In this work, we investigate the production and decay of molecular states with quark content $cc\bar c\bar q$ and $J^P=1^+$ using a phenomenological analysis and an effective Lagrangian approach. Based on an $\textit{SU}$(3) flavor-symmetry analysis to identify golden channels, we further explore the dynamics of these processes under the molecular assumptions of ${\eta_c D^*}$ and ${J/\psi D^*}$ . Our results indicate that the production branching ratio in $B_c$ decays is sizable: it can be of order $10^{-4}$ for the molecular configuration ${{\eta}_cD^*}$ and $10^{-5}$ for the molecule ${J/\psi D^*}$ . In addition, we find that the decay widths of the two molecular configurations ${{\eta}_cD^*}$ and ${J/\psi D^*}$ are not significant, at the level of ${\cal{O}}$ ( $\text{MeV}$ ).

China

Na Li

Ye Xing

Jing-Rui Shi

Analysis of molecular state $\textit{η$_{c}$D}$ $^{*}$ and $\textit{J}$/$\textit{ψD}$ $^{*}$ in the effective Lagrangian approach * Supported by the National Natural Science Foundation of China (NSFC) (12005294)

We report stronger evidence for the $X(7200)$ state and markedly improved measurements of the $X(6900)$ resonance parameters based on a combined analysis of the di- $J/\psi$ mass spectrum using published data from LHCb, ATLAS, and CMS. Through simultaneous fits to the datasets from all three experiments, we observe the $X(6900)$ with overwhelming significance ( $ \gt 12\sigma$ ) and determine its mass and width with improved precision. For the $X(7200)$ , we find consistent signals across multiple interference models, with significances ranging from $3.7\sigma$ to $6.6\sigma$ ; in the best-fit model (the CMS three-resonance scheme), the significance reaches $6.6\sigma$ , providing substantially stronger evidence for this state. Our results underscore the essential role of interference effects in fully charmed tetraquark spectroscopy and offer new constraints on their production mechanisms at the LHC.

Yuan Wang

Ran Li

Bin Zhong

Ya-Qian Wang

Enhanced evidence of $\textit{X}$(7200) and improved measurements of $\textit{X}$(6900) parameters from a combined LHCb-ATLAS-CMS analysis * Supported by the National Natural Science Foundation of China (NSFC) (12475077)

The Kerr/CFT correspondence establishes a correspondence between extremal black holes in higher dimensions and a chiral conformal field theory (CFT) in their near-horizon limit. A generalization of this framework, known as the EVH/CFT correspondence, has been developed for four- and five-dimensional AdS black holes. It was further proposed in [ ${\rm{AdS}}_{D=6,7}$ black holes, a generalized duality between $(D-2)$ -dimensional geometry and $(D-3)$ -dimensional field theory may emerge in a suitably defined extremal vanishing horizon (EVH) limit. In this work, we show that, in the EVH limit, the near-EVH geometries of these ${\rm{AdS}}_{D=6,7}$ black holes reduce to lower-dimensional black holes whose metrics are conformally related to solutions of Einstein-Maxwell-Maxwell-dilaton (EMMD) gravity. This structural resemblance suggests a potential route toward the microscopic counting of non-AdS black hole entropy via higher-dimensional AdS/CFT techniques.

Weichao Bu

Yang Lei

Probing decoupled throats of AdS $\textit{D}$ black holes in $\textit{D}$ = 6, 7 * Supported by National Natural Science Foundation of China (NSFC) (2305081), the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), and the NSFC-Royal Society International Collaboration (W2421035)

