Exotic hadrons beyond the conventional quark model provide a direct window into the dynamics of strong interaction. However, extracting the multiquark spectroscopy has to face the quantum many-body problem, which is still a theoretical challenge. In this case, diquark-antidiquark model is proposed as an approximation. Although this model can describe the spectroscopy roughly, it cannot describe the detailed dynamics. Furthermore, the methods aiming at dealing with many-body problem, e.g., the Gaussian expansion method and diffusion Monte Carlo, are proposed, but face severe computational bottlenecks. In this work, we introduce the neural-network quantum state (NNQS) approach to investigate the spectra of fully heavy multiquark states within the nonrelativistic potential quark model. By employing deep neural networks to represent the complex many-body spatial wave function, and constructing the color-spin part exactly from group theory to enforce fermionic antisymmetry, our approach effectively overcomes the dimensionality obstacles inherent in traditional methods. The results are compared with various model calculations, demonstrating that NNQS offers superior accuracy and flexibility, particularly in treating high-dimensional correlations. This work establishes NNQS as a promising tool for exploring the spectroscopy of exotic hadrons.

The masses of $1^{--}$ P-wave charmoniumlike and bottomoniumlike tetraquark states are calculated in a constituent quark model where the Cornell-like potential and Breit-Fermi interaction are employed. All model parameters were imported from previous work, and predetermined by studying the low-lying conventional S- and P-wave light, charmed, bottom, charmonium, and bottomonium meson mass spectra. The lowest $1^{--}$ tetraquark mass is predicted to be around 4.15 GeV. The decay widths of $1^{--}$ P-wave tetraquark states are calculated for possible two-body strong decay channels within the rearrangement mechanism, including $\omega {\chi }_{cJ}$ and $\eta J/\psi$ for charmoniumlike tetraquarks, and $\omega {\chi }_{bJ}$ for bottomoniumlike tetraquarks. The theoretical results are compared with the selected exotic states, also known as Y states, and tentative assignments are suggested. This study suggests that $\psi (4230)$, $\psi (4360)$, $\psi (4660)$, and $\mathrm{\Upsilon }(10753)$ may be P-wave tetraquark states and that multiple states might exist around 4.36 GeV.

Recent discoveries of exotic hadrons, which cannot be classified within the conventional quark model of $q\overline{q}$ mesons and $qqq$ baryons, strongly imply the existence of dynamically generated hadronic molecules. Some of these hadron-hadron interactions are accompanied by coupled-channel effects, which remain challenging to quantitatively determine. In this work, we demonstrate that femtoscopy provides a sensitive probe of such coupled-channel dynamics. We calculate correlation functions for the double-strangeness pentaquark candidates $P_{css}(4493)$ ($J^P=1/2^{-}$) and $P_{css}(4633)$ ($J^P=1/2^{-}$ or $3/2^{-}$), revealing clear signatures of the attractive interactions that can form bound states. The results are markedly different from those obtained in scenarios that neglect off-diagonal transitions, highlighting the importance of coupled-channel effects for understanding the structure of these hadrons.

We apply the generalized effective-range expansion of Du et al. [Phys. Rev. Lett. 135, 011903 (2025)], which incorporates the left-hand cut from one-pion exchange to low-energy neutron–proton scattering in the ${}^1{S}_0$ and ${}^3{S}_1$ channels. The amplitude zero for the center-of-mass momentum near 0.35 GeV in the ${}^1{S}_0$ channel is naturally accommodated within this framework. We extract the pole position, scattering length, effective range, shape parameter, and the pseudoscalar pion–nucleon coupling constant $g_{\pi N}^2/(4\pi )$ at different expansion orders. The low-energy parameters are stable and consistent with established values, while $g_{\pi N}^2/(4\pi )$ exhibits larger uncertainties. The extraction of $g_{\pi N}^2/(4\pi )$ is data driven, relying on the analytic constraints from the left-hand cut and phase-shift data within the one-pion-exchange approximation. Despite larger uncertainties compared to high-precision extractions, the consistency with established values demonstrates that this framework can probe the left-hand-cut singularity.

We investigate the late-time asymptotic solutions and attractor structure of the spin density in minimal causal spin hydrodynamics in Gubser flow. After deriving the differential equation governing the spin density, we obtain its late-time asymptotic solutions and identify both attractors and repellers in the corresponding numerical solutions. We then map these solutions back to flat Minkowski space and find parameter regions where the spin density exhibits a power-law decay. We further show that, when the characteristic length scale of the system is much larger than the proper time, several components of the spin density can decay as slowly as conventional thermodynamic variables in relativistic hydrodynamics. In this regime, the spin density behaves as a hydrodynamic mode governed by the late-time scaling laws of the flow.

