The charmed baryon was first observed experimentally in 1975, one year after the charm quark's confirmation via the discovery of the $ J/\psi $ particle. Studying charmed baryon decays provides a pathway to investigate both strong and weak interactions, leveraging the weak decays of the embedded charm quark. However, for approximately three decades following its discovery, experimental knowledge of charmed baryons remained significantly limited compared to those of the hidden-charm $\textit{ψ}$ mesons and open-charm $ D_{(s)} $ mesons. This situation changed markedly starting in 2014, when dedicated data collection for charmed baryons commenced at BESIII. In this article, we review the experimental progress achieved since 2014 in understanding the weak decays of the charmed baryons.

China

Pei-Rong Li

Xiao-Rui Lyu

Yangheng Zheng

Experimental overview on the charmed baryon decays * The authors thank Fusheng Yu for useful discussions. The authors are supported in part by National Natural Science Foundation of China (12221005, 12422504); CAS Project for Young Scientists in Basic Research (YSBR-117); Fundamental Research Funds for the Central Universities, Lanzhou University (lzujbky-2025-ytB01, lzujbky-2023-stlt01, lzujbky-2023-it32), University of Chinese Academy of Sciences

Electroweak (EW) amplitudes in the gauge-Goldstone five-component formalism have a distinctive property: gauge symmetry is imprinted in the amplitudes, manifested as the massive Ward identity (MWI) $ k^M{\cal{M}}_M=0 $ . In this study, we used the HELAS package to numerically study gauge symmetry in EW amplitudes. First, we directly tested gauge symmetry by examining the MWI of amplitudes. Second, we modified the couplings within a vertex and among vertices to check if and how the MWI changes. Third, we tested gauge symmetry by considering the couplings modified by operators from the standard model effective field theory (SMEFT). Similar to the standard model, there are relations between different couplings that are protected by gauge symmetry. We observed that, if we modify the couplings to deviate from the relations, the MWI is violated. In contrast, the MWI is restored when the relations between couplings reduce to those in the SMEFT.

Wang-Fa Li

Junmou Chen

Qian-Jiu Wang

Zhao-Huan Yu

Numerical study on the gauge symmetry of electroweak amplitudes * Junmou Chen is supported by National Natural Science Foundation of China (12205118), Wang-Fa Li, Qian-Jiu Wang, and Zhao-Huan Yu are supported by the Guangzhou Science and Technology Planning Project (2024A04J4026)

In this article, the electroweak transition form factors of $$\Lambda _b\rightarrow \Lambda _c$$ and $$\Xi _b\rightarrow \Xi _c$$ are analyzed within the framework of three-point QCD sum rules. In phenomenological side, all possible couplings of interpolating current to hadronic states are considered. In QCD side, the perturbative part and the contributions of vacuum condensates up to dimension 8 are also included. With the estimated form factors, we study the decay widths and branching ratios of semileptonic decays $$\Lambda _b\rightarrow \Lambda _cl\bar{\nu }_l$$ and $$\Xi _b\rightarrow \Xi _cl\bar{\nu }_l$$ ( $$l=e,\mu $$ and $$\tau $$ ). Our results for the branching ratios of $$\Lambda _b\rightarrow \Lambda _cl\bar{\nu }_l$$ are comparable with experimental data and the results from other collaborations. In addition, our prediction for the branching ratio of $$\Xi _b\rightarrow \Xi _cl\bar{\nu }_l$$ can provide a valuable reference for future experimental measurements.

Jie Lu

Guo-Liang Yu

Dian-Yong Chen

Zhi-Gang Wang

Bin Wu

Analysis of the semileptonic decays $$\Lambda _b\rightarrow \Lambda _cl\bar{\nu }_l$$ and $$\Xi _b\rightarrow \Xi _cl\bar{\nu }_l$$ in QCD sum rules

