Papers

Recent measurements of two-particle transverse-momentum correlations, $C_{p_T}$, in Au+Au collisions have revealed a statistically significant non-monotonic beam-energy dependence over the range $\sqrt{s_{NN}}=3.0$–$7.7$~GeV that has been interpreted as potentially indicative of critical phenomena associated with a critical end point (CEP) in the QCD phase diagram. This interpretation is assessed in light of the absence of a controlled framework establishing $C_{p_T}$ as a quantitative proxy for the underlying critical response. The implications of this limitation are examined by considering the expected finite-size and finite-time modification of critical fluctuations, substantial non-critical dynamical contributions, the lack of demonstrated critical scaling, and the sizeable discrepancy between the CEP region inferred from the observed $C_{p_T}$ non-monotonicity and that constrained by susceptibility-based measurements and finite-size scaling analyses. Taken together, these considerations indicate that the observed $C_{p_T}$ non-monotonicity does not, by itself, establish a critical origin nor provide reliable quantitative constraints on the existence or location of a possible CEP.

Glueballs are colour-singlet bound states built from gluons alone. They are an unavoidable consequence of the non-Abelian structure of Quantum Chromodynamics (QCD), and, in the pure Yang–Mills limit, they are the only physical excitations of the theory. The present article reviews what is known about them. After establishing which spin, parity and charge-conjugation quantum numbers two- and three-gluon states can carry, the pure-gauge spectrum is surveyed. Each of the main theoretical approaches and their respective conclusions are briefly presented. They include lattice QCD, constituent-gluon and Coulomb-gauge models, functional Dyson–Schwinger and Bethe–Salpeter equations, holographic models, and QCD sum rules. Particular attention is paid to the scale-setting ambiguity that limits how precisely a quenched glueball mass can be converted into physical units. The discussion then turns to full QCD. After discussing the meaning of a glueball assignment in this context, unquenching effects and questions related to glueball–$q\bar{q}$ mixing are addressed. The large-$N_c$ counting that underpins the mixing picture, as well as mass-matrix and effective-Lagrangian treatments of mixing are presented. The selection rules and dynamical mechanisms that shape glueball decays are also discussed. The gluon-rich production mechanisms used experimentally are finally reviewed. The candidates are assessed sector by sector: $f_0(1370)/f_0(1500)/f_0(1710)$ and the competing interpretations of the scalar sector, $\eta(1405)/\eta(1475)$ and $X(2370)$ in the pseudoscalar sector, the crowded tensor region, and the essentially unexplored $C=-1$ sector and its connection to the Odderon. Outlooks on the programmes that could help in validating some of these candidates or identifying others are reviewed as a conclusion.

We investigate the utility of the locality-preserving Derby-Klassen (DK) fermion-to-qubit mapping [arXiv:2003.06939] for variational quantum simulation of two-dimensional $t$-$V$ and Fermi-Hubbard models. The DK mapping preserves the locality of fermionic interactions with an enlarged Hilbert space, thereby requiring additional constraints that define the physical sector. We incorporate these constraints directly into a Hamiltonian Variational Ansätz (HVA) through Clifford-gate state preparation and use the Variational Quantum Eigensolver (VQE) to show that the low-energy properties of the resulting qubit Hamiltonian are accurately reproduced. We further exploit particle-number conservation inherent in the ansätz to resolve distinct symmetry sectors and reliably access degenerate states. Consequently, we benchmark the DK-HVA against Jordan-Wigner-based variational circuits at nonzero chemical potential, where particle-hole symmetry and the associated half-filled sign-free condition are absent. Finally, we demonstrate the advantage of locality-preserving mappings in higher-dimensional fermionic systems, where the conventional Jordan-Wigner (JW) transformation generates increasingly long Pauli strings and corresponding circuit overheads. We further extend the framework to the spinful Fermi-Hubbard model and identify a tradeoff between fermionic-mode placement and the locality of hopping and on-site interaction terms. These results establish a practical framework combining locality-preserving fermion-to-qubit mappings, constraint-preserving Clifford state preparation, and symmetry-preserving variational circuits, that trades auxiliary-qubit and stabilizer-preparation overhead for reduced operator nonlocality, providing a practical route toward resource-efficient quantum simulation of higher-dimensional interacting fermionic systems.

