We study the charmed baryon two-body decays of → $\textit{M}$ under the SU(3) flavor symmetry, where refers to anti-triplet singly charmed baryons, and and $\textit{M}$ denote decuplet baryons and pseudoscalar mesons, respectively. We consider the released energy dependence of both partial waves and phase space for the SU(3) symmetry breaking effects. With 4 real parameters in total and 8 experimental data points, we achieve a minimal $\textit{χ}$ /d.o.f. value of 0$\textit{.}$81, providing a satisfactory explanation to the experiment results. We evaluate the branching ratios and decay asymmetries with unusual positive decay asymmetry in → $\textit{M}$, indicating the nontrivial SU(3) -breaking effects. The results of the large SU(3) -breaking effects can be verified in the further research by the experiments at BESIII, Belle II and LHCb.

China

Chao-Qiang Geng

Chia-Wei Liu

Sheng-Lin Liu

Two-body charmed baryon nonleptonic weak decays with decuplet baryon involving SU(3)

We investigate the identification of the Wess-Zumino-Witten (WZW) Lagrangian at colliders such as BESIII and the Super-$\textit{τ}$-Charm Facility. Our analysis concentrates on the radiative decays of $\textit{η}$ and $\textit{η}$ mesons, including $\textit{η}$ → $\textit{γγ}$, $\textit{η}$ → $\textit{γℓ}$ $\textit{ℓ}$ , $\textit{η}$ → $\textit{π}$ $\textit{π}$ $\textit{γ}$, and $\textit{η}$ → $\textit{π}$ $\textit{π}$ $\textit{ℓ}$ $\textit{ℓ}$ , as well as semileptonic kaon decays such as $\textit{K}$ → $\textit{π}$ $\textit{π}$ $\textit{ν}$ . Employing the hidden local symmetry framework to incorporate vector meson contributions, we compute the decay amplitudes and form factors. For the decay $\textit{η}$ → $\textit{π}$ $\textit{π}$ $\textit{γ}$, the box anomaly dominates, and we find that the anomalous coupling can be experimentally determined to percent-level precision at BESIII. In contrast, vector meson contributions are significant in the decay $\textit{η}$ → $\textit{π}$ $\textit{π}$ $\textit{γ}$. Using experimental data for $\textit{η}$ → $\textit{π}$ $\textit{π}$ $\textit{γ}$, we obtain $$ {\mathcal{B}}_{\textrm{box}}^{\textrm{exp}} $$ = (1.70 ± 0.05)%, which is approximately ten times larger than previously expected experimentally. We observe good agreement between our calculated anomalous couplings and experimental results. In kaon decays, WZW terms uniquely contribute to the form factor $\textit{H}$, which can be extracted from parity-conserving decay distributions. While predictions at the chiral point closely match experimental values (e.g., $\textit{H}$ = −2.31 versus −2.27 ± 0.10), we find that intermediate vector meson states introduce substantial corrections, potentially as large as 25%. We strongly advocate for revisiting these experiments to achieve improved precision in form factor extractions.

Yue-Liang Wu

Identify hadron anomalous couplings at colliders

<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>

Xiang-Nan Jin

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 investigate thermodynamics of apparent horizon in the ( ) universe with trivial and nontrivial connections. We first explore the perspectives of the first law, generalized second law and – phase transition with trivial connection. We show that the lowest-order correction of entropy has the same form as that in loop quantum gravity, and the critical exponents of the phase transition caused by the lowest-order correction are consistent with those in mean field theory. We then examine the thermodynamic implication of nontrivial connections. We find that nontrivial connections in the ( ) universe imply non-equilibrium states from the perspective of thermodynamics.

Haomin Rao

Chunhui Liu

Thermodynamic of the

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 construct a new stellar compact object model in the regime of anisotropic pressure using the framework of gravitational decoupling via minimal geometric deformation, with the particularity that the seed solution used is the known Kohler–Chao–Tikekar cosmological solution. As an extra condition to close the Einstein’s field equations resulting for this construction, we use a generalised complexity factor for self-gravitating spheres to the well-known Wyman IIa solution. The resulting model fulfils the fundamental physical acceptability stellar conditions for a compactness factor of a pulsar SMC X-1. The stability of the model is also investigated.

