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)

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

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)

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.

The behaviour of spatial string tension $$\sigma _s(T)$$ <math> <mrow> <msub> <mi>σ</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <mi>T</mi> <mo>)</mo> </mrow> </mrow> </math> as a function of the temperature T is found in the framework of the Field Correlator Method (FCM). Here the string tension is calculated using the gluelump Green’s function, where gluons in the gluelump are interacting via the same spatial string tension. The resulting T-dependence was obtained without extra parameters in the region $$T_c&lt; T &lt; 5 T_c$$ <math> <mrow> <msub> <mi>T</mi> <mi>c</mi> </msub> <mo>&lt;</mo> <mi>T</mi> <mo>&lt;</mo> <mn>5</mn> <msub> <mi>T</mi> <mi>c</mi> </msub> </mrow> </math> using the formalism of elliptic functions $$\theta _3$$ <math> <msub> <mi>θ</mi> <mn>3</mn> </msub> </math> , demonstrating good agreement with available lattice data.

Russia

N. Agasian

Z. Khaidukov

Yu. Simonov

The spatial string tension from the field correlator method

The scalar resonances $$X(3915), X(3960), X_0(4140)$$ <math> <mrow> <mi>X</mi> <mrow> <mo>(</mo> <mn>3915</mn> <mo>)</mo> </mrow> <mo>,</mo> <mi>X</mi> <mrow> <mo>(</mo> <mn>3960</mn> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>X</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>4140</mn> <mo>)</mo> </mrow> </mrow> </math> are considered as exotic four-quark states: $$cq\bar{c} \bar{q}, cs\bar{c} \bar{s}, cs\bar{c}\bar{s}$$ <math> <mrow> <mi>c</mi> <mi>q</mi> <mover> <mrow> <mi>c</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mover> <mrow> <mi>q</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mo>,</mo> <mi>c</mi> <mi>s</mi> <mover> <mrow> <mi>c</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mover> <mrow> <mi>s</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mo>,</mo> <mi>c</mi> <mi>s</mi> <mover> <mrow> <mi>c</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mover> <mrow> <mi>s</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math> , while the X(3863) is proved to be the $$c\bar{c}, 2\,^3P_0$$ <math> <mrow> <mi>c</mi> <mover> <mrow> <mi>c</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mo>,</mo> <mn>2</mn> <msup> <mspace width="0.166667em"></mspace> <mn>3</mn> </msup> <msub> <mi>P</mi> <mn>0</mn> </msub> </mrow> </math> state. The masses and the widths of these resonances are calculated in the framework of the Extended Recoupling Model, where a four-quark system is formed inside the bag and has relatively small size ( $$\lesssim 1.0$$ <math> <mrow> <mo>≲</mo> <mn>1.0</mn> </mrow> </math> fm). Then the resonance X(3915) appears due to the transitions: $$J/\psi \omega $$ <math> <mrow> <mi>J</mi> <mo>/</mo> <mi>ψ</mi> <mi>ω</mi> </mrow> </math> into $$D^{*+}D^{*-}$$ <math> <mrow> <msup> <mi>D</mi> <mrow> <mrow></mrow> <mo>∗</mo> <mo>+</mo> </mrow> </msup> <msup> <mi>D</mi> <mrow> <mrow></mrow> <mo>∗</mo> <mo>-</mo> </mrow> </msup> </mrow> </math> (or $$D^{*0}\bar{D}^{*0})$$ <math> <mrow> <msup> <mi>D</mi> <mrow> <mrow></mrow> <mo>∗</mo> <mn>0</mn> </mrow> </msup> <msup> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mrow> <mrow></mrow> <mo>∗</mo> <mn>0</mn> </mrow> </msup> <mrow> <mo>)</mo> </mrow> </mrow> </math> and back, while the X(3960) is created due to the transitions $$D_s^+D_s^-$$ <math> <mrow> <msubsup> <mi>D</mi> <mi>s</mi> <mo>+</mo> </msubsup> <msubsup> <mi>D</mi> <mi>s</mi> <mo>-</mo> </msubsup> </mrow> </math> into $$J/\psi \phi $$ <math> <mrow> <mi>J</mi> <mo>/</mo> <mi>ψ</mi> <mi>ϕ</mi> </mrow> </math> and back, and the $$X_0(4140)$$ <math> <mrow> <msub> <mi>X</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>4140</mn> <mo>)</mo> </mrow> </mrow> </math> is formed in the transitions $$J/\psi \phi $$ <math> <mrow> <mi>J</mi> <mo>/</mo> <mi>ψ</mi> <mi>ϕ</mi> </mrow> </math> into $$D_s^{*+}D_s^{*-}$$ <math> <mrow> <msubsup> <mi>D</mi> <mi>s</mi> <mrow> <mrow></mrow> <mo>∗</mo> <mo>+</mo> </mrow> </msubsup> <msubsup> <mi>D</mi> <mi>s</mi> <mrow> <mrow></mrow> <mo>∗</mo> <mo>-</mo> </mrow> </msubsup> </mrow> </math> and back. The characteristic feature of the recoupling mechanism is that this type of resonances can be predominantly in the S-wave decay channels and has $$J^P=0^+$$ <math> <mrow> <msup> <mi>J</mi> <mi>P</mi> </msup> <mo>=</mo> <msup> <mn>0</mn> <mo>+</mo> </msup> </mrow> </math> . In two-channel case the resonance occurs to be just near the lower threshold, while due to coupling to third channel (like the $$c\bar{c}$$ <math> <mrow> <mi>c</mi> <mover> <mrow> <mi>c</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math> channel) it is shifted up and lies by (20–30) MeV above the lower threshold. The following masses and widths are calculated: $$M(X(3915))=3920$$ <math> <mrow> <mi>M</mi> <mo>(</mo> <mi>X</mi> <mo>(</mo> <mn>3915</mn> <mo>)</mo> <mo>)</mo> <mo>=</mo> <mn>3920</mn> </mrow> </math> MeV, $$\Gamma (X(3915))=20$$ <math> <mrow> <mi>Γ</mi> <mo>(</mo> <mi>X</mi> <mo>(</mo> <mn>3915</mn> <mo>)</mo> <mo>)</mo> <mo>=</mo> <mn>20</mn> </mrow> </math> MeV; $$M(X(3960))=3970$$ <math> <mrow> <mi>M</mi> <mo>(</mo> <mi>X</mi> <mo>(</mo> <mn>3960</mn> <mo>)</mo> <mo>)</mo> <mo>=</mo> <mn>3970</mn> </mrow> </math> MeV, $$\Gamma (X(3960)=45(5)$$ <math> <mrow> <mi>Γ</mi> <mo>(</mo> <mi>X</mi> <mo>(</mo> <mn>3960</mn> <mo>)</mo> <mo>=</mo> <mn>45</mn> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </math> MeV, $$M(X_0(4140))= 4120(20)$$ <math> <mrow> <mi>M</mi> <mo>(</mo> <msub> <mi>X</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>4140</mn> <mo>)</mo> </mrow> <mo>)</mo> <mo>=</mo> <mn>4120</mn> <mrow> <mo>(</mo> <mn>20</mn> <mo>)</mo> </mrow> </mrow> </math> MeV, $$\Gamma (X_0(4140))=100$$ <math> <mrow> <mi>Γ</mi> <mo>(</mo> <msub> <mi>X</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>4140</mn> <mo>)</mo> </mrow> <mo>)</mo> <mo>=</mo> <mn>100</mn> </mrow> </math> MeV, which are in good agreement with experiment.

