We present our results for the twist-3 gluon contribution to the single transverse-spin asymmetry (SSA) in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> production in proton-proton collisions. Although the data were reported by the RHIC experiment more than a decade ago, a theoretical calculation based on rigorous collinear factorization has remained unavailable for the dominant gluonic contribution. Our results show that only the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi></math>-even type twist-3 gluon distribution, which has a direct relationship with the gluon transverse-momentum-dependent distribution function, contributes to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> SSA. Therefore, this observable serves as a key probe to understand the three-dimensional motion of gluons inside the proton. We also perform numerical simulations of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> SSA at RHIC and LHC energies. Our simulations indicate that a sizable SSA could be generated through a mechanism different from that responsible for the SSA in light hadron and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math>-meson production.

Poland

Longjie Chen

China

Shinsuke Yoshida

Twist-3 gluon contribution to the single transverse-spin asymmetry in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> production in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi></math> collisions

Searching for dark matter is a primary goal of modern astronomy and particle physics. Invisible decays of heavy quarkonia are particularly promising for probing light dark matter, attracting broad interest due to their unique sensitivity. Experiments searching for radiative invisible decays of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> have steadily improved upper limits, and upcoming facilities will push sensitivity further—making the precise determination and subtraction of the neutrino background indispensable. Here, we present the first lattice QCD calculation of the Standard Model decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mi>γ</mi><mi>ν</mi><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover></math>, an irreducible background to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mi>γ</mi><mo>+</mo><mtext>invisible</mtext></math>. Our result for the branching fraction is <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Br</mi><mo stretchy="false">(</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mi>γ</mi><mi>ν</mi><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover><mo stretchy="false">)</mo><mo>=</mo><mn>1.04</mn><mo stretchy="false">(</mo><mn>7</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>8</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>10</mn></mrow></msup></math>, where the first uncertainty is statistical and the second is our systematic estimate. This work advances lattice-based determinations of neutrino backgrounds to quarkonium invisible decays, delivering an ab initio benchmark for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mi>γ</mi><mo>+</mo><mtext>invisible</mtext></math>. Our approach generalizes to other quarkonium channels (e.g., <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo>/</mo><mi>ϕ</mi><mo stretchy="false">→</mo><mi>γ</mi><mo>+</mo><mtext>invisible</mtext></math>) and provides critical theoretical support for dark matter searches at colliders.

Yu Meng

Ning Li

Chuan Liu

Haobo Yan

Ke-Long Zhang

Xue-Ze Zhang

Lattice determination of the neutrino background for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mi>γ</mi><mo>+</mo><mi>invisible</mi></math>

We analyze the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><mi>p</mi><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi mathvariant="normal">Ξ</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><mi>p</mi><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi mathvariant="normal">Ξ</mi></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> processes in the energy region <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1.8</mn><mo>&lt;</mo><msqrt><mrow><mi>s</mi></mrow></msqrt><mo>&lt;</mo><mn>2.8</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math> within an effective Lagrangian approach. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mo stretchy="false">(</mo><mn>1800</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Σ</mi><mo stretchy="false">(</mo><mn>2250</mn><mo stretchy="false">)</mo></math> resonances, along with the ground states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Σ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi></math>, are included. Additionally, a possible <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mtext> </mtext><mtext> </mtext><msup><mi mathvariant="normal">Σ</mi><mo>*</mo></msup></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">Λ</mi><mo>*</mo></msup></math> resonance with a mass around 1.9 GeV and a width of approximately 200 MeV is introduced to describe the structure at 2.0 GeV in the total cross section and reproducing the threshold behavior. The two possible solutions corresponding to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">Σ</mi><mo>*</mo></msup><mo stretchy="false">(</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">Λ</mi><mo>*</mo></msup><mo stretchy="false">(</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo stretchy="false">)</mo></math> cannot be distinguished by the existing data. Predictions for the polarization of the final-state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Ξ</mi></math> and the cross section of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>−</mo></msup><mi>n</mi><mo stretchy="false">→</mo><msup><mi>K</mi><mn>0</mn></msup><msup><mi mathvariant="normal">Ξ</mi><mo>−</mo></msup></math> are compared with the experimental data, we find that the results of solution-II with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">Λ</mi><mo>*</mo></msup><mo stretchy="false">(</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo stretchy="false">)</mo></math> are much better. We also discuss the possible interpretations of the introduced <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> hyperon as a pentaquark candidate, e.g., an <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>K</mi><mi mathvariant="normal">Ξ</mi><mo stretchy="false">(</mo><mn>1530</mn><mo stretchy="false">)</mo></math> hadronic molecule. However, since the polarization data suffer from rather large uncertainties, more data inputs are needed in future experiments, for example, J-PARC, HIAF, and JLab.

