We present a lattice quantum chromodynamics calculation of the $x$-dependent isovector quark helicity parton distribution function (PDF) of the proton in the large momentum effective theory (LaMET) framework. Through operator product expansion (OPE) we also extract the $\tilde{d}_2$ moment of the twist-3 PDF $g_T(x)$ for the first time in the $\overline{\rm MS}$ scheme, which is proportional to the average color Lorentz force experienced by the quark in the proton. This calculation is performed on a lattice of spacing $a$ = 0.076 fm at physical quark masses. The quasi-PDF matrix elements are measured in proton states boosted to momenta $P_z=\{0, 0.25, 1.02, 1.53\}$ GeV. We first extract the lowest few helicity PDF moments from the renormalization-group (RG) invariant ratios of the matrix elements with OPE. Combined with the matrix elements relevant for $g_T(x)$, we obtain $\tilde{d}_2^{u-d}(2\ {\rm GeV})=0.0024(46)$ at next-to-leading order in $\overline{\rm MS}$. Then, the helicity quasi-PDF matrix elements are renormalized in the hybrid scheme with linear renormalon resummation and Fourier transformed to the $x$-space after an asymptotic extrapolation. The quasi-PDF is perturbatively matched to the $\overline{\rm MS}$ PDF with RG and threshold resummations at next-to-leading power and next-to-next-to-leading logarithmic accuracies. After resummations, we determine the PDF in the region $x\in[0.25,0.75]$ with controlled systematic uncertainties. The end-point regions are then parameterized, combined with the LaMET prediction at moderate $x$, and fitted to the short-distance matrix elements in coordinate space.

We present continuum-estimated (2+1)-flavor lattice QCD results for second-order fluctuations of conserved charges and the leading-order equation of state in the presence of strong magnetic fields at nonzero baryon chemical potential, using the HISQ action at the physical pion mass. The baryon-electric charge correlation $\chi^{\rm BQ}_{11}$ exhibits striking sensitivity to the magnetic field: $R_{cp}$-like double ratios $\chi^{\rm BQ}_{11}/\chi^{\rm Q}_{2}$ and $\chi^{\rm BQ}_{11}/\chi^{\rm QS}_{11}$ reach enhancements of $\sim2$ and $\sim2.25$ at $eB \simeq 8M_\pi^2$ along the transition line, establishing $\chi^{\rm BQ}_{11}$ as a magnetometer of QCD. To bridge theoretical predictions and experimental observations, we construct HRG-based proxy observables and apply systematic kinematic cuts emulating STAR and ALICE detector acceptances, which retain $\sim80\%$ of the lattice QCD magnetic sensitivity. Extending to the QCD equation of state under strangeness neutrality and isospin asymmetry, we determine the chemical potential ratio $q_1\equiv(\mu_{\rm Q}/\mu_{\rm B})_{\rm LO}$ and the pressure coefficient $P_2$ for magnetic field strengths up to $eB \simeq 0.8~{\rm GeV}^2 \sim 45 M_{\pi}^2$. The results reveal temperature-band crossings, hierarchy reversals, and non-monotonic structures driven by the nontrivial interplay between thermal and magnetic effects.

Reliable approximations for correlation functions at intermediate and strong coupling remain hard to obtain for general quantum field theories. Perturbative expansions are often asymptotic or have a finite radius of convergence, which limits their applicability beyond weak coupling. Here we combine weak- and strong-coupling expansions and propose to use two-point Padé schemes to construct approximants. For lattice $\phi^4$ theory, we show that this two-point interpolation strategy yields accurate global approximations to the two-point correlation function across broad coupling regimes and compares favorably with standard one-point resummation methods. We also provide heuristic explanations for the observed convergence behavior and discuss the practical range of validity of the approach.

