<p>We study the direct <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetries in the decays of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>+</mo></msubsup><msubsup><mover accent="true"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">¯</mo></mover><mi>c</mi><mo>−</mo></msubsup></math> and <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><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><msubsup><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover><mi>c</mi><mo>−</mo></msubsup></math>, emphasizing the critical role of final-state interactions (FSIs). In these channels, the small energy release and annihilation topology suppress short-distance contributions while enhancing long-distance effects. By separating the decay amplitudes into S and P waves, we show that the P-wave component, carrying only a single weak phase, contributes negligibly to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetries. In contrast, the S-wave amplitude—strongly modified by FSIs—acquires a substantial strong phase that enables interference among multiple weak phases, producing large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-violating effects. Numerically, we find sizable asymmetries of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>a</mi><mrow><mi>C</mi><mi>P</mi></mrow><mi>dir</mi></msubsup><mo>=</mo><mn>0.88</mn><mo>±</mo><mn>0.05</mn><mo>±</mo><mn>0.10</mn></math> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>+</mo></msubsup><msubsup><mover accent="true"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">¯</mo></mover><mi>c</mi><mo>−</mo></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>a</mi><mrow><mi>C</mi><mi>P</mi></mrow><mi>dir</mi></msubsup><mo>=</mo><mo>−</mo><mn>0.106</mn><mo>±</mo><mn>0.019</mn><mo>±</mo><mn>0.010</mn></math> for <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><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><msubsup><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover><mi>c</mi><mo>−</mo></msubsup></math>, where the first and second uncertainties stem from the poorly known hadron couplings and the omission of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup><mo stretchy="false">→</mo><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>+</mo></msubsup><msubsup><mover accent="true"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">¯</mo></mover><mi>c</mi><mo>−</mo></msubsup></math> rescattering process. For practical feasibility, we restrict our analysis to intermediate states involving pseudoscalar mesons, which yield tractable loop integrals. Excited intermediate states, such as <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><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>, are omitted because their inclusion would require handling nonrenormalizable interactions, introducing substantial ambiguity. These results, combined with the relatively large branching fractions, make these modes prime targets for experimental searches at LHCb and Belle II, potentially offering new insights into strong dynamics and nonperturbative QCD in heavy-hadron decays.</p>

China

Chao-Qiang Geng

Xiang-Nan Jin

Chia-Wei Liu

Large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetries from final-state interactions in charmful baryonic decays of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>+</mo></msubsup><msubsup><mover accent="true"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">¯</mo></mover><mi>c</mi><mo>−</mo></msubsup></math> and <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><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><msubsup><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover><mi>c</mi><mo>−</mo></msubsup></math>

We study the transverse momentum ( $p_T$ ) differential anisotropic flow and flow fluctuation in Pb+Pb collisions at $\sqrt{s_{_{NN}}}$ =5.02 TeV at the LHC. A (3+1)-dimensional CLVisc hydrodynamics framework with fluctuating TRENTO (or AMPT) initial conditions is utilized to simulate the space-time evolution of the quark-gluon plasma (QGP) medium. The effects of shear viscosity and the sub-nucleon structure on anisotropic flow and flow fluctuation are analyzed. Our result shows that shear viscosity tends to suppress both flow coefficients ( ${v_2\{2}\}$ , ${v_2\{4\}}$ , and ${\langle v_2\rangle}$ ) and flow fluctuation ( ${\sigma_{v_2}}$ ) owing to its smearing effect on local density fluctuation. The flow coefficients appear to be insensitive to the sub-nucleon structure, whereas the flow fluctuation ${\sigma_{v_2}}$ tends to be suppressed by the sub-nucleon structure in central collisions but enhanced in peripheral collisions. After taking into account the sub-nucleon structure effect, our numerical result can qualitatively describe the relative flow fluctuations ( ${v_2\{4\}/v_2\{2\}}$ , $F({v_2})$ ) measured by the ALICE Collaboration at the LHC. We further investigate the effects of shear viscosity, sub-nucleon structure, and initial condition model on the flow angle and flow magnitude decorrelations ( ${A_2^f}$ , ${M_2^f}$ ) using the four-particle correlation method. We find that the flow decorrelation effect is typically stronger in central collisions than in peripheral collisions. The flow angle decorrelation is found to be insensitive to the shear viscosity and sub-nucleon structure, whereas the flow magnitude decorrelation shows quite different behaviors when using the TRENTO and AMPT initial condition models. Our study sheds light on the anisotropic flow, transport properties, and initial structure of the QGP created in high-energy nuclear collisions.