Zheng-Li Luo

Jia-Jun Wu

Bing-Song Zou

Possible <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi mathvariant="normal">Σ</mi></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">Λ</mi><mo>*</mo></msup></math> resonance with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>−</mo></msup><mi>p</mi><mo stretchy="false">→</mo><mi>K</mi><mi mathvariant="normal">Ξ</mi></math> scattering

We perform coupled channel analysis for <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>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>π</mi></math>, and related meson pairs for 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> channel in an effective model of hadrons and quarks. The model incorporates meson exchange potential such as one pion and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> meson exchanges, and quark exchanges. It turns out that the meson exchange potential is small, while the off-diagonal interactions by the quark exchanges at short distances, particularly for transitions between <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><mo>−</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>π</mi></math> are strong, which plays a main role for the scattering amplitudes for 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> channel, in consistent with the results of the lattice simulations of the HALQCD group.

Japan

Yukihiro Abe

Yasuhiro Yamaguchi

Atsushi Hosaka

<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><mo>−</mo><mi>π</mi><mi>J</mi><mo>/</mo><mi>ψ</mi></math> coupled-channel scattering for <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>

In this paper, we calculate the decay widths and branching fractions for the decays $$Z \rightarrow J/\psi +\Upsilon (nS)$$ ( $$n=1,2,3$$ ) at future super $\textit{Z}$ factory and at the CEPC/FCC-ee, including both the relativistic and QCD corrections within the framework of nonrelativistic QCD. Both the relativistic and QCD corrections are found to be large and negative. Compared to the leading-order results, the decay widths are significantly reduced by the higher-order corrections due to significant numerical cancellations. Despite the resulting large theoretical uncertainties, sizable event rates from these rare decay channels could still be anticipated at future high-luminosity electron-positron colliders running around the Z-pole. Ultimately, our results provide an essential theoretical baseline, highlighting the necessity of incorporating even higher-order corrections and resummation techniques for future precision phenomenological studies.

Guang-Yu Wang

Xu-Chang Zheng

Guang-Zhi Xu

Next-to-leading order QCD and relativistic corrections to $$Z \rightarrow J/\psi +\Upsilon (nS)$$

Using a data sample of (10087 ± 44) × 10 $\textit{J}$/$\textit{ψ}$ events collected with the BESIII detector at a center-of-mass energy of $$ \sqrt{s}=3.097 $$ GeV, a dedicated search for the charmonium semileptonic weak decay $$ J/\psi \to {D}_s^{-}{e}^{+}{\nu}_e+\mathrm{c}.\mathrm{c}. $$ is performed. No significant signal is observed. An upper limit on the branching fraction is set at $$ \mathcal{B}\left(J/\psi \to {D}_s^{-}{e}^{+}{\nu}_e+\mathrm{c}.\mathrm{c}.\right)&lt;9.9\times {10}^{-8} $$ at the 90% confidence level. This result improves upon previous constraints by an order of magnitude, representing the most stringent experimental limit to date. It thus provides a critical test of Standard Model predictions and new physics scenarios in heavy-quark dynamics.

M. Ablikim

Russia

M. Achasov

Sweden

P. Adlarson

X. Ai

Germany

R. Aliberti

Italy

A. Amoroso

Q. An

Y. Bai

O. Bakina

Y. Ban

H.R. Bao

V. Batozskaya

Mongolia

K. Begzsuren

N. Berger

M. Berlowski

M. Bertani

D. Bettoni

F. Bianchi

E. Bianco

A. Bortone

I. Boyko

United States

R. Briere

A. Brueggemann

H. Cai

M. Cai

X. Cai

A. Calcaterra

G. Cao

N. Cao

Türkiye

S. Cetin

X. Chai

J. Chang

T. Chang

G. Che

Y. Che

C. Chen

Chao Chen

G. Chen

H. Chen

M. Chen

S. Chen

T. Chen

X. Chen

Y. Chen

Z. Chen

J. Cheng

L. Cheng

South Korea

S. Choi

X. Chu

G. Cibinetto

F. Cossio

United Kingdom

J. Cottee-Meldrum

H. Dai

J. Dai

X. Dai

A. Dbeyssi

R. Boer

D. Dedovich

C. Deng

Z. Deng

A. Denig

I. Denisenko

M. Destefanis

F. Mori

X. Ding

Y. Ding

J. Dong

L. Dong

M. Dong

X. Dong

M. Du

S. Du

X. Du

Y. Duan

Z. Duan

P. Egorov

G. Fan

J. Fan

Y. Fan

J. Fang

S. Fang

W. Fang

Y. Fang

L. Fava

F. Feldbauer

G. Felici

C. Feng

J. Feng

L. Feng

Q. Feng

Y. Feng

M. Fritsch

Search for the charmonium semi-leptonic weak decay $$ J/\psi \to {D}_s^{-}{e}^{+}{\nu}_e+\mathrm{c}.\mathrm{c}. $$

