Multipartite entanglement is a uniquely quantum form of correlation that captures collective properties of a composite quantum state beyond those encoded in its bipartite subsystems. We investigate this phenomenon in the process $e^+e^-\to t\bar tZ$ at a future lepton collider, where the final state spins span the tripartite Hilbert space $\mathscr{H}=\mathbb{C}^{2}\otimes\mathbb{C}^{2}\otimes\mathbb{C}^{3}$. Starting from the Standard Model helicity amplitudes, we reconstruct the full $12\times 12$ spin density matrix and characterise its entanglement structure through one-to-one negativities, one-to-other negativities, and the genuine multipartite negativity, evaluated at three increasingly inclusive levels of phase space integration. Pairwise entanglement is generally suppressed relative to the collective (one-to-other) and the genuine multipartite entanglement, and all measures decrease as more kinematic information is integrated out. Assuming quantum tomography in the fully leptonic decay channel at $\sqrt{s}=1$ TeV, we find that the collective entanglement is accessible at a realistic high-luminosity polarised lepton collider, while a direct observation of genuine multipartite entanglement is challenging and would benefit from further optimisation of the event analysis and observable choice. The study establishes $e^+e^-\to t\bar tZ$ as an attractive laboratory for probing multipartite entanglement in high-energy collisions and provides a general mixed state framework that applies to any tripartite spin system.

We contribute to the systematic analysis of New Physics effects in neutrino experiments using Effective Field Theory (EFT) methods. We review and extend the quantum field-theoretical formalism for generic neutrino interactions, discussing the inclusion of matter effects and deriving the connection with the density matrix formalism. On the phenomenological side, we apply this framework for the first time to medium-baseline reactor neutrino experiments. We derive analytical expressions for the relevant oscillation observables and perform a first EFT analysis of the recent JUNO dataset, extracting bounds on the leading non-standard interaction parameters.

This work proposes a new terrestrial probe for millicharged particles (mCPs) and demonstrates promising discovery prospects. mCPs can be copiously produced in core-collapse supernovae (SNe), and a fraction may escape, travel to Earth and yield distinct signals. The mCP mass induces a time-of-flight (ToF) delay relative to the SN neutrino burst, opening a clean search window after the neutrino signal has passed. We compute the mCP-induced electron-recoil signals at XENONnT, JUNO, DUNE, and Hyper-Kamiokande for benchmark SN scenarios, and find that for $\varepsilon = 10^{-9}$ and sub-MeV to MeV-scale masses, more than 10 events per year can be detected. This search can improve upon existing SN cooling bound on $\varepsilon$ by up to an order of magnitude.

The \texttt{T4-2-i} topology provides a one-loop realization of Majorana neutrino mass and may be viewed as a radiative extension of the type-II seesaw, with a scalar triplet, two inert scalar doublets, and singlet fermions propagating in the loop. A central difficulty in realizing this topology lies in the simultaneous presence of tree-level type-I and type-II seesaw contributions arising from the same particle content. In addition, the stability of the dark-matter candidate typically requires the introduction of an ad hoc discrete symmetry. In this work, we revisit the \texttt{T4-2-i} topology within a non-holomorphic modular-invariant framework based on the double-cover group $T'$. The presence of both even- and odd-weight polyharmonic Maaß forms considerably enlarges the space of allowed modular structures, while the residual $\mathbb{Z}_2$ symmetry associated with the vicinity of the fixed point $\tau=i$ naturally stabilizes the lightest odd state. The modular assignments forbid the dangerous tree-level contributions, determine the flavor structure of the lepton sector, and allow both fermionic and scalar dark-matter candidates. We confront the model with neutrino-oscillation data, charged-lepton-flavor-violating bounds, electroweak precision observables, the Higgs diphoton signal strength, the observed dark-matter relic abundance, the cosmological bound on the sum of neutrino masses, and direct-detection this http URL on the fermionic dark-matter candidate, in which the lightest odd state is the Majorana fermion $N_1$, we find that both normal and inverted neutrino mass orderings remain viable. In the allowed region, the relic abundance is largely controlled by coannihilation with the inert scalar partners, while the spin-independent direct-detection rate remains naturally suppressed because it arises only through a loop-generated Higgs portal.

