Neutrino oscillations provide crucial insights into fundamental particle physics, with two-flavor approximations effectively describing reactor and atmospheric phenomena. This paper explores the use of Physics-Informed Neural Networks (PINNs) to solve the governing differential equations for neutrino evolution in both vacuum and matter environments. We review the theoretical framework, including vacuum mixing and the Mikheyev-Smirnov-Wolfenstein (MSW) effect in matter, and demonstrate PINN implementations for vacuum and constant-density profiles. This Machine learning based approach for reactor (low-energy) and atmospheric (high-energy) neutrinos shows high precision similar to analytical solutions, with mean squared errors of the order of \(10^{-3}-10^{-4)\). Although this work focuses on solving the evolution equation in general cases, we discuss the significant potential advantages of PINNs over traditional solvers, without any mesh requirements, high-dimensionality reduction, and applicability to complex geometries, along with future extensions to three-flavor effects.

We outline the analysis of three-particle interactions and decay processes for leading-order modifications in a Lorentz-violating quantum field theory.

A formalism for radiative correction calculations in exclusive $\eta$ electroproduction on the proton is presented, extending the treatment developed for the pion channel. The EXCLURAD code is used in the radiative correction procedure with EtaMAID-2023 multipole amplitudes. The cross-section correction factor $\delta$ varies by up to ${\sim}\,30\%$ across the resonance region $W = 1.49$-$2.0$ GeV at $E_{\rm beam} = 6.535$ GeV, with a local maximum near $W \simeq 1.66$ GeV driven by the $S_{11}(1535)$ and $S_{11}(1650)$ resonances. The beam-spin asymmetry is suppressed by 15-25% at the same kinematics. Numerical results covering $Q^2 = 0.3$-$4.0$ GeV$^2$ and the full angular range are provided for kinematics relevant to CLAS12 experiments at Jefferson Lab.

We construct an effective light-front mass-squared operator for quark-antiquark systems that incorporates quark dressing effects through a running quark mass. Starting from a Minkowski-space quark propagator constrained by lattice-QCD-inspired parametrization, we derive the disconnected light-front resolvent for a light quark-antiquark system using a generalized spectral representation of an individual quark propagator separating out the instantaneous contributions. By projecting the resolvent onto a constituent-quark helicity basis, we obtain an effective dressed mass-squared operator suitable for light-front Hamiltonian approaches. We introduce an effective light-front quark self-energy and analyze its momentum dependence. As an application, we study pion structure using representative light-front wave-function models and compute unpolarized transverse-momentum-dependent distributions, unpolarized parton distribution functions and distribution amplitudes. Our results show that quark dressing induces sizable infrared modifications while preserving controlled ultraviolet behavior, providing a framework to incorporate nonperturbative QCD dynamics into light-front descriptions of hadrons.

The B-L Supersymmetric Standard Model with Inverse Seesaw (BLSSM-IS) extends the Minimal Supersymmetric Standard Model (MSSM) by incorporating a gauged B-L symmetry, right-handed neutrinos and an additional neutral gauge boson Z'. Searches at the Large Hadron Collider (LHC) constrain the mass of this gauge boson to be as low as only ~ 2.2 TeV in the BLSSM-IS, owing to interference effects with the SM. In this framework, mono-Z' events can arise from the associated production of a Z' boson and a singlet Higgs boson h', where h' subsequently decays into missing energy carried by a pair of the Lightest Supersymmetric Particle (LSP) - either a neutralino or a right-handed sneutrino - which serves as a Dark Matter (DM) candidate. Focusing on leptonic decays of the Z' (electrons and muons), we analyse the kinematic distributions of the final-state leptons and the missing transverse energy in order to extract a signal for this process which is independent of the nature of the BLSSM-IS DM.

We perform coupled channel analysis for $D \bar D^*$, $J/\psi \pi$ and related meson pairs for the $Z_c(3900)$ channel in an effective model of hadrons and quarks. The model incorporates meson exchange potential such as one pion and $D^{(*)}$ meson exchanges, and quark exchanges. It turns out that the meson exchange potential is small, while the off-diagonal interactions by the quark exchanges at short distances, particularly for transitions between $D\bar D^*$-$J/\psi \pi$ are strong, which plays a main role for the scattering amplitudes for the $Z_c(3900)$ channel, in consistent with the results of the lattice simulations of the HALQCD group.

The enhancement of the baryon production relative to mesons in small-collision systems is considered a breakthrough result of the Large Hadron Collider since a similar effect in heavy-ion collisions is understood by invoking the formation of the strongly-interacting quark--gluon plasma. In this letter, a baryon enhancement is reported for $p_{\rm T}^{\rm ch,\, jet}>15$\,GeV/$c$ jets produced in pp collisions at $\sqrt{s}=13$\,TeV simulated with PYTHIA8. The effect can be explained as a transition between quark-initiated jets (low jet multiplicities) to gluon-initiated jets (high jet multiplicities). The present result challenges the interpretation about the multiplicity dependence of the baryon enhancement in terms of collective expansion of the medium and quark recombination.

We investigate the three-body $DDK$ system with quantum numbers $I(J^P) = \frac{1}{2}(0^-)$ within a coupled-channel framework that incorporates both $DDK$ and $D^{*}D^{*}K$ configurations. The $D^{(*)}D^{(*)}$ interactions are described using the one-boson-exchange model constrained by the heavy-quark symmetry and fitted to the pole positions of $X(3872)$, $T_{cc}^+$, and $Z_c(3900)$. The $D^{(*)}K$ interaction is from the chiral effective theory, motivated by the molecular interpretation of $D_{s0}^*(2317)$, and is further constrained by lattice-QCD results for the $DK$ scattering lengths. The resulting three-body problem is solved using the Gaussian expansion method, while the complex scaling method is employed to search for possible resonant states. We find that coupled-channel effects from $D^{*}D^{*}K$ are negligible, and the $DDK$ system supports a deeply bound state across a wide range of parameters. Depending on the long-range behavior of the $DK$ interaction, an additional shallow state may emerge near the particle-dimer ($D$-$DK$) threshold. The deeply bound state exhibits a compact three-body structure, whereas the shallow state displays characteristic features of a three-body halo configuration. No clear resonance poles are identified within the explored parameter region. Similar results are obtained for the $D^{*}D^{*}K$ system. These findings may provide new insight into few-body dynamics in systems involving charmed mesons and kaons.

We calculate the two-loop quarkonium Hamiltonian in the annihilation channel within the framework of potential-NRQCD effective field theory. The result agrees with the previous calculation of the corresponding four-quark operator in NRQCD for SU(N) color gauge group. We further obtain an expression with a more general color structure applicable to other gauge groups. Combined with the recently calculated two-loop Hamiltonian in the non-annihilation channel, this completes the full two-loop quarkonium Hamiltonian.

