<p>Motivated by recent LHCb measurements 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"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub></math> three body decays, we conduct an analysis of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetry in three body decays of bottom baryons utilizing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi></math>-spin symmetry. We first develop a convenient representation that facilitates the incorporation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi></math>-spin symmetry into our analysis. By integrating weak and strong phases into the derived amplitude, we obtain the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetry and establish relationships between <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>U</mi></math>-spin related decay channels. With the help of experimental measurements, we provide numerical predictions for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetries for other decay channels, particularly <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>b</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> under a specific scenario. Furthermore, we provide a quantity that can be used as a null test of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>SU</mi><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo></mrow></math> symmetry and standard model. Deviations from zero would indicate potential new physics if they exceed the expected magnitude of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>SU</mi><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo></mrow></math> breaking effects. These results are valuable for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation measurements in baryon decays, and can be tested in future experiments.</p>

China

Wei Wang

Zhi-Peng Xing

Zhen-Xing Zhao

Implications on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation of charmless three body decays of bottom baryons from a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi></math>-spin analysis

Motivated by the work of Cardoso et al. (2022) <cross-ref refid='br0150' id='crf0030'>[15]</cross-ref> on black holes in galaxies, we derive a new black hole solution surrounded by a Dekel-Zhao (DZ) dark matter profile. The derived metric, influenced by DZ profile parameters, exhibits two distinct regimes: for <math altimg='si1.svg'><mi>r</mi><mo>&#8810;</mo><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant='normal'>c</mi></mrow></msub></math> ( <math altimg='si2.svg'><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant='normal'>c</mi></mrow></msub></math> is a characteristic radius), exponential corrections dominate, producing significant deviations from the Schwarzschild solution near dense cores, while for <math altimg='si3.svg'><mi>r</mi><mo>&#8811;</mo><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant='normal'>c</mi></mrow></msub></math>, these corrections vanish, restoring the Schwarzschild metric at large distances. These findings ensure consistency with general relativity in vacuum. The black hole shadow and deflection angle are analyzed, demonstrating that the shadow radius increases with black hole mass ( <math altimg='si4.svg'><msub><mrow><mi>M</mi></mrow><mrow><mi mathvariant='normal'>BH</mi></mrow></msub></math>), while higher central densities ( <math altimg='si5.svg'><msub><mrow><mi>&#961;</mi></mrow><mrow><mi mathvariant='normal'>ch</mi></mrow></msub></math>) result in smaller shadows, reflecting the environmental impact of dense dark matter halos. Photon dynamics reveal how DZ profiles modify critical impact parameters and effective potentials, with gravitational lensing effects highly sensitive to the characteristic radius ( <math altimg='si2.svg'><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant='normal'>c</mi></mrow></msub></math>). Smaller <math altimg='si2.svg'><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant='normal'>c</mi></mrow></msub></math> values lead to larger deflection angles due to stronger gravitational effects near compact cores. This work highlights the significance dark matter profiles in shaping black hole observables, providing a theoretical foundation for future observational studies and advancing the understanding of dark matter-black hole interactions in astrophysical and cosmological contexts.

Türkiye

Ali Övgün

Philippines

Reggie C. Pantig

Black hole in the Dekel-Zhao dark matter profile

In this work, we investigate the weak decays of ground-state triply heavy baryons. We first obtain the form factors using the light-front quark model in the three-quark picture, and then apply them to arrive at some phenomenological predictions, including the decay widths of semileptonic decays and nonleptonic decays. Our results are expected to be helpful for the experimental search for triply heavy baryons.

Fu-Wei Zhang

Qi Yang

Weak decays of triply heavy baryons

We investigate the purely nonfactorizable <math><msubsup><mi>Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo>→</mo><msup><mi>Ξ</mi><mn>0</mn></msup><msup><mi>K</mi><mo>+</mo></msup></math> decay using light-cone sum rules. To extract the decay amplitudes, a three-point correlation function is defined and calculated at hadron and quark-gluon level, respectively. Both the W-exchange and the W-inward emission diagrams are considered in the quark-gluon level calculation, where the two-particle light-cone distribution amplitudes (LCDAs) of kaon are used as nonperturbative input. We obtain the decay amplitudes contributed from the twist-2 and twist-3 kaon LCDAs, respectively. The obtained P-wave amplitude is consistent with those predicted in the literature, while the S-wave one is much smaller. This significant difference between the S- and P -wave amplitudes leads to small up-down spin asymmetry, close to the experimental measurement.