Germany

Jie Zhu

Canada

Xiang-Yu Wu

Guang-You Qin

Anisotropic flow, flow fluctuation, and flow decorrelation in relativistic heavy-ion collisions: the roles of sub-nucleon structure and shear viscosity * Supported in part by the Natural Science Foundation of China (12225503, 11890710, 11890711, 11935007). Zhu Jie is supported in part by the China Scholarship Council (202306770009). Wu Xiang-Yu is supported in part by the National Science Foundation within the framework of the JETSCAPE collaboration (OAC-2004571) and in part by the Natural Sciences and Engineering Research Council of Canada. Some of the calculations were performed in the Nuclear Science Computing Center at Central China Normal University (NSC$^{3}$), Wuhan, Hubei, China.

Our study focuses on the weak decay of <math><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><mo>→</mo><mi>p</mi><mover><mi>n</mi><mo>¯</mo></mover></math>, which is the only possible two-body baryonic decay in the <math><mi>D</mi></math> meson system. An analysis using perturbative quantum chromodynamics (pQCD) is challenging in this decay due to the small amount of energy released. In particular, naive factorization, suppressed by the light quark masses, results in a minor contribution to this channel. In the framework of final state interactions, the hidden strangeness in the intermediate state naturally avoids this chiral suppression from light quark masses. The branching fraction is predicted to be <math><mi>B</mi><mo>(</mo><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><mo>→</mo><mi>p</mi><mover><mi>n</mi><mo>¯</mo></mover><mo>)</mo><mo>=</mo><mo>(</mo><mn>1.43</mn><mo>±</mo><mn>0.10</mn><mo>)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math>, in agreement with the experimental value of <math><mo>(</mo><mn>1.22</mn><mo>±</mo><mn>0.11</mn><mo>)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math>. We also analyze the decays of <math><mi>B</mi></math> mesons into two charmed baryons involving annihilation-type topological diagrams. In these decays, we conduct a joint analysis of naive factorization and final state interactions. Using the experimental upper bound of <math><mi>B</mi><mo>(</mo><msubsup><mi>B</mi><mi>s</mi><mn>0</mn></msubsup><mo>→</mo><msubsup><mi>Λ</mi><mi>c</mi><mo>+</mo></msubsup><msubsup><mover><mi>Λ</mi><mo>¯</mo></mover><mi>c</mi><mo>−</mo></msubsup><mo>)</mo><mo>&lt;</mo><mn>8</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup></math>, we set a constraint on the coupling constant <math><msub><mi>g</mi><mrow><msup><mi>D</mi><mo>+</mo></msup><msubsup><mi>Λ</mi><mi>c</mi><mo>+</mo></msubsup><mi>n</mi></mrow></msub><mo>&lt;</mo><mn>7.5</mn></math>. Final state interactions lead to a prediction of the decay parameter <math><mi>γ</mi><mo>(</mo><msubsup><mi>B</mi><mi>s</mi><mn>0</mn></msubsup><mo>→</mo><msubsup><mi>Λ</mi><mi>c</mi><mo>+</mo></msubsup><msubsup><mover><mi>Λ</mi><mo>¯</mo></mover><mi>c</mi><mo>−</mo></msubsup><mo>)</mo><mo>&gt;</mo><mn>0.8</mn></math>, whereas pQCD predicts it to be negative. We propose future measurements of <math><msup><mi>B</mi><mn>0</mn></msup><mo>→</mo><msubsup><mi>Ξ</mi><mi>c</mi><mo>+</mo></msubsup><msubsup><mover><mi>Ξ</mi><mo>¯</mo></mover><mi>c</mi><mo>−</mo></msubsup></math>, predicting a significant <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>3</mn><msub><mo>)</mo><mi>F</mi></msub></math> breaking effect with <math><mfrac><mrow><mi>B</mi><mo>(</mo><msup><mi>B</mi><mn>0</mn></msup><mo>→</mo><msubsup><mi>Ξ</mi><mi>c</mi><mo>+</mo></msubsup><msubsup><mover><mi>Ξ</mi><mo>¯</mo></mover><mi>c</mi><mo>−</mo></msubsup><mo>)</mo></mrow><mrow><mi>B</mi><mo>(</mo><msubsup><mi>B</mi><mi>s</mi><mn>0</mn></msubsup><mo>→</mo><msubsup><mi>Λ</mi><mi>c</mi><mo>+</mo></msubsup><msubsup><mover><mi>Λ</mi><mo>¯</mo></mover><mi>c</mi><mo>−</mo></msubsup><mo>)</mo></mrow></mfrac><mo>=</mo><mn>1.4</mn><mo>%</mo></math>, contrary to the naive estimate of 5.3%. We strongly recommend future measurements.

