Based on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> annihilation data collected with the BESIII detector at center-of-mass energies from 4.600 to 4.699 GeV, corresponding to an integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>4.5</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>, we present the first measurement of the longitudinal polarization of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi></math> hyperon produced in the inclusive decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><mi>X</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi></math> denotes any allowed final states. The polarizations are determined to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="script">P</mi><mi mathvariant="normal">Λ</mi></msub><mo>=</mo><mo>−</mo><mn>0.393</mn><mo>±</mo><mn>0.05</mn><msub><mn>5</mn><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.02</mn><msub><mn>0</mn><mrow><mi>syst</mi></mrow></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="script">P</mi><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover></msub><mo>=</mo><mn>0.288</mn><mo>±</mo><mn>0.05</mn><msub><mn>6</mn><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.01</mn><msub><mn>7</mn><mrow><mi>syst</mi></mrow></msub></math>. A search for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation is performed using an asymmetry constructed from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi></math> polarization and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mo stretchy="false">→</mo><mi>p</mi><msup><mi>π</mi><mo>−</mo></msup></math> decay asymmetry parameter, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="script">A</mi><mrow><mi>C</mi><mi>P</mi></mrow><mi>pol</mi></msubsup><mo>=</mo><mn>0.15</mn><mo>±</mo><mn>0.1</mn><msub><mn>2</mn><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.0</mn><msub><mn>3</mn><mrow><mi>syst</mi></mrow></msub></math> was obtained. Furthermore, an updated measurement of the absolute branching fraction is reported as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><mi>X</mi><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>38.07</mn><mo>±</mo><mn>0.3</mn><msub><mn>8</mn><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.4</mn><msub><mn>9</mn><mrow><mi>syst</mi></mrow></msub><mo stretchy="false">)</mo><mo>%</mo></math>, representing a fourfold precision improvement over the previous BESIII measurement. A search for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation in the decay rate yields <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="script">A</mi><mrow><mi>C</mi><mi>P</mi></mrow><mi>dir</mi></msubsup><mo>=</mo><mo stretchy="false">(</mo><mn>1.5</mn><mo>±</mo><msub><mn>1.0</mn><mrow><mi>stat</mi></mrow></msub><mo>±</mo><msub><mn>1.0</mn><mrow><mi>syst</mi></mrow></msub><mo stretchy="false">)</mo><mo>%</mo></math>. No evidence for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation is observed in this inclusive charm baryon decay. The subscripts ‘stat’ and ‘syst’ denote statistical and systematic uncertainties, respectively.

China

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

Precision Studies and Searches for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> Asymmetries in the Inclusive Decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><mi>X</mi></math>

We study the nonleptonic weak decays of doubly charmed baryons (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="script">B</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math>) into singly charmed baryons (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="script">B</mi><mi>c</mi></msub></math>) and vector mesons (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>V</mi></math>), denoted as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="script">B</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo stretchy="false">→</mo><msub><mi mathvariant="script">B</mi><mi>c</mi></msub><mi>V</mi></math>. The short-distance contributions are calculated within the naive factorization hypothesis, while the long-distance final-state interaction effects are modeled via hadronic triangle diagrams. Unlike previous approaches, which compute only the imaginary part using the Cutkosky cutting rule, we evaluate the complete loop integrals to obtain both the real and imaginary parts of the amplitudes. These provide the nontrivial strong phases essential for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation. The model parameters are determined using experimental data. With this improved calculation method, we predict the branching ratios and decay asymmetry parameters for various decay channels, as well as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violations for short-distance dominated and singly Cabibbo-suppressed channels. This strengthens our theoretical framework for future study of doubly charmed baryons. Certain decays, primarily driven by long-distance effects, have been calculated, and their observation in future experiments could help clarify the role of final-state interactions in charm baryon decays. Therefore, our calculation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="script">B</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo stretchy="false">→</mo><msub><mi mathvariant="script">B</mi><mi>c</mi></msub><mi>V</mi></math> provides crucial predictions for branching ratios, decay asymmetry parameters, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation, which are essential for guiding experimental study at LHCb.

