We study the implications for $$B_s - \bar{B}_s$$ mixing and the neutron electric dipole moment (EDM) in a light dark matter model with sizable invisible rare meson decays to accommodate the recent possible deviations from Standard Model (SM) predictions observed in $$B^+\rightarrow K^+\nu \bar{\nu }$$ by Belle II and $$K^+\rightarrow \pi ^+\nu \bar{\nu }$$ by NA62. Given that the neutrinos in these decays escape detection, they can be replaced by other invisible final states. Based on effective operator analysis, it has been proposed that branching ratios for $$B^+\rightarrow K^+ +\text{ invisible }$$ and $$K^+\rightarrow \pi ^+ +\text{ invisible }$$ can naturally be larger than the SM predictions due to the emission of light dark matter pairs. We demonstrate that this scenario can be realized within a UV-complete two-Higgs-doublet model (2HDM) where neutral Higgs bosons mediating dark matter interactions induce significant low-energy effects especially for $$B_s-\bar{B}_s$$ mixing and neutron EDM. Within the allowed parameter space, we find non-negligible contributions to $$B_s - \bar{B}_s$$ mixing. For the neutron EDM, there is a cancellation due to the exchange of neutral spin-zero particles, but QCD renormalization group evolution will lift this cancellation which in fact is generally true for any neutral Higgs contribution. However, we demonstrate that such a cancellation does not occur for charged scalar contributions. Ultimately, the allowed CP-violating phases in the Yukawa sector can generate a neutron EDM at a level consistent with the current experimental bound.

China

Xuan Hong

Xiao-Gang He

Ming-Wei Li

A light DM model for large $$B \rightarrow K + \text{ invisible }$$ and $$K \rightarrow \pi + \text{ invisible }$$ decays and its implications for $$B_s-\bar{B}_s$$ mixing and neutron EDM

We investigate the existence of the three-body molecular state composed of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup></math> within the one-boson-exchange model. A major challenge is that while the pseudoscalar-meson couplings are well determined, the couplings for scalar- and vector-meson exchanges render significant model dependence. To ensure the reliability of our predictions and reduce model dependence, we recalibrate the coupling constants of the one-boson-exchange model. We treat the pole position of <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>, or equivalently the scalar <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>σ</mi></math>-exchange coupling constant, as the only unknown parameter. The coupling constants for the vector <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ω</mi></math> exchanges are determined by the pole positions of the well-established states <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> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo stretchy="false">(</mo><mn>3875</mn><mo stretchy="false">)</mo></math>. We demonstrate that these parameter sets also successfully describe the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>s</mi><mn>0</mn></mrow></msub><mo stretchy="false">(</mo><mn>2870</mn><mo stretchy="false">)</mo></math> without further tuning. For the three-body system, our results indicate that an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mrow><mo stretchy="false">(</mo><msup><mi>J</mi><mi>P</mi></msup><mo stretchy="false">)</mo></mrow><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn><mrow><mo stretchy="false">(</mo><msup><mn>0</mn><mo>−</mo></msup><mo stretchy="false">)</mo></mrow></math> three-body molecular bound state exists when <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> is a virtual state located within approximately <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>10</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> of the <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> threshold. Furthermore, we extend our analysis to the complex energy plane using the complex scaling method to search for molecular resonances, though no evidence of resonances is found in considered channels. We also apply this formalism to the bottom analog <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><msup><mi>B</mi><mo>*</mo></msup><msup><mi>K</mi><mo>*</mo></msup></math> system. In this sector, the conditions for the existence of a three-body bound state are more relaxed, as a <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> virtual state located within <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>25</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> below the threshold suffices, although three-body molecular resonances remain absent. We suggest that future experiments precisely measure the pole position of <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> or search for the three-body bound state in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mi>D</mi><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mi>π</mi><mi>π</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mi>D</mi><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover></math> channels, as these efforts would mutually illuminate the nature of the associated states.