For supersymmetric extensions of the Standard Model we construct some expressions that include Yukawa couplings for the third and second generations and receive relatively small quantum corrections. This implies that they slightly depend on scale and are therefore approximate renormalization group invariants. Using these invariants we try to analyse possible relations between the Yukawa couplings at the unification scale $M_X$ as well as the predictions for values of $\mbox{tg}\,\beta$ and $\alpha(M_X)$. In particular, we suggest two variants of such relations and investigate whether they agree with the experimental values of elementary particle masses. It is demonstrated that the Yukawa unification for the third and second generations consistent with them can be achieved by adding exotic superfields forming 3 representations $5+\bar{5}$ of the group $SU(5)$ to the MSSM field content. We argue that this may indicate the possible underlying $E_6$ gauge symmetry.

The invariant mass spectrum of $e^+e^-$ pairs produced in high-energy Pb-emulsion collisions at 160 A GeV at CERN SPS exhibits a complex structure of many resonances resting on top of a broad enhancement at invariant masses below 50 MeV, with the prominent resonance at 19 $\pm$1 MeV providing independent support for the hypothetical X17 particle. We show that this complex structure may be coherently described as signatures for the neutral color-singlet $q\bar q$ quark matter in both its deconfined and confined phases. That is, the broad enhancement may arise from thermal annihilation of QED(U(1))-deconfined quarks and antiquarks into $e^+e^-$ pairs at the phase transition temperature $T_c$(QED), theoretically estimated to be 4.75 $\pm$ 1.2 MeV from the transitional equilibrium condition. The observed 3$\pm$1 and 7$\pm$1 MeV resonances may correspond to the QED(U(1))-deconfined $d\bar d$ and $u\bar u$ Coulomb bound states near their quark rest masses, respectively, whereas the observed 19 $\pm$ 1 MeV resonance may correspond to the QED(U(1))-confined isoscalar QED meson. The approximate agreement between the theoretical and the experimental spectrum suggests that both QED(U(1))-confined and QED(U(1))-deconfined neutral color-singlet $q\bar q$ quark matter may have been produced in these high-energy Pb-emulsion collisions. We propose future experiments to confirm or refute these findings.

We review recent developments on the QCD phase diagram at small chemical potentials and increasing temperature. There are three regimes/phases in QCD which differ by symmetries, degrees of freedom and N_c scaling: the hadron gas below the chiral restoration temperature T_ch, the stringy fluid between T_ch and the deconfinement temperature T_d and the quark-gluon plasma above T_d.

We study the kaon quasi-distribution amplitude (quasi-DA) and distribution amplitude (DA) within the large-momentum effective theory (LaMET) combined with the first-principles functional QCD. Using quark correlation functions and the kaon Bethe-Salpeter amplitude in the Euclidean space from the 2+1 flavour functional QCD [1] as inputs, we obtain the kaon quasi DA in the large longitudinal momentum region with the contour deformation method [2] in the complex plane of momentum. By performing $1/P_z^2$ and $1/P_z^4$ order extrapolations of the kaon quasi-DA for the choices of the maximal longitudinal momentum $P_z^{\max}\in[2,2.5]$ GeV, we obtain a single-peaked and asymmetric kaon DA with the uncertainties arising from the extrapolation interval and ansatz. We find the first and second order moments of the kaon DA, $\langle \xi \rangle_K = 0.020(3)$ and $\langle \xi^2 \rangle_K = 0.253(12)$, respectively.

Ultralight bosons sourced by macroscopic objects can generate long-range spin-independent and spin-dependent potentials that are accessible to precision interferometry. Such potentials induce phase shifts in Josephson junctions, detectable through precision current measurements. We propose three experimental scenarios to probe photophilic scalar interactions, Lorentz-violating scalar-mediated interactions, and axion-mediated monopole-dipole interactions, depending on the nature (unpolarized or polarized) of the source. The proposed setups provide sensitivities to novel mixed couplings that are largely unconstrained by existing bounds and enables the exploration of new forces at centimeter to micrometer length scales.

We report a detailed simulation study of the search for $s$-channel Higgs boson production in $e^+e^-$ collisions at a center-of-mass (c.m.) energy of $\sqrt{s}=125\,\mathrm{GeV}$ at the CERN Future Circular Collider (FCC-ee), as a means to constrain the electron Yukawa coupling, $y_e$. The process of interest is $e^+e^-\to H\to WW^*\to \ell^\pm\nu + jj$ with four different $WW^*$ final states considered, involving both on- and off-shell $W$ bosons decaying either into dileptons ($\ell^\pm = e^\pm$ and $\mu^\pm$, including those from $\tau^\pm$ decays) or into dijets ($jj$). Signal and background events are discriminated through a multiclass gradient boosted decision tree exploiting a comprehensive set of kinematic and topological variables across the four final-state categories. Assuming a monochromatized c.m. energy spread of 4.1 MeV, yielding a $\sigma_{e^+e^-\to H} = 280\,\mathrm{ab}$ resonant cross section, and an integrated luminosity of $10\,\mathrm{ab}^{-1}$, the analysis achieves a combined statistical significance of 2.0 standard deviations. This corresponds to an upper limit on the coupling modifier $\kappa_e = y_e/y_e^{\rm SM} \lesssim 1.35$ at 95\% confidence level, and provides the most stringent constraint on the electron Yukawa coupling achieved in simulation-based studies to date.

This contribution reviews recent progress in the low-lying scalar mesons and glueballs. We propose a new classification for the scalar nonet that includes $f_0(980)$ and $a_0(980)$ as the lowest states, while we identify $f_0(1500)$ as a primary glueball candidate. We demonstrate that the production yields of these states in heavy-ion collisions are mutually consistent across statistical, coalescence, and S-matrix frameworks. To investigate their internal structure, we move beyond standard phenomenology by describing glueballs as topological solitons. This approach yields an energy spectrum in excellent agreement with lattice QCD and experimental data, while interpreting $f_0(2470)$ as a tightly bound glueballonium to explain its anomalously long lifetime. This non-perturbative framework provides a predictive basis for the future experimental verification of exotic scalar states.

As the lightest isovector vector meson, the $\rho$ meson is an important object for investigating the structure of resonant states in strong interactions. Owing to its strong coupling to the $\pi\pi$ channel and its large decay width, the conventional constituent quark model treatment, in which it is simply regarded as a pure $q\bar q$ bound state while the hadronic-channel coupling effects are neglected, is insufficient to fully characterize its physical properties. To this end, in the present work we establish a unified framework for studying the structure and resonant properties of the $\rho$ meson by combining the quark-gluon and hadronic degrees of freedom. At the quark-gluon level, we first determine the parameters of the chiral quark model by refitting a set of narrow mesons for which open OZI-allowed strong-decay channels are absent or strongly suppressed. With these parameters fixed, the bare mass of the $\rho$ meson is obtained and used as the input for the subsequent hadronic-level analysis. At the hadronic level, based on inverse scattering theory, we construct a model including the coupling between the bare state and the $\pi\pi$ continuum, extract the $\rho_0-\pi\pi$ interaction using the $P$-wave $\pi\pi$ scattering phase-shift data, and further calculate the width of the $\rho$ meson as well as the bare-state component in the physical state. The present work also provides a generalizable analytical framework for further studies of other hadronic resonances with significant channel-coupling effects.