In this article, the vector, axial vector and tensor form factors of <italic>B<inf>c</inf></italic> to <italic>D</italic>-wave charmonia <italic>&#968;<inf>J</inf></italic> ( <math altimg='si138.svg'><mrow><mi>J</mi><mo linebreak='goodbreak'>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></mrow></math>) and <italic>&#951;</italic> <inf><italic>c</italic>2</inf> are analyzed within the framework of three-point QCD sum rules. With the predicted vector and axial vector form factors, we study the decay widths and branching ratios of semileptonic decays <math altimg='si139.svg'><mrow><msub><mi>B</mi><mi>c</mi></msub><mo>&#8594;</mo><msub><mi>&#968;</mi><mi>J</mi></msub><mi>l</mi><mover accent='true'><msub><mi>&#957;</mi><mi>l</mi></msub><mo>&#175;</mo></mover></mrow></math> and <math altimg='si140.svg'><mrow><msub><mi>B</mi><mi>c</mi></msub><mo>&#8594;</mo><msub><mi>&#951;</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mi>l</mi><mover accent='true'><msub><mi>&#957;</mi><mi>l</mi></msub><mo>&#175;</mo></mover></mrow></math>. Our results indicate that the semileptonic decay branching ratios of <italic>B<inf>c</inf></italic> to <italic>D</italic>-wave charmonia decreases as the total angular momentum of the final state <italic>D</italic>-wave charmonia increases. For decay processes <math altimg='si141.svg'><mrow><msub><mi>B</mi><mi>c</mi></msub><mo>&#8594;</mo><msub><mi>&#968;</mi><mn>1</mn></msub><mi>l</mi><msub><mover accent='true'><mi>&#957;</mi><mo>&#175;</mo></mover><mi>l</mi></msub></mrow></math>, <math altimg='si142.svg'><mrow><msub><mi>B</mi><mi>c</mi></msub><mo>&#8594;</mo><msub><mi>&#968;</mi><mn>2</mn></msub><mrow><mo>[</mo><msub><mi>&#951;</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo>]</mo></mrow><mi>l</mi><msub><mover accent='true'><mi>&#957;</mi><mo>&#175;</mo></mover><mi>l</mi></msub></mrow></math> and <math altimg='si143.svg'><mrow><msub><mi>B</mi><mi>c</mi></msub><mo>&#8594;</mo><msub><mi>&#968;</mi><mn>3</mn></msub><mi>l</mi><msub><mover accent='true'><mi>&#957;</mi><mo>&#175;</mo></mover><mi>l</mi></msub></mrow></math>, the branching ratios can reach the order of magnitude <math altimg='si100.svg'><msup><mn>10</mn><mrow><mo>&#8722;</mo><mn>3</mn></mrow></msup></math>, <math altimg='si144.svg'><msup><mn>10</mn><mrow><mo>&#8722;</mo><mn>4</mn></mrow></msup></math> and <math altimg='si145.svg'><msup><mn>10</mn><mrow><mo>&#8722;</mo><mn>5</mn></mrow></msup></math>, respectively, which can provide a valuable reference for future experimental measurements for <italic>B<inf>c</inf></italic> meson by LHCb collaboration. Furthermore, these results also can provide useful information to study the properties of <italic>B<inf>c</inf></italic> meson and <italic>D</italic>-wave charmonia.

Systematic analysis of the transition form factors of <italic>B<inf>c</inf></italic> to <italic>D</italic>-wave charmonia and corresponding semileptonic decays

The high-density region of the QCD phase diagram displays an intricate competition between color superconductivity and the QCD Kondo effect due to color exchange in quark matter containing a single heavy quark impurity. We explore the characteristic impurity-induced superconducting subgap states arising in such systems by generalizing the surrogate model solver, recently considered in the context of condensed matter physics [<a href="http://dx.doi.org/10.1103/PhysRevB.108.L220506">Phys. Rev. B 108, L220506 (2023)</a>]. The method consists of approximating the full superconducting bulk by only a small number of effective levels whose parameters are chosen so as to best reproduce the Matsubara frequency dependence of the impurity-bulk hybridization function. We numerically solve a surrogate QCD Kondo model describing a quantum impurity color exchange coupled to a two-color two-flavor superconducting bulk. The results directly indicate the presence of multiple phase transitions as the coupling of the impurity to the bulk is increased, due to the interplay between various overscreened states. The methods introduced here are straightforward enough to be extended to more realistic QCD scenarios.