Yan-Ke Chen

Lu Meng

Jun-Zhang Wang

Shi-Lin Zhu

Existence of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><msup><mi>B</mi><mo>*</mo></msup><msup><mi>K</mi><mo>*</mo></msup></math> three-body molecular states

We analyze the charmless two-body decays of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> meson into a pseudoscalar and a vector meson, referred to as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>P</mi><mi>V</mi></math> decay, within the framework of the modified perturbative QCD (PQCD) approach, which was originally developed to solve the long-standing puzzles, the so-called <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>K</mi></math> puzzles. In this method, based on the conventional PQCD calculations, soft form factors and contributions arising from color-octet quark-antiquark components in the final state are introduced, which involve essentially nonperturbative dynamics. By employing the flavor SU(3) symmetry and its breaking effect, the parameters describing soft contributions are correlated and subsequently reduced into a more concise set of SU(3) parameters. Through a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>χ</mi><mn>2</mn></msup></math> analysis procedure applied to the experimental data, these parameters are determined, from which the corresponding theoretical results for the branching ratios and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetries in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>P</mi><mi>V</mi></math> decays are derived. Within this framework, it is demonstrated that the theoretical calculations align well with experimental measurements, suggesting that the method developed for solving <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>K</mi></math> puzzles can be extended to more decay modes of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> meson. The numerical analysis shows that these soft contributions have a significant influence on the theoretical results. Furthermore, more precise experimental data are needed for deeper investigations of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetries.

Sheng Lü

Ru-Xuan Wang

Mao-Zhi Yang

Phenomenological analysis of charmless <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>P</mi><mi>V</mi></math> decays in the modified perturbative QCD approach

We investigate rare special dileptonic decays of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Σ</mi><mi>b</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></math> baryons in the standard model and context of the general two-Higgs-doublet model with Type III. Specifically, we consider the decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Σ</mi><mi>b</mi></msub><mo stretchy="false">→</mo><mi mathvariant="normal">Σ</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></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><mi mathvariant="normal">Ξ</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>ℓ</mo></math> represents <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>τ</mi></math> lepton. By studying these rare decays, we aim to assess the impact of the two-Higgs-doublet model with Type III on various observables, such as the differential decay width, the total decay width, the differential branching ratio, the total branching ratio, and lepton forward-backward asymmetries using the decay amplitude and the transition matrix elements in terms of form factors calculated via light cone QCD in full theory. We compare our results to those of the standard model, as well as existing lattice QCD predictions and experimental data, to assess the agreement and viability of the two-Higgs-doublet model with Type III. Furthermore, we highlight the potential for experimental investigations of these decay channels in the near future. The soon-to-be updated LHCb and/or Belle II detectors, renowned for their capabilities in studying rare decays, present excellent opportunities for probing the predicted branching ratios.

Türkiye

Z. Tavukoğlu

A.T. Olgun

Iran

K. Azizi

Comprehensive analyses of rare <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Σ</mi><mi>b</mi></msub><mo stretchy="false">→</mo><mi mathvariant="normal">Σ</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></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><mi mathvariant="normal">Ξ</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math> decays in the 2HDM

We study the semileptonic decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>s</mi></msub><mo stretchy="false">→</mo><msubsup><mi>D</mi><mi>s</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup><mi>τ</mi><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover></math> as a promising probe for new physics (NP) beyond the standard model (SM). The extension of the SM is done through the introduction of four-fermion operators beyond the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>V</mi><mo>−</mo><mi>A</mi></math> structure with the corresponding Wilson coefficients characterizing their contribution. The constraints on these coefficients are obtained from recent experimental data. Form factors describing hadron transitions are calculated in our covariant quark model with infrared confinement. Theoretical predictions for the full set of observables in these channels are provided. We analyze possible NP effects to be tested in future experiments.

JINR

M.A. Ivanov

India

J.N. Pandya

Italy

P. Santorelli

N.R. Soni

Vietnam

C.T. Tran

H.C. Tran

Vo Quoc Phong

Detailed analysis of possible new-physics effects in the semileptonic decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>s</mi></msub><mo stretchy="false">→</mo><msubsup><mi>D</mi><mi>s</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup><mi>τ</mi><mover accent="true"><mi>ν</mi><mo stretchy="false">¯</mo></mover></math>

Germany

Simon Mutke

Leon Heuser

Ingrid Dax

Bastian Kubis

Sweden

Stefan Leupold

Publisher Correction: Dispersive analysis of $\textit{D}$- and $\textit{B}$-meson form factors with chiral and heavy-quark constraints

Belgium

A. Sánchez-Fernández

S. Bara

W. Ryssens

S. Goriely

Corrigendum to “Accurate spontaneous fission half-lives from a microscopic large-scale nuclear structure model” [Physics Letters B 140287 (2026)]

This paper presents a detailed description of a model-independent method for the direct measurement of the Υ(4$\textit{S}$) → $\textit{B}$ $\textit{B}$ and Υ(4$\textit{S}$) → $$ {B}^0{\overline{B}}^0 $$ production fractions at $\textit{B}$ factories. The method is based on counting single- and double-inclusive charmed meson production at the Υ(4$\textit{S}$) resonance, providing statistical tagging of $$ {B}^0{\overline{B}}^0 $$ and $\textit{B}$ $\textit{B}$ events. A feasibility study indicates that a precision comparable to the current world average can be achieved without making any underlying assumptions, as the calculations rely solely on event yields.