We study the phenomenology of heavy neutral leptons (HNLs) in $B$-meson decays as probes of physics beyond the Standard Model. Focusing on the leptonic channels $B \to \mu N$ and $B \to \tau N$, we constrain the allowed regions in the $M_N$--$|U_{\ell N}|^2$ plane using current experimental data. Using these constraints, we investigate lepton-number violating ($\Delta L=2$) processes mediated by on-shell HNLs, including $B_{(c)}^- \to \pi^+ \mu^- \mu^-$ and $B_c^- \to J/\psi\, \pi^+ \mu^- \mu^-$. For benchmark values $|U_{\mu N}|^2 = 10^{-6}$ and $M_N = 2$-- $3\,\mathrm{GeV}$, the predicted branching ratios lie in the range $\mathcal{O}(10^{-13})$--$\mathcal{O}(10^{-8})$. Among the channels, $B_c^- \to \pi^+ \mu^- \mu^-$ shows the largest enhancement, while $B_c^- \to J/\psi\, \pi^+ \mu^- \mu^-$ is strongly suppressed. These results indicate a clear channel dependence, with $B_c$ modes providing enhanced sensitivity to HNL effects and offering promising avenues for future searches of lepton number violation.

The LHCb collaboration has recently observed the rare hyperon decay $\Sigma^+\to p\mu^+\mu^-$. It can also measure the corresponding antihyperon channel with comparable precision and is thus in a position to extract information on $CP$ violation in this mode. Interestingly, the long-distance contributions that dominate it within the standard model provide large absorptive phases that could drive substantial $CP$ violation through interference with potential new-physics contributions. Here we explore this possibility, finding that the decay rate asymmetry is currently allowed to be as high as tens of percent, which can be probed by LHCb in the near future. We additionally consider the same with regard to the dielectron mode $\Sigma^+\to pe^+e^-$ as well as the related radiative one $\Sigma^+\to p\gamma$.

Naturally tiny neutrino masses can be explained by the low scale seesaw with heavy neutral lepton $N$ coupling to the neutrinophilic Higgs doublet $\Phi_\nu$, which obtains a much smaller vacuum expectation value than the standard Higgs doublet $\Phi$. Within this model, the neutrino masses originate from the new Yukawa interaction $y \overline{L}\tilde{\Phi}_\nu N$. In this paper, we propose the novel same-sign tetralepton signature at the 2 TeV same-sign muon mode $\mu^+\mu^+$ of $\mu$TRISTAN. We investigate two distinct channels of this signature, which are both generated by the Yukawa interaction $y \overline{L}\tilde{\Phi}_\nu N$. One is from the pair production of charged Higgs $\mu^+\mu^+\to H^+ H^+\to \mu^+N +\mu^+ N\to \mu^+ \mu^+ jj + \mu^+ \mu^+ jj\to 4\mu^+ + 4j$, and the other one is from the single production of charged Higgs $\mu^+\mu^+ \to \mu^+ N H^+ \to \mu^+N +\mu^+ N\to \mu^+ \mu^+ jj + \mu^+ \mu^+ jj\to 4\mu^+ + 4j$. We then perform a detailed simulation of this same-sign tetralepton signature, and obtain the promising region at $\mu$TRISTAN.

In this paper, we present the production of double SM-like Higgs $ (h) $ at the future electron positron colliders within the context of $ S_{3} $ model with three Higgs doublets (S3-3H) and no CP violation to describe beyond the Standard Model Higgs Physics. We focus first on the numerically allowed parameter space of the model, taking into account theoretical bounds from perturbative unitarity and vacuum stability, as well as by data at the Large Hadron Collider (LHC) and the Tevatron. The double Higgs production in the S3-3H model can deviate from the SM predictions up to a few orders of magnitude in both the $ e^+e^- \rightarrow hhZ $ and the $ e^+ e^- \rightarrow h h\nu_{e} \bar{\nu}_{e}$ channels. Thus, our findings indicate that the S3-3H model can lead to measurable deviations from the SM predictions of Higgs production at future $ e^+ e^- $ colliders. These results highlight the importance of studies at such colliders for searching physics beyond the Standard Model.

We study the magnetic fields produced in the early Universe during the electroweak symmetry breaking by considering random configurations of an inhomogeneous Higgs field. By exploiting the inherent randomness of the initial configurations the spectrum of the produced magnetic field is essentially analytic, which bypasses the need for costly lattice simulations. On the numerical side, we devise a simulation framework which results in continuous fields capable of resolving the small-scale structure of the fields that was inaccessible for the lattice-based calculation. Finally, by revisiting the effects of statistical isotropy and causality on the spectrum, we define general correlation functions that are then fitted to the simulation data and compared to the analytic results.

Both scalar and vector dark matter can be produced during a cosmological first order phase transition if the dark matter is coupled to the field undergoing the transition. Both kinds of particle are also produced by the plasma through the normal freeze out scenario. For different dark matter masses, we identify the regions of parameter space where there are significant deviations from the normal freeze out scenario and discover there are some rather general predictions. For dark matter particles in the traditional thermal relic GeV-TeV window, dark sector phase transitions around a GeV affect scalar dark matter and dark sector phase transitions around 10 MeV affect vector dark matter abundances (and therefore should take place in a dark sector). When the phase transitions are in the interesting temperature range, the normal range of dark matter masses are different to those predicted by thermal freeze out. We calculate the expected gravitational wave signal of these phase transitions.

Heavy quark (HQ) momentum ($\kappa$) and spatial diffusion ($D_s$) coefficients are computed in a non-perturbative thermal QCD medium in the presence of a background magnetic field of arbitrary strength. Both perturbative and non-perturbative effects are incorporated via the in-medium HQ potential, obtained from the resummed gluon propagator. We find that the momentum diffusion coefficients become anisotropic even in the static heavy quark limit, with the magnetic field direction defining the axis of anisotropy. This anisotropy originates from restrictions on longitudinal momentum diffusion in the gluon spectral function, and naturally leads to two spatial diffusion coefficients ($D_s^L$, $D_s^T$). Non-perturbative effects are found to be dominant at low temperatures. These results provide a more consistent input for Langevin based calculations of the heavy quark directed flow at RHIC and LHC energies.

We investigate the dynamics and mass spectra of charged pseudoscalar ($\pi^+$) and vector ($\rho^+$) mesons in a background magnetic field at finite temperature using the two-flavor Nambu-Jona--Lasinio (NJL) model. By employing a quark propagator that isolates the Schwinger phase from its Landau level expansion, we formulate an exact non-commutative phase-space framework utilizing the Wigner-Weyl transform and the Moyal star product. This approach enables the algebraic diagonalization of the Bethe-Salpeter equations for composite states with asymmetric fractional constituent charges. For the pseudoscalar channel, we analytically verify the exact cancellation between the dynamical random phase approximation spatial sum rules and the vacuum gap equation. This identity preserves the generalized Goldstone theorem, causing the $\pi^+$ pole mass to strictly track the kinematic zero-point energy drift at order of $eB$. In the vector channel, our full phase-space evaluation reveals that the Zeeman spin-splitting emerges dynamically from microscopic threshold truncations governed by the chiral Dirac algebra. Notably, we find that the tachyonic instability of the spin-aligned $\rho^+$ state is quenched. The magnetic catalysis of the chiral condensate drives the continuum threshold ($2M$) upwards, overtaking the Zeeman attraction and preventing vector meson condensation within this mean-field framework. Furthermore, finite-temperature evaluations show a monotonic thermal suppression of the meson masses driven by Pauli blocking, yet all modes remain bound without undergoing Mott dissociation prior to chiral symmetry restoration.