A. Badalian

The scalar exotic resonances $$X(3915), X(3960), X_0(4140)$$ <math> <mrow> <mi>X</mi> <mrow> <mo>(</mo> <mn>3915</mn> <mo>)</mo> </mrow> <mo>,</mo> <mi>X</mi> <mrow> <mo>(</mo> <mn>3960</mn> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>X</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>4140</mn> <mo>)</mo> </mrow> </mrow> </math>

Numerous resonances in the $$c{{\bar{c}}}$$ <math> <mrow> <mi>c</mi> <mover> <mrow> <mi>c</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math> and 4q systems, containing $$c{{\bar{c}}}$$ <math> <mrow> <mi>c</mi> <mover> <mrow> <mi>c</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math> plus $$s{{\bar{s}}}$$ <math> <mrow> <mi>s</mi> <mover> <mrow> <mi>s</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math> quarks (or light $$q{{\bar{q}}}$$ <math> <mrow> <mi>q</mi> <mover> <mrow> <mi>q</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math> ) were observed during last decades and recently the LHCb has found a remarkable narrow peak $$T_{cc}(3875)$$ <math> <mrow> <msub> <mi>T</mi> <mrow> <mi>cc</mi> </mrow> </msub> <mrow> <mo>(</mo> <mn>3875</mn> <mo>)</mo> </mrow> </mrow> </math> in the $$D D^*$$ <math> <mrow> <mi>D</mi> <msup> <mi>D</mi> <mo>∗</mo> </msup> </mrow> </math> system. Besides there are several highly excited charmonium-like resonances, which can be treated as the shifted standard charmonium states. We analyze all these groups of the resonances in the mass region (3900–4700) MeV, using relativistic strong coupling theory with possible channel coupling phenomena. For the shifted charmonium states conventional charmonium spectrum is presented, being calculated with the relativistic string Hamiltonian, which does not contain fitting parameters, while for high excitations the universal flattened confining potential is used. It is shown that X(4274), X(4500), X(4700) can be identified as $$3\,^3P_1, 4\,^3P_0, 5\,^3P_0$$ <math> <mrow> <mn>3</mn> <msup> <mspace width="0.166667em"></mspace> <mn>3</mn> </msup> <msub> <mi>P</mi> <mn>1</mn> </msub> <mo>,</mo> <mn>4</mn> <msup> <mspace width="0.166667em"></mspace> <mn>3</mn> </msup> <msub> <mi>P</mi> <mn>0</mn> </msub> <mo>,</mo> <mn>5</mn> <msup> <mspace width="0.166667em"></mspace> <mn>3</mn> </msup> <msub> <mi>P</mi> <mn>0</mn> </msub> </mrow> </math> states. The group of exotic states are considered using the Extended Recoupling Model, where two mesons $$m_1,m_2$$ <math> <mrow> <msub> <mi>m</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>m</mi> <mn>2</mn> </msub> </mrow> </math> transfer into another pair of mesons $$m_3, m_4$$ <math> <mrow> <msub> <mi>m</mi> <mn>3</mn> </msub> <mo>,</mo> <msub> <mi>m</mi> <mn>4</mn> </msub> </mrow> </math> and back (infinite number of times), creating the four-quark resonance. Within this approach the resonances – $$T_{cc}(3875), Z_c(3900), X(3915), Z_{cs}(3985), X(4014)$$ <math> <mrow> <msub> <mi>T</mi> <mrow> <mi>cc</mi> </mrow> </msub> <mrow> <mo>(</mo> <mn>3875</mn> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>Z</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mn>3900</mn> <mo>)</mo> </mrow> <mo>,</mo> <mi>X</mi> <mrow> <mo>(</mo> <mn>3915</mn> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>Z</mi> <mrow> <mi>cs</mi> </mrow> </msub> <mrow> <mo>(</mo> <mn>3985</mn> <mo>)</mo> </mrow> <mo>,</mo> <mi>X</mi> <mrow> <mo>(</mo> <mn>4014</mn> <mo>)</mo> </mrow> </mrow> </math> , and X(4140) – can be explained as the exotic four-quark states in the S-wave decay channels.