Xiao Yu

Hidden strangeness in meson weak decays to baryon pair

We study CP violation in b-baryon decays of <math altimg='si1.svg'><msubsup><mrow><mi mathvariant='normal'>&#926;</mi></mrow><mrow><mi>b</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow></msubsup><mo stretchy='false'>&#8594;</mo><msup><mrow><mi mathvariant='normal'>&#926;</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow></msup><mi>D</mi></math> with <math altimg='si2.svg'><mi>D</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><mo>,</mo><msup><mrow><mover accent='true'><mrow><mi>D</mi></mrow><mrow><mo stretchy='false'>&#175;</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup></math> and <math altimg='si3.svg'><msub><mrow><mi>D</mi></mrow><mrow><mi>i</mi></mrow></msub><mspace width='0.25em' /><mo stretchy='false'>(</mo><mi>i</mi><mo linebreak='badbreak' linebreakstyle='after'>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo stretchy='false'>)</mo></math>. We find that these baryonic decay processes provide an ideal opportunity to measure the weak phase due to the absence of the relative strong phase. Explicitly, we relate <math altimg='si4.svg'><mover accent='true'><mrow><mi>&#961;</mi></mrow><mrow><mo stretchy='false'>&#175;</mo></mrow></mover></math> and <math altimg='si5.svg'><mover accent='true'><mrow><mi>&#951;</mi></mrow><mrow><mo stretchy='false'>&#175;</mo></mrow></mover></math> the CKM elements with the decay rate ratios of <math altimg='si6.svg'><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mi mathvariant='normal'>&#915;</mi><mo stretchy='false'>(</mo><msubsup><mrow><mi mathvariant='normal'>&#926;</mi></mrow><mrow><mi>b</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow></msubsup><mo stretchy='false'>&#8594;</mo><msup><mrow><mi mathvariant='normal'>&#926;</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow></msup><msub><mrow><mi>D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy='false'>)</mo><mo stretchy='false'>/</mo><mi mathvariant='normal'>&#915;</mi><mo stretchy='false'>(</mo><msubsup><mrow><mi mathvariant='normal'>&#926;</mi></mrow><mrow><mi>b</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow></msubsup><mo stretchy='false'>&#8594;</mo><msup><mrow><mi mathvariant='normal'>&#926;</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow></msup><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy='false'>)</mo></math> without the charge conjugate states. As a complementary, we also examine the decay distributions of <math altimg='si7.svg'><msub><mrow><mi mathvariant='normal'>&#923;</mi></mrow><mrow><mi>b</mi></mrow></msub><mo stretchy='false'>&#8594;</mo><mi mathvariant='normal'>&#923;</mi><mo stretchy='false'>(</mo><mo stretchy='false'>&#8594;</mo><mi>p</mi><msup><mrow><mi>&#960;</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow></msup><mo stretchy='false'>)</mo><mi>D</mi></math>. There are in total 32 decay observables, which can be parameterized by 9 real parameters, allowing the experiments to extract the angle <math altimg='si8.svg'><mi>&#947;</mi><mo>&#8801;</mo><mi mathvariant='normal'>arg</mi><mo>&#8289;</mo><mo stretchy='false'>(</mo><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>u</mi><mi>d</mi></mrow></msub><msubsup><mrow><mi>V</mi></mrow><mrow><mi>u</mi><mi>b</mi></mrow><mrow><mo>&#8270;</mo></mrow></msubsup><mo stretchy='false'>/</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>c</mi><mi>d</mi></mrow></msub><msubsup><mrow><mi>V</mi></mrow><mrow><mi>c</mi><mi>b</mi></mrow><mrow><mo>&#8270;</mo></mrow></msubsup><mo stretchy='false'>)</mo></math> in the CKM unitarity triangle. In addition, the feasibilities of the experimental measurements are discussed. We find that <math altimg='si4.svg'><mover accent='true'><mrow><mi>&#961;</mi></mrow><mrow><mo stretchy='false'>&#175;</mo></mrow></mover></math> and <math altimg='si5.svg'><mover accent='true'><mrow><mi>&#951;</mi></mrow><mrow><mo stretchy='false'>&#175;</mo></mrow></mover></math> can be extracted at LHCb Run3 from <math altimg='si1.svg'><msubsup><mrow><mi mathvariant='normal'>&#926;</mi></mrow><mrow><mi>b</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow></msubsup><mo stretchy='false'>&#8594;</mo><msup><mrow><mi mathvariant='normal'>&#926;</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow></msup><mi>D</mi></math>, and a full analysis of <math altimg='si7.svg'><msub><mrow><mi mathvariant='normal'>&#923;</mi></mrow><mrow><mi>b</mi></mrow></msub><mo stretchy='false'>&#8594;</mo><mi mathvariant='normal'>&#923;</mi><mo stretchy='false'>(</mo><mo stretchy='false'>&#8594;</mo><mi>p</mi><msup><mrow><mi>&#960;</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo></mrow></msup><mo stretchy='false'>)</mo><mi>D</mi></math> is available at LHCb Run4.