Romania

Virgil V. Baran

Denmark

Jens Paaske

Yu-Shiba-Rusinov states in color-superconducting quark matter

In the framework of the relativized quark model, the mass spectra of the doubly heavy baryons are rigorously calculated in the three-quark system under the heavy-quark dominance mechanism, by using the Gaussian expansion method and the infinitesimally-shifted Gaussian basis functions. With the obtained mass spectra of all doubly heavy baryon families, the contribution of each Hamiltonian term to the energy levels is analyzed. It is found that the spin splitting is mainly determined by the spin-dependent interactions associated with the light quark. Moreover, it is shown that the spin splitting evolves regularly with the mass of heavy quarks by the evolution of the spectral structure, which is consistent with the heavy quark symmetry. Meanwhile, the orbital excitation is dominated by the $$\rho $$ -mode, which is different from that of the singly heavy baryons. At last, our analysis indicates that the $$\Xi _{cc}^{+}(3520)$$ state should not exist truly and the $$\Xi _{cc}^{++}(3621)$$ should be the true ground state with $$J^{P}$$ = $$\frac{1}{2}^{+}$$ . It is recommended to design the corresponding experiments to search for the $$\Xi _{cc}^{*}$$ in the energy range from 3694 to 3714 MeV.

Zhen-Yu Li

Jian-Zhong Gu

Hong-Tao Shen

Mass spectra of doubly heavy baryons in the relativized quark model with heavy-quark dominance

The rigorous calculation of the spin-orbit terms in a three-quark system is realized based on the Gaussian expansion method and the infinitesimally-shifted Gaussian basis functions in the framework of the relativized quark model, by ignoring the mixing between different excited states. Then, the complete mass spectra of the singly heavy baryons are obtained rigorously, under the heavy-quark dominance mechanism. Accordingly, systematical analyses are performed for the reliability and predictive power of the model, the fine structure of the singly heavy baryon spectra, the assignments of the excited baryons, and some important topics about heavy baryon spectroscopy, such as the missing states, 'spin-orbit puzzle,' and clustering effect. The results confirm that, under the heavy-quark dominance mechanism, the relativized quark model can describe the excitation spectra and the fine structures of the singly heavy baryons correctly and precisely.

Mass spectra of singly heavy baryons in the relativized quark model with heavy-quark dominance * Supported by the Open Project of Guangxi Key Lab of Nuclear Physics and Technology (NLK2023-04), the Central Government Guidance Funds for Local Scientific and Technological Development in China (Guike ZY22096024), the Natural Science Foundation of Guizhou Province-ZK[2024](General Project)650, the National Natural Science Foundation of China (11675265, 12175068), the Continuous Basic Scientific Research Project (WDJC-2019-13) and the Leading Innovation Project (LC 192209000701)

This study is devoted to calculating the form factors of $B_c \to D^{*}$ , $B_c \to D$ , $B_c \to D_s^{*}$ , and $B_c \to D_s$ transitions in the framework of three-point QCD sum rules. At the QCD side, the contributions of $\langle\overline{q}q\rangle$ , $\langle\overline{q}g_{s}\sigma Gq\rangle$ , $\langle g_{s}^{2}G^{2}\rangle$ , $\langle g^{3}f_{abc}G^{3}\rangle$ , and $\langle\overline{q}q\rangle \langle g_{s}^{2}G^{2}\rangle$ are taken into account. With the obtained form factors, the decay widths and branching ratios of several two-body nonleptonic decay processes, $B_c \to \eta_c D^{*}$ , $\eta_c D$ , $ J/\psi D^{*}$ , $ J/\psi D$ , $\eta_c D_s^{*}$ , $\eta_c D_s$ , $J/\psi D_s^{*}$ , and $J/\psi D_s$ , are predicted. These results on the form factors and decay properties of the $B_c$ meson provide useful information for us to study the heavy-quark dynamical behavior.

