We study QCD with three degenerate flavors of dynamical quarks using first-principles lattice simulations. For a specific choice of imaginary isospin chemical potential, this theory possesses an exact center symmetry, just like pure gauge theory. This exact symmetry is expected to be intact at low temperatures and spontaneously broken in the high-temperature regime. By analyzing the finite-size scaling of the Polyakov loop distribution, obtained with a dedicated multihistogram approach, we demonstrate that there is a first-order deconfinement phase transition in between. Our results are obtained employing stout-smeared rooted staggered quarks at one lattice spacing. Using simulations at different quark masses we sketch the behavior of QCD in the mass-isospin chemical potential plane, shedding new light on this corner of the fundamental phase diagram of the strong interactions.

Lattice QCD provides a first-principles framework for solving quantum chromodynamics. However, its application to off-shell partons has been largely restricted to the Landau gauge, as achieving high-precision $\xi$ gauge fixing on the lattice poses significant challenges. Motivated by a universal power-law dependence of off-shell parton matrix elements on gauge-fixing precision in the Landau gauge, we propose an empirical precision-extrapolation method to approximate high-precision $\xi$ gauge fixing. By properly defining the bare gauge coupling and then the effective $\xi$, we validate our $\xi$ gauge-fixing procedure by successfully reproducing the $\xi$-dependent regularization-independent momentum-subtraction renormalization constants for local quark bilinear operators at 0.3% level, up to $\xi \sim 1$.

In this work, we investigate the interactions between an excited anticharm meson doublet $({\overline{D}}_1,{\overline{D}}_2^{*})$ and ground-state octet baryons $(N,\mathrm{\Lambda },\mathrm{\Sigma },\mathrm{\Xi })$ with the aim of identifying possible molecular pentaquark states. A systematic analysis is performed within the one-boson-exchange model, which incorporates both $S$- and $P$-wave interactions, $S\text{−}D$-wave mixing, and coupled-channel effects. By solving the Schrödinger equations, we can predict a rich spectrum of loosely bound anticharm molecular pentaquarks with strangeness $|S|=0$, 1, 2. Our results provide specific quantum number assignments and mass range predictions to guide future experimental searches at facilities such as LHCb and Belle II. The discovery of such states would significantly enrich the hadron spectrum and serve as a critical test of theoretical models for hadronic interactions.

We consider the case of a free real massive bulk scalar in $D=4$ dimensions, and embed two parallel plates as interfaces on which we impose nonlinear boundary conditions, either Dirichlet- or Neumann-like, parametrized by a new coupling constant $g$. The system mimics a non-Abelian gauge theory supplemented with boundary conditions on surfaces embedded in the bulk. We present the first evidence for a nonperturbative $\frac{1}{g^2}$ boundary mass generation and its ensuing correction to the standard Casimir energy. This result becomes possible by incorporating dynamical corrections to the effective boundary fields, which are used to build in the boundary conditions directly at the action level.

We investigate the influence of QCD phase transition and critical fluctuations of the critical end point (CEP) on the deuteron yield within the functional renormalization group (fRG) approach, by using the nucleon coalescence model and a low energy effective field theory of quarks and mesons. It is found that the two-point baryon density correlation function is enhanced in a narrow region radiated from the CEP along the phase boundary. Meanwhile, the deuteron-to-proton yield ratio $N_d/N_p$ presents a monotonically increasing trend with decreasing collision energy, in which the leading-order uncorrelated contribution is dominant. The density correlation correction only shows a weak peaklike structure in the energy region of $\sqrt{s_{NN}}=3–7\mathrm{GeV}$, whose magnitude is significantly smaller than that of the leading-order contribution.

Recently, LHCb reported the radiative-decay ratio ${\mathcal{R}}^{\psi \gamma }\equiv \mathcal{B}[X(3872)\to {\psi }^{\prime }\gamma ]/\mathcal{B}[X(3872)\to J/\psi \gamma ]=1.67\pm 0.25$ extracted from $B^{+}\to K^{+}(J/\psi \gamma ,{\psi }^{\prime }\gamma )$. This result differs markedly ($\sim 4.6\sigma$) from the BESIII value obtained from $e^{+}{e}^{-}\to \gamma (J/\psi \gamma ,{\psi }^{\prime }\gamma )$, ${\mathcal{R}}^{\psi \gamma }=-0.04\pm 0.28$. Such a significant tension suggests that more than one state in the $X(3872)$ region contributes to the processes. We therefore propose a two-state scenario: a shallow $D^{*0}{\overline{D}}^0$ bound state with $J^{PC}=1^{++}$ and a $2^{-+}$ charmonium candidate, ${\eta }_{c2}$, slightly above the $D^{*0}{\overline{D}}^0$ threshold. We show that this hypothesis consistently describes these ratios along with other branching fractions and line shapes across multiple processes. By contrast, fits without the ${\eta }_{c2}$ component fail to reproduce the radiative-ratio data. We also predict helicity-angle distributions that motivate the future experiments to test the two-state hypothesis and search for the so-far missing ${\eta }_{c2}$.