We perform a systematic QCD sum rule study of light tetraquark states with $J^{PC}=1^{--}$ in the diquark-antidiquark picture. A complete set of local interpolating currents is constructed and projected onto six flavor-isospin configurations ($q=u/d$): the isoscalar $qq\overline{q}\overline{q}$, $qs\overline{q}\overline{s}$, and $ss\overline{s}\overline{s}$ sectors, the isovector $qq\overline{q}\overline{q}$ and $qs\overline{q}\overline{s}$ sectors, and the isotensor $qq\overline{q}\overline{q}$ sector. From the nonderivative currents studied in the present work, the extracted masses of the $qq\overline{q}\overline{q}$, $qs\overline{q}\overline{s}$, and $ss\overline{s}\overline{s}$ configurations lie in the ranges 1.53–2.37 GeV, 1.86–2.51 GeV, and 2.46–2.60 GeV, respectively. For the $ss\overline{s}\overline{s}$ vector sector, we also quote the previous derivative-current result ${2.34}_{-0.30}^{+0.23}\mathrm{GeV}$ as a complementary benchmark. We further compare the present $1^{--}$ tetraquark spectrum with previous QCD sum rule results for the $1^{-+}$ tetraquark and hybrid states [N. Su, E.-L. Cui, Y.-W. Jiang, and H.-X. Chen, Eur. Phys. J. C 86, 724 (2026).], aiming to provide useful information for distinguishing tetraquark and hybrid configurations in the light hadron spectrum. As an additional improvement, we complete the previously missing isotensor $1^{-+}$ tetraquark entry and obtain its lowest mass to be $M=2.19_{-0.24}^{+0.26}\mathrm{GeV}$, which is included in the spectral comparison.

Within the QCD sum-rule framework, we investigate hidden-heavy tetraquark channels with the exotic quantum number $J^{\mathrm{PC}}=0^{--}$ using four representative local color-octet–octet interpolating currents. The currents include both vector-axialvector and scalar-pseudoscalar Dirac structures. The operator product expansion is carried out up to dimension-eight condensates. The four diagonal sum rules yield mutually consistent mass estimates in the range 10.8–11.1 GeV for the hidden-bottom sector and around 4.3–4.6 GeV for the corresponding hidden-charm sector, with the bottom sector exhibiting the clearest Borel stability. Since local tetraquark currents with the same quantum numbers are related by Fierz rearrangements, the current-dependent results do not by themselves imply four distinct states or uniquely defined internal color structures. We also discuss quantum-number-allowed decay channels and emphasize the absence of the lowest pseudoscalar-pseudoscalar heavy-meson modes for a neutral $0^{--}$ state. The results provide theoretical guidance for future experimental searches at Belle II, LHCb, and BESIII.

We present a systematic analysis of the fall-apart decays for the $1S$, $1P$, and $2S$-wave fully-strange tetraquark states. It shows that most of the fully-strange tetraquark states have a relatively narrow fall-apart decay width of $\mathcal{O}(10)\mathrm{MeV}$. The newly observed axial-vector state $X(2300)$ at BESIII may favor the low-lying $1S$-wave $1^{+-}$ state $T_{(4s)1^{+-}}(2323)$, while the $X(2500)$ resonance observed in the earlier BESIII experiment may favor the low-lying $1P$-wave $0^{-+}$ state $T_{(4s)0^{-+}}(2481)$. Some fully-strange tetraquark states predicted in theory can be searched for in their dominant fall-apart decay channels in experiments, such as $\varphi \varphi$, $\varphi \varphi (1680)$, ${\eta }^{(\prime )}\varphi$, ${\eta }^{(\prime )}{h}_1(1415)$, and $\varphi f_2^{\prime }(1525)$, to which they have relatively large couplings.

We derive the expressions for the one-point energy correlator (OPEC) in deep inelastic scattering in the high-energy (small-$x$) limit within the Color Glass Condensate (CGC) framework. The OPEC is computed as a function of the angle between the energy flow and the target proton or nucleus, enabling a systematic exploration of different momentum scales in the scattering process. Owing to the momentum sum rule, the dependence on fragmentation functions cancels, leaving the dipole amplitude as the only nonperturbative input. As a result, the OPEC provides a sensitive and promising probe of gluon saturation dynamics at small $x$. We present numerical results for representative kinematic configurations relevant to the future Electron-Ion Collider, demonstrating sizable nuclear suppression effects within the CGC framework and highlighting the consistency of this observable with predictions from gluon saturation.