We construct exact many-body scar towers in two dimensional gauge theories with two flavors of massless fundamental fermions. For oppositely charged fermions, the scar subspace is generated by a gauge-neutral $\eta$-pairing operator, and admits a purely algebraic construction. Exact diagonalization methods reveal anomalously low entanglement and long-range pair correlations in the scar states. Charge conjugation maps the $\eta$-tower to a vector-flavor polarization sector of the equal charge model, yielding an interpretation as a coherent flavor mode with Josephson-like phase dynamics. Finite fermion masses mix the protected pair with an orthogonal channel and destroy the exact tower. The identified scar tower can be algebraically realized in a large family of lattice field theories, revealing a universal character of these states. Our results provide an analytical construction of invariant scar subspaces in a gauge theory with a nontrivial continuum interpretation.

Incorporating dynamical fermions is a central challenge for diffusion samplers of lattice gauge theories. We propose an analytic pseudofermion sampler based on continuous Hasenbusch transport as a component for gauge diffusion. The construction uses shifted linear solves and a finite-path correction, requiring neither explicit fermion determinant evaluation nor a learned pseudofermion model. We demonstrate the coupling in the two-flavour Schwinger model without neural networks, obtaining corrected physical observables compatible with independent references. We also show why accurate covariance transport can leave large weight fluctuations, tracing them to the backward transition density. This analysis leads to a correction based on the Wilson operator trace that reduces log-weight variance without changing the generated fields or increasing the number of Dirac operator applications. The predicted improvement is verified on previously unused gauge backgrounds. These results provide an analytic option for incorporating fermions in gauge diffusion and a guide to controlling its correction weights.

In this paper we investigate accelerated gluodynamics for a broad intervals of temperature and acceleration. Our study is carried out within lattice simulation in the co-moving reference frame parameterized by the Rindler coordinates. We developed the renormalization prescription that allowed us to calculate renormalized Polyakov loop as a function of coordinate in the Rindler spacetime. Using the data for the renormalized local Polyakov loop, we calculated spatial dependence of the static quark free energy and effective mass of static quark. Besides the Rindler coordinates, it is believed that accelerated gluodynamics can be approximated utilizing non-accelerated gluodynamics with a properly adjusted temperature gradient in accordance with the Tolman-Ehrenfest law. We compared these approaches for the observables under study. It was found that they agree quite well close to the critical temperature and demonstrate disagreement at higher temperatures. We believe that this disagreement might be attributed to the Tolman-Ehrenfest law corrections which appear in the Rindler gluodynamics.

The Division of Particles and Fields (DPF) of the American Physical Society would like to thank SCAC for providing an opportunity for input to the SCAC facilities subpanel. The DPF represents scientists working at U.S. Universities and DOE Laboratories on understanding fundamental particles and forces. We are focused on Discovery Physics. The subpanel has been asked to consider two proposed DPF-related projects, the DUNE Phase II Detectors and supporting infrastructure and U.S. contributions to a future Higgs Factory. In this note, we briefly describe the questions driving our field and the P5 strategic plan and other community prioritization documents that form the backbone of our comment. The following sections provide short descriptions of the two projects, highlighting information relevant to your charge, answers to your specific questions, and a description of the process that produced this note.

We present an extraction of the unpolarised transverse momentum dependent (TMD) parton distribution functions (PDFs) for the valence quarks in the pion from experimental mea- surements of the Drell-Yan process. The procedure adopted in this project relies on the framework of TMD factorisation, and the inputs of nucleon TMDPDF, pion collinear PDF, as well as the Collins-Soper kernel. The non-perturbative behaviour of the TMDPDFs is parameterised using an ansatz function that contains three unknown parameters and implements an exponential decay at large transverse distances. This work employs the most recent results in perturbation theory, and utilises a precise estimation of the nucleon TMDPDF. We perform an investigation of data used in the fit. This investigation leads to important observations regarding the effects of the kinematics and binning methods in the experimental data. Our results agree qualitatively with the previous determinations from phenomenology and a lattice computation