Xiao-Hui Hu

Fu-Sheng Yu

Ye Xing

Final-state rescattering mechanism of doubly-charmed baryon decays: <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="script">B</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo stretchy="false">→</mo><msub><mi mathvariant="script">B</mi><mi>c</mi></msub><mi>V</mi></math>

We study the effect of boundary deformations on the von Neumann entropy of subregions in two-dimensional boundary conformal field theories (BCFTs) at zero and finite temperature. The deformations considered are infinitesimal global conformal transformations that move the boundary and can equivalently be viewed as the leading-order effect of certain BCFT perturbations with the boundary displacement operator.

Dominik Neuenfeld

Christopher Tellinger

Large-c BCFT entanglement entropy with deformed boundaries from emergent JT gravity

We investigate the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave scatterings of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><msub><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover><mi>c</mi></msub></math> systems within a unified chiral effective field theory framework up to next-to-leading order. The contact low-energy coupling constants are determined by fitting to the lattice QCD results for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub></math> scattering phase shift at an unphysical pion mass. After extrapolating to the physical pion mass, we find a repulsive interaction in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo stretchy="false">(</mo><msup><mi>J</mi><mi>P</mi></msup><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mo stretchy="false">(</mo><msup><mn>0</mn><mo>+</mo></msup><mo stretchy="false">)</mo><mtext> </mtext><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub></math> channel, consistent with the lattice QCD simulation. On the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><msub><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover><mi>c</mi></msub></math> side, using the fitted contact low-energy constants, we predict the phase shifts and potentials for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><msub><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover><mi>c</mi></msub></math> scattering in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo stretchy="false">(</mo><msup><mi>J</mi><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mo stretchy="false">(</mo><msup><mn>0</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0</mn><mo stretchy="false">(</mo><msup><mn>1</mn><mrow><mo>−</mo><mo>−</mo></mrow></msup><mo stretchy="false">)</mo></math> channels. Attractive interactions are found in both channels, each allowing for the formation of bound states. In particular, the attraction in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0</mn><mo stretchy="false">(</mo><msup><mn>1</mn><mrow><mo>−</mo><mo>−</mo></mrow></msup><mo stretchy="false">)</mo><mtext> </mtext><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><msub><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover><mi>c</mi></msub></math> channel is stronger. In addition, our analysis reveals that the spin-spin term caused by the two-pion exchange contributes significantly to the interactions, leading to a distinct mass splitting between the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0</mn><mo stretchy="false">(</mo><msup><mn>0</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0</mn><mo stretchy="false">(</mo><msup><mn>1</mn><mrow><mo>−</mo><mo>−</mo></mrow></msup><mo stretchy="false">)</mo><mtext> </mtext><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><msub><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover><mi>c</mi></msub></math> channels.

Zhe Liu

Hao Xu

Zhan-Wei Liu

Xiang Liu

Scattering of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><msub><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover><mi>c</mi></msub></math> in chiral effective field theory

A four-dimensional gauge-gravity unification based on local <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>S</mi><mi>L</mi><mo stretchy="false">(</mo><mn>2</mn><mi>N</mi><mo>,</mo><mi>C</mi><mo stretchy="false">)</mo></mrow></math> symmetry is developed in a universal Yang-Mills-type setting, which, however, appears dynamically consistent only in the symmetry-broken phase. In the exact symmetry limit, the theory may only be formulated in a premetric framework, where the accompanying tetrad multiplets, though promoted to dynamical fields, do not yet satisfy the conventional invertibility conditions. An ordinary Einstein-Cartan spacetime geometry emerges only in the broken postsoldering phase, in which the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>L</mi><mo stretchy="false">(</mo><mn>2</mn><mi>N</mi><mo>,</mo><mi>C</mi><mo stretchy="false">)</mo></math> tetrad multiplets are treated as constrained dynamical fields selecting a neutral internal symmetry branch. This realizes the breaking <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>L</mi><mo stretchy="false">(</mo><mn>2</mn><mi>N</mi><mo>,</mo><mi>C</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mspace linebreak="goodbreak"></mspace><mi>S</mi><mi>L</mi><mo stretchy="false">(</mo><mn>2</mn><mo>,</mo><mi>C</mi><mo stretchy="false">)</mo><mo>×</mo><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></math>, thereby lifting all noncompact internal directions, while the surviving neutral tetrad is, as usual, associated with the gravitational field. A special ghost-free curvature-squared Lagrangian provides a consistent quadratic sector for the spin connection, propagating only admissible connection modes: the massless <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></math> vector fields together with massive axial-vector and pseudoscalar multiplets. The Einstein-Cartan linear curvature term is argued to arise radiatively from fermion loops, thereby relating the gravitational scale to the same <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>L</mi><mo stretchy="false">(</mo><mn>2</mn><mi>N</mi><mo>,</mo><mi>C</mi><mo stretchy="false">)</mo></math>-covariant matter sector that defines the unified gauge coupling. Finally, the matter sector points to a deeper elementarity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>L</mi><mo stretchy="false">(</mo><mn>2</mn><mi>N</mi><mo>,</mo><mi>C</mi><mo stretchy="false">)</mo></math> spinors, identified with preon constituents whose bound states form the observed quarks and leptons. Anomaly matching between preons and composites singles out <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>=</mo><mn>8</mn></math>. The chain <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>L</mi><mo stretchy="false">(</mo><mn>16</mn><mo>,</mo><mi>C</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>S</mi><mi>L</mi><mo stretchy="false">(</mo><mn>2</mn><mo>,</mo><mi>C</mi><mo stretchy="false">)</mo><mo>×</mo><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>8</mn><mo stretchy="false">)</mo></math> then naturally yields three composite quark-lepton families, while filtering out extraneous heavy states.

