In the present work, the strong decays of the discovered $ P_c(4380) $ , $ P_c(4440) $ , $ P_c(4457) $ and their possible isospin cousins are systematically studied via the assignment that they are meson-baryon molecular states. In detail, the strong decay constants and partial decay widths of their decay channels are calculated under the framework of QCD sum rules. The decay widths of the discovered $ P_c(4380) $ , $ P_c(4440) $ , and $ P_c(4457) $ are in good agreement with the experiments. The predictions of the decays of these three related possible isospin cousins are presented, which would shed light on their findings in experiments. In return, this may testify to the assignments of the discovered $ P_c $ states.

China

Xiu-Wu Wang

Xin Li

Zhi-Gang Wang

Systematic study of the strong decays of the $\textit{P}$ $\textit{c}$ states and their possible isospin cousins via the QCD sum rules * Supported by the National Natural Science Foundation of China (12575083) and the Natural Science Foundation of Hebei Province (A2024502002)

The exploration of symmetry laws stands as a cutting-edge direction in modern physics research. This study delves into the examination of $\textit{P}$ and $\rm CP$ symmetry properties within the charm quark system by analyzing asymmetry parameters in the two-body decay process of $ \Omega_c $ . By accounting for the polarization effects of electron and positron beams and employing the helicity formalism, we systematically analyze the decay characteristics of $ \Omega_c $ and its subsequent hyperon decays through specific asymmetry parameters. A comprehensive formulation of the angular distribution for these decay processes has been developed. The research assesses the detection sensitivity of asymmetry parameters in the $ \Omega_c\rightarrow \Omega^-\pi^+ $ decay mode across different experimental conditions, including varying data sample sizes and beam polarization configurations. These results contribute to enriching a theoretical foundation for forthcoming experimental endeavors at the STCF, offering significant implications for symmetry studies in the charm sector.

Yunlu Wang

Yunlong Xiao

Pengcheng Hong

Phenomenological study of Ω $\textit{c}$ → Ω$^{−}$ $\textit{π}$ $^{+}$ at polarized electron-positron collider

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 ${\cal{O}}$ ( $\text{MeV}$ ).

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 investigate the $\textit{b}$ → $\textit{c}$ semileptonic sum rule in the presence of a massive sterile neutrino. Recent measurements of charged-current semitauonic $\textit{B}$-meson decays exhibit a ∼ 4$\textit{σ}$ deviation from the Standard Model predictions, whereas no such tension has been reported for the lowest-lying baryonic counterpart, the Λ decay. Since these decay rates are related through the sum rule, accommodating such a mismatch beyond the level of uncertainties is nontrivial. We revisit this issue by considering dimension-six operators involving a massive sterile neutrino, and evaluate the resulting violation of the sum rule. We find that the induced effect remains negligible compared with the current experimental uncertainties, further strengthening the sum rule as a consistency check for the experimental data.

Japan

Motoi Endo

Syuhei Iguro

Germany

Tim Kretz

Satoshi Mishima

$\textit{b}$ → $\textit{c}$ semileptonic sum rule: exploring a sterile neutrino loophole

Strong decays allowed by the Okubo–Zweig–Iizuka rule play a decisive role in determining the properties of particles. The widely used $$^{3}P_{0}$$ model is non-relativistic and contains unknown adjustable parameter $$\gamma $$ that need to be determined experimentally. Based on the Bethe–Salpeter equation, we have derived a relativistic calculation formula in which the effective strength related to the $$^{3}P_{0}$$ parameter $$\gamma $$ is not introduced as an independent fitting parameter, but is consistently determined by the interaction kernel of the Bethe–Salpeter equation. Using this method, we present the total width of $$h_{c}(2P)$$ and allows a theoretical determination of the parameter $$\gamma $$ in the $$^{3}P_{0}$$ model within the present framework.

Yi-Yi Rui

Tianhong Wang

Zhi-Hui Wang

Tai-Fu Feng

Guo-Li Wang

Relativistic Bethe–Salpeter study of OZI-rule allowed strong decays: determination of total width of $$h_{c}(2P)$$ and $$^{3}P_{0}$$ model parameter