The nature of low-lying scalar and axial-vector charmed mesons has long been debated, specifically whether they are best explained as hadronic molecules or compact tetraquark systems. These two scenarios exhibit quite different features for the accessible $SU(3)$ multiplets in the scalar and axial-vector sectors. To resolve this debate, we performed $N_f=3+1$ lattice simulations and calculated the energy levels of the $SU(3)$ $[6]$ and $[\overline{15}]$ multiplets for both the scalar and axial-vector mesons in an $SU(3)$ flavor-symmetric setting. In both sectors we find attractive states for the [6] and repulsive interactions for the $[\overline{15}]$. This is consistent with the hadronic molecule picture, but not the compact tetraquark picture which predicts a low-lying $[\overline{15}]$ states in the axial-vector sector but not in the scalar sector.

The QCD Anderson transition is believed to be connected to both deconfinement and chiral crossovers. These crossovers are substantially affected when external magnetic fields ($B$) are present, most prominently, e.g., via magnetic catalysis and inverse magnetic catalysis. In this work, we use lattice QCD to investigate the Anderson transition in two different setups: (1) at $B=0$ by studying the low-lying eigenmodes of the overlap operator using gauge configurations with $2+1+1$ quark flavors of twisted-mass Wilson fermions. We estimate the mobility edge below which eigenmodes are localized via the inflection point of the so-called relative volume. Previous work has shown that, contrary to expectations, this estimate does not vanish at the temperature of the chiral phase transition. A possible scenario for this apparent contradiction was discussed, and in this work, we present an alternative observable for measuring localization that supports this scenario. And (2) by studying the localization properties of the staggered Dirac operator at $B\neq0$ on configurations with $2+1$ dynamical staggered fermions and 2 stout-smearing steps. Our preliminary results on two lattice spacings ($24^3\times 6$ and $24^3\times 8$) indicate a non-monotonic behavior of the mobility edge with the magnetic field across different temperatures, which hints at a reduction in the Anderson transition temperature in the presence of an external magnetic field.

The static energy is an excellent observable for extracting the strong coupling $\alpha_s$ on the lattice. For short distances, the static energy can be calculated both on the lattice using Wilson line correlators, and with perturbation theory up to three loop accuracy with leading ultrasoft log resummation. Comparing the perturbative expression and lattice data allows for precise determination of $\alpha_s$. We present early results for 1-loop lattice perturbation theory improvement of the Wilson loop and show how it improves the $\alpha_s$ extraction. We present a preliminary reanalysis of the TUMQCD (2+1)-flavor QCD data.

We consider a quenched SU(2)$\times$U(1) gauge Higgs theory on the lattice, coupled to a static vector-like fermion which, in this case, is in the same gauge group representation as the Higgs field. Physical (i.e. locally gauge invariant) electrically charged and electrically neutral states of matter particles in the electroweak theory were described decades ago, but those constructions do not exhaust all the possibilities, and new types of electrically charged/neutral states, orthogonal to former constructions, are described here. The difference has to do with how the static source, which by itself does not create a physical state, is dressed by dynamical fields. We find that, unsurprisingly, the neutral static fermion is much lighter than any of the charged fermion states. But a lattice study of the propagation of the charged fermion states indicates the existence of (at least) two particle states with different masses in charged particle spectrum.

To overcome the fast oscillatory behavior of correlation functions for extracting scattering phase shift in real-time quantum simulations encountered in Ref.\cite{Guo:2026qkx}, we propose and test two solutions in the present work. One is to simulate Hermitian systems in imaginary time, the other is to simulate non-Hermitian systems in real time. We demonstrate that both approaches lead to the problem of non-unitary quantum evolution which can be solved by combining two quantum algorithms: block encoding and Hadamard test. The combined quantum algorithm does not require mid-circuit measurements or adjustment of the input parameters of the Hamiltonian, and can be easily implemented on quantum computers. Both the size and length of quantum circuits grow linearly with evolution time. Numerical tests on quantum simulators show that both approaches agree with exact solutions for a sufficiently long time before the signal is lost in statistical fluctuations. The results bode well for using non-Hermitian and imaginary-time simulations to circumvent oscillations inherent in real-time simulation of other quantum systems.