Using a sample of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>2712.4</mn><mo>±</mo><mn>14.3</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>6</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo></mrow></math> events collected with the BESIII detector, we perform a search for the isospin-violating decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>χ</mi></mrow><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><mover accent="true"><mrow><mi mathvariant="normal">Σ</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><msup><mrow><mtext> </mtext></mrow><mrow><mn>0</mn></mrow></msup><mo>+</mo><mi mathvariant="normal">c</mi><mo>.</mo><mi mathvariant="normal">c</mi><mo>.</mo><mo stretchy="false">(</mo><mi>J</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo stretchy="false">)</mo></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>η</mi></mrow><mrow><mi>c</mi></mrow></msub><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><mover accent="true"><mrow><mi mathvariant="normal">Σ</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><msup><mrow><mtext> </mtext></mrow><mrow><mn>0</mn></mrow></msup><mo>+</mo><mi mathvariant="normal">c</mi><mo>.</mo><mi mathvariant="normal">c</mi></mrow></math>. No significant signal for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>c</mi></msub></math> is observed in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mover accent="true"><mrow><mi mathvariant="normal">Σ</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><msup><mrow><mtext> </mtext></mrow><mrow><mn>0</mn></mrow></msup></math> invariant mass distribution. The upper limits on the branching fractions at the 90% confidence level are set to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msub><mrow><mi>χ</mi></mrow><mrow><mi>c</mi><mn>0</mn></mrow></msub><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><mover accent="true"><mrow><mi mathvariant="normal">Σ</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><msup><mrow><mtext> </mtext></mrow><mrow><mn>0</mn></mrow></msup><mo>+</mo><mi mathvariant="normal">c</mi><mo>.</mo><mi mathvariant="normal">c</mi><mo>.</mo><mo stretchy="false">)</mo></mrow><mo>&lt;</mo><mn>1.5</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msub><mrow><mi>χ</mi></mrow><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><mover accent="true"><mrow><mi mathvariant="normal">Σ</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><msup><mrow><mtext> </mtext></mrow><mrow><mn>0</mn></mrow></msup><mo>+</mo><mi mathvariant="normal">c</mi><mo>.</mo><mi mathvariant="normal">c</mi><mo>.</mo><mo stretchy="false">)</mo><mo>&lt;</mo><mn>1.6</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msub><mrow><mi>χ</mi></mrow><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><mover accent="true"><mrow><mi mathvariant="normal">Σ</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><msup><mrow><mtext> </mtext></mrow><mrow><mn>0</mn></mrow></msup><mo>+</mo><mi mathvariant="normal">c</mi><mo>.</mo><mi mathvariant="normal">c</mi><mo>.</mo><mo stretchy="false">)</mo><mo>&lt;</mo><mn>1.7</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup></mrow></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msub><mrow><mi>η</mi></mrow><mrow><mi>c</mi></mrow></msub><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><mover accent="true"><mrow><mi mathvariant="normal">Σ</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><msup><mrow><mtext> </mtext></mrow><mrow><mn>0</mn></mrow></msup><mo>+</mo><mi mathvariant="normal">c</mi><mo>.</mo><mi mathvariant="normal">c</mi><mo>.</mo><mo stretchy="false">)</mo><mo>&lt;</mo><mn>6.2</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>5</mn></mrow></msup></mrow></math> for the first time.