Using <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>10</mn><mtext> </mtext><mn>087</mn><mo>±</mo><mn>44</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>6</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> events collected with the BESIII detector, a full angular analysis is carried out on the process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><mover accent="true"><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mo stretchy="false">→</mo><mi>n</mi><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><mover accent="true"><mrow><mi>p</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>+</mo><mi mathvariant="normal">c</mi><mo>.</mo><mi mathvariant="normal">c</mi></mrow></math>. The decay parameters <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mn>0</mn></msub></math> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mo stretchy="false">→</mo><mi>n</mi><msup><mi>π</mi><mn>0</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mover accent="true"><mi>α</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msub></math> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mover accent="true"><mrow><mi mathvariant="normal">Λ</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mo stretchy="false">→</mo><mover accent="true"><mrow><mi>n</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> are measured to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>0.668</mn><mo>±</mo><mn>0.007</mn><mo>±</mo><mn>0.002</mn></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>0.677</mn><mo>±</mo><mn>0.007</mn><mo>±</mo><mn>0.003</mn></math>, respectively, yielding the most precise test for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> symmetry of neutral decays of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>A</mi></mrow><mrow><mi>C</mi><mi>P</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>=</mo><mo stretchy="false">(</mo><msub><mrow><mi>α</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>+</mo><msub><mrow><mover accent="true"><mrow><mi>α</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msub><mo stretchy="false">)</mo><mo>/</mo><mo stretchy="false">(</mo><msub><mrow><mi>α</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>−</mo><msub><mrow><mover accent="true"><mrow><mi>α</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msub><mo stretchy="false">)</mo></mrow></math>, to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>0.006</mn><mo>±</mo><mn>0.007</mn><mo>±</mo><mn>0.002</mn></math>. The ratios <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mn>0</mn></msub><mo>/</mo><msub><mi>α</mi><mo>−</mo></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mover accent="true"><mi>α</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msub><mo>/</mo><msub><mi>α</mi><mo>+</mo></msub></math> are determined to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0.884</mn><mo>±</mo><mn>0.013</mn><mo>±</mo><mn>0.006</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0.885</mn><mo>±</mo><mn>0.013</mn><mo>±</mo><mn>0.004</mn></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mo>−</mo></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mo>+</mo></msub></math> are the decay parameters of <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> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover><mo stretchy="false">→</mo><mover accent="true"><mi>p</mi><mo stretchy="false">¯</mo></mover><msup><mi>π</mi><mo>+</mo></msup></math>, respectively. The ratios, found to be smaller than unity by more than <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>5</mn><mi>σ</mi></math>, confirm the presence of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><mi>I</mi><mo>=</mo><mn>3</mn><mo>/</mo><mn>2</mn></math> transition in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover></math> decays, which is expected to improve the theoretical calculations for isospin amplitudes, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>A</mi><mrow><mi>C</mi><mi>P</mi></mrow></msub></math>, in hyperon decays. In all results, the first and second uncertainties are statistical and systematic, respectively.

M. Ablikim

Russia

M.N. Achasov

Sweden

P. Adlarson

X.C. Ai

R. Aliberti

Italy

A. Amoroso

Q. An

Y. Bai

JINR

O. Bakina

Y. Ban

H.R. 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

X.R. Chen

X.T. Chen

X.Y. Chen

Y.B. Chen

Y.Q. Chen

Z.K. Chen

J.C. 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.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

J.H. Feng

L. Feng

Q.X. Feng

Y.T. Feng

M. Fritsch

Test of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> Symmetry in the Neutral Decays of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi></math> via <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover></math>

We present an effective field theory (EFT) framework for coupled-channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> scattering, applying it to recent lattice QCD results by Alexandrou et al. [<a href="http://dx.doi.org/10.1103/PhysRevLett.132.151902">Phys. Rev. Lett. 132, 151902 (2024)</a>]. Two complementary EFT approaches are developed: (1) a low-energy theory near the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</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>J</mi><mo>=</mo><mn>0</mn></math>) and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>*</mo></msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>=</mo><mn>1</mn></math>) thresholds, where coupled-channel effects are integrated out; (2) coupled-channel formulation, where all relevant momentum scales are treated as soft, incorporating contact interactions and one-pion exchange (OPE). Importantly, OPE contributes to the lowest channels only through off-diagonal transitions, thus resulting in the appearance of the left-hand cut from two-pion exchange. The two approaches yield mutually consistent results, supporting the existence of shallow bound states in both channels, in agreement with the lattice findings. The finite-volume spectra and extracted pole positions show a near-degeneracy in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>=</mo><mn>0</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>=</mo><mn>1</mn></math> channels, consistent with heavy-quark spin symmetry (HQSS). Using HQSS, we predict additional shallow bound states near the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>*</mo></msup><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup></math> thresholds, which are accessible to future lattice simulations. The effect of OPE on the finite volume spectra is found to be small, with only moderate impact on HQSS partners.

Michael Abolnikov

Lu Meng

Vadim Baru

Evgeny Epelbaum

Arseniy A. Filin

Ashot M. Gasparyan

Shallow <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>b</mi><mi>c</mi></mrow></msub></math> states from an EFT analysis of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> scattering on the lattice