Zheng-Yi Wei

Jiabao Zhang

New extraction of CP violation in b-baryon decays

The BESIII collaboration has recently reported the first time measurement of the decay asymmetry <math><mrow><mi>α</mi><mo>(</mo><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>→</mo><msup><mrow><mi>Ξ</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>)</mo><mo>=</mo><mn>0.01</mn><mo>±</mo><mn>0.16</mn><mo>(</mo><mi>stat</mi><mo>)</mo><mo>±</mo><mn>0.03</mn><mo>(</mo><mi>syst</mi><mo>)</mo></mrow></math> and also a sizable phase shift of <math><msub><mi>δ</mi><mi>P</mi></msub><mo>−</mo><msub><mi>δ</mi><mi>S</mi></msub><mo>=</mo><mo>−</mo><mn>1.55</mn><mo>±</mo><mn>0.25</mn></math> or <math><mn>1.59</mn><mo>±</mo><mn>0.25</mn></math> between S- and P-wave amplitudes. This implies significant strong phase shifts in the decay amplitudes. The strong phases indicate the existence of rescattering or loop effects, which are challenging to calculate due to nonperturbative effects. By employing the flavor <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>3</mn><msub><mo>)</mo><mi>F</mi></msub></math> symmetry and applying the Körner-Pati-Woo theorem to reduce the number of parameters, we find that the current data already allow us to obtain, for the first time, model-independent decay amplitudes and their strong phases. The establishment of the existence of sizable strong phases opens a window for future investigations into <math><mi>C</mi><mi>P</mi></math> violation. In our fit, a notable discrepancy emerges in the branching ratio of <math><msubsup><mi>Ξ</mi><mi>c</mi><mn>0</mn></msubsup><mo>→</mo><msup><mi>Ξ</mi><mo>−</mo></msup><msup><mi>π</mi><mo>+</mo></msup></math>. The direct relationship between <math><mi>Γ</mi><mo>(</mo><msubsup><mi>Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo>→</mo><mi>Λ</mi><msup><mi>e</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>e</mi></msub><mo>)</mo></math> and <math><mi>Γ</mi><mo>(</mo><msubsup><mi>Ξ</mi><mi>c</mi><mn>0</mn></msubsup><mo>→</mo><msup><mi>Ξ</mi><mo>−</mo></msup><msup><mi>e</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>e</mi></msub><mo>)</mo></math>, along with newly discovered <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>3</mn><msub><mo>)</mo><mi>F</mi></msub></math> relations, collectively suggests an underestimation of <math><mi>B</mi><mo>(</mo><msubsup><mi>Ξ</mi><mi>c</mi><mn>0</mn></msubsup><mo>→</mo><msup><mi>Ξ</mi><mo>−</mo></msup><msup><mi>π</mi><mo>+</mo></msup><mo>)</mo></math> in experimental findings.