The precision of the electromagnetic proton-neutron mass difference $\delta m_\mathrm{QED}$ extracted from the Cottingham formula hinges on a subtraction function whose low-energy normalization $\bar S(0)$ is fixed by the isovector combination of the proton and neutron polarizabilities, $(\alpha_{E1}-\beta_{M1})^{p-n}$. We derive a dispersive sum rule for this combination in terms of $s$-channel photoabsorption cross sections and the product of $t$-channel $\gamma\gamma\to\pi\eta/K\bar K_{I_t=1}$ and $\pi\eta/K\bar K_{I_t=1}\to N\bar N$ amplitudes, without invoking Reggeon dominance. Combining empirical pion-photoproduction multipoles with coupled-channel Muskhelishvili–Omnès representations of the scalar-isovector $\pi\eta/K\bar K$ amplitudes, we obtain $(\alpha_{E1}-\beta_{M1})^{p-n}=-2.26(73)\times10^{-4}\,\mathrm{fm}^3$, fixing its sign and reducing the uncertainty by a factor of 4 compared with the previously known value. This result yields $\bar S(0)=-1.76(61)\,\mathrm{GeV}^{-2}$, leading to $\delta m_\mathrm{QED}=0.71^{+0.03}_{-0.06}\,\mathrm{MeV}$, substantially more precise than previous Cottingham determinations. The negative $\bar S(0)$ also provides a stringent low-energy test of Reggeon dominance in the subtraction function.

Wetterich showed that certain 1+1D probabilistic cellular automata are equivalent to fermionic QFTs and posed the 3D construction as an open problem. We construct one: a layered automaton ("coincube") whose conversion blocks form the real quaternion representation of Cl(0,3), controlled by binary environment fields whose streaming outruns the carrier ("fresh tape") – no bit is consulted twice, and the single-particle ensemble propagator equals the annealed Bloch operator at every time. Exact results: the step operator is unitary for an explicit complex structure; the local Grassmann action is extracted mechanically; the single-carrier excitation is a Weyl fermion with an isotropic leading cone (slope ratios 1 within errors, factorized transport excluded by >=10 error bars); at finite momentum the node carries a parity-odd anisotropy c(q)kx ky kz/|k|, cancelled on the Dirac branch whose gap is 2 arctan[qm/(1-qm)], while off-resonant spectators stay massless; media-mediated interaction obeys Ug = (1-2gq^2) U. Obstructions: ballistic transport admits only finite velocity sets; Abelian sign gauges leave the factorized surface; no protected 2-component node survives an exhaustive search. Finally, a dichotomy for the quaternionic event class: an isotropic cone forces overdamping – Q = w_0/Gamma <= pi/(2 ln 2) at all densities, 0.66 at working density – while in-state unitarity forces factorized transport. Postselected two-boundary amplitudes evade this, exactly unitary at all times under the fresh tape, with induced weight positivity open: the relativistic object here is an amplitude whose probabilistic reading is unsettled.

A first-principles investigation of heavy-light meson behaviour in hot QCD matter is essential for the interpretation of experimental results associated with open heavy flavour productions in relativistic heavy-ion collision experiments. Using anisotropic lattice ensembles from the FASTSUM collaboration with Nf=2+1 dynamical Wilson-clover fermions at non-zero temperatures, we study the B and B_s spectra at non-zero temperature. We use relativistic light quark propagators, while the b quark propagators are computed with a non-relativistic effective theory (NRQCD). We find that above T_c, thermal effects on the B meson states are more significant than those on the B_s states. Also, our results support the dissolution of the B-meson bound states above T_c.

