Bilinear Euclidean quark and gluon correlators with Wilson links have been used widely for applications of large-momentum effective field theories to computing non-perturbative collinear and soft parton physics. Due to color confinement, these correlators decay exponentially at large spatial distances, a behavior crucial for computing momentum-space Fourier transformations with controlled errors from lattice QCD data. Using heavy-quark effective theory reduction, dispersive analysis, Lorentz symmetry, and heavy-flavor spectra, we determine the leading and next-to-leading asymptotic behaviors and relate the expansion parameters to binding energies of heavy-flavor hadrons. We demonstrate the results through two-loop calculations in $\phi^3$ theory and from the perspective of locality and analyticity. We also study the impact of the asymptotic analysis on realistic lattice QCD data and demonstrate reliable error estimates.

We present results for the one-loop value of the improvement coefficient $c_\mathrm{SW}$ for Wilson and Brillouin fermions subject to stout smearing or Wilson flow, in combination with Wilson or Symanzik glue. To this end we use a recently developed method that allows one to modify an existing perturbative calculation, like the one for $c_\mathrm{SW}^{(1)}$, to include stout smearing or Wilson flow at arbitrary stout parameters ($\varrho$, $n_\mathrm{stout}$) or flow times $t/a^2$, respectively. Our results indicate that already a small amount of smoothing makes the perturbative series well behaved, suggesting that a non-perturbatively determined $c_\mathrm{SW}$ might be close to its one-loop value for couplings $g_0^2\simeq 1$.

We present the first lattice-QCD validation of multiple sum rules associated with quark-gluon decomposition of hadron mass by computing all components from first principles. We achieve this through nonperturbative renormalization of the QCD energy-momentum tensor, including its trace, in a gradient-flow scheme, followed by continuum extrapolations, two-loop matching to the $\overline{\mathrm{MS}}$ scheme, and zero-flow-time extrapolations. These ingredients enable a direct and simultaneous verification, in a common renormalization scheme and scale, of multiple energy-density-based and trace-based mass decomposition sum rules proposed in the literature. We demonstrate the framework for the $\eta_c$ and $J/\psi$ charmonia using three fine lattice spacings with a physical strange-quark and near-physical up- and down-quark masses. We present the first lattice-QCD results for the gravitational form factor $\bar{C}$. We find sizable gluonic contributions to charmonia masses at the hadronic scale, $\sim 15\%$ in the Lorcé and Metz-Pasquini-Rodini decompositions. The trace-anomaly contribution in the Ji sum rule is $\sim 6\%$, while the gluonic component of the trace anomaly in the Hatta-Rajan-Tanaka sum rule is $\sim 35\%$. The method is general and can be straightforwardly adopted for lattice-QCD calculations of mass and spin decompositions as well as gravitational form factors of other hadrons and nuclei.

Nonequilibrium dynamics of quantum many-body systems is one of the main targets of quantum simulations. This focus - together with rapid advances in quantum-computing hardware - has driven increasing applications in high-energy physics, particularly in lattice gauge theories. However, most existing experimental demonstrations remain restricted to (1+1)-dimensional and/or abelian gauge theories, such as the Schwinger model and the toric code. It is essential to develop quantum simulations of nonabelian gauge theories in higher dimensions, addressing realistic problems in high-energy physics. To fill the gap, we demonstrate a quantum simulation of thermalization dynamics in a (2+1)-dimensional $q$-deformed $\mathrm{SU}(2)_3$ Yang-Mills theory using a trapped-ion quantum computer. By restricting the irreducible representations of the gauge fields to the integer-spin sector of $\mathrm{SU}(2)_3$, we obtain a simplified yet nontrivial model described by Fibonacci anyons, which preserves the essential nonabelian fusion structure of the gauge fields. We successfully simulate the real-time dynamics of this model using quantum circuits that explicitly implement $F$-moves. In our demonstrations, the quantum circuits execute up to 47 sequential $F$-moves. We identify idling errors as the dominant error source, which can be effectively mitigated using dynamical decoupling combined with a parallelized implementation of $F$-moves.