Taiwan

Xiao-Gang He

Chang Yang

Complete determination of <math><mrow><mi>S</mi><mi>U</mi><mo>(</mo><mn>3</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>F</mi></mrow></msub></mrow></math> amplitudes and strong phase in <math><mrow><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>→</mo><msup><mrow><mi>Ξ</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math>

We study the CP-odd and CP-even observables of the B mesons decaying into a baryon and antibaryon. We estimate these observables through the <math><mmultiscripts><mrow><mi>P</mi></mrow><mrow><mn>0</mn></mrow><none></none><mprescripts></mprescripts><none></none><mrow><mn>3</mn></mrow></mmultiscripts></math> model and chiral selection rule. The decay branching ratio of <math><msup><mrow><mi>B</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>→</mo><mi>p</mi><mover><mrow><mi>Λ</mi></mrow><mo>‾</mo></mover></math> is calculated to be <math><mo>(</mo><mn>2.31</mn><mo>±</mo><mn>0.69</mn><mo>)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>7</mn></mrow></msup></math>, which is consistent with the current experiments. The effects of the <math><mi>B</mi><mo>−</mo><mover><mrow><mi>B</mi></mrow><mo>‾</mo></mover></math> oscillations are considered, which largely suppress the direct CP asymmetries in the <math><msubsup><mrow><mi>B</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>0</mn></mrow></msubsup></math> decays. We suggest the experiments to visit <math><msubsup><mrow><mi>B</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>→</mo><mi>Λ</mi><mo>(</mo><mo>→</mo><mi>p</mi><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>)</mo><mover><mrow><mi>Λ</mi></mrow><mo>‾</mo></mover><mo>(</mo><mo>→</mo><mover><mrow><mi>p</mi></mrow><mo>‾</mo></mover><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>)</mo></math>, where the time-averaged CP-odd observables are estimated to be large. The direct CP asymmetries of <math><msup><mrow><mi>B</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>→</mo><mi>p</mi><mover><mrow><mi>Λ</mi></mrow><mo>‾</mo></mover></math> and <math><msup><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msup><mo>→</mo><mi>p</mi><mover><mrow><mi>p</mi></mrow><mo>‾</mo></mover></math> are found to be <math><mo>(</mo><mn>26.2</mn><mo>±</mo><mn>7.9</mn><mo>)</mo><mtext>%</mtext></math> and <math><mo>(</mo><mo>−</mo><mn>3.1</mn><mo>±</mo><mn>0.9</mn><mo>)</mo><mtext>%</mtext></math> for a positive strong phase and <math><mo>(</mo><mo>−</mo><mn>36.9</mn><mo>±</mo><mn>11.1</mn><mo>)</mo><mtext>%</mtext></math> and <math><mo>(</mo><mn>4.2</mn><mo>±</mo><mn>1.3</mn><mo>)</mo><mtext>%</mtext></math> for a negative strong phase, respectively.

