Existing pion+nucleus Drell-Yan and electron+pion scattering data are used to develop ensembles of model-independent representations of the pion generalized parton distribution (GPD). Therewith, one arrives at a data-driven prediction for the pion mass distribution form factor, $\theta_2^\pi $. Compared with the pion elastic electromagnetic form factor, $\theta_2^\pi$ is harder: the ratio of the radii derived from these two form factors is $r_\pi^{\theta_2}/r_\pi = 0.79(3)$. Our data-driven predictions for the pion GPD, related form factors and distributions should serve as valuable constraints on theories of pion structure.

The quantum chromodynamics (QCD) coupling $\alpha_{\rm s}$ is the most important parameter for achieving precise QCD predictions. By using the well measured effective coupling $\alpha^{g_1}_{\rm s}(Q)$ defined from the Bjorken sum rules as a basis, we suggest a novel self-consistency way to fix the $\alpha_{\rm s}$ at all scales: The QCD light-front holographic model is adopted for its infrared behavior, and the fixed-order pQCD prediction under the principle of maximum conformality (PMC) is used for its high-energy behavior. Using the PMC scheme-and-scale independent perturbative series, and by transforming it into the one under the physical V scheme, we observe that a precise $\alpha_{\rm s}$ running behavior in both the perturbative and nonperturbative domains with a smooth transition from small to large scales can be achieved.

Parton distribution functions (PDFs) are defining expressions of hadron structure. Exploiting the role of effective charges in quantum chromodynamics, an algebraic scheme is described which, given any hadron's valence parton PDFs at the hadron scale, delivers predictions for all its PDFs (unpolarized and polarized) at any higher scale. The scheme delivers results that are largely independent of both the value of the hadron scale and the pointwise form of the charge; and, inter alia, enables derivation of a model-independent identity that relates the strength of the proton's gluon helicity PDF, $\Delta G_p^\zeta$, to that of the analogous singlet polarized quark PDF and valence quark momentum fraction. Using available data fits and theory predictions, the identity yields $\Delta G_p(\zeta_{_{\scriptstyle \rm C}}=\sqrt{3}\,{\rm GeV})=1.48(10)$. It furthermore entails that the measurable quark helicity contribution to the proton spin is $\tilde a_{0p}^{\zeta_{_{\scriptstyle \rm C}}}=0.32(3)$, thereby reconciling contemporary experiment and theory.

We investigate the decays of $B^0 \to K^0 X(3872)$ and $B^+ \to K^+ X(3872)$ based on the picture where the $X(3872)$ resonance is strongly coupled to the $D\bar{D}^* + c.c.$ channel. In addition to the decay mechanism where the $X(3872)$ resonance is formed from the $c\bar{c}$ pair hadronization with the short-distance interaction, we have also considered the $D\bar{D}^*$ rescattering diagrams in the long-distance scale, where $D$ and $\bar{D}^*$ are formed from $c$ and $\bar{c}$ separately. Because of the difference of the mass thresholds of charged and neutral $D\bar{D}^*$ channels, and the rather narrow width of the $X(3872)$ resonance, at the $X(3872)$ mass, the loop functions of $D^0\bar{D}^{*0}$ and $D^+\bar{D}^{*-}$ are much different. Taking this difference into account, the ratio of $\mathcal{B}[B^0\to K^0X(3872)]/\mathcal{B}[B^+ \to K^+ X(3872)] \simeq 0.5$ can be naturally obtained. Based on this result, we also evaluate the decay widths of $B_s^0 \to \eta(\eta') X(3872)$. It is expected that future experimental measurements of these decays can be used to elucidate the nature of the $X(3872)$ resonance.

Machine learning is a novel and powerful technology and has been widely used in various science topics. We demonstrate a machine-learning-based approach built by a set of general metrics and rules inspired by physics. Taking advantages of physical constraints, such as dimension identity, symmetry and generalization, we succeed to approach the Gell-Mann–Okubo formula using a technique of symbolic regression. This approach can effectively find explicit solutions among user-defined observables, and can be extensively applied to studying exotic hadron spectrum.

