374)

In this article, the vector, axial vector and tensor form factors of <italic>B<inf>c</inf></italic> to <italic>D</italic>-wave charmonia <italic>&#968;<inf>J</inf></italic> ( <math altimg='si138.svg'><mrow><mi>J</mi><mo linebreak='goodbreak'>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></mrow></math>) and <italic>&#951;</italic> <inf><italic>c</italic>2</inf> are analyzed within the framework of three-point QCD sum rules. With the predicted vector and axial vector form factors, we study the decay widths and branching ratios of semileptonic decays <math altimg='si139.svg'><mrow><msub><mi>B</mi><mi>c</mi></msub><mo>&#8594;</mo><msub><mi>&#968;</mi><mi>J</mi></msub><mi>l</mi><mover accent='true'><msub><mi>&#957;</mi><mi>l</mi></msub><mo>&#175;</mo></mover></mrow></math> and <math altimg='si140.svg'><mrow><msub><mi>B</mi><mi>c</mi></msub><mo>&#8594;</mo><msub><mi>&#951;</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mi>l</mi><mover accent='true'><msub><mi>&#957;</mi><mi>l</mi></msub><mo>&#175;</mo></mover></mrow></math>. Our results indicate that the semileptonic decay branching ratios of <italic>B<inf>c</inf></italic> to <italic>D</italic>-wave charmonia decreases as the total angular momentum of the final state <italic>D</italic>-wave charmonia increases. For decay processes <math altimg='si141.svg'><mrow><msub><mi>B</mi><mi>c</mi></msub><mo>&#8594;</mo><msub><mi>&#968;</mi><mn>1</mn></msub><mi>l</mi><msub><mover accent='true'><mi>&#957;</mi><mo>&#175;</mo></mover><mi>l</mi></msub></mrow></math>, <math altimg='si142.svg'><mrow><msub><mi>B</mi><mi>c</mi></msub><mo>&#8594;</mo><msub><mi>&#968;</mi><mn>2</mn></msub><mrow><mo>[</mo><msub><mi>&#951;</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo>]</mo></mrow><mi>l</mi><msub><mover accent='true'><mi>&#957;</mi><mo>&#175;</mo></mover><mi>l</mi></msub></mrow></math> and <math altimg='si143.svg'><mrow><msub><mi>B</mi><mi>c</mi></msub><mo>&#8594;</mo><msub><mi>&#968;</mi><mn>3</mn></msub><mi>l</mi><msub><mover accent='true'><mi>&#957;</mi><mo>&#175;</mo></mover><mi>l</mi></msub></mrow></math>, the branching ratios can reach the order of magnitude <math altimg='si100.svg'><msup><mn>10</mn><mrow><mo>&#8722;</mo><mn>3</mn></mrow></msup></math>, <math altimg='si144.svg'><msup><mn>10</mn><mrow><mo>&#8722;</mo><mn>4</mn></mrow></msup></math> and <math altimg='si145.svg'><msup><mn>10</mn><mrow><mo>&#8722;</mo><mn>5</mn></mrow></msup></math>, respectively, which can provide a valuable reference for future experimental measurements for <italic>B<inf>c</inf></italic> meson by LHCb collaboration. Furthermore, these results also can provide useful information to study the properties of <italic>B<inf>c</inf></italic> meson and <italic>D</italic>-wave charmonia.

Jie Lu

Guo-Liang Yu

Zhi-Gang Wang

Systematic analysis of the transition form factors of <italic>B<inf>c</inf></italic> to <italic>D</italic>-wave charmonia and corresponding semileptonic decays

<list id='lst0001'><list-item id='lstitem0001'><label>&#8226;</label><para id='p0001'>We investigate a classical model of coupled harmonic oscillators (CHO) as the classical counterpart of the Lee model. In this classical model, the divergence of the fundamental frequency and its renormalization precisely reproduce the divergence and renormalization of the physical mass of the particle, revealing that mass divergence in the Lee model is not solely a quantum phenomenon.</para></list-item><list-item id='lstitem0002'><label>&#8226;</label><para id='p0002'>We derive the necessary conditions that any renormalization must satisfy for the two-oscillator system corresponding to the single-mode Lee model.</para></list-item><list-item id='lstitem0003'><label>&#8226;</label><para id='p0003'>We examine the classical analog of the <italic>N</italic>-<italic>&#952;</italic> scattering process in the Lee model and demonstrate that the cutoff-dependent behavior of the scattering strength parallels the quantum scenario, indicating that the suppression of scattering also has a classical origin.</para></list-item></list>

Kang Xu

C.P. Sun

Classical analog of the T. D. Lee model for renormalization

We develop a systematic framework for understanding symmetries in topological phases in 2 + 1 dimensions using the string-net model, encompassing both gauge invariances that preserve anyon types and global symmetries permuting anyon types, including both invertible symmetries describable by groups and noninvertible symmetries described by categories. As an archetypal example, we reveal the first noninvertible categorical gauge invariance of topological orders in 2 + 1 dimensions: the Fibonacci gauge invariance of the doubled Fibonacci topological order, described by the Fibonacci fusion 2-category. Our approach involves two steps: first, classifying and establishing dualities between different string-net models describing the same topological order; and second, constructing symmetry transformations within the same string-net model when the dual models have isomorphic input data, achieved by composing duality maps with isomorphisms of degrees of freedom between the dual models.

Yu Zhao

Yidun Wan

Noninvertible gauge invariance in (2+1)d topological orders: a string-net model realization

The recently observed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><mo stretchy="false">(</mo><mn>1690</mn><mo stretchy="false">)</mo></math> has been identified as a supernumerary pseudoscalar resonance signal in the strange-meson spectrum predicted by quark model calculations. It is the best candidate of a strange cryptoexotic state. In this work, we systematically study the hadron masses of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>u</mi><mi>d</mi><mover accent="true"><mi>d</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math> tetraquark states with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>0</mn><mo>−</mo></msup></math> in the method of QCD sum rules. For ten interpolating currents, we calculate the correlation functions up to dimension-8 nonperturbative condensates. To calculate the trigluon condensate, we comprehensively consider the contributions from different operators with and without covariant derivatives. The infrared safety can be guaranteed for the completely calculated trigluon condensate by properly addressing the IR divergences in Feynman diagrams. It is demonstrated that the trigluon condensate provides significant contributions to the sum-rule analyses in these light tetraquark systems. Our results support the interpretation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><mo stretchy="false">(</mo><mn>1690</mn><mo stretchy="false">)</mo></math> resonance to be a pseudoscalar <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>u</mi><mi>d</mi><mover accent="true"><mi>d</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math> tetraquark state.

Jin-Peng Zhang

Xu-Liang Chen

Zi-Xi Ou-Yang

Xiang Yu

Wei Chen

Jia-Jun Wu

Unraveling <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><mo stretchy="false">(</mo><mn>1690</mn><mo stretchy="false">)</mo></math> as a pseudoscalar <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>u</mi><mi>d</mi><mover accent="true"><mi>d</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math> tetraquark state