CP asymmetries in Meson Two-body Baryonic Decays

We study the <math><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>−</mo><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>′</mo></mrow></msubsup></math> mixing effects in the semileptonic decays the doubly charm baryons of <math><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow></msub></math>. We focus on the ratio of <math><mi>R</mi><mo>(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>)</mo><mo>≡</mo><mi>B</mi><mo>(</mo><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo>→</mo><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>′</mo></mrow></msubsup><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mi>e</mi></mrow></msub><mo>)</mo><mo>/</mo><mi>B</mi><mo>(</mo><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo>→</mo><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow></msub><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mi>e</mi></mrow></msub><mo>)</mo></math> and find that <math><mo>(</mo><mi>R</mi><mo>(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo><mo>,</mo><mi>R</mi><mo>(</mo><mo>−</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo><mo>)</mo><mo>=</mo><mo>(</mo><mn>0.46</mn><mo>±</mo><mn>0.01</mn><mo>,</mo><mn>7.33</mn><mo>±</mo><mn>0.23</mn><mo>)</mo></math> with <math><msub><mrow><mi>θ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><mn>0.137</mn><mi>π</mi></math>, which are in sharp contrast to <math><mi>R</mi><mo>(</mo><mn>0</mn><mo>)</mo><mo>=</mo><mn>2.15</mn><mo>±</mo><mn>0.11</mn></math> without the mixing. The ratio is enhanced (suppressed) by a factor of four for a negative (positive) <math><msub><mrow><mi>θ</mi></mrow><mrow><mi>c</mi></mrow></msub></math>. In addition, the polarization asymmetries of <math><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>(</mo><mo>′</mo><mo>)</mo></mrow></msubsup></math> are found to be <math><mi>α</mi><mo>(</mo><mo>−</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo><mo>=</mo><mn>0.32</mn><mspace width="0.25em"></mspace><mo>(</mo><mo>−</mo><mn>0.76</mn><mo>)</mo></math> and <math><mi>α</mi><mo>(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo><mo>=</mo><mo>−</mo><mn>0.82</mn><mspace width="0.25em"></mspace><mo>(</mo><mo>−</mo><mn>0.38</mn><mo>)</mo></math>. As <math><mi>R</mi></math> and α are highly sensitive to <math><msub><mrow><mi>θ</mi></mrow><mrow><mi>c</mi></mrow></msub></math> and unaffected by the W-exchange contributions, they provide excellent opportunities to determine <math><msub><mrow><mi>θ</mi></mrow><mrow><mi>c</mi></mrow></msub></math> in the ongoing experiments.