We study how the ground-state properties of the rho meson respond when the number of light-quark flavors N_f is driven towards the conformal window. The interaction is a symmetry-preserving, confining vector–vector contact interaction whose effective coupling carries a flavor dependence designed to encode the screening produced by fermion loops in the deep infrared. That interaction feeds the Schwinger–Dyson equation for the dressed-quark propagator and the homogeneous Bethe–Salpeter equation in the rainbow-ladder truncation, regularized in the Schwinger proper-time scheme so that quark production thresholds are absent while chiral symmetry remains broken. Raising N_f weakens the coupling, suppresses the dynamically generated mass and restores chiral symmetry together with deconfinement at a critical flavor number N^{c}_{f}. The vector channel responds differently from the pseudoscalar one. Because the $\rho$ is not a Goldstone boson, its mass is not protected by the symmetry that is being restored, and it simply follows the shrinking constituent scale, while the canonically normalized amplitude E_rho and the leptonic decay constant f_rho soften along the way. In this framework the rho sits above the nominal q\bar{q} threshold for every flavor number examined, so the state survives only as long as confinement removes that threshold. Dissociation is therefore governed by the divergence of the confinement length scale rather than by a crossing of the bound-state mass, and we contrast both criteria. The three elastic electromagnetic form factors G_E, G_M and G_Q, computed in the generalized impulse approximation, flatten as N_f grows, the zero crossing of G_E migrates towards the infrared and the charge radius expands, whereas the magnitude of the quadrupole moment decreases. The rho thus becomes a larger and rounder object as the theory approaches conformality.

We provide a manifestly gauge-invariant description of the Higgs mechanism in the Standard Model, casting it not as the breaking of a local symmetry, but as a smooth, analytic crossover from a high-temperature symmetric phase to a low-temperature Higgs phase. Taking the vacuum expectation value of a gauge-invariant local scalar operator and constructing composite quasi-particle states from the original fields of the Lagrangian usually introduces contact-term divergences. Previous attempts to circumvent this issue via bilocal operators remain unsatisfactory. Here we demonstrate that the gradient flow at a flow time $t$ provides a clean, structurally sound, and Lorentz-covariant regularization that permits a consistent, renormalon-free matching onto the standard $\overline{\text{MS}}$ scheme at a scale $\mu \sim 1/\sqrt{2t}\gg m_t$. Beyond its theoretical appeal, this construction clarifies a number of conceptional and practical questions. We demonstrate the utility of this framework at the one-loop level, thereby establishing the foundation for future electroweak precision physics in this approach.

We investigate the twist-2 and twist-3 tensor-polarized partonic structures of the spin-1 deuteron. Using the operator product expansion with local operators, we derive a Wandzura-Wilczek (WW)-like twist-2 relation between the tensor-polarized twist-2 quark distribution $f_{1LL}$ and the twist-3 distribution $f_{LT}$, together with a Burkhardt-Cottingham (BC)-like sum rule. The local-operator formalism makes the Lorentz structure and rotational invariance manifest and provides useful constraints on the twist-3 sector. We then use a phenomenological parametrization of the twist-2 distribution $f_{1LL}(x)$, constrained by HERMES data on the deuteron structure function $b_1$ at $Q^2=2.5~\text{GeV}^2$, to quantitatively estimate the twist-3 distribution $f_{LT}(x)$ within the WW approximation. The resulting $f_{LT}(x)$ has a shape and magnitude comparable to those of $f_{1LL}(x)$, indicating that subleading-twist effects may be relevant for future experiments at relatively low $Q^2$. In this contribution, we summarize the theoretical derivation of the WW-like relation and BC-like sum rule and present a phenomenological estimate of the tensor-polarized twist-3 quark distribution $f_{LT}$ in the deuteron.

The search for physics beyond the Standard Model in low-energy weak interaction processes requires a precise knowledge of the Standard Model background at tree- and loop-level. In many such cases, radiative corrections represent one of the major sources of theory uncertainty due to the non-perturbative structures of nucleon or nuclei. In this review, I discuss several modern strategies based on dispersion relation, lattice gauge theory and nuclear many-body calculations to pin down the hadronic and nuclear uncertainties in the radiative corrections to low-energy weak interaction processes such as beta decays and parity-violating electron-nucleus scattering.