Georgia

J.L. Chkareuli

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>L</mi><mo stretchy="false">(</mo><mn>2</mn><mi>N</mi><mo>,</mo><mi>C</mi><mo stretchy="false">)</mo></math> Yang-Mills theories: Direct internal forces and emerging gravity

The production of exotic hadrons <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> and <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 <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi></math> collisions at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>7</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math> is compared using the parton and hadron cascade model together with the dynamically constrained phase-space coalescence model. In the simulation, the compact tetraquark state and the loose molecular state are formed in the partonic and hadronic levels, respectively. Our analysis of the transverse momentum spectra reveals a significant discrepancy between the compact state and the molecular states. Furthermore, the production asymmetry between <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>−</mo></msubsup></math> is investigated. Finally, the coalescence parameters are extracted from the calculated spectra to further characterize the emission source properties. These distributions are proposed as valuable criteria for distinguishing between these states and investigating their internal structures in experimental measurements.

Hongge Xu

Tianqi Luo

Yi-Long Xie

Zhi-Lei She

Ning Yu

Zuman Zhang

Comparative study of <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> versus <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> production in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>p</mi><mi>p</mi></mrow></math> collisions at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>7</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math>

We search for the reaction channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy="false">→</mo><mi>η</mi><mi>η</mi><mi>J</mi><mo>/</mo><mi>ψ</mi></math> in a data sample with center-of-mass energies from 4.226 to 4.950 GeV that was collected by the BESIII detector operating at the Beijing Electron Positron Collider (BEPCII). The data analysis is performed with two different reconstruction methods, exclusive and semi-inclusive, enabling a comparison and combination of the results. Only at a few energy points is a nonzero cross section observed with a statistical significance of more than <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>3</mn><mi>σ</mi></math> using one of the methods. Therefore, the corresponding upper limits of the cross section at the 90% confidence level are determined. The energy-dependent results show clear deviations from the line shape expected from three-body phase space alone. Since the statistical significance for almost all center-of-mass energies is low, the upper limits for the reaction channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy="false">→</mo><mi>η</mi><mi>η</mi><mi>J</mi><mo>/</mo><mi>ψ</mi></math> also serve as limits for the existence of a possible isospin partner to the charmonium-like isospin triplet <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mi mathvariant="normal">c</mi></msub><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math> which decays to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>η</mi></math>.

M. Bertani

S.L. Chen

Z. Chen

Z.J. Chen

J.J. Cui

I. Denysenko

B. Ding

R. Farinelli

J.H. Feng

L. Feng

Q.X. Feng

Search for the reaction channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy="false">→</mo><mi>η</mi><mi>η</mi><mi>J</mi><mo>/</mo><mi>ψ</mi></math> and the isospin partner of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math> at center-of-mass energies <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>4.226</mn><mtext> </mtext><mi>−</mi><mtext> </mtext><mn>4.950</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>

We calculate the fragmentation functions for a gluon into $\textit{P}$-wave $\textit{B}$ mesons within the nonrelativistic QCD factorization framework, incorporating color-singlet and color-octet contributions. Ultraviolet divergences arising from phase-space integrals are removed via operator renormalization in the modified minimal subtraction scheme. The resulting fragmentation functions are presented in both graphical form and as fitted analytic expressions.