The Fierz rearrangement, based on the various internal symmetries of hadrons, can be used to study their decay properties in a largely model-independent way. We have developed a semiautomatic Mathematica program to implement this method, with which we calculate the relative branching ratios of two-gluon glueballs with $J^{PC}=0^{++}/0^{-+}$ and three-gluon glueballs with $J^{PC}=0^{++}/1^{+-}$. In total, we derive nearly 100 ratios for these glueballs. Our results suggest that the $f_0(1710)$ and $\eta (2370)$ likely contain a significant gluon component, whereas the gluon component in $f_0(1500)$ appears to be small. Furthermore, we propose observing the three-gluon glueball with $J^{PC}=0^{++}$ in the $\pi \pi \omega$ and $K\overline{K}\varphi$ channels, and the three-gluon glueball with $J^{PC}=1^{+-}$ in the $\pi \pi \omega$, $\pi \pi \varphi$, and $K\overline{K}\varphi$ channels. This study enhances our understanding of the gluonic structure of exotic hadrons and will assist future experimental searches in high-energy physics.

We investigate the impact of a uniform spin density on the critical temperature of the chiral phase transition in finite-temperature QCD in the scope of the linear $\sigma$ model. We demonstrate that at a finite spin potential ${\mu }_{\mathrm{\Sigma }}$, corresponding to a finite spin density, the predictive power of the model is challenged by an ambiguity associated with a contribution of the vacuum renormalization term to the free energy. Eliminating the regularization freedom through comparison with recent low-${\mu }_{\mathrm{\Sigma }}$ lattice data, we extend the phase diagram of QCD at finite spin density to regions inaccessible to lattice simulations. We show that, as the spin potential increases, the temperature of the chiral crossover transition diminishes and the chiral crossover turns into a first-order transition at a second-order critical end point $(T,{\mu }_{\mathrm{\Sigma }}{)}_{\mathrm{CEP}}\simeq (0.142,0.098)\mathrm{GeV}$. With increasing spin potential, the critical temperature touches the zero-temperature axis at ${\mu }_{\mathrm{\Sigma }}=0.310\mathrm{GeV}$, implying that the chiral symmetry is restored at higher potentials at any temperature.

We explain that the logic behind the derivation of the Noumi-Shiraishi function can be applied directly to the Baker-Akhiezer function (BAF). This amounts to changing an ansatz for BAF to a nested one, where the BAF of $N+1$ variables is recursively expressed as a sum over BAFs of $N$ variables. This may be seen as a generalization of symmetrization trick from [A. Mironov, A. Morozov, and A. Popolitov, arXiv:2601.10500] but for the generally nonsymmetric BAF. We demonstrate that, for usual nontwisted ($a=1$) BAFs, this method correctly reproduces the Noumi-Shiraishi formula directly from linear equations, resolving the ambiguity related to nonsimple roots. For the first nontrivial twisted case ($N=3$, $a=2$) this method also fixes this ambiguity, moreover, answers for the first few layers of coefficients are in the form of direct quantization of the above article.

Following the previously developed approach to the calculation of quantum corrections to the effective potential in arbitrary scalar field theories in the leading logarithmic approximation, we extended it to the next-to-leading order. Based on Bogoliubov-Parasiuk-Hepp-Zimmerman renormalization procedure and the Bogoliu-bov-Parasiuk theorem, we construct recurrence relations and renormalization group equations that allow one to sum up the leading and subleading logarithms in all orders of perturbation theory. The formalism is applicable to an arbitrary scalar potential, renormalizable or not. To verify the results, we compare them with a renormalizable model treated within the standard renormalization group approach.