Yu-Ji Shi

Light-cone sum rules study on the purely nonfactorizable <math><msubsup><mi>Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo>→</mo><msup><mi>Ξ</mi><mn>0</mn></msup><msup><mi>K</mi><mo>+</mo></msup></math> decay

In traditional QCD sum rules, the simple hadron spectral density model of the “delta-function-type ground state + theta-function-type continuous spectrum” determines that there is no perfect parameter selection. In recent years, inverse problem methods, particularly the inverse matrix method, have shown better handling of QCD sum rules. This work continues to develop the inverse matrix method. Considering that the narrow-width approximation may still be a good approximation, we separate the ground state from the spectral density. We then follow the general steps of the inverse matrix method to extract physical quantities such as decay constants that we may be more interested in.

Yi-Peng Xing

Run-Hui Li

A progress in the inverse matrix method in QCD sum rules

Heavy quark expansion can nicely explain the lifetime of  $$\Lambda _{b}$$  <math> <msub> <mi>Λ</mi> <mi>b</mi> </msub> </math>  . However, there still exist sizable uncertainties from the four-quark operator matrix elements of  $$\Lambda _{b}$$  <math> <msub> <mi>Λ</mi> <mi>b</mi> </msub> </math>   in  $$1/m_{b}^{3}$$  <math> <mrow> <mn>1</mn> <mo>/</mo> <msubsup> <mi>m</mi> <mrow> <mi>b</mi> </mrow> <mn>3</mn> </msubsup> </mrow> </math>   corrections, which describe the spectator effects. In this work, these four-quark operator matrix elements are investigated using full QCD sum rules for the first time. At the QCD level, contributions from up to dimension-6 four-quark operators are considered. Our method for calculating high-dimensional operator matrix elements holds promise for use in resolving the  $$\Omega _{c}$$  <math> <msub> <mi>Ω</mi> <mi>c</mi> </msub> </math>   lifetime puzzle.

Xiao-Yu Sun

On the four-quark operator matrix elements for the lifetime of  $$\Lambda _{b}$$  <math> <msub> <mi>Λ</mi> <mi>b</mi> </msub> </math>

There exists a significant deviation between the most recent lattice quantum chromodynamics (QCD) simulation and experimental measurement by Belle for <math><msubsup><mi>Ξ</mi><mi>c</mi><mn>0</mn></msubsup><mo>→</mo><msup><mi>Ξ</mi><mo>−</mo></msup><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math>. In this work, we investigate the <math><msub><mi>Ξ</mi><mi>c</mi></msub><mo>→</mo><mi>Ξ</mi></math> form factors in QCD sum rules. To this end, the two-point correlation functions of <math><msub><mi>Ξ</mi><mi>c</mi></msub></math> and <math><mi>Ξ</mi></math>, and the three-point correlation functions of <math><msub><mi>Ξ</mi><mi>c</mi></msub><mo>→</mo><mi>Ξ</mi></math> are calculated. At the QCD level, contributions from up to dimension-6 four-quark operators are considered, and the leading order results of the Wilson coefficients are obtained. For the form factors, relatively stable Borel windows can be found. Our form factors are comparable with those of lattice QCD, except for <math><msub><mi>f</mi><mo>⊥</mo></msub></math>. The obtained form factors are then used to predict the branching ratios of <math><msub><mi>Ξ</mi><mi>c</mi></msub><mo>→</mo><mi>Ξ</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math>, and our predictions are consistent with the most recent data of ALICE and Belle, and those of lattice QCD within error. Given that the branching ratios only contain limited information, we suggest the experimentalists directly measure the form factors of <math><msub><mi>Ξ</mi><mi>c</mi></msub><mo>→</mo><mi>Ξ</mi></math>.

Ya-Ting Yang

Semileptonic form factors of <math><mrow><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>→</mo><mi>Ξ</mi></mrow></math> in QCD sum rules