We present a comprehensive theoretical assessment of the masses of possible baryonic configurations characterized by the presence of two heavy top quarks, including $\Xi_{ttu}$, $\Xi_{ttd}$, $\Omega_{tts}$, $\Omega_{ttc}$, and $\Omega_{ttb}$ systems. This analysis is rigorously executed within the specialized framework of two-point $\mathrm{QCD}$ sum rules, focusing on their predicted ground state masses. Our interest in these systems arises from recent CMS and ATLAS reports indicating a pseudoscalar excess close to $t\bar{t}$ threshold. Our evaluation incorporates both perturbative terms and nonperturbative effects, including condensate contributions up to dimension eight. Based on our results, the extracted central masses for all channels are slightly above the sum of the constituent quark masses, which is consistent with the inherent uncertainties of the method. These quantitative predictions provide a useful first-principle theoretical reference, which may help future experimental searches for such heavy configurations at the LHC and inform sensitivity studies at next-generation facilities such as the FCC.

We address issues related to the presence of defects at topological transitions, in particular when defects are modeled in terms of further variables associated with a quenched disorder, corresponding to the limit in which the defect dynamics is very slow. As a paradigmatic model, we consider the three-dimensional lattice ${\mathbb Z}_2$ gauge model in the presence of quenched uncorrelated disorder associated with the plaquettes of the lattice, whose topological transitions are characterized by the absence of a local order parameter. We study the critical behaviors in the presence of weak disorder. We show that they belong to a new topological universality class, different from that of the lattice ${\mathbb Z}_2$ gauge models without disorder, in agreement with the Harris criterium for the relevance of uncorrelated quenched disorder when the pure system undergoes a continuous transition with positive specific-heat critical exponent.

We perform a systematical investigation of the existence of the deuteron-like singly bottomed dibaryon resonance states with strangeness $S=-1,~-3,~-5$ in the chiral quark model. Two resonance states with strangeness $S=-1$ are obtained in the baryon-baryon scattering process. The first candidate is $\Sigma\Sigma_b$ in the $\Lambda\Lambda_b$ and $N\Xi_b^*$ scattering process, with the resonance energy 6974.22 MeV - 6975.37 MeV and the decay width 14.450 MeV, respectively; the other one is $\Sigma \Sigma_b^*$ in the $N\Xi_b$ and $N\Xi'_b$ scattering process, with the resonance energy 6990.69 MeV - 7008.37 MeV and the decay width 43.790 MeV, respectively. The Root Mean Square (RMS) radius calculation shows that the former tends to be in a compact structure, while the latter tends to be in a molecular structure. Both of these resonance states are worthy of experimental exploration. Furthermore, it should be emphasized that the effect of channel-coupling is of great importance in exploring exotic hadron states, and investigating the scattering process may serve as an effective approach to identifying genuine resonances.

Quantifying non-stabilizerness (``magic'') in interacting fermionic systems remains a formidable challenge, particularly for extracting high order correlations from quantum Monte Carlo simulations. In this Letter, we establish the two-point stabilizer Rényi entropy (SRE) and its mutual counterpart as robust, computationally accessible probes for detecting magic in diverse fermionic phases. By deriving local estimators suitable for advanced numerical methods, we demonstrate that these metrics effectively characterize quantum phase transitions: in the one-dimensional spinless $t$-$V$ model, they sharply identify the Luttinger liquid to charge density wave transition, while in the two-dimensional honeycomb lattice via determinant quantum Monte Carlo, they faithfully capture the critical exponents of the Gross-Neveu-Ising universality class. Furthermore, extending our analysis to the fractional quantum Hall regime, we unveil a non-trivial spatial texture of magic in the Laughlin state, revealing signatures of short-range exclusion correlations. Our results validate the two-point SRE as a versatile and sensitive diagnostic, forging a novel link between quantum resource theory, critical phenomena, and topological order in strongly correlated matter.