Ecuador

B. Siza

J. Andrade

D. Santana

Pakistan

Azerbaijan

Tayyab Naseer

Anisotropic extension of the Kohler–Chao–Tikekar cosmological solution with like Wyman IIa complexity factor

This work explores the construction of spherically symmetric models of stellar interiors by incorporating the null complexity factor (CF) as an additional constraint. This supplementary condition helps us to close an array of stellar structure equations resulting from the process of gravitational decoupling. By making use of MGD-type gravitational decoupling we analyze the role of gravitational decoupling and its impact on the complexity of static, self-gravitational systems. We begin by considering an anisotropic seed solution described by the Kohler–Chao–Tikekar metric ansatz. We then apply the minimal geometric deformation technique to this seed solution, imposing the constraint that the effective anisotropic factor vanishes. This constraint leads to the generation of an isotropic stellar solution. Furthermore, we construct a second family of solutions in which the CF, remains the same for both the seed solution and its minimally deformed counterpart. Our analysis further investigated the influence of both the deformation parameter and the CF on the structural properties of the static and spherically symmetric stellar objects.

Saudi Arabia

Abeer Albalahi

Z. Yousaf

S. Khan

Akbar Ali

Anisotropic interior models with Kohler–Chao–Tikekar-like complexity factor

We explored a new approach to search for a low-mass   $ Z^{\prime} $   particle through   $ Z^{\prime} $   decays by identifying its existence through parity-violating phenomena in the isospin-violating final states of   $ Z^{\prime} $   and the corresponding charge conjugated states of   $ Z^{\prime} $  . Our investigation centered on a generation-independent and leptophobic   $ Z^{\prime} $   with mass below 10 GeV. Given the present experimental conditions at Beijing Spectrometer III (BESIII) and the anticipated opportunities at the Super Tau Charm Factory (STCF), we conducted Monte-Carlo simulations to predict possible events at both facilities. Notably, we foresee a substantial enhancement in the precision of the lower limit estimation of   $ Z^{\prime} $   as well as a reduction in statistical uncertainty with upcoming STCF experiments. Furthermore, it is essential to highlight that a null result in the measurement of   $ Z^{\prime} $   would impose stringent constraints, requiring the   $ Z^{\prime} $   couplings to be in the order of   $ Z^{\prime} $  .

Jiabao Zhang

New signature of low mass ′ in / Decays  

The scalar mesons have been established for a long time, but their nature is still an open question. In this paper, we investigate the potential of categorizing their <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>3</mn><msub><mo>)</mo><mi>f</mi></msub></math> representations via <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><mi>S</mi><mi>V</mi></math> and <math><mi>γ</mi><mi>S</mi></math>, offering a criterion that may illuminate this issue. Here, <math><mi>S</mi></math> (<math><mi>V</mi></math>) denotes scalar (vector) mesons. Using the <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>3</mn><msub><mo>)</mo><mi>f</mi></msub></math> symmetry with the current data, we find that <math><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>500</mn><mo>)</mo></math> and <math><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>980</mn><mo>)</mo></math> are mostly made of singlet and octet <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>3</mn><msub><mo>)</mo><mi>f</mi></msub></math> representations, respectively, with the singlet-octet mixing angle of <math><mi>θ</mi><mo>=</mo><mo>(</mo><mn>82.9</mn><mo>±</mo><mn>4.4</mn><mo>)</mo><mo>°</mo></math>. This conclusion is consistent with the caculations of the quark-antiquark (<math><mi>q</mi><mover><mi>q</mi><mo>¯</mo></mover></math>) hypothesis. For the scalar mesons in the range of 1–2 GeV, we discuss the mixings between <math><mi>q</mi><mover><mi>q</mi><mo>¯</mo></mover></math> and glueballs. Our numerical results suggest that <math><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>1710</mn><mo>)</mo></math> is likely composed of the scalar glueball. We urge our experimental colleagues to measure <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><mi>ρ</mi><msub><mi>a</mi><mn>0</mn></msub><mo>(</mo><mn>980</mn><mo>,</mo><mn>1450</mn><mo>,</mo><mn>1710</mn><mo>)</mo></math>, <math><msup><mi>K</mi><mo>*</mo></msup><mo>(</mo><mn>892</mn><msup><mo>)</mo><mo>±</mo></msup><msup><mi>K</mi><mo>*</mo></msup><mo>(</mo><mn>700</mn><mo>,</mo><mn>1430</mn><mo>,</mo><mn>1950</mn><msup><mo>)</mo><mo>∓</mo></msup></math>, and <math><mi>ω</mi><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>500</mn><mo>)</mo></math>, which provide useful information in the <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>3</mn><msub><mo>)</mo><mi>f</mi></msub></math> analysis.

Ao-Wen Zhou

Categorizing <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>3</mn><msub><mo>)</mo><mi>f</mi></msub></math> representations of scalar mesons by <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> decays

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.