At low temperatures $T$ where $1/T=\beta\gg1$ the naïve implementation of determinant quantum Monte Carlo (DQMC) methods suffers from loss of precision and numerical instabilities when evaluating the fermion determinant. This instability propagates into the calculation of observables that rely on the evaluation of the inverse of the fermion matrix, or the Greens function. For DQMC methods that rely on the Hamiltonian Monte Carlo (HMC) algorithm, an additional complication comes from evaluating the force terms required for integrating Hamilton's equations of motion, since here loss of precision and numerical instabilities are also prevalent. We show how to address all these issues using various choices of matrix decompositions, allowing us to simulate at $\beta\gtrsim 90$, which corresponds to room temperature for graphene structures. Furthermore, our implementation has numerical costs that scale similarly to the naïve implementation, namely as $\mathcal{O}(N_x^3N_t)$, where $N_x$ ($N_t$) is the number of spatial (temporal) sites.

The $\Lambda_c p$ momentum correlation functions are investigated using $\Lambda_c N$ interactions derived within the covariant chiral effective field theory. Our analysis reveals that the interaction is weakly attractive in the spin-singlet ${}^1S_0$ channel. In contrast, the ${}^3S_1$ channel exhibits a pronounced sensitivity to coupled-channel effects, i.e., the inclusion of $S$--$D$ mixing results in a repulsive $\Lambda_c p$ interaction; its absence leads to a weakly attractive one. Consequently, the spin-averaged correlation function -- dominated by the triplet state weight -- exhibits repulsive behavior when the $S$-- $D$ mixing is present. Furthermore, the source size dependence of the correlation functions is examined, demonstrating that the resulting variations remain experimentally resolvable within the precision of current femtoscopic measurements. A systematic comparison with non-relativistic chiral effective field theory and phenomenological models yields distinct discrepancies in the femtoscopic correlation functions. These findings underscore the capacity of femtoscopy to discriminate between different theoretical descriptions of the $\Lambda_c N$ interaction and provide useful references for upcoming experimental data.

We review the current state of knowledge of the phase diagram of QCD through lattice, effective field theories, and chiral models. Several sections through the three dimensional phase diagram are known for $N_f=2+1$ with good precision. Due to technical advances in lattice techniques over the last decade or so, new aspects of the phase diagram can now be explored. We review current lattice results. The newly acquired knowledge can be used to reconstruct the full phase diagram for physical QCD, \ie, $N_f=1+1+1$. We remark on the computations which would help understand this better, and what the current constraints are on matter in neutron star cores. We also remark on the physics of the chiral transition and neutron stars in the 't Hooft large $N_c$ limit.

We provide a non-perturbative determination of the scheme- and scale-independent low-energy constant $\ell_{\scriptscriptstyle{7}}$, appearing in the QCD effective chiral Lagrangian at next-to-leading order, by means of lattice QCD simulations with $N_{\scriptscriptstyle{\rm f}}=2+1$ quark flavors. We adopt staggered fermions and extract $\ell_{\scriptscriptstyle{7}}$ from the pion mass splitting by suitably generalizing the method introduced in [Phys. Rev. D 104 (2021) 074513] for the Wilson discretization. Adopting 12 gauge ensembles with 3 different values of the pion mass, and 4 different values of the lattice spacing, we are able to achieve controlled extrapolations towards the continuum, infinite volume, and chiral limits. Our final result $\ell_{\scriptscriptstyle{7}} \,\times \, 10^3 = 2.79(58)_{\scriptscriptstyle{\rm stat}}(19)_{\scriptscriptstyle{\rm syst}} = 2.79(61)_{\scriptscriptstyle{\rm tot}}$ agrees with and substantially improves on previous determinations.

We summarize the application of derivatives of the QCD pressure, calculated within the framework of lattice QCD, in constructing observables that probe aspects of the QCD phase diagram at physical quark masses. We outline how the behavior of energy-like and magnetization-like observables at physical quark masses is influenced by the $(2+1)$-flavor chiral phase transition. We describe features of the chiral crossover at vanishing and non-vanishing chemical potentials and discuss deconfinement at zero chemical potential. We address the relevance of the convergence properties of the Taylor expansion of the QCD pressure in the search for the QCD critical endpoint.