Nucleon decays into a lepton and two pseudoscalar mesons represent key channels for probing baryon number violation, complementing conventional two-body modes. In this Letter, we model-independently correlate two- and three-body processes within the framework of low-energy effective field theory, performing a global analysis that avoids single-operator-dominance assumption. We derive significantly improved bounds on 15 three-body modes with a lepton ($e^+,\,\mu^+,\hat\nu=\nu/\bar\nu$) and two non-strange mesons ($\pi,\eta$). For charged-lepton modes, our lower limits on partial lifetimes ($\Gamma^{-1}$) surpass current Particle Data Group (PDG) values by more than three orders of magnitude. For 5 (anti)neutrino modes, we establish for the first time $\Gamma^{-1}\gtrsim 10^{34}\,\rm yr$. Additionally, our analysis improves constraints on two-body processes $n\to e^+\pi^-$, $n\to \mu^+\pi^-$, and $p\to \hat\nu \pi^+$ by approximately a factor of 2 compared to the PDG limits. These results highlight the importance of leveraging correlations among different processes to better probe new physics, enabling more stringent constraints on experimentally challenging processes from well-measured ones.

There are two $R$-factors frequently used in the phenomenology of exclusive processes at small values of the Bjorken $x$ variable. One $R$-factor takes into account the effects of non-zero longitudinal momentum transfer, which is assumed to be zero in the dipole scattering amplitude. Another $R$-factor accounts for the real part of the elastic scattering amplitude which is often neglected, with the standard dipole scattering amplitude giving only the imaginary part of the elastic amplitude. In this work we present two new theoretical developments aimed at eliminating the need for the two $R$-factors. We argue that the $R$-factors can be replaced by (i) modifying the argument of the dipole scattering amplitude and by (ii) augmenting the initial conditions for its non-linear small-$x$ evolution. Specifically, we show that to account for the effects of non-zero skewness $\xi$, one has to replace the rapidity argument $Y = \ln (1/x)$ of the eikonal dipole amplitude $N$ and the odderon dipole amplitude $\cal O$ by $Y = \ln \min \left\{ 1/|x|, 1/|\xi|\right\}$. The prescription applies to the elastic scattering cross sections, as well as for calculations of the Generalized Parton Distributions and Generalized Transverse Momentum Dependent parton distributions at small $x$ and at small but non-zero skewness $\xi$. We also show that the real part of the scattering amplitude, proportional to Im~$N$, which is intimately connected to the signature factor of the amplitude, can be accounted for by a more careful evaluation of the initial condition for the evolution and by writing the non-linear evolution equation in an integral form. One can similarly construct Im~$\cal O$ for the odd-signature odderon amplitude. We hope that future implementation of our prescriptions presented here will eliminate the need for both phenomenological $R$-factors.

High-fidelity simulation of particle-matter interactions provides the essential theoretical reference for diverse physics disciplines, yet generating synthetic datasets at the scale of current and future experiments has become prohibitive. Here, we introduce PHIN-GAN, a novel physics-informed generative adversarial network designed to address this challenge. We derive a set of analytical probability density functions, that effectively describe the ``straggling function'' identified with Landau. For the first time, this enables their continuous evaluation across the entire phase-space. These analytical forms are leveraged to enforce a parametric distribution-level learning objective. Rooted in first principles, PHIN-GAN offers a generalizable, interpretable and scalable proof-of-concept approach for a lossless generative model that maintains the high fidelity of the standard-bearer for simulating such interactions, namely GEANT4, at a fraction of the computational cost.

Deep-inelastic $e/\mu$ scattering data off targets ranging from deuterium to lead indicate that the nuclear modifications to the structure functions of bound nucleons are minimal in the kinematic region around the peak of the valence quark distributions. An analysis of world measurements of the isoscalar cross-section ratios $\sigma^A/\sigma^{{}^2\text{H}}$ in the region of $0.25 \leq x \leq 0.35$ shows a remarkable cancellation across all nuclei, with an average value of $0.9985 \pm 0.0022$. We discuss these results and possible interpretations in the context of a microscopic model of nuclear modifications of the structure functions.

Preheating after inflation proceeds through parametric resonance, leading to efficient particle production in scalar field models. In this work, we investigate the structure of parametric resonance in the $\phi^4$ chaotic inflationary model during the preheating phase by performing a fully numerical analysis of the coupled dynamical equations governing the inflaton field and the mode function of the produced particles, thereby avoiding the approximations commonly employed in earlier studies. Our results reveal resonance patterns that differ significantly from those obtained with approximate analytical treatments. In the weak coupling regime, short-wavelength modes rapidly settle into oscillations with nearly constant amplitude, while the corresponding occupation numbers approach saturation. However, the long-wavelength modes exhibit gradual amplitude growth, with occupation numbers transitioning into a non-linear oscillatory regime. As the coupling strength increases, the dynamics becomes increasingly nonlinear, leading to the emergence of stochastic behavior. In the strong coupling regime, short-wavelength modes display a step-like (staircase) evolution in the occupation number, indicative of intermittent bursts of particle production. However, the long-wavelength modes exhibit a more gradual, monotonic growth with small superimposed fluctuations. These findings highlight the rich, coupling-dependent, structure of parametric resonance in the quartic inflationary model and underscore the importance of exact numerical treatment in accurately capturing preheating dynamics.

We explore the viability of scalar field dark matter halo models through the rotation curve analysis of the Andromeda galaxy (M31), taking into account a realistic description of its baryonic structure. The mass model includes a stellar disk described by the Freeman profile and two alternative bulge configurations: a classical single de Vaucouleurs bulge and a two-component structure consisting of inner and main bulges modeled by exponential sphere profiles. The dark matter halo is modeled using three scalar field motivated models: fuzzy dark matter (FDM), Bose-Einstein condensate and multistate scalar-field dark matter. The model parameters are determined through the Levenberg-Marquardt nonlinear least-squares fitting, and the relative performance of the models is evaluated using the Bayesian Information Criterion which allows a direct comparison with previous phenomenological halo studies performed for the same galaxy. We find that the two-bulge baryonic configuration ensures a better statistical description of the M31 rotation curve, independently of the adopted halo model. The results also suggest that, within scalar field dark matter scenarios, smooth cored halos, such as FDM, provide the most consistent description of the M31 kinematics.

We suggest a non-minimal renormalization scheme based on dimensional regularization that naturally incorporates threshold effects of heavy particles. By renormalizing couplings and masses to subtract all poles in $d \geq 4$, the resulting scheme is mass-dependent and circumvents shortcomings of mass-independent schemes like minimal subtraction. At the same time, many advantages of minimal subtraction such as gauge independence are retained. Through explicit one-loop computations in QCD, we demonstrate that this scheme reduces to minimal subtraction at high energies while providing smooth transitions at particle thresholds and implementing the Appelquist-Carazzone theorem. Potential future applications and extensions are discussed.