Ao-Wen Zhou

Semileptonic decays of doubly charmed baryons with Mixing

We study the ratio of <math><mi>R</mi><mo>=</mo><mn>2</mn><mi>Γ</mi><mo>(</mo><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>→</mo><msup><mrow><mi>Ξ</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mi>e</mi></mrow></msub><mo>)</mo><mo>/</mo><mn>3</mn><mi>Γ</mi><mo>(</mo><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>→</mo><mi>Λ</mi><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mi>e</mi></mrow></msub><mo>)</mo></math>, which is found to be <math><mi>R</mi><mo>=</mo><mn>1</mn><mspace width="0.25em"></mspace><mo>(</mo><mn>0.8</mn><mo>)</mo></math> from the exact (broken) <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>3</mn><mo>)</mo></math> flavor symmetry, in sharp contrast to the average value of <math><msub><mrow><mi>R</mi></mrow><mrow><mi>a</mi><mi>v</mi></mrow></msub><mo>=</mo><mn>0.59</mn><mo>±</mo><mn>0.10</mn></math> from the ALICE collaboration and lattice QCD results. We propose to use the mixing of <math><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>−</mo><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>′</mo></mrow></msubsup></math> to resolve the puzzle. From the mass spectra, we find that the mixing angle is <math><mo>|</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>|</mo><mo>=</mo><mn>0.137</mn><mo>(</mo><mn>5</mn><mo>)</mo><mi>π</mi></math>, which suppresses <math><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>→</mo><mi>Ξ</mi><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mi>e</mi></mrow></msub></math> about 20% model-independently, resulting in <math><mi>R</mi><mo>≈</mo><mn>0.6</mn></math> with the <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>3</mn><mo>)</mo></math> flavor breaking effect. We explicitly demonstrate that <math><mi>R</mi><mo>=</mo><mn>0.70</mn><mo>±</mo><mn>0.09</mn></math> from the bag model, which is also consistent with <math><msub><mrow><mi>R</mi></mrow><mrow><mi>a</mi><mi>v</mi></mrow></msub></math>. To test the mixing mechanism, we recommend the experiments to measure the decays of <math><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>→</mo><msup><mrow><mi>Ξ</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>(</mo><mn>1530</mn><mo>)</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mi>e</mi></mrow></msub></math>, whose branching fractions are determined to be <math><mo>(</mo><mn>4.4</mn><mo>∼</mo><mn>8.7</mn><mo>)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></math> and <math><mo>(</mo><mn>1.3</mn><mo>∼</mo><mn>2.6</mn><mo>)</mo><mtext>%</mtext></math> for <math><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msubsup></math> and <math><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup></math>, respectively, but vanish without the mixing. In addition, nonvanishing values of <math><mi>B</mi><mo>(</mo><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>→</mo><msup><mrow><mi>Ξ</mi></mrow><mrow><mo>′</mo><mn>0</mn></mrow></msup><mo>(</mo><mn>1530</mn><mo>)</mo><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>)</mo></math> and <math><mi>B</mi><mo>(</mo><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>→</mo><msup><mrow><mi>Σ</mi></mrow><mrow><mo>′</mo><mo>+</mo></mrow></msup><mo>(</mo><mn>1385</mn><mo>)</mo><msup><mrow><mover><mrow><mi>K</mi></mrow><mo>‾</mo></mover></mrow><mrow><mn>0</mn></mrow></msup><mo>)</mo></math> will also be evidences of the mixing based on the Körner-Pati-Woo theorem, which are calculated as <math><mo>(</mo><mn>3.8</mn><mo>∼</mo><mn>7.5</mn><mo>)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></math> and <math><mo>(</mo><mn>6.6</mn><mo>∼</mo><mn>13</mn><mo>)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>4</mn></mrow></msup></math>, respectively. We emphasize that <math><msub><mrow><mi>θ</mi></mrow><mrow><mi>c</mi></mrow></msub></math> is sizable and should be given serious considerations in future studies on the heavy baryon systems.