The two-channel exotic charmonium-like resonances in the mass region (3900–4700) MeV

The infinite chain of transitions of one pair of mesons (channel I) into another pair of mesons (channel II) can produce bound states and resonances in both channels even if no interactions inside channels exist. These resonances which can occur also in meson-baryon channels are called channel-coupling (CC) resonances. A new mechanism of CC resonances is proposed where transitions occur due to a rearrangement of confining strings inside each channel — the recoupling mechanism. The amplitude of this recoupling mechanism is expressed via overlap integrals of the wave functions of participating mesons (baryons). The explicit calculation with the known wave functions yields the peak at E = 4.12 GeV for the transitions <math> <mi>J</mi> <mo>/</mo> <mi>ψ</mi> <mo>+</mo> <mi>ϕ</mi> <mo>↔</mo> <msubsup> <mi>D</mi> <mi>s</mi> <mo>∗</mo> </msubsup> <mo>+</mo> <msubsup> <mover> <mi>D</mi> <mo>¯</mo> </mover> <mi>s</mi> <mo>∗</mo> </msubsup> </math> $$ J/\psi +\phi \leftrightarrow {D}_s^{\ast }+{\overline{D}}_s^{\ast } $$ , which can be associated with χ c1 (4140), and a narrow peak at 3.98 GeV with the width 10 MeV for the transitions <math> <msubsup> <mi>D</mi> <mi>s</mi> <mo>−</mo> </msubsup> <mo>+</mo> <msubsup> <mi>D</mi> <mn>0</mn> <mo>∗</mo> </msubsup> <mo>↔</mo> <mi>J</mi> <mo>/</mo> <mi>ψ</mi> <mo>+</mo> <msup> <mi>K</mi> <mrow> <mo>∗</mo> <mo>−</mo> </mrow> </msup> </math> $$ {D}_s^{-}+{D}_0^{\ast}\leftrightarrow J/\psi +{K}^{\ast -} $$ , which can be associated with th recently discovered Z cs (3985).

Recoupling mechanism for exotic mesons and baryons

Using the vector exchange interaction in the local hidden gauge approach, which in the light quark sector generates the chiral Lagrangians and has produced realistic results for 
					 and the hidden charm pentaquark states, we study the meson-baryon interactions in the coupled channels that lead to the 
					 and 
					 excited states of the molecular type. We obtain seven states of the 
					 type with energies between 
					 and 
					 MeV, and one 
					 state at 
					 MeV.
				

Brazil

J. M. Dias

Qi-Xin Yu

Wei-Hong Liang

Zhi-Feng Sun

Ju-Jun Xie

Spain

E. Oset

Ξbb and Ωbbb molecular states Partly supported by the National Natural Science Foundation of China (11975083, 11947413, 11847317, 11565007, 11735003, 1191101015). Q. X Yu acknowledges the support from the National Natural Science Foundation of China (11775024, 11575023, 11805153) and China Scholarship Council. Partly supported by the Spanish Ministerio de Economia y Competitividad and European FEDER funds (FIS2017- 84038-C2-1-P B, FIS2017-84038-C2-2-P B), and the Generalitat Valenciana in the program Prometeo II-2014/068, and the project Severo Ochoa of IFIC, SEV-2014-0398