A derivation of the relative velocity used in the definition of the relativistic cross-section is given in terms of manifestly Lorentz invariant quantities. Along the way we find that there is a certain arbitrariness in the usual definition of cross-section.

We show that the Weyl (trace) anomaly gives rise to a new non-dissipative vector current in accelerated relativistic fluids. The anomaly uniquely fixes the second-order transport coefficient governing the coupling between the electromagnetic field and the fluid acceleration. We derive this result by extending hydrodynamic anomaly matching to include the trace anomaly, and independently reproduce it in boundary quantum field theory by treating the Rindler horizon of an accelerated observer as an effective boundary. From the boundary perspective, the electric- and magnetic-field sectors correspond to screening and vacuum magnetization effects near the boundary. In the local rest frame, the electric-field contribution induces an additional charge density, while the magnetic-field contribution generates a transverse current with a Nernst-like, more generally thermomagnetic Hall-like, tensor structure. Our results reveal a new class of anomaly-induced transport governed by the trace anomaly.

We study nonlinear effective field theories (EFTs) with factorially growing perturbative expansions, focusing on a class in which the relative entropy encodes an infinite tower of higher-dimensional operators. Using the resummed relative entropy, we derive bounds on EFT coefficients: the non-negativity of the resummed relative entropy fixes the sign of their asymptotic growth, while its violation signals instabilities. In fermionic QED, analytic continuation from Euclidean to Minkowski spacetime yields a concrete example: the Schwinger effect, a nonperturbative instability captured by the resummed relative entropy.

We introduce a new regularization scheme for divergent integrals in quantum field theory. The framework is based on the structural decomposition of the integrand asymptotic expansion, which distinguishes between contributions that drive UV singularities and those that remain finite. This asymptotic regularization method isolates the genuinely singular sector and enables a consistent subtraction of divergences while maintaining covariance and gauge symmetry. In single-scale theories, we show that the renormalized quantities exhibit a non-local logarithmic dependence uniquely determined by the UV asymptotics, offering a derivation of logarithmic terms that is independent of standard renormalization-group flows. Because it relies only on asymptotic structure rather than on standard relativistic power counting, the method is naturally applicable to theories with modified dispersion relations and non-standard UV scaling. Although formulated here for ultraviolet divergences, the underlying strategy extends straightforwardly to infrared singularities.

Through analyzing the quark propagator under the magnetic field, we establish that the axial anomaly originates from an additional Dirac structure in quark propagator induced by the magnetic field. This Dirac structure also allows one to connect the axial anomaly with the topological properties of the system by checking the axial vector Ward identity. For the tree level propagator, we reproduce the result of the anomalous axial current as in the Dirac Hamiltonian approach and kinetic theory. Particularly, we confirm that the chiral magnetic effect (CME) comes from the same term that is in charge of the axial anomaly, specifically, as the anomaly of the transversal axial vector Ward Identity. The identity guarantees that the CME conductivity $C_{\rm CME}$ is a constant as $C_{\rm CME}=\frac{1}{2\pi^2}$, and is robust against the temperature, chemical potential, magnetic field and also interaction. Finally, we verify this numerically by applying the full quark propagator under magnetic field calculated from the functional QCD methods.

Numerical analysis to determine the form of the scalar power spectrum in Warm Inflationary paradigm is inevitable. One further needs numerical techniques to analyse any Warm Inflation model with the current observational data through the MCMC codes that are available publicly, like COSMOMC or Cobaya. We present \texttt{SWIM} (Stochastic Warm Inflation Module) written in C++ and Python, that not only helps generate the Warm Inflationary scalar power spectrum, either semi-analytically or fully numerically, but also is integrated with Cobaya enabling the user to constrain the model parameters with current CMB data and thus to put any Warm Inflation model to test. \texttt{SWIM} numerically solves the standard stochastic perturbation equations of Warm Inflation without any approximations, uses machine learning techniques to speed up the MCMC analysis while analysing the fully numerical power spectrum that significantly reduces the computational cost, and is able to accommodate any Warm Inflation model with any form of inflationary potential and dissipative coefficient for numerical analysis. We show that \texttt{SWIM}, in most of the cases, outperforms other numerical codes on Warm Inflation that are designed to yield only the semi-analytical power spectrum as far as the runtimes are concerned. We further point out that there can be situations where the semi-analytical way of determining the scalar power spectrum in Warm Inflation can fall short, and one needs the full numerical power spectrum for parameter estimation given the observational data. In such cases, \texttt{SWIM} is the only code available so far that is designed to perform the task. Hence, \texttt{SWIM} offers a complete numerical platform for thorough analysis of Warm Inflation models against the current cosmological data. \texttt{SWIM} has been made publicly available at this https URL.

We have evaluated the electromagnetic spectral function and its spectral properties by computing the one-loop photon polarization tensor in presence of magnetic field, particularly in a strong field approximation compared to the thermal scale. When the magnetic scale is higher than the thermal scale the lowest Landau level (LLL) becomes effectively (1+1) dimensional strongly correlated system that provides a kinematical threshold based on the mass scale. Beyond this threshold the photon strikes the LLL and the spectral strength starts with a high value due to the dimensional reduction and then falls off with increase of the photon energy due to LLL dynamics in a strong field approximation. This strongly enhances the dilepton rate over the thermal perturbative leading order (Born) rate at very low invariant mass. We have also investigated the electromagnetic screening by computing the Debye screening mass and it depends distinctively on three different scales (mass of the quasiquark, temperature and the magnetic field strength) of a hot magnetized system. The mass dependence of the Debye screening supports the occurrence of a magnetic catalysis effect in the strong field approximation.

The boost invariant longitudinal position space variable $\sigma$, which is the Fourier conjugate to skewness $\xi$, unravels the longitudinal impact parameter information in a proton. Here, we investigate the skewness sensitivity of T-odd leading twist GTMDs within the Dokshitzer Gribov Lipatov Altarelli Parisi (DGLAP) region, considering a momentum transfer to longitudinal as well as transverse direction. The $\sigma$-space distributions of the T-odd sector show oscillatory patterns that are sensitive to the square of the total momentum transfer $-t$, which is analogous to the diffraction scattering of waves in Optics. An additional effect on the diffraction pattern is reported, caused by interference between transverse momentum transfer $\bfd$ to the transverse momentum $\bfp$ of quarks. We also present the correlation of proton spin to the transverse momentum of constituents through Sivers and Boer-Mulders Wigner Distributions in boost invariant longitudinal position space.

This paper investigates the influence of heavy-quark momentum on their interaction rate and the resulting drag coefficient in a quark-gluon plasma. To go beyond simplified treatments, the drag coefficient is derived by expressing the energy loss coefficients as polynomial expansions of momentum. This work introduces a phenomenological extension of the drag coefficient, providing a flexible framework to test the sensitivity of heavy-quark observables to additional momentum dependence in transport coefficients. Furthermore, the effects of particle momentum on radiative and collisional energy loss are determined more accurately. The study focuses on calculating the nuclear modification factor $R_{AA}$ of charm and bottom quarks in Pb-Pb collisions at $\sqrt{S_{NN}} = 5.02 TeV$. The initial distribution functions are evolved numerically using the Fokker-Planck equation. The results are compared with the latest experimental data from ALICE and ATLAS, collected in 2021 and 2022.