Resolving puzzle in With Mixing Spectrum Within the Quark Model

We present a systematic study of <math><msubsup><mi>Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo>→</mo><msub><mi>B</mi><mi>q</mi></msub><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math> with <math><msub><mi>B</mi><mi>q</mi></msub><mo>=</mo><mo>(</mo><mi>Λ</mi><mo>,</mo><mi>n</mi><mo>)</mo></math> and <math><mo>ℓ</mo><mo>=</mo><mo>(</mo><mi>e</mi><mo>,</mo><mi>μ</mi><mo>)</mo></math>, examining all the possible decay observables based on the homogeneous bag model (HBM) and lattice QCD (LQCD). With the HBM, we find that the branching fractions and polarization asymmetries of the daughter baryon <math><mi>Λ</mi></math> are <math><mi>B</mi><mo>(</mo><msubsup><mi>Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo>→</mo><mi>Λ</mi><msup><mi>e</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>e</mi></msub><mo>,</mo><mi>Λ</mi><msup><mi>μ</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>μ</mi></msub><mo>,</mo><mi>n</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub><mo>)</mo><mo>=</mo><mo>(</mo><mn>3.78</mn><mo>±</mo><mn>0.25</mn><mo>,</mo><mn>3.67</mn><mo>±</mo><mn>0.23</mn><mo>,</mo><mn>0.40</mn><mo>±</mo><mn>0.04</mn><mo>)</mo><mo>%</mo></math> and <math><msub><mi>α</mi><mi>Λ</mi></msub><mo>(</mo><msubsup><mi>Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo>→</mo><mi>Λ</mi><msup><mi>e</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>e</mi></msub><mo>,</mo><mspace></mspace><mi>Λ</mi><msup><mi>μ</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>μ</mi></msub><mo>)</mo><mo>=</mo><mo>(</mo><mo>−</mo><mn>82.6</mn><mo>,</mo><mo>−</mo><mn>82.3</mn><mo>)</mo><mo>%</mo></math>, respectively. From the LQCD, we obtain that <math><msub><mi>α</mi><mi>Λ</mi></msub><mo>(</mo><msubsup><mi>Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo>→</mo><mi>Λ</mi><msup><mi>e</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>e</mi></msub><mo>,</mo><msup><mi>μ</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>μ</mi></msub><mo>)</mo><mo>=</mo><mspace></mspace><mo>(</mo><mo>−</mo><mn>87.4</mn><mo>±</mo><mn>1.0</mn><mo>,</mo><mo>−</mo><mn>87.2</mn><mo>±</mo><mn>1.0</mn><mo>)</mo><mo>%</mo></math>. We also explore the time-reversal asymmetries due to new physics beyond the standard model. All our results are consistent with the current experimental data, while some of them are accessible to the experiments at BESIII and Belle II.

Anatomy of <math><msubsup><mi>Λ</mi><mi>c</mi><mo>+</mo></msubsup></math> semileptonic decays

We study the heavy quark symmetry with the homogeneous bag model (HBM) and light-front quark model (LFQM) based on the decays of <math><mrow><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>b</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>→</mo><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>−</mo></mrow></msup><msub><mrow><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>ℓ</mo></mrow></msub><mo>(</mo><mo>ℓ</mo><mo>=</mo><mi>e</mi><mo>,</mo><mi>μ</mi><mo>,</mo><mi>τ</mi><mo>)</mo></mrow></math>. In particular, we calculate various parameters in the heavy quark expansions, including the Isgur-Wise functions and their first order corrections. The parameters in the HBM are fitted from the mass spectra, while the ones in the LFQM are tightly constrained by the heavy quark symmetry, granting the predictive power of our results. We explicitly obtain that <math><mrow><mi>B</mi><mo>(</mo><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>b</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>→</mo><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup><msub><mrow><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>e</mi></mrow></msub><mo>)</mo><mo>=</mo><mo>(</mo><mn>5.69</mn><mo>±</mo><mn>0.58</mn><mo>,</mo><mn>5.35</mn><mo>±</mo><mn>0.50</mn><mo>)</mo></mrow></math>, <math><mrow><mi>B</mi><mo>(</mo><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>b</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>→</mo><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup><msub><mrow><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>μ</mi></mrow></msub><mo>)</mo><mo>=</mo><mo>(</mo><mn>5.67</mn><mo>±</mo><mn>0.58</mn><mo>,</mo><mn>5.33</mn><mo>±</mo><mn>0.49</mn><mo>)</mo></mrow></math>, and <math><mrow><mi>Γ</mi><mo>(</mo><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>b</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>→</mo><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><msup><mrow><mi>τ</mi></mrow><mrow><mo>−</mo></mrow></msup><msub><mrow><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>τ</mi></mrow></msub><mo>)</mo><mo>/</mo><mi>Γ</mi><mo>(</mo><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>b</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>→</mo><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup><msub><mrow><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>μ</mi></mrow></msub><mo>)</mo><mo>=</mo><mo>(</mo><mn>0.3243</mn><mo>±</mo><mn>0.0126</mn><mo>,</mo><mn>0.3506</mn><mo>±</mo><mn>0.0046</mn><mo>)</mo></mrow></math> for the numerical values of (HBM, LFQM). Our results of the branching fractions in both models agree well with the experimental data and lattice QCD calculations. In addition, we find that the hard gluon corrections decrease the branching fractions around 10%.