The different QCD processes, which can produce a heavy quark-antiquark ($Q\overline{Q}$) pair, induce different correlations between the heavy quarks. Employing the epos4hq event generator, we study the consequences of these correlations and compare the calculation with experimental results on open and hidden heavy flavor mesons, measured in proton-proton ($pp$) collisions at RHIC and LHC energies. We find that the measured correlations between heavy mesons are a direct image of the different ways in which the heavy quark pair is produced. They also contribute differently to the transverse momentum distribution of open and hidden heavy flavor mesons. The latter are calculated in a Wigner density approach, which also enables us to reproduce quantitatively the measured $B_c$ spectra. This agreement allows conclusions on the spatial distribution of the heavy quark creation processes.

The microphysics underlying nonbaryonic dark matter remains unknown. I derive the two-species Schrödinger-Poisson-Yukawa system for spin-$\frac{1}{2}$ dark-sector fermion fields, $\psi$ (mass $m_1$) and $\chi$ (mass $m_2$), coupled through a scalar mediator of mass $m_{\varphi }$ via a universal Yukawa coupling, within an orbital-free density-functional framework with the Kirzhnits gradient coefficient ${\lambda }_{\mathrm{B}}=1/9$. A central result is that the Bohm potential, far from being negligible in the Thomas-Fermi regime, contributes a species-dependent surface-energy correction analogous to the nuclear liquid-drop model; the heavier fermion species generates an outward quantum-pressure wall whilst the lighter species provides an inward surface tension, with degeneracy pressure furnishing the bulk confinement. In the single-species Schrödinger-Poisson limit the ground state recovers the benchmarked invariants $M_{\dim }\simeq 3.883$ and $x_T\simeq 2.562$, yielding $M{R}_T\simeq 9.95{\lambda }_{\mathrm{B}}{\hslash }^2/(G{m}_1^2)$. For polytropic index $\gamma =5/3$ the mass-radius relation satisfies $R\propto M^{-1/3}$; for $\gamma =4/3$ a limiting mass emerges above which no stable equilibrium exists. Illustrative configurations span $M={10}^{-8}–5M_{\odot }$, $m_1\sim {10}^{-14}-{10}^{-6}\mathrm{eV}$, and radii from a few km to $\sim {10}^3{R}_{\odot }$, with gravitational-wave contact frequencies in the Einstein Telescope and LISA bands and microlensing signatures accessible to current surveys. The predictive rigidity of the resulting mass-radius relation, in which the single microphysical parameter $m_1$ determines the equilibrium radius once the total mass is specified, furnishes a reproducible, first-principles reference for constraining the dark-fermion mass in multicomponent dark sectors.

In view of the recent theoretical developments in the fixed center approximation for the scattering of a particle with a a two-body cluster, implementing elastic unitarity on the standard fixed center formalism, and the imminent availability of ALICE data on the correlation function of the $p{f}_1(1285)$ system, we update the results of a previous work for this correlation function and the low-energy scattering observables. The new results show appreciable changes in some observables and should provide valuable input for comparison with the forthcoming experimental data. Such a comparison is expected to yield relevant information on the nature of the axial-vector meson states.

$CP$ violation in hadronic multibody decays has been extensively studied, and the experimental breakthrough in the heavy baryon sector was made recently. Partial-wave $CP$ asymmetries (PWCPAs) in multibody decays of heavy hadrons, which although provide us with more interference information, suffer from the normalization problem, as is pointed out in this paper. We propose a novel solution to this problem. We introduce a set of extra factors to rescale the PWCPAs to the proper sizes. Instead of determining the set of factors according to the normalization requirement, we demand that all the PWCPAs have the same statistical errors. In this way, we obtain a set of quasi-normalized PWCPAs, in the sense that they are close to the ideal normalized ones. As an application, we perform an analysis of PWCPAs in the decay channel $B^{\pm }\to {\pi }^{+}{\pi }^{-}{\pi }^{\pm }$. We focus on the phase space region where the invariant mass of the ${\pi }^{+}{\pi }^{-}$ pair varies around the vector resonance ${\rho }^0(1450)$. Based on the data of the LHCb Collaboration, the interference patterns among the resonances ${\rho }^0(1450)$, $f_2(1270)$, and $f_0(1500)$ and their contributions to the quasinormalized PWCPAs are analyzed. The analysis indicates that the quasi-normalized PWCPAs can avoid potential misleading or distorted results comparing with some other alternatively defined ones.