M. Ablikim

Russia

M.N. Achasov

Sweden

P. Adlarson

X.C. Ai

Italy

C.S. Akondi

Germany

R. Aliberti

A. Amoroso

Q. An

Y.H. An

Y. Bai

JINR

O. Bakina

Y. Ban

H.R. Bao

X.L. Bao

Poland

V. Batozskaya

Mongolia

K. Begzsuren

N. Berger

M. Berlowski

M.B. 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

Türkiye

S.A. Cetin

X.Y. Chai

J.F. Chang

T.T. 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.M. Chen

T. Chen

W. Chen

X.R. Chen

X.T. Chen

X.Y. Chen

Y.B. Chen

Y.Q. Chen

Z.K. Chen

J. Cheng

L.N. Cheng

South Korea

S.K. Choi

X. Chu

G. Cibinetto

F. Cossio

United Kingdom

J. Cottee-Meldrum

H.L. Dai

J.P. Dai

X.C. Dai

A. Dbeyssi

R.E. de Boer

D. Dedovich

C.Q. Deng

Z.Y. Deng

A. Denig

I. Denisenko

M. Destefanis

F. De Mori

X.X. Ding

Y. Ding

Y.X. Ding

J. Dong

L.Y. Dong

M.Y. Dong

X. Dong

M.C. Du

S.X. Du

X.L. Du

Y.Q. Du

Y.Y. Duan

Z.H. Duan

P. Egorov

G.F. Fan

J.J. Fan

Y.H. Fan

J. Fang

S.S. Fang

W.X. Fang

Y.Q. Fang

L. Fava

F. Feldbauer

G. Felici

C.Q. Feng

Search for the isospin-violating decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>χ</mi></mrow><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><mover accent="true"><mrow><mi mathvariant="normal">Σ</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><msup><mrow><mtext> </mtext></mrow><mrow><mn>0</mn></mrow></msup><mo>+</mo><mi mathvariant="normal">c</mi><mo>.</mo><mi mathvariant="normal">c</mi><mo>.</mo></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>η</mi></mrow><mrow><mi>c</mi></mrow></msub><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><mover accent="true"><mrow><mi mathvariant="normal">Σ</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><msup><mrow><mtext> </mtext></mrow><mrow><mn>0</mn></mrow></msup><mo>+</mo><mi mathvariant="normal">c</mi><mo>.</mo><mi mathvariant="normal">c</mi><mo>.</mo></mrow></math>

We present HAPS-pPDF1.0, a new global determination of the helicity-dependent parton distribution functions (PDFs) of the proton, based on inclusive deep-inelastic scattering (DIS) and semi-inclusive DIS (SIDIS) data within a consistent next-to-leading order (NLO) QCD framework. In addition to existing measurements, we incorporate simulated pseudodata for the future Electron-Ion Collider (EIC), considering two beam-energy configurations, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>e</mi></mrow></msub><mo>×</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>=</mo><mn>5</mn><mo>×</mo><mn>41</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>GeV</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>18</mn><mo>×</mo><mn>275</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>GeV</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math>, corresponding to an extended kinematic reach down to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi><mo>∼</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup></math>. We focus on longitudinal double-spin asymmetries <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>A</mi><mn>1</mn><mi>h</mi></msubsup></math> for charge-separated pion and kaon production in SIDIS off a longitudinally polarized proton target. These projected measurements significantly improve the flavor separation of sea-quark polarized PDFs (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><mover accent="true"><mi>u</mi><mo stretchy="false">¯</mo></mover></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><mover accent="true"><mi>d</mi><mo stretchy="false">¯</mo></mover></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><mi>s</mi></math>) and reduce the uncertainties on both quark and gluon helicity distributions, with the largest impact at small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>. Polarized PDFs are extracted using a neural-network parametrization and a Monte Carlo replica methodology to propagate experimental uncertainties, while theoretical constraints such as positivity are imposed during the fit. We demonstrate that the inclusion of EIC pseudodata leads to a substantially more precise determination of polarized PDFs, with the largest impact in the small-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> region. The resulting polarized PDF sets are provided in the LHAPDF format.

Iran

Hamzeh Khanpour

Maryam Soleymaninia

Majid Azizi

Michael Klasen

Hadi Hashamipour

Maral Salajegheh

Ulf-G. Meißner

Toward precision helicity PDFs from global DIS and SIDIS fits with projected EIC measurements

We present a novel method for extracting the energy spectrum of ultracold neutrons from magnetically induced spin depolarization measurements using the n2EDM apparatus. This method is also used to exploit sensitivity to the storage properties of the materials used to trap ultracold neutrons, specifically, whether collisions are specular or diffuse. To do so, we utilize tomat simulation to map storage properties to correlation times of the ultracold neutrons to induced magnetic nonuniformities. We highlight the sensitivity of this new technique by comparing the two different storage chambers of the n2EDM experiment, which host different ultracold neutron energy spectra. This method should prove to be invaluable to assess systematic effects in experiments utilizing spin-polarized systems with precise magnetic control and long spin-spin coherence time relative to the observation time, such as neutron electric dipole moment and neutron lifetime experiments worldwide.

Switzerland

N.J. Ayres

France

G. Ban

G. Bison

K. Bodek

V. Bondar

T. Bouillaud

D. Bowles

G.L. Caratsch

E. Chanel

P.J. Chiu

C.B. Crawford

V. Czamler

M. Daum

C.B. Doorenbos

M. Ferry

M. Fertl

A. Fratangelo

D. Galbinski

W.C. Griffith

Serbia

Z.D. Grujic

K. Kirch

V. Kletzl

B. Lauss

T. Lefort

A. Lejuez

Belgium

R. Li

K. Michielsen

J. Micko

P. Mullan

A. Mullins

O. Naviliat-Cuncic

D. Pais

F.M. Piegsa

G. Pignol

C. Pistillo

D. Rebreyend

I. Rienäcker

D. Ries

S. Roccia

D. Rozpedzik

W. Saenz-Arevalo

L. Sanchez-Real Zielniewicz

P. Schmidt-Wellenburg

E.P. Segarra

L. Segner

N. Severijns

K. Svirina

K.S. Tanaka

J. Thorne

J. Vankeirsbilck

N. von Schickh

N. Yazdandoost

J. Zejma

N. Ziehl

G. Zsigmond

Ultracold Neutron Energy Spectrum and Storage Properties from Magnetically Induced Spin Depolarization