Two-color QCD provides a unique first-principles laboratory for strongly interacting matter at finite baryon density, where a diquark condensate realizes a baryonic superfluid. We investigate the internal physics of its quantized superfluid vortices in the chiral limit. We find that a vortex localizes an exact and normalizable $S^3\simeq SU(2)$ family of pion modes. Remarkably, the bulk Wess–Zumino–Witten (WZW) term induces a quantized WZW term for these modes, driving the vortex theory in the infrared to the $SU(2)_1$ WZW conformal field theory with central charge $c=1$. Thus a strongly coupled conformal theory emerges on a vortex in a nonconformal bulk theory. The mechanism extends to pseudoreal $Sp(2N)$ gauge theories, where the corresponding minimal vortex theory flows to $SU(2)_N$, with the level directly encoding the microscopic anomaly coefficient.

We consider Yang-Mills theory with two infinite parallel plates, separated by a distance \(L\), that are perfect magnetic conductors (PMC) or perfect electric conductors (PEC). Recently, it was shown that the Gribov copy problem persists in such a setting. We then study the Gribov-Zwanziger (GZ) action in the presence of those boundaries using functional integral methods. Lagrange multiplier fields allow one to lift the boundary conditions into the action, after which the boundary modifications to the gluon propagator can straightforwardly be determined. In the PEC case, we provide evidence that, even when translation invariance is (partially) broken, the usual horizon term in the GZ action still restricts the functional integral to the Gribov region. We compute the Casimir energy for GZ with PMC or PEC plates, both directly from the functional integral and from the energy-momentum tensor, obtaining consistent results. We compare our analytical results with recent lattice data, in both 4D and 3D. A priori, one might expect that the boundary-modified gluon propagator introduces new \(L\)-dependencies into the GZ gap equation. This would make the Gribov mass \(\gamma\) dynamically dependent on \(L\), implying an interesting interplay with the Casimir energy. However, we show that no such dynamical \(L\)-dependence occurs within the current approximation.

We present a lattice-QCD determination of properties of the lightest scalar, pseudoscalar, vector, and axial-vector heavy-strange mesons. This includes the decay constants of all mesons, and the binding energies and Weinberg compositeness parameters of the positive-parity states. The calculations are performed with domain-wall fermions for the light and strange quarks and anisotropic clover actions for the charm and bottom quarks. We use seven ensembles generated by RBC/UKQCD with pion masses ranging from 431 MeV to 139 MeV and lattice spacings ranging from 0.114 fm to 0.073 fm, which allows us to perform combined chiral and continuum extrapolations. For the negative-parity mesons, we obtain $f_{D_s}=251.4(2.1)(0.4)(2.5)\:{\rm MeV}$, $f_{D_s^*}=272.5(4.3)(1.0)(2.7)\:{\rm MeV}$, $f_{B_s}=228.4(5.8)(0.5)(2.3)\:{\rm MeV}$, $f_{B_s^*}=229.2(4.4)(0.8)(2.3)\:{\rm MeV}$, $f_{D_s^*}/f_{D_s}=1.086(14)(11)$, and $f_{B_s^*}/f_{B_s}=1.003(22)(10)$. In the positive-parity sector, the finite-volume energies and decay constants are extracted using the GEVP from correlation matrices with three different types of hadron interpolating operators, including operators with covariant derivatives and meson-meson-scattering operators at both source and sink. After extrapolation to the physical point, we obtain $f_{D^*_{s0}}=136.6 (8.0)(4.0)(1.4)$ MeV, $f_{D_{s1}}=200 (33)(24)(2)$ MeV, $f_{B^*_{s0}}=207 (12)(8)(2)$ MeV, and $f_{B_{s1}}= 196 (16)(11)(2)$ MeV. Our results for $f_{B^*_{s0}}$ and $f_{B_{s1}}$ are the first from lattice QCD. Lüscher's method is used to find the infinite-volume bound-state masses. At the physical point, we obtain $m_{D^*_{s0}}-m_D-m_K=-48 (14)(4)$ MeV, $m_{D_{s1}}-m_{D^*}-m_K=-61 (15)(2)$ MeV, $m_{B^*_{s0}}-m_B-m_K= -69 (13)(4)$ MeV, and $m_{B_{s1}}-m_{B^*}-m_K=-77 (10)(5)$ MeV. Our analysis shows consistency with the positive-parity states being predominantly molecular.