Russia

M. Yasaveev

P. Pakhlov

N. Peters

A. Mufazalova

A model independent method for measurement of $\textit{B}$ ± and $\textit{B}$ 0 meson production fractions at Υ(4$\textit{S}$)

In this work, to establish a more abundant <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub></math> baryon spectrum, we discuss the production potentials of the excited <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub></math> baryons through <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub></math> hadronic weak decays within a constituent quark model. Based on our successful explanations of the existing experimental data for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub><mo stretchy="false">→</mo><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><mo stretchy="false">(</mo><msup><mi>π</mi><mo>−</mo></msup><mo>,</mo><msup><mi>K</mi><mo>−</mo></msup><mo>,</mo><msup><mi>D</mi><mo>−</mo></msup><mo>,</mo><msubsup><mi>D</mi><mi>s</mi><mo>−</mo></msubsup><mo>,</mo><msubsup><mi>D</mi><mi>s</mi><mrow><mo>*</mo><mo>−</mo></mrow></msubsup><mo stretchy="false">)</mo></math> processes, we further calculate the decay rates of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub></math> baryon into the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>P</mi></math>-, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>D</mi></math>-, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>S</mi></math>-, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>3</mn><mi>S</mi></math>-, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>P</mi></math>-, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>F</mi></math>-, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>D</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub></math> excited states. It is found that these <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub></math> excitations have large production rates in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub></math> hadronic weak decay process associated with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>−</mo></msup></math> meson emitting, i.e., <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub><mo stretchy="false">→</mo><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>*</mo></msubsup><msup><mi>π</mi><mo>−</mo></msup></math>, their branching fractions can reach up to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup><mo stretchy="false">)</mo></math>. To search for the higher <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>3</mn><mi>S</mi></math>-, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>P</mi></math>-, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>F</mi></math>-, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>D</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub></math> states, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub><mo stretchy="false">→</mo><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>3</mn><mi>S</mi><mo stretchy="false">)</mo><msup><mi>π</mi><mo>−</mo></msup><mo stretchy="false">→</mo><msup><mi>D</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup><mi>p</mi><msup><mi>π</mi><mo>−</mo></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub><mo stretchy="false">→</mo><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>2</mn><mi>P</mi><mo>,</mo><mn>2</mn><mi>D</mi><mo>,</mo><mn>1</mn><mi>F</mi><mo stretchy="false">)</mo><msup><mi>π</mi><mo>−</mo></msup><mo stretchy="false">→</mo><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mn>0</mn></mrow></msup><mi>p</mi><msup><mi>π</mi><mo>−</mo></msup></math> decays are worth observing in future experiments.

Kai-Lei Wang

Ya-Mei Cao

Hui-Xiao Duan

Xian-Hui Zhong

Production of excited <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup></math> baryons through <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub></math> hadronic weak decays

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

United Kingdom

A.S.W. Abdelmotteleb

Switzerland

C. Abellan Beteta

F. Abudinén

T. Ackernley

United States

A.A. Adefisoye

Spain

B. Adeva

M. Adinolfi

P. Adlarson

France

C. Agapopoulou

C.A. Aidala

Z. Ajaltouni

S. Akar

K. Akiba

Poland

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

Z.B. Bai

P. Baladron Rodriguez

V. Balagura

A. Balboni

W. Baldini

Z. Baldwin

L. Balzani

H. Bao

J. Baptista de Souza Leite

C. Barbero Pretel

M. Barbetti

I.R. Barbosa

R.J. Barlow

M. Barnyakov

S. Barsuk

W. Barter

J. Bartz

S. Bashir

B. Batsukh

P.B. Battista

A. Bavarchee

A. Bay

A. Beck

M. Becker

F. Bedeschi

I.B. Bediaga

N.A. Behling

S. Belin

A. Bellavista

K. Belous

I. Belov

I. Belyaev

G. Benane

G. Bencivenni

E. Ben-Haim

A. Berezhnoy

R. Bernet

A. Bertolin

F. Betti

J. Bex

O. Bezshyyko

S. Bhattacharya

M.S. Bieker

N.V. Biesuz

A. Biolchini

M. Birch

F.C.R. Bishop

A. Bitadze

A. Bizzeti

T. Blake

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