Xu-Chang Zheng

Xing-Gang Wu

Fragmentation functions for gluon into $\textit{P}$-wave $\textit{B}$ $\textit{c}$ mesons

Within the NRQCD factorization framework, we investigate the color-singlet contribution to $$ {e}^{+}{e}^{-}\to J/\psi +{X}_{\mathrm{non}\ c\overline{c}} $$ at B factories, computing the 𝒪($\textit{α}$ ), 𝒪($\textit{v}$ ), and 𝒪($\textit{α}$ $\textit{v}$ ) corrections to both the unpolarized cross section and the $\textit{J}$/$\textit{ψ}$ angular distribution. The 𝒪($\textit{α}$ $\textit{v}$ ) correction is obtained for the first time, and the validity of NRQCD factorization at this order is explicitly verified. Using the differential equation method, the short-distance coefficients are obtained as asymptotic expansions in $$ r={m}_c/\sqrt{s} $$ up to $\textit{r}$ , which reproduce exact results with high precision at B factory energies, achieving relative errors around 10 for the cross section and around 10 for the angular distribution. Notably, with the same input parameters, our 𝒪($\textit{α}$ ) and 𝒪($\textit{v}$ ) corrections are consistent with those reported in the literature. Phenomenologically, the 𝒪($\textit{α}$ ) correction (with $$ {\mu}_R=\sqrt{s}/2 $$ ) reaches about 50% of the leading-order cross section, while the 𝒪($\textit{v}$ ) and 𝒪($\textit{α}$ $\textit{v}$ ) corrections are accidentally small. After including feeddown contributions from $\textit{ψ}$(2$\textit{S}$), the predicted cross section $$ {0.523}_{-0.197}^{+0.285} $$ pb agrees with the Belle measurement within uncertainties. However, the predicted angular distribution parameter $$ {0.120}_{-0.036}^{+0.041} $$ deviates from the experimental value 5.71 ± 2.51 by more than 2$\textit{σ}$, calling for further experimental and theoretical investigations.

Cong Li

Hao-Yang Liu

Xu-Dong Huang

Wen-Long Sang

Semi-analytical results for $$ {e}^{+}{e}^{-}\to J/\psi +{X}_{\mathrm{non}\ c\overline{c}} $$ up to 𝒪($\textit{α}$ $\textit{s}$ $\textit{v}$ 2) at B factories

We investigate the lineshape of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> cross section in the vicinity of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>+</mo><mi mathvariant="italic">c</mi><mo>.</mo><mi mathvariant="italic">c</mi><mo fontstyle="italic">.</mo></math> threshold, where the “so-called” <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math> is observed in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy="false">→</mo><mi>D</mi><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover></math> channel. To take into account the possible <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>+</mo><mi mathvariant="italic">c</mi><mo>.</mo><mi mathvariant="italic">c</mi><mo fontstyle="italic">.</mo></math> open channel effects or possible contributions from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math>, we include the intermediate meson loop transitions in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math>. As a consequence, a triangle singularity (TS) is fulfilled which can produce nontrivial structures in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>π</mi></math> invariant-mass spectrum. Moreover, the TS transition also allows access to exotic quantum number of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mi>I</mi><mo>,</mo><msup><mi>J</mi><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>C</mi><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>1</mn><mo>,</mo><msup><mn>1</mn><mrow><mo>−</mo><mo stretchy="false">(</mo><mo>−</mo><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo></math> in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>π</mi></math> invariant-mass spectrum. We present predictions for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>π</mi></math> invariant-mass spectrum and our results clarify the different manifestations of the kinematic effects and genuine resonances. In particular, we show that resonance structures arising from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover></math> scatterings or hidden charm tetraquark state with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mi>I</mi><mo>,</mo><msup><mi>J</mi><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>C</mi><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>1</mn><mo>,</mo><msup><mn>1</mn><mrow><mo>−</mo><mo stretchy="false">(</mo><mo>−</mo><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo></math> can be identified by the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>π</mi></math> invariant mass spectrum. It can provide a theoretical guidance for future experimental searches for these exotic candidates.

Jun Wang

Qiang Zhao

Study of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> lineshape near the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo></mrow></msup><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mo>+</mo><mi fontstyle="italic" mathvariant="italic">c</mi><mo>.</mo><mi mathvariant="italic">c</mi><mo fontstyle="italic">.</mo></mrow></math> threshold and possible signals for exotic hidden charm states