We present a one-loop renormalization analysis of the improved gluonic energy-momentum tensor in pure SU(3) lattice gauge theory, employing a tadpole-improved tree-level Symanzik gauge action and a three-loop-improved clover discretization of the field-strength tensor. The calculation is conducted in Landau gauge by matching the amputated two-gluon matrix element of the lattice energy-momentum tensor to the continuum MSbar scheme. The one-loop correction is separated into sail, operator-tadpole, and external-leg contributions, each expressed in terms of a minimal set of scalar Brillouin-zone integrals. This approach yields explicit expressions for the finite lattice coefficient B_lat(u0) and the multiplicative renormalization factor Z_T(u0) associated with the traceless spin-2 component of the energy-momentum tensor. A key result is the clear distinction between the spin-2 sector, governed by Z_T, and the scalar trace sector, which encodes the Yang-Mills trace anomaly. We demonstrate that the improved lattice construction maintains the correct continuum anomaly structure, with the trace determined by the scalar operator F_{rho sigma}F_{rho sigma} and the Yang-Mills beta function, rather than by the spin-2 renormalization factor. The resulting renormalized energy-momentum tensor alters the normalization and short-distance behavior of Euclidean energy-density correlators through both traceless and scalar-channel contributions. Comparison with existing lattice thermodynamic data indicates that the improved operator accurately reproduces the expected temperature dependence of the trace anomaly and provides a systematically improvable framework for studying the equation of state, gluon condensate, and transport coefficients in lattice QCD.

We analyze the effects of the magnetic field on the quark and gluon propagators within the functional QCD framework. By solving the coupled Dyson-Schwinger equations for the quark and gluon propagators, we find that the quark mass is generally enhanced in the presence of a magnetic field, leading to magnetic catalysis of the chiral condensate. Meanwhile, the magnetic field also induces an increase in the gluon screening mass. The enhancement of the gluon screening mass suppresses the quark-gluon interaction and thereby weakens the strength of dynamical chiral symmetry breaking, establishing a competing mechanism against magnetic catalysis. In particular, this enhancement of the gluon screening mass becomes dominant near the chiral phase transition, which in turn gives rise to inverse magnetic catalysis.

We study the out-of-equilibrium scaling behavior of the particle density in quantum fermionic Kitaev wires, after instantaneous quantum quenches (QQs) of the chemical potential within their quantum critical region. The critical scaling of the ground-state particle density is known to be subleading at its Ising-like quantum transition, hidden by regular and logarithmic terms arising from peculiar mixings with the identity operator. This situation changes along the out-of-equilibrium dynamics arising from QQs of the chemical potential to the critical point, starting from the ground state for Hamiltonian parameters within the critical region. We analytically show that the difference between the post-QQ particle density and its critical value develops an out-of-equilibrium scaling behavior, in terms of the dynamic scaling variable $\theta\sim t/\xi^z$ (where $t>0$ is the post-QQ time, $\xi$ is the length scale of the initial state, and $z$ is the dynamic critical exponent) associated with the post-QQ time evolution. The scaling function turns out to have a peculiar singular behavior in the $\theta\to 0$ limit, apparently related to the anomalous equilibrium scaling behavior of the particle density at the starting point of the QQ protocol. This provides analytical evidence of earlier conjectures on the general emergence of post-QQ dynamic scaling behaviors of the subtracted particle density (supported by numerical finite-size scaling analyses), unlike their equilibrium counterpart which turns out to be dominated by nonuniversal contributions.

Probing the internal organization of hidden-charm pentaquarks -- including the spin-color correlations that distinguish compact diquark-diquark-antiquark configurations from loosely bound hadronic molecules -- requires observables beyond mass spectroscopy. We argue that multi-current QCD light-cone sum rules (LCSR) provide a diagnostic framework through exact analytic relations among flavor-sector contributions enforced by the algebra of the interpolating currents. We identify two such signatures: (i) the light-quark contributions satisfy $\mu_{u}/\mu_{d}=e_{u}/e_{d}=-2$ in all four currents considered, reflecting a common Lorentz-color kernel; and (ii) for the $J_{3}(x)$ current the charm contribution vanishes identically, $\mu_{c}=0$, from the Dirac structure of the anti-charm coupling rather than the pseudoscalar charm-diquark embedding alone. Using four diquark-diquark-antiquark currents $J_{1}(x)$-$J_{4}(x)$ with $J^{P}=\tfrac{1}{2}^{-}$, we obtain $\mu_{J_{1}}=-1.35^{+0.35}_{-0.28}\,\mu_{N}$, $\mu_{J_{2}}=3.14^{+0.65}_{-0.50}\,\mu_{N}$, $\mu_{J_{3}}=1.01^{+0.25}_{-0.20}\,\mu_{N}$, $\mu_{J_{4}}=-1.79^{+0.41}_{-0.34}\,\mu_{N}$. These predictions are paired with the $P_{\psi s}^{\Lambda}(4338)$ and $P_{\psi s}^{\Lambda}(4459)$ on mass grounds as a working hypothesis, since the $\pm 0.11~\text{GeV}$ uncertainties accommodate either state within $1\sigma$ of all four currents. The magnitudes $|\mu|\sim 1$-$3\,\mu_{N}$ lie above quark-model and heavy pentaquark chiral perturbation theory expectations ($|\mu|\lesssim 0.5\,\mu_{N}$). Applying the same procedure to two previous molecular LCSR analyses yields $\mu_{u}/\mu_{d}=-1/2$ rather than $-2$, providing an LCSR-internal contrast at the flavor-decomposed level even when total magnitudes are comparable. The two signatures are immune to the state-to-current pairing and offer falsifiable tests of the compact picture.