Nonergodic features of chaotic quantum many-body systems are commonly characterized through local observables, fidelity, and entanglement entropy. Here, using global and nonlocal measures of nonstabilizerness (magic), we study quantum many-body scars near infinite temperature in $(1+1)$-dimensional Abelian $\mathbb{Z}_2$ and U$(1)$ lattice gauge theories, both analytically and numerically. We derive an exact closed-form expression for the nonlocal trace distance magic solely from the Schmidt spectrum, reducing the optimization over local unitaries to a finite maximization over stabilizer-compatible Schmidt ranks. We find that scar eigenstates can exhibit extensive global magic despite their anomalously low entanglement, while retaining anomalously large nonlocal magic compared with ergodic states. We further show that constrained Hilbert spaces can generate irreducible nonlocal magic through stabilizer-incompatible Schmidt ranks, even for a flat entanglement spectrum.

We examine how $s$-channel unitarization changes the dynamical gluon mass scale $m_g$ inferred from high-energy elastic $pp$ scattering. The Born input is the Reggeized Landshoff–Nachtmann exchange of two nonperturbative gluons in a color-singlet state. We fit the ATLAS and TOTEM forward data separately, using eikonal and $U$-matrix unitarizations with logarithmic and power-law running masses derived from Schwinger–Dyson analyses. At the common reference cut $|t|_{\rm max}=0.12~\GeV^2$, the Born fits give $m_g=297$–$427~\MeV$; the eikonal and $U$-matrix fits give $265$–$360~\MeV$ and $243$–$328~\MeV$, respectively. Unitarization changes the fitted values of the intercept parameter $\epsilon$, $m_g$, and the exponential slope $a_1$ of the proton form factor together. Over $0.10\leq |t|_{\rm max}\leq0.14~\GeV^2$, the $U$-matrix parameters vary less with the cut, while the eikonal fits to TOTEM show a pronounced drift. Replacing the infrared continuation of the logarithmic effective charge by a Curci–Ferrari prescription changes $m_g$ by a mean absolute relative shift of $1.77\%$ over twenty comparisons, with a maximum of $2.17\%$. The inferred scale remains in the few-hundred-MeV region, but its fitted value depends on the nonperturbative input and on the unitarization prescription.

Quantum Monte Carlo (QMC) algorithms are among the most powerful classical methods for simulating quantum systems, yet their accuracy is often limited by the systematic errors in the approximations used, such as Trotterization. Here we introduce randomly compiled quantum Monte Carlo (RC-QMC) as a general framework that suppresses these systematic errors by averaging over a family of approximations rather than relying on a single fixed one. This strategy is grounded in the concept of randomized compiling from quantum computing, which suppresses errors by sampling over quantum gates, at essentially no additional computational cost. Consequently, our framework achieves a computational advantage over standard QMC methods when estimating a target state to a desired level of accuracy. We illustrate this advantage on two key Monte Carlo algorithms: (1) path integral quantum Monte Carlo for estimating thermal states, and (2) the quantum trajectories method for simulating open system dynamics. In aggregate, these results represent a cross-fertilization of quantum and classical algorithms, are readily generalizable to other QMC methods, and suggest wider applications in classical simulation.

A critical component of relativistic three-body scattering amplitudes is the one-particle exchange (OPE) process, wherein a single particle is exchanged between incoming and outgoing two-body subsystems. We present an improved, finite-sum expression for the partial-wave OPE that is valid for three massive, spinless particles in arbitrary angular momentum configurations. A collection of analytic and numerical checks demonstrate that our finite-sum expression reproduces the known properties of the partial-wave OPE, including its threshold scaling behavior and singularity structure. Compared with previous work, this result more efficiently handles the rapid proliferation of partial waves contributing to any total angular momentum $J$, enabling the construction of robust wavesets for three-body amplitude analyses.

