Highlights
  • Tilted-axis-cranking covariant density functional theory for high-spin spectroscopy of 69Ga
    The tilted-axis-cranking covariant density functional theory is applied to investigate the three newly-observed positive-parity bands SI, SII, and SIII in 69Ga. The energy spectra and angular momenta are calculated, and they agree closely with experimental data. For band SI, pairing correlations are crucial for the states with spin $I\leq 23/2\hbar$. Bands SII and SIII are suggested to be signature partner bands with positive and negative signatures, respectively. By analyzing the angular momentum alignments, we reveal that the $g_{9/2}$ protons and neutrons are crucial in the collective structures of 69Ga. The transition probabilities $B(E2)$ for these bands are predicted, awaiting further experimental verification.
  • Null test of cosmic curvature using deep learning method
    Determining the spatial curvature of the Universe, a fundamental parameter defining the global geometry of spacetime, remains crucial yet contentious due to existing observational tensions. Although Planck satellite measurements have provided precise constraints on spatial curvature, discrepancies persist regarding whether the Universe is flat or closed. Here, we introduce a model-independent approach leveraging deep learning techniques, specifically residual neural networks (ResNet), to reconstruct the dimensionless Hubble parameter E(z) and the normalized comoving distance D(z) from H(z) data and multiple SNe Ia compilations. Our dual-block ResNet architecture, which integrates a model-driven block informed by $ \Lambda $CDM and a purely data-driven block, yields smooth and robust reconstructions and enables the derivation of D'(z). By combining these reconstructed quantities, we assess the curvature diagnostic function $ {\cal{O}}_k(z) $. Analyses of the Pantheon+ sample support spatial flatness at the 1$ \sigma $ level over 0 < z < 2.5, with a mild tendency toward negative curvature at high redshift. Reconstructions based on Union3 and DESY5, however, show stronger departures toward negative curvature at intermediate and high redshifts. These results highlight the need for expanded and refined observational datasets to conclusively resolve these tensions and comprehensively investigate cosmic geometry.
  • Extracting the kinetic freeze-out properties of high energy pp collisions at the LHC with event shape classifiers
    Event shape measurements are crucial for understanding the underlying event and multiple-parton interactions (MPIs) in high energy proton-proton (pp) collisions. In this study, the Tsallis blast-wave model with independent non-extensive parameters for mesons and baryons was applied to analyze the transverse momentum spectra of charged pions, kaons, and protons in pp collision events at $ \sqrt{s}=13 $ TeV classified by event shape estimators such as relative transverse event activity, unweighted transverse spherocity, and flattenicity. Our analysis reveals consistent trends in the kinetic freeze-out temperature and non-extensive parameter across different collision systems and event shape classes. The use of diverse event-shape observables in pp collisions has significantly expanded the accessible freeze-out parameter space, enabling a more comprehensive exploration of its boundaries. Among these event shape classifiers, flattenicity emerges as a unique observable for disentangling hard process contributions from additive MPI effects, which helps isolate collective motion effects encoded by the radial flow velocity. Through the analysis of the interplay between event-shape measurements and kinetic freeze-out properties, we gain deeper insights into mechanisms responsible for flow-like signatures in pp collisions.
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  • Study of the EEC discrimination power on quark and gluon jet quenching effects in heavy-ion collisions at${\sqrt{s}=}$ 5.02 TeV
    2026, 50(2): 023114-023114-12. doi: 10.1088/1674-1137/ae056c
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    We present a systematic investigation of flavor-dependent jet quenching using energy-energy correlators (EEC) in $ \sqrt{s}=5.02 $ TeV Pb+Pb collisions. Employing the improved SHELL model, which incorporates collisional and radiative energy loss, as well as medium response, we quantify distinct quenching signatures for quark and gluon jets. Key findings include: (1) Pure quark jets exhibit strong EEC enhancement at large angular scales, while gluon jets show a bimodal enhancement pattern at small and large scales; (2) Dual-shift decomposition in the EEC ratio reveals shifts toward large angles is primarily driven by energy loss, while small-${R_{{\rm{L}}}}$ shifts extend beyond selection bias and indicate intrinsic enhancement of the gluon-initiated jets; (3) Quark jets experience global suppression of averaged energy weight $ \langle{\rm{weight}}\rangle({R_{{\rm{L}}}}) $, whereas gluon jets exhibit concentration toward small ${R_{{\rm{L}}}}$; (4) Mechanism decomposition identifies elastic energy loss concentrating $ \langle{\rm{weight}}\rangle({R_{{\rm{L}}}}) $ toward small ${R_{{\rm{L}}}}$, radiative loss dominating quark jet modification, and medium response amplifying large ${R_{{\rm{L}}}}$ enhancement via soft hadrons. The observed flavor dependence in EEC modifications is dominantly driven by intrinsic jet structure differences rather than medium-induced mechanisms. We propose photon-tagged jets as quark proxies and inclusive charged-hadron jets as gluon proxies, demonstrating that they reproduce the respective flavor-specific quenching patterns. Our work establishes the EEC as a precision probe of color-charge-dependent jet-medium interactions, providing new constraints for the detailed $ \hat{q} $ extraction and QGP tomography, while highlighting the critical role of pre-quenching flavor asymmetries.
  • Off-shell modifications of pion generalized parton distributions and transverse momentum dependent parton distributions
    2026, 50(3): 033109-033109-13. doi: 10.1088/1674-1137/ae28ea
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    Off-shell characteristics of pion generalized parton distributions (GPDs) and transverse momentum dependent parton distributions (TMDs) are examined within the framework of the Nambu–Jona-Lasinio model. In our previous studies, we separately investigated the properties of on-shell pion GPDs and light-front wave functions. Comparing the differences between on-shell and off-shell pion GPDs is particularly intriguing becuase it enables us to explore the effects associated with off-shellness. The absence of crossing symmetry causes the moments of GPDs to incorporate odd powers of the skewness parameter, resulting in new off-shell form factors. Through our calculations, we derived correction functions that account for modifications in pion GPDs attributed to off-shell effects. Unlike their on-shell counterparts, certain properties break down in the off-shell scenario; for example, symmetry properties and polynomiality conditions may no longer hold. In addition, we evaluate off-shell TMDs and compare them with their on-shell equivalents while also investigating their dependence on $ {\boldsymbol{k}}_{\perp} $.
  • Classical interpretation of nonrelativistic quark potential model: Color charge definition and meson mass-radius relationship
    2026, 50(3): 033106-033106-8. doi: 10.1088/1674-1137/ae28e9
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    Quantum chromodynamics (QCD) is a fundamental theory describing quark interactions. Thus far, various quark models based on QCD have been widely used to study the properties of hadrons, including their structures and mass spectra. However, unlike quantum electrodynamics and Bohr's model of the hydrogen atom, a direct classical analogy is lacking for hadronic structures. This paper presents a classical interpretation of the nonrelativistic quark potential model, providing a more intuitive and visualizable description of strong interactions through the quantitative formulation of color charge and color flux. In addition, we establish the relationship between meson mass and its structural radius in the nonrelativistic framework and estimate key parameters of our model using available data from $ \eta_b(1S) $ and $ \Upsilon(1S) $. Subsequently, we extend this relationship to a broader range of excited meson states and obtain their structural radii, which show good agreement with the root mean square radius or charge radius predicted by QCD calculations.
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