We calculate the 1-loop $\gamma Z$ box-graph correction to electron-quark scattering at low energy and low momentum transfer. Both electron and quark masses are kept non-zero. From our result, we extract coupling constants for the low-energy effective Lagrangian with parity-violating 4-fermion interaction terms. We study the zero-mass limits and show that a non-zero electron mass is sufficient to obtain finite, well-defined couplings which are insensitive to a hadronic mass cutoff. We finally discuss the impact of our results on the determination of the weak charge of the proton from polarized electron-proton scattering.

We evaluate the QED coupling in the gradient-flow scheme in three and four space-time dimensions. Our general result applies to any theory with a U(1) gauge field coupled to arbitary other fields via arbitrary interactions. As an example, we consider QED with $n_\text{f}$ flavors in three and four space-time dimensions and evaluate the corresponding $\beta$ functions. In four dimensions, we find that the perturbative expansion of the $\beta$ function behaves much better than the corresponding expression in QCD. In three dimensions, we recover both the ultraviolet as well as the infrared fixed points of the QED coupling in the large-$n_\text{f}$ limit.

The deconfining transition in $SU(3)$ gauge theory, traditionally interpreted through the Gross-Witten-Wadia (GWW) model as a sharp third-order phase transition in the large-$N_c$ limit, appears as a smooth crossover in lattice QCD. This work demonstrates that the transition is topologically smoothed into a crossover by incorporating the fractal momentum space structure inherent to thermofractals. By matching the non-extensive $\beta$-function to one-loop QCD results, a fundamental scaling of the thermofractal index $q$ is derived as a function of the number of flavours $N_f$. It is proven that applying a $q$-deformed derivative operator $\mathcal{D}_q$ to the $q$-logarithm of the eigenvalue distance results in a non-extensive measure that effectively smears the topological stiffness of the gauge vacuum. A unified master equation for the Polyakov loop $\langle L \rangle$ is presented, governed by the thermofractal index $q$ and a single variance parameter $\sigma^2(T)$ that scales as $T^{1/(q-1)}$. The observed phase dynamics are shown to be asymptotic limits of this unified density: a ``soft'' algebraic growth $\langle L \rangle \propto T^{11}$ in the 1D string-like confined regime for $N_f=0$, and a rapid $1 - \langle L \rangle \propto T^{-21}$ suppression in the 3D deconfined volume for $N_f=3$. This approach provides a microscopic foundation for partial deconfinement theory and reproduces lattice QCD data with a reduced $\chi^2 \approx 1.12$, offering a rigorous reconciliation between matrix model topology and the continuous QCD crossover.

The determination of whether the ground state of baryon matter in Quantum Chromodynamics (QCD) is the ordinary nucleus or a quark matter state remains a long-standing question in physics. A critical parameter in this investigation is the bag parameter $B$, which quantifies the QCD vacuum energy and can be computed using nonperturbative methods such as Lattice QCD (LQCD). By combining the equation of state derived from perturbative QCD (pQCD) with the bag parameter to fit the LQCD-simulated data for isospin-dense matter, we address the stability of quark matter within the LQCD+pQCD framework. Our findings suggest that the current data imposes an upper bound on $B^{1/4} \lesssim 160$ MeV, approaching a conclusive statement on quark matter stability. Given the lower bound on $B$ from the quark condensate contribution to the vacuum energy, the stable 2-flavor quark matter remains possible, whereas the stable 2+1-flavor quark matter is excluded, assuming complete deconfinement and chiral-symmetry restoration and the reliability of pQCD at baryon chemical potentials around the proton mass. Additionally, we derive more general thermodynamic bounds on the quark matter energy-per-baryon and $B$, which, while weaker, provide complementary insights.