We predict a new physical phenomenon, induced fission-like process and chain reaction of hadronic molecular states. As a molecular state, if induced by a $D$ meson, the $X(3872)$ can split into $D\bar{D}$ final state which is forbidden due to the spin-parity conservation. The breeding of the $D$ meson of the reaction, such as $D^0X(3872)\to D^0\bar{D}^0D^0$, makes the chain reaction of $X(3872)$ matter possible. We estimate the cross section of the $D$ meson induced fission-like process of $X(3872)$ into two $D$ mesons. With very small $D^0$ beam momentum of 1 eV, the total cross section reaches an order of 1000 b, and decreases rapidly with the increasing beam momentum. With the transition of $D^*$ meson in molecular states to a $D$ meson, the $X(3872)$ can release large energy, which is acquired by the final mesons. The momentum distributions of the final $D$ mesons are analyzed. In the laboratory frame, the spectator $D$ meson in molecular state concentrates in the low momentum area. The energy from the transition from $D^*$ to $D$ meson is mainly acquired by two scattered $D$ mesons. The results suggest that the $D$ meson environment will lead to the induced fission-like process and chain reaction of the $X(3827)$. Such a phenomenon can be extended to other hadronic molecular states.

The Large High Altitude Air Shower Observatory (LHAASO) has reported the detection of a large number of multi-TeV-scale photon events also including several PeV-scale gamma-ray-photon events with energy as high as 1.4 PeV. The possibility that some of these events may have extragalactic origins is not yet excluded. Here we propose a mechanism for the traveling of very-high-energy and ultra-high-energy photons based upon the axion-photon conversion scenario, which allows extragalactic above-threshold photons to be detected by observers on the Earth. We show that the axion-photon conversation can serve as an alternative mechanism, besides the threshold anomaly due to Lorentz invariance violation, for the very-high-energy features of the newly observed gamma ray burst GRB 221009A.

We systematically investigate the mass spectrum, spatial configuration and magnetic moment of the ground and p-wave states $[cu][\bar{c}\bar{s}]$ with various color-spin configurations in a multiquark color flux-tube model. Numerical results indicate that the state $Z_{cs}(4000)^+$ can be described as the compact state $[cu][\bar{c}\bar{s}]$ with $1^3\!S_1$. Its main color-spin configuration is $[cu]^{1}_{\boldsymbol{6}_c} [\bar{c}\bar{s}]^{1}_{\bar{\boldsymbol{6}}_c}$ and its magnetic moment is 0.73$\mu_{\scriptscriptstyle{N}}$. The state $Z_{cs}(4220)^+$ can be depicted as the compact state $[cu][\bar{c}\bar{s}]$ with $1^1\!P_1$ (or $1^3\!P_1$). Its main color-spin configuration is $[cu]^{0}_{\bar{\boldsymbol{3}}_c}[\bar{c}\bar{s}]^{0}_{\boldsymbol{3}_c}$ (or $[cu]^{0}_{\bar{\boldsymbol{3}}_c}[\bar{c}\bar{s}]^{1}_{\boldsymbol{3}_c}$) and its magnetic moment is 0.12$\mu_{\scriptscriptstyle{N}}$ (or 0.64$\mu_{\scriptscriptstyle{N}}$). The physical state should be the mixture of these two different color-spin configurations and deserves further investigation. In addition, we also predict the properties of the states $[cu][\bar{c}\bar{s}]$ with other quantum numbers in the model.

We investigate the nature of the strong coupling constant and related physics. Through the analysis of accumulated experimental data around the world, we employ the ability of machine learning to unravel its physical laws. The result of our efforts is a formula that captures the expansive panorama of the distribution of the strong coupling constant across the entire energy range. Importantly, this newly derived expression is very similar to the formula derived from the Dyson–Schwinger equations based on the framework of Yang–Mills theory. By introducing the Euler number $e$ into the functional formula of the strong coupling constant at high energies, we successfully solve the puzzle of the infrared divergence, which allows for a seamless transition of the strong coupling constant from the perturbative to the non-perturbative energy regime. Moreover, the obtained ghost and gluon dressing function distribution results confirm that the obtained strong coupling constant formula can well describe the physical properties of the non-perturbed regime. In addition, we study the quantum-chromodynamics strong coupling constant result of the Bjorken sum rule $\varGamma_1^{p-n}$ and the quark–quark static energy $E_0(r)$, and find that the global energy scale can effectively interpret the experimental data. The present results shed light on the puzzling properties of quantum chromodynamics and the intricate interplay of strong coupling constants at both low and high energy scales.