Yang-Mills theories at $\theta$ and $\theta+2\pi$ are unitarily equivalent, but their $2\pi$ periodicity has a nontrivial realization. Recent developments in generalized global symmetries show that confinement vacua at $\theta=0$ and $2\pi$ should belong to different symmetry-protected topological (SPT) states with the $1$-form center symmetry. For its examination, we measure the Wilson-'t Hooft loop operators at $\theta=2\pi$ for the $SU(2)$ Wilson lattice gauge action and discuss their long-distance behaviors. This requires us to identify the gauge topological charge in the presence of defects, and we employ the $1$-form covariant DBW2 gradient flow to smear lattice gauge fields. We then obtain numerical evidence consistent with dyon condensation at $\theta=2\pi$, rather than monopole condensation, as theoretically predicted.

We demonstrate that the orbifold lattice Hamiltonian -- an approach known for its efficiency in simulating SU($N$) Yang-Mills theory and QCD on digital quantum computers -- can reproduce the Kogut-Susskind Hamiltonian in a controlled limit. While the original Kogut-Susskind approach faces significant implementation challenges on quantum hardware, we show that it emerges naturally as the infinite scalar mass limit of the orbifold lattice formulation, even at finite lattice spacing. Our analysis provides both a general analytical framework applicable to SU($N$) gauge theories in arbitrary dimensions and specific numerical evidence for $(2+1)$-dimensional SU($N$) Yang-Mills theories ($N=2,3$). Using Euclidean path integral methods, we quantify the convergence rate by comparing the standard Wilson action with the orbifold lattice action, matching lattice parameters, and systematically extrapolating results as the bare scalar mass approaches infinity. This reformulation resolves longstanding technical obstacles and offers a straightforward implementation protocol for digital quantum simulation of the Kogut-Susskind Hamiltonian with exponential speedup compared to classical methods and previously known quantum methods, modulo a standard assumptions made also for the original Kogut-Susskind approach.

We present an investigation into the semileptonic and nonleptonic weak decays of bottom baryons $\Omega^{*}_{b}$ and $\Omega_{b}$ within the framework of three-point QCD sum rules. In the semileptonic sector, the $\Omega^{*}_b\rightarrow\Omega_c\ell\bar{\nu}_{\ell}$ and $\Omega_b\rightarrow\Omega^*_c\ell\bar{\nu}_{\ell}$ transitions are specifically considered. Utilizing the operator product expansion up to dimension six, the responsible form factors of these decays are obtained. The acquired form factors enable us to determine the decay widths in three leptonic channels. Branching ratios related to the $\Omega_{b}$ baryon semileptonic decays are also presented. These invariant form factors are subsequently employed as inputs to determine the nonleptonic weak decay widths in various modes with emitting a pseudoscalar or vector meson. An extensive investigation into all possible decay channels of bottom baryons provides valuable information for future experiments to examine the SM predictions, explores the new physics effects in heavy baryonic decays, and advances the understanding of the internal structure of heavy baryons.

We show that, in the replica-broken sector of the Serreau--Tissier (ST) gauge fixing, the expansion of the replica determinant in the regulator $\zeta$ induces a nonlocal bilinear gluonic kernel with the same color and Lorentz structure as the quadratic part of the BRST-invariant Gribov horizon functional. This establishes an effective leading-order correspondence with the refined Gribov-Zwanziger (RGZ) horizon sector, rather than a reconstruction of the full nonlinear functional $H(A^h)$. The induced scale satisfies $\gamma_{\mathrm{ind}}^4\propto \zeta$ at leading order, up to scheme-dependent normalization and higher-order corrections. Depending on the replica phase, the ST sector yields either a local Curci--Ferrari (CF) screening mass or an induced RGZ-type horizon kernel, avoiding double counting of infrared scales.

We present a comprehensive theoretical investigation of the magnetic moments of open heavy-flavor molecular pentaquarks with quark compositions $b\bar{c}qqq$ and $c\bar{b}qqq$ (where $q=u,d,s$). Employing a molecular picture in which the pentaquarks are treated as S-wave bound states of a heavy baryon and a meson, we systematically construct the complete spin--flavor wavefunctions for the two distinct SU(3)$_f$ octet representations, $8_{1f}$ and $8_{2f}$, arising from symmetric and antisymmetric light-diquark configurations, respectively. Within the framework of the constituent quark model, we calculate the magnetic moments of spin-parity configurations, $J^P = \frac{1}{2}^-(\frac{1}{2}^+\otimes 0^-)$ and $J^P = \frac{1}{2}^-, \frac{3}{2}^-(\frac{1}{2}^+\otimes 1^-)$, for each member of the $b\bar{c}$ and $c\bar{b}$ octets. Our results reveal a striking hierarchy: in the $8_{2f}$ representation, the $\frac{1}{2}^+\otimes 0^-$ states exhibit near-universal magnetic moments ($\mu \approx -0.062\,\mu_N$ for $b\bar{c}qqq$ and $\mu \approx +0.362\,\mu_N$ for $c\bar{b}qqq$), as a direct consequence of the spin-singlet light-diquark that suppresses light-quark contributions. In contrast, the $8_{1f}$ representation shows a broad spectrum of values with frequent sign changes, reflecting the active role of the symmetric light-diquark. The clear differences between the $b\bar{c}$ and $c\bar{b}$ families demonstrate explicit heavy-quark flavor symmetry breaking in electromagnetic observables. These predictions provide a detailed set of electromagnetic benchmarks that can serve as discriminants for the internal flavor structure and spin configuration of future experimentally observed open heavy-flavor pentaquarks, offering valuable guidance for ongoing and future searches at facilities such as LHCb and Belle II.