We study in detail the fully inhomogeneous non-linear dynamics of axion inflation, identifying three regimes: weak-, mild-, and strong-backreaction, depending on the duration of inflation. We use lattice techniques that explicitly preserve gauge invariance and shift symmetry, and which we validate against other computational methods of the linear dynamics and of the homogeneous backreaction regime. Notably, we demonstrate that the latter fails to accurately describe the truly local dynamics of strong backreaction. We investigate the convergence of simulations of local backreaction, determining the requirements to achieve an accurate description of the dynamics, and providing useful parametrizations of the delay of the end of inflation. Additionally, we identify key features emerging from a proper local treatment of strong backreaction: the dominance of magnetic energy against the electric counterpart, the excitation of the longitudinal mode, and the generation of a scale-dependent chiral (im)balance. Our results underscore the necessity to accurately capture the local nature of the non-linear dynamics of the system, in order to correctly assess phenomenological predictions, such as e.g. the production of gravitational waves and primordial black holes.

A Quantum Cellular Automaton (QCA) is essentially an operator driving the evolution of particles on a lattice, through local unitaries. Because $\Delta_t=\Delta_x = \epsilon$, QCAs constitute a privileged framework to cast the digital quantum simulation of relativistic quantum particles and their interactions with gauge fields, e.g., $(3+1)$D Quantum Electrodynamics (QED). But before they can be adopted, simulation schemes for high-energy physics need prove themselves against specific numerical issues, of which the most infamous is Fermion Doubling (FD). FD is well understood in particular in the real-time, discrete-space \emph{but} continuous-time settings of Hamiltonian Lattice Gauge Theories (LGTs), as the appearance of spurious solutions for all $\Delta_x=\epsilon\neq 0$. We rigorously extend this analysis to the real-time, discrete-space \emph{and} discrete-time schemes that QCAs are. We demonstrate the existence of FD issues in QCAs for $\Delta_t =\Delta_x = \epsilon \neq 0$. By applying a covering map on the Brillouin zone, we provide a flavor-staggering-only way of fixing FD that does not break the chiral symmetry of the massless scheme. We explain how this method coexists with the Nielsen-Ninomiya no-go theorem, and give an example of neutrino-like QCA showing that our model allows to put chiral fermions interacting via the weak interaction on a spacetime lattice, without running into any FD problem.

The quantum bootstrap method is applied to determine the bound-state spectrum of Quarkonium systems using a non-relativistic potential approximation. The method translates the Schrödinger equation into a set of algebraic recursion relations for radial moments $\langle r^m \rangle$, which are constrained by the positive semidefiniteness of their corresponding Hankel matrices. The numerical implementation is first validated by calculating the $1S$ and $1P$ mass centroids for both charmonium ($c\bar{c}$) and bottomonium ($b\bar{b}$) systems, finding deviations of less than 0.5\% from experimental data from the Particle Data Group (PDG). This analysis is then extended to the hypothetical toponium ($t\bar{t}$) system, predicting a $1S$ ground state mass of $M \approx 344.3 \text{ GeV}$. This theoretical mass is in agreement with the energy of the recently observed resonance-like enhancement in the $t\bar{t}$ cross-section by the ATLAS and CMS collaborations. This result provides theoretical support for the interpretation of this experimental phenomenon as the formation of a quasi-bound toponium state and highlights the predictive power of the non-relativistic potential approach for systems of two massive quarks.

Van der Waals potentials describing interactions between color-singlet mesons and/or baryons vanish at leading order in potential nonrelativistic quantum chromodynamics (pNRQCD). This result and constraints from Gauss's law are used to prove that weakly-coupled pNRQCD van der Waals potentials in generic non-Abelian gauge theories with only heavy quarks are too weak to form bound states whose color state is a product of color-singlets. Quantum Monte Carlo calculations of four, five, and six quarks with equal masses provide numerical evidence that exotic color configurations are higher energy than products of color-singlet hadrons, suggesting that equal-mass fully-heavy tetraquark, pentaquark, and hexaquark bound states do not exist at next-to-leading order in pNRQCD and at all orders in QCD-like theories in which all quark masses are asymptotically large. Mechanisms for generating hadron-hadron bound states are identified, which necessarily involve large quark-mass hierarchies, relativistic effects arising from the presence of sufficiently light quarks, or nonperturbative effects outside the scope of weakly-coupled pNRQCD.