In the past 20 years, many new hadrons that are difficult to explain within the conventional quark model have been discovered in the quarkonium region; these are called exotic hadrons. The Belle II experiment, as the next-generation $B$ factory, provides a good platform for exploring them. The charmonium-like states can be produced at Belle II in several ways, such as $B$ meson decays, initial-state radiation processes, two-photon collisions and double charmonium production. Bottomonium-like states can be produced directly in $e^+e^-$ colliding energies at Belle II with low continuum backgrounds. Belle II plans to perform a high-statistics energy scan from the $B\bar B$ threshold up to the highest possible energy of 11.24 GeV to search for new $Y_b$ states with $J^{\scriptscriptstyle{\rm PC}}$ = $1^{--}$, $X_b$ [the bottom counterpart of $\chi_{c1}(3872)$, also known as $X(3872)$] and partners of $Z_b$ states. We give a mini-review on the status and prospects of exotic hadrons at Belle II.

Within the extended vector meson dominance model, we investigate the $e^+ e^- \to \varLambda^+_c \bar{\varLambda}^-_c$ reaction and the electromagnetic form factors of the charmed baryon $\varLambda_c^+$. The model parameters are determined by fitting them to the cross sections of the process $e^+e^-\rightarrow \varLambda_c^+ \bar{\varLambda}_c^-$ and the magnetic form factor $|G_{\scriptscriptstyle{\rm M}}|$ of $\varLambda^+_c$. By considering four charmonium-like states, called $\psi(4500)$, $\psi(4660)$, $\psi(4790)$, and $\psi(4900)$, we can well describe the current data on the $e^+ e^- \to \varLambda^+_c \bar{\varLambda}^-_c$ reaction from the reaction threshold up to $4.96$ GeV. In addition to the total cross sections and $|G_{\scriptscriptstyle{\rm M}}|$, the ratio $|G_{\scriptscriptstyle{\rm E}}/G_{\scriptscriptstyle{\rm M}}|$ and the effective form factor $|G_{\mathrm{eff}}|$ for $\varLambda^+_c$ are also calculated, and found that these calculations are consistent with the experimental data. Within the fitted model parameters, we have also estimated the charge radius of the charmed $\varLambda_c^+$ baryon.

The structure of light diquarks plays a crucial role in formation of exotic hadrons beyond the conventional quark model, especially with regard to the line shapes of bottomed hadron decays. We study the two-body hadronic weak decays of bottomed baryons and bottomed mesons to probe the light diquark structure and to pin down the quark–quark correlations in the diquark picture. It is found that the light diquark does not favor a compact structure. For instance, the isoscalar diquark $[ud]$ in $\varLambda_{b}^{0}$ can be easily split and rearranged to form $\varSigma_{c}^{(*)}\bar{D}^{(*)}$ via the color-suppressed transition. This provides a hint that the hidden charm pentaquark states produced in $\varLambda^0_b$ decays could be the $\varSigma_{c}^{(*)}\bar{D}^{(*)}$ hadronic molecular candidates. This quantitative study resolves the apparent conflicts between the production mechanism and the molecular nature of these $P_c$ states observed in experiment.

Jet quenching parameter $\hat{q}$ is essential for characterizing the interaction strength between jet partons and nuclear matter. Based on the quark-meson model, we develop a new framework for calculating $\hat{q}$ at finite chemical potentials, in which $\hat{q}$ is related to the spectral function of the chiral order parameter. A mean field perturbative calculation up to the one-loop order indicates that the momentum broadening of jets is enhanced at both high temperature and high chemical potential, and approximately proportional to the parton number density in the partonic phase. We further investigate the behavior of $\hat{q}$ in the vicinity of the critical endpoint (CEP) by coupling our calculation with a recently developed equation of state that includes a CEP in the universality class of the Ising model, from which we discover the partonic critical opalescence, i.e., the divergence of scattering rate of jets and their momentum broadening at the CEP, contributed by scatterings via the $\sigma$ exchange process. Hence, for the first time, jet quenching is connected with the search of CEP.

In 2021, the Belle collaboration reported the first observation of a new structure in the $\psi(2S) \gamma$ final state produced in the two-photon fusion process. In the hadronic molecule picture, this new structure can be associated with the shallow isoscalar $D^*\bar{D}^*$ bound state and as such is an excellent candidate for the spin-2 partner of the $X(3872)$ with the quantum numbers $J^{\rm PC}=2^{++}$ conventionally named $X_2$. In this work we evaluate the electronic width of this new state and argue that its nature is sensitive to its total width, the experimental measurement currently available being unable to distinguish between different options. Our estimates demonstrate that the planned Super $\tau$-Charm Facility offers a promising opportunity to search for and study this new state in the invariant mass distributions for the final states $J/\psi\gamma$ and $\psi(2S)\gamma$.