According to the $B$-mesogenesis framework, the baryon asymmetry of the Universe and dark matter can be simultaneously generated through CP-violating $B$-meson oscillations. In this mechanism, $B$-mesons decay into a Standard Model baryon and a dark-sector antibaryon, denoted by $\psi_{DS}$. Within this scenario, we investigate the allowed mass window for $\psi_{DS}$ using Light Cone Sum Rules (LCSR) for $B_d\rightarrow\Lambda \, \psi_{DS}$ decay. To include non-perturbative effects, we employ contributions up to twist-6 of the $\Lambda$ distribution amplitudes in the operator product expansion (OPE). We derive the branching fraction as a function of dark antibaryon mass and, by comparing with the experimental limits by the BaBar and Belle collaborations, determine the mass ranges of $\psi_{DS}$ consistent with the $B$-mesogenesis mechanism.

We investigate the description of quark confinement in terms of confining strings or flux tubes. We show that compact QED with a topological $\theta$-term, in the dyon condensation phase, is described by a massive two-form field $B_{\mu \nu}$ that gives rise to a string theory with an IR Brazovskii-Lifshitz fixed point at strong coupling. This corresponds to a quantum consistent "free string" in (3+1) dimensions, representing the dual of asymptotic freedom in the UV. Contrary to critical strings, which correspond to trivial Gaussian fixed points, this string is stabilized by a finite thickness, determined by the mass of the $B_{\mu \nu}$ field, instead of living in a higher-dimensional space. It correspondingly contains a massive world-sheet resonance, in addition to the Nambu-Goto phonons, that improves fitting with data. We compute the confining potential and show that it reproduces a generalized Arvis potential $V(L) = aL \sqrt{1 - c/L^2}$ with running parameters $a(L), c(L)$. We compute the mass difference ratios for the heaviest quarkonium and find 2.5 percent agreement with experiment already at the infrared fixed point. We also compute the intercept of Regge trajectories and find that the thickness of Brazovskii-Lifshitz strings tends to increase it from the Nambu-Goto value $\alpha_0 = 1/12$. Overall, our findings strongly support Polyakov's longstanding conjecture on universality of confining gauge theories in the IR.

We propose a novel, machine-learning-based framework for constructing lattice fermions using Physics-Informed Neural Networks (PINNs). Our approach treats the formulation of the Dirac operator as an optimization problem guided by physical requirements, such as symmetries, locality and doubler-decoupling conditions. We first demonstrate that, when trained to satisfy the Ginsparg-Wilson (GW) relation as a soft constraint, a neural network reproduces the overlap fermion operator to high numerical accuracy and learns an effective sign-function mapping without explicitly using a prescribed polynomial or rational approximation. Secondly, we extend the framework from operator construction to machine-assisted algebraic discovery. Within a generalized polynomial ansatz, the network autonomously drives higher-order terms to zero and recovers the standard Ginsparg-Wilson relation. Remarkably, by changing the initial search bias, the same framework also finds a distinct solution corresponding to a Fujikawa-type generalized GW relation.

Prompted by an observation about the integral of exponential functions of the form $f(x)=\lambda e^{\alpha x}$, we investigate the possibility to exactly integrate families of functions generated from a given function by scaling or by affine transformations of the argument using nonlinear generalizations of quadrature formulae. The main result of this paper is that such formulae can be explicitly constructed for a wide class of functions, and have the same accuracy as Newton-Cotes formulae based on the same nodes, with the latter emerging as the linear case of our general formalism. We also derive explicit bounds on the error of the nonlinear quadrature formulae, which in the linear case devolve into the well-known bounds for Newton-Cotes formulae.

We present a systematic QCD sum-rule analysis of the in-medium properties of the charged kaon doublet $K^{\pm}$ over the full $(T,\rho)$ plane relevant to current and forthcoming heavy-ion experiments. Working within the QCD sum-rule framework and incorporating temperature-and density-dependent quark, gluon, and mixed condensates, we derive Borel-transformed sum rules for the effective masses $m_{K^{\pm}}$, the pseudoscalar decay constants $f_{K^{\pm}}$, and the vector self-energy $\Sigma_{v}$ of both charged states simultaneously. Our vacuum results, $m_{K^{-}} = 494.6^{+4.9}_{-6.9}$~MeV and $f_{K^{-}} = 157.3^{+4.1}_{-2.9}$~MeV (with near-degenerate $K^{+}$ values), are in excellent agreement with Particle Data Group values at the sub-percent level. In the medium, $m_{K^{\pm}}$ decreases monotonically with increasing baryon density and temperature, signalling progressive partial restoration of chiral symmetry. A pronounced mass splitting $\Delta m = m_{K^{-}} - m_{K^{+}}$ develops in baryonic matter, driven by the opposite sign of the Weinberg--Tomozawa vector interaction for the two charge states; it reaches $|\Delta m| \sim 0.35$~GeV near $\rho \simeq 3.2\,\rho_{\rm sat}$ at $T = 0$ and is partially quenched by thermal fluctuations. A central outcome of this study is the extraction of the critical onset density $\rho_c$, defined as the threshold beyond which the in-medium modifications of $K^{-}$ properties signal the onset of the transition toward the chirally restored phase. We stress that $\rho_c(T)$ should not be interpreted as a precise determination of the QCD critical point-a task beyond the reach of any current effective framework-but rather as an indicator ....