In this work, we perform a QCD sum rules analysis on  $$\Xi _{Q}-\Xi _{Q}^{\prime }$$  <math> <mrow> <msub> <mi>Ξ</mi> <mi>Q</mi> </msub> <mo>-</mo> <msubsup> <mi>Ξ</mi> <mrow> <mi>Q</mi> </mrow> <mo>′</mo> </msubsup> </mrow> </math>   mixing. Contributions from up to dimension-6 four-quark operators are considered. However, it turns out that only dimension-4 and dimension-5 operators contribute, which reveals the non-perturbative nature of mixing. In particular, we observe that only the diagrams with the two light quarks participating in gluon exchange contribute to the mixing. Our results indicate that the mixing angle  $$\theta _{c}=(1.2\sim 2.8)^{\circ }$$  <math> <mrow> <msub> <mi>θ</mi> <mi>c</mi> </msub> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mn>1.2</mn> <mo>∼</mo> <mn>2.8</mn> <mo>)</mo> </mrow> <mo>∘</mo> </msup> </mrow> </math>   for the  $$Q=c$$  <math> <mrow> <mi>Q</mi> <mo>=</mo> <mi>c</mi> </mrow> </math>   case and  $$\theta _{b}=(0.28\sim 0.34)^{\circ }$$  <math> <mrow> <msub> <mi>θ</mi> <mi>b</mi> </msub> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mn>0.28</mn> <mo>∼</mo> <mn>0.34</mn> <mo>)</mo> </mrow> <mo>∘</mo> </msup> </mrow> </math>   for the  $$Q=b$$  <math> <mrow> <mi>Q</mi> <mo>=</mo> <mi>b</mi> </mrow> </math>   case. Our prediction of  $$\theta _{c}$$  <math> <msub> <mi>θ</mi> <mi>c</mi> </msub> </math>   is consistent with the most recent Lattice QCD result within error. Such a small mixing angle seems unlikely to resolve the tension between the recent experimental measurement from Belle and Lattice QCD calculation for the semileptonic decay  $$\Xi _{c}^{0}\rightarrow \Xi ^{-} e^{+}\nu _{e}$$  <math> <mrow> <msubsup> <mi>Ξ</mi> <mrow> <mi>c</mi> </mrow> <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> </mrow> </math>  .

Revisiting  $$\Xi _{Q}-\Xi _{Q}^{\prime }$$  <math> <mrow> <msub> <mi>Ξ</mi> <mi>Q</mi> </msub> <mo>-</mo> <msubsup> <mi>Ξ</mi> <mrow> <mi>Q</mi> </mrow> <mo>′</mo> </msubsup> </mrow> </math>   mixing in QCD sum rules

In this work, a three-quark picture is constructed using a bottom-up approach for baryons in a light-front quark model. The shape parameters, which characterize the momentum distribution inside a baryon, are determined with the help of the pole residue of the baryon. The relation between the three-quark picture and the diquark picture is clarified. When building the model, we find that Lorentz boost plays a crucial role, and the bottom-up modeling approach can be generalized to multiquark states. Based on this, a unified theoretical framework for describing multiquark states may be established. As a by-product of model construction, we can easily obtain a newly improved definition of baryon interpolating current. The hadron interpolating currents are the starting point of lattice QCD and QCD sum rules, and therefore are of great importance.

Xiao-Hui Hu

Baryons in the light-front approach: The three-quark picture

We calculate the <math><mi>W</mi></math>-exchange contribution to the <math><msubsup><mi>Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo>+</mo><mo>+</mo></mrow></msubsup><mo>→</mo><msubsup><mi>Ξ</mi><mi>c</mi><mrow><mo>+</mo><mo>(</mo><mo>′</mo><mo>)</mo></mrow></msubsup><msup><mi>π</mi><mo>+</mo></msup></math> decay using light-cone sum rules. The two-particle light-cone distribution amplitudes of the pion are used as nonperturbative input for the sum rules calculation, and the perturbative kernel is calculated at the leading order. We obtain the corresponding decay branching fractions by combining our <math><mi>W</mi></math>-exchange amplitudes with the factorizable amplitudes given by various theoretical methods from the literature. It is shown that with the factorizable amplitudes from heavy quark effective theory, we obtain the branching fraction ratio <math><mi>B</mi><mo>(</mo><msubsup><mi>Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo>+</mo><mo>+</mo></mrow></msubsup><mo>→</mo><msubsup><mi>Ξ</mi><mi>c</mi><mrow><mo>+</mo><mo>′</mo></mrow></msubsup><msup><mi>π</mi><mo>+</mo></msup><mo>)</mo><mo>/</mo><mi>B</mi><mo>(</mo><msubsup><mi>Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo>+</mo><mo>+</mo></mrow></msubsup><mo>→</mo><msubsup><mi>Ξ</mi><mi>c</mi><mo>+</mo></msubsup><msup><mi>π</mi><mo>+</mo></msup><mo>)</mo><mo>=</mo><mn>1.42</mn><mo>±</mo><mn>0.78</mn></math>, which is consistent with the experimental value of <math><mn>1.41</mn><mo>±</mo><mn>0.17</mn><mo>±</mo><mn>0.1</mn></math>.

Germany

Ye Xing

Georgia

Ulf-G. Meißner

<math><mi>W</mi></math>-exchange contribution to the decays <math><msubsup><mi>Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo>+</mo><mo>+</mo></mrow></msubsup><mo>→</mo><msubsup><mi>Ξ</mi><mi>c</mi><mrow><mo>+</mo><mo>(</mo><mo>′</mo><mo>)</mo></mrow></msubsup><msup><mi>π</mi><mo>+</mo></msup></math> using light-cone sum rules