In the late 1990s, Suzuki and Yasuta proposed a compact formula that extracts the decay rate per unit volume of a false vacuum in the $D$-dimensional $O(N)$ $\lambda(\phi^2)^2$ theory with an unbounded potential from conventional perturbative coefficients of the vacuum energy density, i.e., vacuum bubble diagrams. The idea was to identify the imaginary part arising from the Borel integral along the discontinuity of the Borel transform with that of the vacuum energy density. While the formula works quite well for~$D=1$, i.e., quantum mechanics, its validity remained unclear for~$D\geq2$ because only the first three perturbative coefficients for~$D=2$ were available and the result showed no sign of convergence. In the present paper, we reexamine this approach using the first seven nontrivial perturbative coefficients (up to nine loops) for~$D=2$ and~$N=1$ obtained by Serone, Spada, and~Villadoro. Introducing two tunable parameters in the finite-order truncated Borel transform following these authors, we find that the imaginary part converges as the perturbative order increases, with the last few orders agreeing to within a few percent. In the intermediate range of the coupling constant, $3\lesssim\widetilde{g}\lesssim8$, this approach yields an imaginary part rather close to the leading-order semi-classical approximation with the one-loop determinant; it is $10$–$20\%$ larger than the semi-classical result with the two-loop correction computed by Malatesta, Parisi, and~Rizzo.

We perform a quantitative analysis of the $B^{0}$ meson spectroscopic parameters in a hot and dense medium. Within the framework of QCD two-point sum rules, we calculate the mass and decay constant of the $B^{0}$ meson with the help of the perturbative spectral density and nonperturbative contributions up to mass dimension five as functions of temperature $T$ and baryon chemical potential $\mu_B$. For various fixed values of the baryon chemical potential, our numerical results indicate that both the mass and decay constant of the $B^{0}$ meson initially increase with temperature, reach a maximum, and then gradually decrease before eventually vanishing at sufficiently high temperatures. The corresponding vanishing points are found to be in the temperature intervals $(0.182-0.273)~\mathrm{GeV}$ and $(0.118-0.173)~\mathrm{GeV}$, for the mass and decay constant, respectively. Moreover, these temperatures move toward lower values as the baryon chemical potential increases. On the other hand, for various fixed temperatures, both the mass and decay constant exhibit a slight initial increase with increasing baryon chemical potential, followed by a subsequent decrease, eventually vanishing at sufficiently high chemical potentials. The vanishing points for the decay constant is determined to be in baryon chemical potential interval $(0.23-0.83)~\mathrm{GeV}$. For the mass, the decrease at $T=0$ is much weaker than at finite temperatures; excluding this case, the vanishing points for the mass are determined to be in baryon chemical potential interval $(0.38-1.43)~\mathrm{GeV}$ for different fixed temperatures. It is further observed that the baryon chemical potential values corresponding to the vanishing of both the mass and decay constant move to lower values as the temperature increases. In the $T \to 0$ and $\mu_B \to 0$ limit ...

Quantum computers can circumvent the numerical sign problem in gauge theories at finite density or in real time. Quantum simulations of gauge theories require a finite-dimensional representation of continuous gauge fields. Replacing a continuous gauge group by a finite subgroup can substantially reduce the required quantum resources, but introduces digitization errors that must be controlled in the Hamiltonian, or continuous-time, limit. Previous studies, using the isotropic Euclidean lattices showed that the freezing transition of the discrete subgroup can make it a bad approximation for the continuous group at large Euclidean couplings. Here, we study the digitization of U(1) by its Z($N$) subgroups in 2+1 dimensions using anisotropic Euclidean lattices. We derive the trajectories of the spatial and temporal gauge couplings along which the Hamiltonian limit is approached at fixed Hamiltonian coupling. While the temporal coupling exhibits power-law scaling in the continuous U(1) theory, it grows only logarithmically for finite Z($N$). Using classical lattice simulations and exact diagonalization, we verify that these trajectories reproduce the corresponding Hamiltonian theories. We find that the freezing transition persists in the Hamiltonian limit of discrete gauge groups and that finite-$N$ theories can differ substantially from U(1) even outside the frozen regime, in contrast to the behavior on isotropic Euclidean lattices, where for small couplings, the discrete group provides a very accurate approximation of the continuous group. Our results provide a classical benchmark for quantifying the systematic errors due to gauge-field digitization in quantum simulations.