We develop a formalism, based on spinor-helicity techniques, to generalize the formulation of partial wave unitarity bounds. We discuss unitarity bounds for $N \to M$ (with $N,M \geq 2$) scattering processes -- relevant for high-energy future colliders -- and spin-2 or higher-spin theories -- relevant for effective field theories of gravity -- that are not approachable by standard methods. Moreover, we emphasize the power and complementarity of positivity and partial wave unitarity bounds to constrain the parameter space of effective field theories.

We propose a mechanism for relaxing a gauge theory CP violating phase in discrete steps to very small values. The idea is that the CP violating phase includes the magnetic dual of a $4$-form flux which can discharge by the nucleation of membranes. Inside the bubbles surrounded by the membranes, the total CP violating phase is reduced. When the bubbles are produced rapidly during radiation domination in the early universe, near the chiral symmetry breaking scale, they will collide and percolate, melting away into gauge theory radiation and dramatically relaxing CP violation.

We propose a model for the cosmological formation of superheavy Q-Balls in the mass range $10^{-7} \, M_{\odot}$ to $10^{6} \, M_{\odot}$. The model is based on a hidden sector scalar potential motivated by broken scale invariance, for which analytic Q-ball solutions and numerical simulations of condensate fragmentation exist. We show that this potential can produce superheavy Q-balls during the radiation-dominated era. As an example, we show that it is possible to produce Q-balls of mass $ \sim \,10^{6} \, M_{\odot}$ and diameter $\sim$ 100 light years, with a number density $\sim 1$ per galaxy. Such early-forming superheavy Q-balls could play a role in galaxy and supermassive black hole (SMBH) formation. We also show that it is possible to form smaller mass Q-balls with large numbers per galaxy volume, that could form SMBH by merging. Finally, we show that it is possible to produce asteroid mass Q-balls that could account for all of the dark matter whilst remaining consistent with observational limits on MACHOs.

We introduce a two real scalar singlet extension of the two Higgs doublet model. We study the vacuum structure, the bounded from below conditions, the restrictions from the oblique parameters S,T and U, as well as the unitarity constraints. We submit the model to collider and Dark Matter experimental constraints and explore its allowed parameter space. We compare randomly populated simulations, simulations starting near the alignment limit, and a Machine Learning based exploration. Using Evolutionary Strategies, we efficiently search for regions with a viable Dark Matter candidate.

Gravitational effects are known to violate global symmetries, threatening the Peccei-Quinn (PQ) solution to the strong CP problem. Ultraviolet completions featuring a gauged $U(1)$ symmetry, where $U(1)_{\rm PQ}$ arises as an accidental global symmetry, can suppress Planck-suppressed operators, enabling high-quality axions in a mass window where it can also account for the observed dark matter (DM) in the Universe. We show that in such models, the spontaneous breaking of the $U(1)$ gauge symmetry generates a strong stochastic gravitational wave background (SGWB) from gauge cosmic string loops. Even in the most conservative scenario, for breaking scales $\gtrsim 10^{14}$ GeV, the SGWB signal strength can exceed astrophysical foregrounds across a broad frequency range. Such quality axion models have a characteristic IR break frequency originating from the dynamics of the string-wall network collapse. We propose this characteristic SGWB frequency-amplitude region, identified as \textit{Signature-Window-Axion-Gravitational waves} (SWAG), to be a novel probe of high-quality axion DM at future space and ground-based interferometers.

We perform a detailed computation of the helicity-dependent next-to-leading power leading logarithms in W+jet production, originating from next-to-soft gluon radiation and soft (anti-)quark emissions. These contributions are systematically captured via helicity-sensitive spinor shifts and soft quark operators. The resulting expressions exhibit full agreement with a recently proposed universal structure of NLP corrections for processes involving the production of an arbitrary massive colourless final state in association with a jet.

We present a fully automated framework to compute production spin-density matrices for generic collider processes at tree level within \textsc{MadGraph5\_aMC@NLO}. The method assembles helicity amplitudes into event-by-event production matrices. These are written to the LHE file in a compact form, together with run metadata, enabling direct post-processing of quantum observables. The implementation supports bi- and multipartite qubit and qutrit final states, configurable reference frames, and both polarised and unpolarised initial states. A companion, easy-to-extend library provides analysis routines to determine key quantum-information measures and witnesses. These include purity, concurrence, and entanglement of formation for qubits; Peres--Horodecki tests and negativity; spin-polarisation vectors and correlation matrices; $D$-coefficients; and stabiliser-based ``magic'' measures. As a result, multi-particle quantum correlations can be quantified systematically. We validate the implementation against known results for $t\bar t$ and $VV$ ($V=W^\pm,Z$) production in $pp$ and $e^+e^-$ collisions and in heavy-resonance decays. We then consider new applications and study quantum correlations in several LHC final states: $t\bar t W^\pm$, $tW^-$ vs.\ $t(\bar t\to W^- \bar b)$, and $t\bar t t$ vs. $t\bar t t\bar t$.

We consider the Standard Model (SM) extended by a secluded $U(1)_D$ gauge sector encompassing a Dirac fermion ($\chi$) dark matter (DM), an abelian gauge boson $Z^\prime$ and a SM-singlet complex-scalar field $\Phi$, whose radial component drives cosmic inflation. When the Higgs portal coupling is small, the $Z^\prime$ then acts as a {\it ``reheaton''}, dominating the energy budget of the Universe before finally yielding the SM bath, with reheating temperature $< O(10)$ TeV, through the gauge portal interaction. We explore the possibility that DM freezes-in via non-thermal $Z^\prime$ decays before reheating ends, giving rise to substantial viable parameter space. We account for non-perturbative effects, relevant during the initial stages of reheating, using lattice simulations. We additionally show how the cosmological gravitational wave (GW) background produced by preheating and inflation allow for a direct probe of the reheating mechanism.

Motivated by the discrepancies noted recently between the theoretical predictions of the electromagnetic $J/\psi \to \pi^0 \gamma^*$ transition form factor and the BESIII data, we reanalyze this transition form factor using the dispersive Khuri-Treiman equations, with final-state interactions in both the direct channel and the crossed channels properly considered. This improved framework incorporates $\rho$-$\omega$ mixing effects. The effect of four-pion states is evaluated through a dispersively improved vector-meson-dominance model. From this information, we propose a two-parameter fit that provides an excellent description of the BESIII data over the broad energy range from 0 to 2.8GeV. We demonstrate that the $\rho\pi^0$ decay mode of the $J/\psi$ is dominated by strong interaction, while the $\omega\pi^0$ mode is dominated by one-photon exchange. From this, we extract the relative phase between the strong and the one-virtual-photon (electromagnetic) modes in hadronic decays of $J/\psi$ as $(62 \pm 21)^{\circ}$. This could provide useful information in understanding the long-standing $\rho \pi$ puzzle in $J/\psi$ decays.