Ze Zhou

Analysis of the form factors of B$_{c}$ → $\textit{D}$ $^{(*)}$, $\textit{D}$ $\textit{s}$ $^{(*)}$ and relevant nonleptonic decays * Supported by the National Natural Science Foundation (12175068) and Natural Science Foundation of HeBei Province (A2024502002)

In this article, we firstly analyze the mass and pole residue of negative parity nucleon $$N^*(1535)$$ within the two-point QCD sum rules. Basing on these results, we continuously study the strong coupling constants of vertices $$\Lambda _cDN^*$$ , $$\Lambda _cD^*N^*$$ , $$\Lambda _bBN^*$$ and $$\Lambda _bB^*N^*$$ in the framework of three-point QCD sum rules. At hadron side, all possible couplings of interpolating current to hadronic states are considered. At QCD side, the contributions of vacuum condensate terms $$\langle \bar{q}q\rangle $$ , $$\langle g_s^2GG\rangle $$ , $$\langle \bar{q} g_s\sigma Gq\rangle $$ , $$\langle \bar{q}q\rangle ^2$$ and $$g_s^2\langle \bar{q}q\rangle ^2$$ are also considered. By setting the four momentum of $$D^{(*)}[B^{(*)}]$$ mesons off-shell, the strong coupling constants in deep space-like regions ( $$Q^2=-q^2\gg \Lambda _{QCD}^2$$ ) are obtained. Then, the momentum dependent coupling constants in space-like regions are fitted into analytical function $$G(Q^2)$$ and are extrapolated into time-like regions ( $$Q^2<0$$ ). Finally, the on-shell values of strong coupling constants are obtained by taking $$Q^{2}=-m_{D^{(*)}[B^{(*)}]}^2$$ . The results are $$G_{\Lambda _cDN^*}(Q^2=-m_D^2)=4.06^{+0.96}_{-0.75}$$ , $$f_{\Lambda _cD^*N^*}(Q^2=-m_{D^*}^2)=3.73^{+0.68}_{-0.16}$$ , $$g_{\Lambda _cD^*N^*}(Q^2=-m_{D^*}^2)=9.22^{+3.16}_{-0.36}$$ , $$G_{\Lambda _bBN^*}(Q^2=-m_B^2)=9.11^{+1.54}_{-1.61}$$ , $$f_{\Lambda _bB^*N^*}(Q^2=-m_{B^*}^2)=8.55^{+2.69}_{-2.21}$$ and $$g_{\Lambda _bB^*N^*}(Q^2=-m_{B^*}^2)=-\,0.25^{+0.16}_{-0.01}$$ .

Analysis of the strong vertices $$\Lambda _cD^{(*)}N^*(1535)$$ and $$\Lambda _bB^{(*)}N^*(1535)$$ in QCD sum rules

We study $ \cos2\phi $ azimuthal asymmetry in doubly longitudinally polarized proton-proton Drell-Yan collisions within the transverse momentum dependent factorization framework. The asymmetry arises from the convolution of the longitudinal transversity distribution $ h_{1L}^{\perp} $ for both protons. Using the Bacchetta-Delcarro-Pisano-Radici-Signori parameterization for the nonperturbative Sudakov form factor and the Wandzura-Wilczek approximation for collinear $ h_{1L}^{\perp} $ , we predict the double spin asymmetry $ A_{LL}^{\cos2\phi} $ at RHIC and NICA kinematics. Our results demonstrate sensitivity to sea quark distributions, with the asymmetry reaching up to 25% for maximal sea quark contributions. These predictions highlight the potential of polarized Drell-Yan measurements to probe sea quark dynamics and advance our understanding of nucleon structures.

Hui Li

Ting Hu

Liang-Liang Liu

Xiao-Yu Wang

Zhun Lu

Asymmetry ${{\boldsymbol A}_{\boldsymbol{LL}}^{\bf\cos2\boldsymbol\phi}} $ in the polarized proton-proton Drell-Yan process within TMD factorization * Hui Li is supported by Fundamental Research Program of Shanxi Province (202203021222224) and Natural Science Foundation of Shanxi Normal University (JCYJ2023021). Xiao-Yu Wang is supported by the Natural Science Foundation of Henan Province (242300421377, 232300421140)