We investigate the strong decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><msup><mi>ρ</mi><mo>+</mo></msup><msup><mi>ρ</mi><mo>−</mo></msup><mi>ω</mi></math> and the radiative decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mi>γ</mi><msup><mi>ρ</mi><mn>0</mn></msup><mi>ω</mi></math>, taking into account 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"><msup><mi>K</mi><mo>*</mo></msup><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi><mi>ω</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi><mi>ϕ</mi></math> final-state interactions, which dynamically generate the scalar meson <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>1710</mn><mo stretchy="false">)</mo></math>. Our results demonstrate that a clear peak structure emerges around 1.8 GeV in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>ρ</mi><mo>+</mo></msup><mi>ω</mi></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>ρ</mi><mo>−</mo></msup><mi>ω</mi></math>) invariant mass distribution of the strong decay, which can be associated with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>1710</mn><mo stretchy="false">)</mo></math> resonance. Similarly, a distinct peak is predicted in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>ρ</mi><mn>0</mn></msup><mi>ω</mi></math> invariant mass distribution of the radiative decay. Our results indicate that clear signals of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>1710</mn><mo stretchy="false">)</mo></math> production could be observed in future measurements of these processes at BESIII, Belle II, and the planned Super Tau-Charm Facility, thereby helping to determine its mass and width more precisely.

Spain

Wen-Tao Lyu

Luis Roca

Eulogio Oset

Role of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>1710</mn><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><mo stretchy="false">→</mo><msup><mi>ρ</mi><mo>+</mo></msup><msup><mi>ρ</mi><mo>−</mo></msup><mi>ω</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mi>γ</mi><msup><mi>ρ</mi><mn>0</mn></msup><mi>ω</mi></math> reactions

We investigate the low-energy interactions between the charmonium state <italic>J</italic>/ <italic>&#968;</italic> and the light pseudoscalar mesons ( <italic>&#960;</italic> and <italic>K</italic>) within the framework of dispersion relations. We demonstrate that the symmetry-breaking terms in the chiral Lagrangian induce mixing between the bare charmonium fields, necessitating a diagonalization procedure to correctly identify the physical <italic>J</italic>/ <italic>&#968;</italic> and <italic>&#968;</italic>&#8242; states. Using the resulting diagonalized Lagrangian, we construct the crossed-channel amplitudes for <math altimg='si4.svg'><mrow><mi>J</mi><mo linebreak='goodbreak'>/</mo><mi>&#968;</mi><mi>J</mi><mo linebreak='goodbreak'>/</mo><mi>&#968;</mi><mo>&#8594;</mo><mi mathvariant='script'>P</mi><mover accent='true'><mi mathvariant='script'>P</mi><mo>&#175;</mo></mover></mrow></math> and incorporate the <italic>&#960;&#960;</italic> and <math altimg='si5.svg'><mrow><mi>K</mi><mover accent='true'><mi>K</mi><mo>&#175;</mo></mover></mrow></math> rescattering effects through dispersion relations. This framework is used consistently both in the phenomenological extraction of the transition parameters from <italic>&#968;</italic>&#8242;&#8239;&#8594;&#8239; <italic>J</italic>/ <italic>&#968;&#960;&#960;</italic> and in the continuation of the crossed amplitudes to the near-threshold <math altimg='si8.svg'><mrow><mi>J</mi><mo linebreak='goodbreak'>/</mo><mi>&#968;</mi><mi mathvariant='script'>P</mi><mspace width='0.33em' /><mo>(</mo><mi mathvariant='script'>P</mi><mo linebreak='goodbreak'>=</mo><mi>&#960;</mi><mo>,</mo><mi>K</mi><mo>)</mo></mrow></math> region. As a result, we determine both the scattering lengths and the effective ranges. We obtain the upper-bound estimates <math altimg='si9.svg'><mrow><msub><mi>a</mi><mrow><mi>J</mi><mo>/</mo><mi>&#968;</mi><mi>&#960;</mi></mrow></msub><mo>&#8818;</mo><mo>&#8722;</mo><mn>0.0037</mn></mrow></math> fm and <math altimg='si10.svg'><mrow><msub><mi>a</mi><mrow><mi>J</mi><mo>/</mo><mi>&#968;</mi><mi>K</mi></mrow></msub><mo>&#8818;</mo><mo>&#8722;</mo><mn>0.049</mn></mrow></math> fm, where the negative sign indicates an attractive interaction without a bound state in our convention. Our results show that the <italic>J</italic>/ <italic>&#968;K</italic> interaction is moderately enhanced relative to the pion channel, driven by explicit chiral symmetry breaking. Furthermore, a quantitative comparison of the coupled-channel mechanism, where <italic>J</italic>/ <italic>&#968;&#960;</italic> and <italic>J</italic>/ <italic>&#968;K</italic> couple to open-charm channels, reveals that both <italic>J</italic>/ <italic>&#968;&#960;</italic> and <italic>J</italic>/ <italic>&#968;K</italic> scatterings are predominantly governed by the soft-gluon exchange mechanism.