We establish the multipole structure of the $N\to \mathrm{\Delta }$ transition at the level of the generalized parton distributions (GPDs). We decompose the four transition GPDs into one monopole, two dipole, and one quadrupole components in the transverse plane by a multipole expansion of the covariant transition matrix element in terms of the three-dimensional spin-transition tensors and the transverse momentum transfer. These multipole components are in one-to-one correspondence with the light-front helicity amplitudes. In the zero-skewness limit, the multipole GPDs define impact-parameter transition densities, which generalize the transverse transition charge densities to the $x$-dependent level. These transition densities arise from nondiagonal matrix elements between two distinct hadronic states and must therefore be distinguished from the diagonal densities of the nucleon and the $\mathrm{\Delta }$. The multipole transition densities visualize the monopole, dipole, and quadrupole structures of the partonic $N\to \mathrm{\Delta }$ transition in the transverse plane.

A search for proton decay via $p\to l^{+}+X$, where $l^{+}$ is a positively charged lepton and $X$ is an invisible, massless, neutral particle, was performed using a $401\mathrm{kton}·\mathrm{years}$ exposure representing the entire pure water phase of Super-Kamiokande. No significant indication of a proton decay was observed beyond the expected atmospheric neutrino background. Lower limits on the partial lifetime of the proton were set to $1.72\times {10}^{33}\mathrm{years}$ for $p\to e^{+}+X$ and $0.61\times {10}^{33}\mathrm{years}$ for $p\to {\mu }^{+}+X$ at the 90% confidence level. These results improve on previous limits by factors of 2 and 1.5, respectively.

Predictions for observables involving the cosmological 21-cm background require calculations of spatial correlations of star formation rate densities (SFRDs), which have a nonlinear dependence on the baryon-dark matter relative velocity. Prior work derived these SFRD correlations with a simplifying assumption that neglected the difference between the correlations of the components of the velocity parallel and perpendicular to the separation between the two points being correlated. Here we calculate the full joint PDF of the squares of the peculiar velocity at two different points. The error that arises in predictions for 21-cm fluctuations if this subtlety is overlooked is generally less than a few percent, but it can be larger for some values of wave number $k$ and redshift $z$ if there are cancellations between different contributions to the total signal. The correct expression is easily implemented and increases the run time of the code by only a few percent.

The relation between spin and statistics in quantum field theory relies on Poincaré invariance, a symmetry that is lost in the presence of a gravitational field, and replaced in general relativity by the principle of general covariance. In a nonperturbative approach to quantum gravity, beyond the picture of gravitational perturbations propagating on a flat background, it is an open question whether the gravitational field must still satisfy a bosonic statistics. By implementing the principle of general covariance through the requirement of invariance under active diffeomorphisms in loop quantum gravity, we find that the space of kinematical states of the gravitational field includes not only bosonic states, but also subspaces of fermionic and mixed statistics.

We show that scalar discrete-series unitary irreducible representations (UIRs) ${\mathrm{\Pi }}_{p,0}$ ($p=1,2,\dots$) of the de Sitter (dS) group ${\mathrm{SO}}_0(1,4)$ admit a dS-covariant Krein realization on the dS hyperboloid, endowed with a dS-invariant nondegenerate Klein-Gordon (KG) sesquilinear form, in which the group action is indecomposable and organizes naturally into a Gupta-Bleuler triplet. The positive- and negative-norm sectors are already present in the underlying Krein space, whereas a null sector emerges only at an intermediate stage, where the induced KG form becomes degenerate, and its radical leads canonically to the physical quotient carrying the UIR ${\mathrm{\Pi }}_{p,0}$. We further show that suitable limits of the bulk theory at the “future” and “past” conformal boundaries ${\mathcal{I}}^{\pm }$ give rise to dS-invariant boundary realizations endowed with induced kernel inner products. While the bulk negative-norm sector admits no independent boundary counterpart, the boundary realization retains the physical and gauge structures inherited from the bulk. The resulting boundary module nevertheless remains indecomposable, with its physical quotient carrying the discrete-series representation ${\mathrm{\Pi }}_{p,0}$. The antipodal symmetry provides a natural relation between the realizations on ${\mathcal{I}}^{+}$ and ${\mathcal{I}}^{-}$, ensuring the consistency of the boundary construction and its geometric interpretation. At the heart of the analysis lies a Fourier-type bulk-boundary transform that provides a dS-covariant identification of the bulk and boundary physical sectors, establishing a one-to-one intertwining correspondence between the bulk and boundary realizations of ${\mathrm{\Pi }}_{p,0}$ while preserving reflection positivity.

Building on the framework developed by Perche [Phys. Rev. D 106, 025018 (2022)], we study two localized nonrelativistic quantum particles propagating along timelike geodesics in a curved spacetime background. Each particle is coupled to a quantum clock that operationally records the time spent in a prescribed spatial region. We compute the covariance of the resulting time observables for separable and entangled two-particle states, comparing flat and curved backgrounds. We then reformulate the protocol as a Bell-like experiment and show that the Bell parameter can acquire a curvature-induced correction. In particular, a protocol calibrated to saturate the classical bound in flat spacetime can be driven above this bound in curved spacetime for entangled states. We focus on two-dimensional curved backgrounds in which the local tidal term induces an effective harmonic potential in the Fermi-frame description. Our results show that spacetime curvature can modify operationally defined quantum correlations and suggest entangled quantum clocks as probes of spacetime curvature.