In this article, the electroweak transition form factors of $\Sigma_b\to\Sigma_c$, $\Xi'_b\to\Xi'_c$ and $\Omega_b\to\Omega_c$ are analyzed within the framework of three-point QCD sum rules. In phenomenological side, all possible couplings of interpolating current to hadronic states are considered, and the Dirac structure dependence on the form factors is systematically eliminated. In QCD side, our calculation incorporates both the perturbative part and the contributions from vacuum condensates up to dimension 8. This systematic inclusion of higher-dimensional terms accounts for a broader set of Feynman diagrams, thereby enhancing the comprehensiveness and reliability of the operator product expansion. Using the obtained form factors, we study the partial widths of semileptonic decays $\Sigma_b\to\Sigma_cl\bar{\nu}_l$, $\Xi'_b\to\Xi'_cl\bar{\nu}_l$ and $\Omega_b\to\Omega_cl\bar{\nu}_l$ ($l=e$, $\mu$ and $\tau$). The results indicate that these decay widths approximately satisfy SU(3) flavor symmetry. Next, we calculate the branching ratios for the decay process $\Omega_b\to\Omega_cl\bar{\nu}_l$ and compare them with the results from other collaborations. Furthermore, the lepton universality ratios and some asymmetry parameters of these decay processes are also analyzed, which provide information for the study of new physics. We hope that these results will serve as a useful reference for future theoretical and experimental studies of weak decays involving heavy flavor baryons.

We investigate the freeze-in of MeV-scale fermionic dark matter (DM) that couples to the Standard Model via a new vector mediator to assess the potential that future direct detection experiments have to observe new physics in either the DM or neutrino sectors. We study the minimal kinetic mixing dark photon of a secluded $U(1)_D$ as well as gauge bosons of the anomaly-free $U(1)_{L_i-L_j}$, with $i,j=e,\mu,\tau$, and $U(1)_{B-L}$ gauge extensions, exploring the impact of low reheating temperatures on the DM production rates. For the ultralight dark photon scenario, we show that current experimental constraints from electron recoil data in DAMIC-M and PandaX-4T can be avoided if the DM fermion is only a subcomponent (smaller than 40%) of the total cold DM and that future detectors can be sensitive to a DM fraction below 1% for masses above 1 MeV. For a massive dark photon, there are allowed regions of the parameter space with masses in the range 50 MeV $\lesssim m_{\rm DM}\lesssim$ 500 MeV that can be within the reach of direct detection experiments through nuclear recoils if freeze-in occurred at a low reheating temperature. Finally, the case of $U(1)_{L_i-L_j}$ and $U(1)_{B-L}$ is particularly interesting since the discovery of new physics can come from either the DM or the neutrino sector, which features new interactions. We find that freeze-in at low reheating temperatures can reproduce the observed abundance in large parts of the parameter space up to gauge couplings of $g_X\sim10^{-2}$ for MeV DM. Most notably, direct detection experiments will be sensitive to considerable parts of this parameter space in nuclear recoils for 50 MeV $\lesssim m_{\rm DM}\lesssim$ 500 MeV. Additionally, the enhanced signal from solar neutrino coherent scattering is observable in these scenarios, which can serve as a further handle to identify the underlying particle physics model.

We present a systematic analysis of the Higgs signal strengths at 125 GeV and 95 GeV in a non-supersymmetric $U(1)_X$ model with vector-like fermions ($U(1)_X$VLFM). This model extends the SM by introducing an additional $U(1)_X$ gauge symmetry, three right-handed neutrinos, two singlet Higgs fields ($\phi$ and $S$), and one generation of vector-like quarks and leptons. The scalar fields mix with each other in the neutral CP-even sector, leading to two Higgs-like states around 95 GeV and 125 GeV. A $\chi^2$ analysis is performed by combining the Higgs signal strength measurements at 125 GeV from ATLAS and CMS, including the $\gamma\gamma$, $WW^*$, $ZZ^*$, $b\bar{b}$, and $\tau\bar{\tau}$ channels, with the 95 GeV excesses observed in the diphoton and $b\bar{b}$ final states reported by CMS and LEP. Our results indicate that the $U(1)_X$VLFM can successfully reproduce the observed signal strengths of the 125 GeV Higgs while simultaneously explaining the 95 GeV excess. The parameters $g_X$, $g_{YX}$, $v_S$, $v_P$, and the new Yukawa couplings play a crucial role in achieving this consistency.

In the first part of the talk, I review general properties of $SO(10)$-inspired leptogenesis. This high-scale leptogenesis scenario is based on the simple assumption that the neutrino Dirac mass matrix is not too different from the up quark mass matrix. After showing how this necessarily implies a production of the asymmetry from the next-to-lightest right handed neutrino decays, so-called $N_2$-leptogenesis, I discuss how this results into important testable constraints on low energy neutrino parameters. In particular inverted ordering is not viable if strict $SO(10)$-inspired conditions are assumed. This is an important test in view of the expected results from the JUNO experiment. I also discuss how a subset of the $SO(10)$-inspired leptogenesis solutions realises strong thermal leptogenesis, where the final asymmetry is independent of the initial conditions. In this case a signal might be discovered by next generation $0\nu\beta\beta$ decay experiments. In the second part, I present some new results from \cite{DiBari:2025zlv}, where the impact of flavour coupling on $SO(10)$-inspired leptogenesis has been studied in detail.

Neutrino oscillation experiments are entering an era of precision, requiring both fast calculations and reliable uncertainty estimates. We present a compact three-flavor oscillation calculator for constant-density matter, built on analytic perturbative formulas and validated against established series expansions. Using the NuFIT 6.0 global-fit covariance matrix, the tool incorporates up-to-date parameter values and correlations. It accurately computes appearance and disappearance probabilities over 0.3-5 GeV at a 295 km baseline, offering two computation modes: exact Hamiltonian diagonalization for high-fidelity results, and a faster perturbative approximation that runs roughly 27x quicker. A hybrid scheme handles the MSW resonance region, combining speed with accuracy. Uncertainties can be propagated via Monte Carlo sampling or a fast linearized approach, producing reliable confidence bands. The implementation preserves unitarity, reproduces vacuum and resonance limits, and captures high-energy suppression effects. This calculator provides a fast, reliable framework for parameter scans, phenomenological studies, and sensitivity estimates for current and future long-baseline experiments like Hyper-Kamiokande and DUNE.

The main aim of this thesis is to reveal some interesting aspects of the purely affine theory of gravity and its cosmological implication. A particular attention will be devoted to its consequences when applied to cosmological inflation. Primarily, affine spacetime, composed of geodesics with no notion of length and angle, accommodates gravity but not matter. The thesis study is expected to reveal salient properties of matter dynamics in affine spacetime and may reveal an intimate connection between vacuum state and metrical gravity. An interesting application of the framework is the inflationary regime, where it is shown that affine gravity prefers only a unique metric tensor such that the transition from nonminimal to minimal coupling of the inflaton is performed only via redefinition of the latter. This allows us to avoid the use of the so called conformal frames. In fact, unlike metric gravity, the metric tensor in affine gravity is generated and not postulated a priori, thus this tensor is absent in the actions and conformal transformation does not make sense. Last but not least, we try to show how metric gravity can be induced through a simple structure that contains only affine connection and scalar fields. General relativity arises classically only at the vacuum, and this view of gravity may be considered as a new way to inducing metric elasticity of space, not through quantum corrections as in standard induced gravity, but only classically. The thesis is concluded by analyzing affine gravity in a particular higher-dimensional manifold (product of two spaces) in an attempt to understand both, the cosmological constant and matter dynamically.