To shed light on the inner structure of the observed single-bottom strange baryons, in this work we systematically study the Okubo-Zweig-Iizuka allowed strong decay properties of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>P</mi></math>- and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>S</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mo>′</mo></msubsup></math> baryons within the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>j</mi><mtext>−</mtext><mi>j</mi></math> coupling scheme in the framework of the quark pair creation model. For a comparison, we also give the predictions of the chiral quark model. The calculations indicate that (i) The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>P</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi></math>-mode <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub></math> states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub><mo stretchy="false">|</mo><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo>,</mo><mn>1</mn><msub><mo stretchy="false">⟩</mo><mi>λ</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub><mo stretchy="false">|</mo><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo>,</mo><mn>1</mn><msub><mo stretchy="false">⟩</mo><mi>λ</mi></msub></math> are highly promising candidates for the observed state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub><mo stretchy="false">(</mo><mn>6087</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub><mo stretchy="false">(</mo><mn>6095</mn><mo stretchy="false">)</mo><mo>/</mo><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub><mo stretchy="false">(</mo><mn>6100</mn><mo stretchy="false">)</mo></math>, respectively. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>P</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi></math>-mode <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mo>′</mo></msubsup></math> states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mo>′</mo></msubsup><mo stretchy="false">|</mo><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo>,</mo><mn>2</mn><msub><mo stretchy="false">⟩</mo><mi>λ</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mo>′</mo></msubsup><mo stretchy="false">|</mo><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>5</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo>,</mo><mn>2</mn><msub><mo stretchy="false">⟩</mo><mi>λ</mi></msub></math> are likely candidates for the state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub><mo stretchy="false">(</mo><mn>6227</mn><mo stretchy="false">)</mo></math>. Meanwhile, we cannot rule out the possibility that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub><mo stretchy="false">(</mo><mn>6227</mn><mo stretchy="false">)</mo></math> could be a candidate of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>P</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi></math>-mode <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub></math> state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub><mo stretchy="false">|</mo><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo>,</mo><mn>2</mn><msub><mo stretchy="false">⟩</mo><mi>ρ</mi></msub></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub><mo stretchy="false">|</mo><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>5</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo>,</mo><mn>2</mn><msub><mo stretchy="false">⟩</mo><mi>ρ</mi></msub></math>. (ii) For the other <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>P</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi></math>-mode <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub></math> states and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>P</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi></math>-mode <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mo>′</mo></msubsup></math> states, they may be moderate states with a width of several tens of MeV. Their main decay channels are <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub><mi>π</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mo>′</mo></msubsup><mi>π</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mo>*</mo></msubsup><mi>π</mi></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover></math>. The width of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>P</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi></math>-mode <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mo>′</mo></msubsup></math> states are slightly broader, approximately several tens to over one hundred MeV, and the dominant decay channels are <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mo>′</mo></msubsup><mi>π</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mo>*</mo></msubsup><mi>π</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Σ</mi><mi>b</mi></msub><mi>K</mi></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Σ</mi><mi>b</mi><mo>*</mo></msubsup><mi>K</mi></math>. (iii) The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>S</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi></math>-mode <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mo>′</mo></msubsup></math> states are most likely to be relatively narrow state with a width of only a few to around ten MeV, and they mainly decay into <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mo>′</mo></msubsup><mi>π</mi></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mo>*</mo></msubsup><mi>π</mi></math>. Meanwhile, the decay process of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>S</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi></math>-mode <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mo>′</mo></msubsup></math> states into the final states containing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>P</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub></math> baryons should not be overlooked either. We hope that the theoretical results can provide some reference for future experimental investigations.

Yu-Bin Zhang

Yi-Heng Wang

Probing the inner structures of the observed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mo>′</mo></msubsup></math> resonances