We consider the classical scattering of two gravitating compact objects in the presence of a massive scalar mediator, providing a simple model of exotic phenomena. Through dimensional analysis, we argue that such a process can only be classical in the presence of gravity, a consequence of which is that perturbing in the coupling of the scalar to a worldline is not separate from the post-Minkowskian expansion. When computing asymptotic observables, the massive mediator complicates the Fourier transforms to impact-parameter space at next-to-leading order. We reduce these to univariate parametric integrals—amenable to numerical integration—and produce analytic results for the linear impulse and the scattering angle to the second post-Minkowskian order. The scattering angle exhibits a maximum when the range of the scalar-mediated force is comparable to the impact parameter, a possible signature of a massive scalar mediator. In the opposite, large-mass regime we uncover a screening effect: integrating out the scalar sourced by each compact object reduces its gravitational mass by an amount linear in the scalar’s mass. Both of these phenomena are next-to-leading-order effects.

We present the spectrum of stationary black hole solutions associated with the first nontrivial member of the Dym family of boundary conditions. The analysis combines the holonomy conditions provided by the Chern-Simons formulation of ${\mathrm{AdS}}_3$ gravity with the periodic solutions of the stationary Dym equation. The resulting spacetimes are characterized by two positive real parameters, two positive integers, and a relative phase, generically describing stationary, nonaxisymmetric black holes.

Extreme-mass-ratio inspirals (EMRIs) are among the most promising sources for future space-based gravitational-wave (GW) detectors, such as the Laser Interferometer Space Antenna. To fully leverage the scientific potential, the GW templates required for parameter estimation must be modeled with high accuracy for eccentric precessing binary systems with nonzero spins. This work introduces a practical and efficient framework for incorporating the effects of secondary spin in fully generic, eccentric, and off-equatorial EMRIs to the first postadiabatic order. We utilize recently found analytic solutions for the trajectories of spinning bodies in Kerr spacetime to significantly simplify the calculation of the corresponding asymptotic GW fluxes. Furthermore, thanks to the recently proven flux-balance laws, we show how to express the rates of change of the constants of motion, including the Carter-Rüdiger constant, using asymptotic Teukolsky amplitudes and purely geodesic functions that are already established in the literature. Finally, we show how this framework performs in the case of nearly spherical inspirals and numerically demonstrate that the linear-in-spin part of the phases is gauge independent. A Wolfram Mathematica implementation of the code developed in this work is publicly available in the kerrspinningfluxes package.

We study the collisional disruption of primordial black hole (PBH) clusters in the Milky Way halo. Encounters between clusters strip PBHs into a diffuse component, and the fraction of PBH mass in this smooth component along a sightline determines how microlensing constraints divide between isolated compact objects and extended cluster lenses. We combine an analytic Navarro-Frenk-White-based collision-rate model, 72 direct N-body binary collision simulations that calibrate the escaped-mass fraction as a universal function $\tilde{f}(\tilde{v},\tilde{b})$ of the relative velocity and impact parameter in units of the cluster velocity scale and half-mass radius, and cosmological N-body simulations of a Milky Way-like halo ($M_{200}\simeq 8\times {10}^{11}{M}_{\odot }$, $c_{200}\simeq 11$) that record the encounter history of every cluster from $z=9$ to $z=0$. For ${10}^6$ and ${10}^7{M}_{\odot }$ clusters, which lie on either side of the characteristic cluster mass at $z=9$, the local encounter rate at the solar circle is $2.9\times {10}^{-3}$ and $1.2\times {10}^{-2}{\mathrm{Myr}}^{-1}$, consistent with the simulations to within $\sim 40\%$. Because the peak-disruption velocity of Carr-radius clusters ($12–20\mathrm{km}{\mathrm{s}}^{-1}$) lies far below typical halo encounter velocities, the mass loss accumulates over many weak encounters, and most of it occurs early, during halo assembly, when the encounter velocities are still low: half of the total mass loss happens before $z\approx 2$, which analytic estimates made at $z=0$ do not account for. The surviving mass fraction at the solar circle is $S\simeq 0.50$ (${10}^6{M}_{\odot }$) and 0.04 (${10}^7{M}_{\odot }$), and the dark matter-mass-weighted smooth fraction toward the large Magellanic cloud and small Magellanic cloud is 0.49 and 0.92, respectively. Cluster-cluster disruption is therefore substantial over the lifetime of the Galaxy, and reanalyses of microlensing surveys should use the radially varying smooth fraction $f_{\mathrm{sm}}(r)$ obtained here.