Recent developments have established exact bosonization and fermionization with a $\mathbb{Z}_2$ symmetry as dualities through gauging. In this work, we apply fermionic gauging, which realizes generalized Jordan-Wigner transformations, to the Bose-Hubbard (BH) model with a global $U(1)$ symmetry and derive an exact dual description in terms of fermionic composites, built from bosons and fermions. In 1D, this duality generalizes the exact mapping between the extended hard-core BH model and the spinless Fermi-Hubbard model to include soft-core bosons. At low energies, the mapping reduces to the well-known equivalence between the sine-Gordon model and the Thirring model. The oscillation wave vector of the fermionic composite correlation function in the gapless phase is fixed by their density, providing a novel manifestation of Luttinger's theorem. We verify the exact duality using density matrix renormalization group (DMRG) calculations and demonstrate that the gapless phase and the phase transition are governed by the compact boson conformal field theory. Our construction naturally extends to generic bosonic systems and higher dimensions, opening new avenues for studying Bose-Fermi mixtures in optical lattices and other strongly correlated quantum systems.

Topological fluctuations are essential to nonperturbative gauge theories but become increasingly difficult to sample toward the continuum limit, where Markov chains can freeze in sectors of fixed topological charge. We introduce a generative sampler, a mixture of sector-resolved samplers (MSRS) that explicitly resolves these sectors and exploits a key advantage of generative models, the ability to directly evaluate the domain-restricted partition function and thereby determine the relative weights of disconnected sectors. We train a generative model in a reference topological sector combined with a bijective topological shift that deterministically maps its samples to other sectors. We demonstrate the method in two-dimensional compact U (1) lattice gauge theory, where it reproduces the topological-charge distribution and yields an unbiased susceptibility in a regime where hybrid Monte Carlo is frozen and overrelaxation gives inaccurate estimates. Our approach also outperforms existing flow-based samplers by orders of magnitude. These results demonstrate that explicit sector resolution provides a promising route to overcoming topological barriers in lattice gauge theory.

Lattice gauge theories are a low-energy regularization of quantum field theories. They are the basis for the development of numerical algorithms that provide insight into the non-perturbative regime of quantum field theories which is difficult to achieve through other methods. We present a python package, ggpeps, implementing gauged Gaussian projected entangled pair states (GGPEPS), specialized to study lattice gauge theories. We give a an overview of the considered systems, describe the GGPEPS ansatz and provide a usage guide for the ggpeps package.

Nucleon sigma terms are important for the decomposition of the nucleon mass and for searches for new physics beyond the Standard Model involving scalar interactions. A persistent tension between lattice QCD and phenomenological determinations may be due to uncontrolled excited-state contamination in lattice QCD analyses. In previous work at $m_\pi=429~\rm MeV$, we showed that this contamination is dominated by $N\sigma$ states and can be strongly suppressed with a variational analysis using $N$ and $N\sigma$ operators. In this talk, we present preliminary results at $m_\pi=222~\rm MeV$, where the $\sigma$ becomes unstable and decays into $\pi\pi$. We investigate whether the same small variational basis can remove the expected $N\pi\pi$ contamination through the overlap of the $N\sigma$ operator with these states.

The nucleon axial form factor is analyzed in terms of a dispersion relation comprising chiral perturbation theory (ChPT) and perturbative QCD (pQCD) in the low- and high-momentum regimes respectively, which implies a set of superconvergence sum rules for the $A \to N \bar N$ spectral function. In the timelike region below the $N \bar N$ production threshold we include the $a_1$ and $a_1'$ resonances, with finite-width effects modeled through $\rho \pi$ and $\sigma \pi$ intermediate states. Above the $N \bar N$ threshold, we model an infinite tower of radially excited $1^{++}$ resonances with a non-integer power fall-off, eventually matching pQCD. In this setup, we find that both the ChPT and pQCD contributions are tiny. In turn, the dominant $\rho\pi$ triangle provides the leading deviations from axial meson dominance. Our calculation is not a fit; it contains parameters with a priori uncertainties estimates. The axial radius is predicted to be $r_A^2 =(0.28-0.33)~\textrm{fm}^2 = ( 0.47-0.57~\textrm{fm})^2$ in agreement with recent lattice QCD results but inconsistent with the MINER$\nu$A determination. A simple semiempirical formula is provided accounting for the main physical effects.