Motivated by the recent <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>3.9</mn><mi>σ</mi></mrow></math> evidence for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation from the LHCb collaboration in decays of an antitriplet beauty baryon to a charmonium, an octet baryon, and a pseudoscalar meson, we perform, for the first time, a systematic analysis of this class of decays within the framework of flavor <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo></math> symmetry. Several predictions for branching ratios and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violating relations that can be tested in future experiments are found, in particular <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><msub><mi>A</mi><mrow><mi>C</mi><mi>P</mi></mrow></msub><mo>=</mo><msub><mi>A</mi><mrow><mi>C</mi><mi>P</mi></mrow></msub><mo stretchy="false">(</mo><msubsup><mi mathvariant="normal">Λ</mi><mi>b</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><mi>p</mi><msup><mi>π</mi><mo>−</mo></msup><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">)</mo><mo>−</mo><msub><mi>A</mi><mrow><mi>C</mi><mi>P</mi></mrow></msub><mo stretchy="false">(</mo><msubsup><mi mathvariant="normal">Λ</mi><mi>b</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><mi>p</mi><msup><mi>K</mi><mo>−</mo></msup><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">)</mo><mo>=</mo><msub><mi>A</mi><mrow><mi>C</mi><mi>P</mi></mrow></msub><mo stretchy="false">(</mo><msubsup><mi mathvariant="normal">Λ</mi><mi>b</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><mi>n</mi><msup><mi>π</mi><mn>0</mn></msup><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">)</mo><mo>−</mo><mspace linebreak="goodbreak"></mspace><msub><mi>A</mi><mrow><mi>C</mi><mi>P</mi></mrow></msub><mo stretchy="false">(</mo><msubsup><mi mathvariant="normal">Λ</mi><mi>b</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><mo stretchy="false">(</mo><mi>n</mi><msub><mi>K</mi><mi>S</mi></msub><mo>,</mo><mi>n</mi><msub><mi>K</mi><mi>L</mi></msub><mo stretchy="false">)</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">)</mo></math>. Our results provide guidance to test the availability of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo></math> symmetry and search for possible <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation effects in this class of decays.

Jin Sun

Zhi-Peng Xing

Xiao-Gang He

Predictions for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation in antitriplet beauty baryon to charmonium decays

Recently, a semi-microscopic structure model has been presented to study the structure of a weakly-bound, two-body nucleus with a deformed core, including Pauli-blocking effects. The model has been successfully applied within the adiabatic distorted wave approximation (ADWA) reaction framework to study the reactions 16C(d, p) 17C, restricting the analysis to bound states of the residual 17C nucleus. In these calculations, the structure of 17C is described using the recently presented semimicroscopic Nilsson+AMD model (NAMD), considering different Pauli-blocking methods. In the present work, the analysis is extended to unbound states of this nucleus with the aim of constraining the location of the 1 <italic>d</italic> <inf>3/2</inf> single-particle strength and infer the <math altimg='si3.svg'><mrow><mi>N</mi><mo linebreak='goodbreak'>=</mo><mn>16</mn></mrow></math> shell-gap. Comparing the measured energy differential cross section for this reaction with calculations in which the position of the 1 <italic>d</italic> <inf>3/2</inf> orbital is arbitrarily varied, we conclude that a large shell-gap (&#8239;&gt;&#8239;5 MeV) is required, in agreement with recently reported value from [J. Lois-Fuentes et al., Phys. Lett. B 867, 139600 (2025)].

Spain

P. Punta

J.A. Lay

A.M. Moro

J. Lois-Fuentes

B. Fernández-Domínguez

Constraining the N=16 shell gap in 17C via transfer to the continuum in the 16C( <italic>d, p</italic>) 17C reaction

Recently, LHCb reported the radiative-decay ratio <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="script">R</mi><mrow><mi>ψ</mi><mi>γ</mi></mrow></msup><mo>≡</mo><mi mathvariant="script">B</mi><mo stretchy="false">[</mo><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msup><mi>ψ</mi><mo>′</mo></msup><mi>γ</mi><mo stretchy="false">]</mo><mo>/</mo><mi mathvariant="script">B</mi><mo stretchy="false">[</mo><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>γ</mi><mo stretchy="false">]</mo><mo>=</mo><mn>1.67</mn><mo>±</mo><mn>0.25</mn></math> extracted from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mo>+</mo></msup><mo stretchy="false">(</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>γ</mi><mo>,</mo><msup><mi>ψ</mi><mo>′</mo></msup><mi>γ</mi><mo stretchy="false">)</mo></math>. This result differs markedly (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>∼</mo><mn>4.6</mn><mi>σ</mi></math>) from the BESIII value obtained from <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>γ</mi><mo stretchy="false">(</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>γ</mi><mo>,</mo><msup><mi>ψ</mi><mo>′</mo></msup><mi>γ</mi><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="script">R</mi><mrow><mi>ψ</mi><mi>γ</mi></mrow></msup><mo>=</mo><mo>−</mo><mn>0.04</mn><mo>±</mo><mn>0.28</mn></math>. Such a significant tension suggests that more than one state in the <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> region contributes to the processes. We therefore propose a two-state scenario: a shallow <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup></math> bound state with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><msup><mn>1</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup></math> and a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>2</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup></math> charmonium candidate, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></math>, slightly above the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup></math> threshold. We show that this hypothesis consistently describes these ratios along with other branching fractions and line shapes across multiple processes. By contrast, fits without the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></math> component fail to reproduce the radiative-ratio data. We also predict helicity-angle distributions that motivate the future experiments to test the two-state hypothesis and search for the so-far missing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></math>.

Satoshi X. Nakamura

Two nearby states in the <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> region: Resolving the radiative-decay ratio tension with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></math>