We introduce a new causal spinfoam vertex for 4D Lorentzian quantum gravity. The causal data are encoded in Toller $T$-matrices, which add to Wigner $D$-matrices $T^{(+)}+T^{(-)}=D$, and for which we provide a Feynman $\mathrm{i}ϵ$ representation. We discuss how the Toller poles cancel in the Engle-Pereira-Rovelli-Livine vertex, how the Livine-Oriti model is obtained in the Barrett-Crane limit, and how spinfoam causal data are distinct from Regge causal data. In the large-spin limit, we show that only Lorentzian Regge geometries with causal data compatible with the spinfoam data are selected, resulting in a single exponential $\exp (+\mathrm{i}{S}_{\text{Regge}}/\hslash )$ and a new form of causal rigidity.

The chiral SYK model [Lian et al. The chiral SYK model, J. High Energy Phys. 09 (2019) 067] is a $1+1$-dimensional generalization of the Sachdev-Ye-Kitaev model with chiral Majorana fermions and homogeneous random interactions. In the large-$N$ limit, the model admits an exact solution of the two-point function due to its scaling symmetry and exhibits a quantized thermal Hall conductance consistent with that of a $2+1$-dimensional gapped topological system. We study two chiral SYK systems coupled by a relevant quadratic interaction that explicitly breaks scaling and time-reversal symmetry. Working in the regime of weak intersystem coupling, we solve the Dyson-Schwinger equations perturbatively and obtain analytic expressions for two-point functions at finite temperature. Unlike the coupled SYK model in $0+1$ dimensions, the $1+1$-dimensional chiral system does not develop a mass gap, and no thermal phase transition is observed. We show that the leading correction to the thermodynamic free energy is temperature independent, implying that the entropy density remains identical to that of two uncoupled chiral SYK systems. A real-time analysis of the retarded correlator reveals the emergence of massless collective bosonic modes propagating between the two subsystems at zero temperature, signaling quasiparticle tunneling without gap generation. Our results demonstrate a sharp qualitative distinction between relevant deformations of SYK models in zero and one spatial dimensions and highlight the robustness of gapless chiral edge dynamics against explicit scaling symmetry-breaking interactions.

Three-dimensional supersymmetric gauge theories with eight supercharges possess a unique duality known as 3D mirror symmetry. Under this correspondence, the Coulomb branch of one theory is equivalent to the Higgs branch of its mirror dual, and vice versa. Over the past decades, extensive effort has been devoted to charting the landscape of 3D mirror pairs, though progress has often been constrained by the need to identify suitable brane configurations. In this first installment, we introduce a new quiver-based algorithm, termed growth and fusion, which completes a quartet of Higgsing algorithms alongside decay and fission, quiver subtraction, and quiver addition. Together, these four algorithms provide a systematic framework that circumvents the limitations of brane constructions, enabling us to determine the mirror dual of a given quiver and to systematically bootstrap new 3D mirror pairs. We demonstrate the power of this approach on a new class of circular 3D mirror pairs.

Symmetry under a particular class of nonstrictly canonical transformation may be used to identify, and subsequently excise degrees of freedom which do not contribute to the closure of the algebra of dynamical observables. Such redundant degrees of freedom may physically be identified with empirically inaccessible measures of global scale. In this article, we present a mathematical framework which extends the symmetry reduction procedure to theories of classical fields, in both the Lagrangian and Hamiltonian settings. In order to maintain Lorentz covariance, while simultaneously working with a finite-dimensional phase space, we employ the De Donder-Weyl formalism, for which the natural description is formulated in terms of the fibered manifolds of multisymplectic geometry. We subsequently analyze a number of simple examples, and provide a discussion of the broader implications of our construction.

We study renormalization group (RG) flows in far-from-equilibrium states. The study is made tractable by focusing on states that are spatially homogeneous, time independent, and scale invariant. Such states, in which mode $k$ has occupation numbers $n_k\sim k^{-\gamma }$, are well known in nonlinear physics. RG flow in such states is qualitatively different from that in the vacuum—a positive $\gamma$ decreases the dimension of an operator, turning marginal interactions into relevant interactions. We compute one-loop beta functions. Depending on the sign of the beta function, backreaction may either cause a minor shift of the state in the IR or completely change the nature of the state. Focusing on nearly marginal interactions, we construct an analog of the epsilon expansion and IR fixed points, with epsilon now set by the scaling of the interaction rather than the spacetime dimension. In the language of RG flow, critical balance scaling—which has applications in fields as varied as astrophysics and ocean waves—corresponds to the state dynamically adjusting itself along the RG flow until the interaction becomes marginal.