Jiang Yan

Xiong-Hui Cao

Meng-Lin Du

Feng-Kun Guo

Low-energy scattering of the <italic>J</italic>/ <italic>&#968;&#960;</italic> and <italic>J</italic>/ <italic>&#968;K</italic> systems

The time-dependent <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetry in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow><mi>ρ</mi><mo stretchy="false">(</mo><mn>770</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> decays is measured using proton-proton collision data corresponding to an integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>6</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>, collected with the LHCb detector at a center-of-mass energy of 13 TeV during the years 2015–2018. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-violation parameters for this process are determined to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><msubsup><mrow><mi>β</mi></mrow><mrow><mi>c</mi><mover accent="true"><mrow><mi>c</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mi>d</mi></mrow><mrow><mi>eff</mi></mrow></msubsup><mo>=</mo><mn>0.710</mn><mo>±</mo><mn>0.084</mn><mo>±</mo><mn>0.051</mn><mtext> </mtext><mtext> </mtext><mi>rad</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">|</mo><mi>λ</mi><mo stretchy="false">|</mo><mo>=</mo><mn>1.019</mn><mo>±</mo><mn>0.034</mn><mo>±</mo><mn>0.024</mn></mrow></math>, where the first uncertainty is statistical and the second systematic. This constitutes the first observation of time-dependent <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow><mi>ρ</mi><mo stretchy="false">(</mo><mn>770</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> decays. Assuming approximate SU(3) flavor symmetry, these results are combined with the previous consistent LHCb measurement to set the most stringent constraint on the penguin contribution, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><msub><mi>ϕ</mi><mi>s</mi></msub></math>, to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-violating phase <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ϕ</mi><mi>s</mi></msub></math> in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>s</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow><mi>ϕ</mi><mo stretchy="false">(</mo><mn>1020</mn><mo stretchy="false">)</mo></math> decays, yielding <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><msub><mi>ϕ</mi><mi>s</mi></msub><mo>=</mo><mn>5.0</mn><mo>±</mo><mn>4.6</mn><mtext> </mtext><mtext> </mtext><mi>mrad</mi></math>.

Netherlands

R. Aaij

A.S.W. Abdelmotteleb

Switzerland

C. Abellan Beteta

F. Abudinén

T. Ackernley

A.A. Adefisoye

B. Adeva

M. Adinolfi

France

C. Agapopoulou

C.A. Aidala

Z. Ajaltouni

S. Akar

K. Akiba

M. Akthar

P. Albicocco

J. Albrecht

R. Aleksiejunas

CERN

F. Alessio

P. Alvarez Cartelle

R. Amalric

Brazil

S. Amato

J.L. Amey

Y. Amhis

L. An

L. Anderlini

M. Andersson

P. Andreola

M. Andreotti

S. Andres Estrada

A. Anelli

D. Ao

C. Arata

F. Archilli

Z. Areg

M. Argenton

Costa Rica

S. Arguedas Cuendis

L. Arnone

A. Artamonov

M. Artuso

E. Aslanides

R. Ataíde Da Silva

M. Atzeni

B. Audurier

J.A. Authier

D. Bacher

I. Bachiller Perea

S. Bachmann

M. Bachmayer

J.J. Back

Observation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> Violation in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>ρ</mi><mo stretchy="false">(</mo><mn>770</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> Decays