This paper initiates the systematic study of thermal field theory for generic equilibrium density matrices, which feature arbitrary values not only of temperature and chemical potentials, but also of average angular momentum. The focus here is on scalar fields, although some results also apply to fields with arbitrary spins. A general technique to compute ensemble averages is provided. Moreover, path-integral methods are developed to study thermal Green's functions (with an arbitrary number of points) in generic theories, which cover both the real-time and imaginary-time formalism. It is shown that, while the average angular momentum, like the chemical potentials, does not contribute positively to the Euclidean action, its negative contributions can be compensated by some other contributions that are instead positive, at least in some cases, e.g. when the chemical potentials vanish. As an application of the developed general formalism, it is shown that the production of particles weakly coupled to a rotating plasma can be significantly enhanced compared to the non-rotating case. The Higgs boson production through a portal coupling to a dark sector in the early universe is studied in some detail. The findings of this paper can also be useful, for example, to investigate the physics of rotating stars, ordinary and primordial black holes and more exotic compact objects.

The discovery of massive, high redshift galaxies with the James Webb Space Telescope (JWST) has been argued to challenge $\Lambda$CDM (cold dark matter): such systems would require extremely rare halos and baryon-to-stellar-mass conversion efficiencies unphysically approaching -- or exceeding -- $100\%$. If confirmed at galaxy-formation--forbidden efficiencies, these galaxies could signal new physics beyond standard cosmological structure formation. We develop a galaxy model framework that ties the linear power spectrum to the inferred efficiencies of galaxy growth while incorporating multiple sources of uncertainties in order to test the structure formation models. The sources of error include (i) observational sample variance, (ii) asymmetric scatter induced by the steepness of the high-mass halo tail, and (iii) systematic uncertainties in stellar mass estimates. We find that the inferred star-formation efficiency is largely controlled by systematic uncertainties in the stellar mass estimates derived from spectral energy distribution modeling of JWST-detected galaxies. Because of the inherent Eddington-like bias, systematic uncertainties amplify the asymmetry of the scatter, in some cases by orders of magnitude, thereby bringing the inferred efficiencies into closer agreement with expectations from early galaxy formation models. We also present how these uncertainties can be applied to the inferred UV luminosity function. Our framework can be used to test $\Lambda$CDM as errors are reduced and further detections are made.

We classify the non-Abelian anomaly of the Euclidean conformal group $SO(2n+1,1)$ in $2n$ dimensions via Stora-Zumino descent from its Euler invariant polynomial in $2n+2$ dimensions. In this way, we place the conformal anomaly on the same footing as ordinary perturbative 't Hooft anomalies. We also explore the relation of the non-Abelian anomaly to the known \textit{type-A Weyl anomaly}, which involves projecting into a Weyl cocycle. We discuss implications for anomaly inflow, and 't Hooft anomaly matching for the full conformal group with a Wess-Zumino-Witten term. In 4d, this enables the construction of a dilaton effective action matching the full non-Abelian $SO(5,1)$ conformal anomaly.

The effective potential for a scalar theory with $\lambda\phi^4$ interaction, coupled to a massless fermion through Yukawa interaction is calculated by summing over infinite number of two particle irreducible (2PI) diagrams of two different types and a 2PI diagram of a third type using Cornwall, Jackiw and Tomboulis (CJT) method. There is an inversion symmetry present in the effective potential under $\phi\rightarrow -\phi$. When the value of coupling constant falls beyond an open set of positive real numbers, the effective potential exhibits both maxima and minima above and below the zero potential line respectively on either side of its minimum at $\phi=0$. The fermion acquires a mass in this region of coupling constant when the system settles into the minimum at positive, non-zero $\phi$ breaking the inversion symmetry of the vacuum. However, the effective potential exhibits a minimum only at $\phi=0$ and also the fermion remains massless when the coupling constant assumes any value from this open set.

We prove that off-shell massless scalar three-point Feynman integrals are self-dual under Fourier transformation. This implies that a momentum space integral can be expressed as the position space integral of the same Feynman graph with transformed edge-weights (not the dual graph) if external vertices are labeled accordingly. In particular, any off-shell massless scalar three-point Feynman integral can be expressed as a graphical function. The result follows immediately from a theorem by M. Golz, E. Panzer and the author on parametric representations of position space integrals (2015), but it was only observed by X. Jiang in 2025 in the context of four-dimensional $\mathcal{N}=4$ Super-Yang-Mills theory. We generalize Jiang's result and discuss the consequences of the self-duality in the context of graphical functions. In particular, we derive a new identity for graphical functions and a new twist relation for scalar integrals (Feynman periods) in $\phi^4$ theory.

We analyze various gravity theories involving de-Sitter, quadratic $\mathcal{R}^2$ and non-minimally coupled scalar in the light of application of the Dyson-Schwinger technique involving exact background solution of the Green's function. We denote specific set of solutions for the metric to move towards a quantum analysis of the theory. This kind of solutions is identified as conformally flat metric. Such a conclusion naturally arises in the use of the Dyson-Schwinger equations in the study of the Yang-Mills theory through the mapping theorem. We show a sequence of cosmological phase transitions starting from the breaking of such conformal invariance that can be hindered by the presence of the non-minimal coupling.

We study the linear cosmological evolution of inelastic self-interacting dark matter in a two-component dark sector with a small mass splitting, assuming thermal initial conditions for the two species. We derive the coupled background and perturbation equations for inelastic conversion between the two species, considering both power-law and low-velocity saturation cross sections. Exothermic conversion injects kinetic energy into the light component, generating pressure support that suppresses small-scale structure and produces dark acoustic oscillations in the matter power spectrum. The resulting cutoff at scale $k > 1\,h\,\mathrm{Mpc}^{-1}$ depends on the normalization and velocity dependence of the cross section, the dark matter mass and the mass splitting. Using linear power spectra computed with a modified Boltzmann solver, we apply recast constraints from Lyman-$\alpha$ forest data and high-redshift UV luminosity functions, finding non-monotonic but closed exclusion regions driven by the competition between efficient conversion and rapid depletion of the heavy component. These results show that the internal thermodynamics of a secluded multi-component dark sector can leave observable imprints on structure formation, providing a complementary probe of secluded dark matter.

Pohl et al. measured the energy difference between the 2P and 2S states of muonic hydrogen and used it to determine a precise value of the proton radius. The result disagreed significantly from values extracted from electronic hydrogen and elastic electron-proton scattering. This discrepancy was exciting because it indicated a breakdown of Coulomb's law. In more technical terms, the discrepancy indicated that a fundamental property of the Standard Model, known as lepton universality, could be violated. This chapter explains the origins, meaning and significance of the puzzle. A resolution, based on very recent experiments, is stated. The proton radius puzzle is no more.