We demonstrate that treating Earth matter effects via a constant-density approximation introduces a fundamental systematic error in long-baseline neutrino oscillation analyses. Using exact numerical propagation through realistic PREM profiles, we show that matter-profile mismodeling does not merely affect the $\nu_{\mu}\rightarrow\nu_{e}$ appearance probability, but generates correlated biases across the $\nu_{\mu}\rightarrow\nu_{\tau}$ and $\nu_{\mu}\rightarrow\nu_{\mu}$ channels as dictated by PMNS unitarity. Our stochastic analysis reveals that the $\nu_{\mu}\rightarrow\nu_{\tau}$ channel is the most volatile carrier of the geophysical systematic. Across varying correlation lengths at baselines like $5000$ km and $7000$ km, the $\tau$-appearance channel consistently carries a larger mean bias and variance than the standard $\nu_{\mu}\rightarrow\nu_{e}$ appearance channel. These findings demonstrate that spatially resolved density treatments are a mathematical necessity for the analysis frameworks of future precision neutrino facilities.

We investigate a predictive and testable framework in which dark matter (DM), heavy-neutrino dynamics, and the BAU originate from correlated interactions within a local $U(1)_{B-L}$ extension of the SM. Unlike conventional $B-L$ constructions based on the type-I seesaw, we employ an inverse-seesaw mechanism realized through a sterile fermion $S_{1}$ and a complex scalar field $\phi$, whose vacuum expectation value simultaneously generates the masses of the heavy neutrinos $N_{1,2}$ and the Majorana DM fermion $\chi$ via Yukawa couplings. The small lepton-number-violating parameter induced by a higher-dimensional operator leads to naturally light active neutrinos together with TeV-scale heavy neutrinos and sizable active-sterile mixing, yielding distinctive collider signatures unavailable in minimal $B-L$ models. The relic abundance of $\chi$ is governed by annihilation channels mediated by the same scalar and gauge interactions, producing a direct and model-specific correlation between successful leptogenesis and the observed DM relic density. A combined parameter-space analysis incorporating neutrino oscillation data, lepton-flavor-violating processes, direct-detection limits, and collider bounds on $N_{1,2}$ and $Z^\prime$ reveals a narrow yet robust region consistent with all these constraints. Representative benchmark points in this region are examined at a future multi-TeV muon collider. Heavy-neutrino production through electroweak processes yields striking signatures in the dilepton plus missing energy ($2\ell + E\!\!\!/_T$) and single-lepton plus di-jet plus missing energy ($1\ell + 2j + E\!\!\!/_T$) final states. These channels demonstrate that next-generation muon colliders offer a powerful and complementary probe of the inverse-seesaw origin of neutrino masses, the DM relic density, and the TeV-scale leptogenesis within such an extended $U(1)_{B-L}$ framework.

We investigate whether a minimal $\mathbb{Z}_4$-symmetric fermion-scalar extension of the Standard Model can simultaneously realise viable dark matter, a strong electroweak phase transition, and a stochastic gravitational-wave signal. The model contains a real scalar singlet and a Dirac fermion, allowing thermal two-component dark matter, mixed WIMP-FIMP histories, and an effectively fermionic relic abundance generated by scalar decays. We impose theoretical consistency, the correct electroweak vacuum, and dark-matter constraints from relic density, direct detection, and invisible Higgs decays before using the surviving points as input for the finite-temperature analysis. This reveals that the compatibility between dark matter and a strong first-order electroweak phase transition is highly selective. After current dark-matter constraints are imposed, the strong-transition criterion along the Higgs direction is satisfied only in two viable regimes: the thermal two-component case with $M_\psi<M_S<2M_\psi$ and the decay-driven WIMP-FIMP case with $M_S>2M_\psi$. By contrast, the thermal regime with $M_S<M_\psi$ and the stable mixed WIMP-FIMP scenario with $M_S<2M_\psi$ are largely concentrated at small portal couplings or near the Higgs-resonance region, and do not yield a strong transition in the parameter space considered. The successful transitions typically proceed through an intermediate singlet-like phase. For representative nucleating benchmark points in the viable strong-transition regions, we compute the gravitational-wave spectra from sound waves and turbulence. Some spectra enter the projected reach of future space-based interferometers, showing that detectable signals arise only in selected dark-matter-compatible regions where a sufficiently active Higgs portal appears in correlated combination with the scalar mass and the remaining dark sector parameters.

We explicitly compute the axial anomaly in dense matter and show that its form remains unchanged from that in vacuum, even in the massless limit. This result follows from a subtle cancellation in the anomalous Ward identity between the medium-induced contributions to the divergence of the axial current and to the pseudoscalar density. We then revisit the chiral magnetic effect in a fermionic medium coupled to an axial chemical potential under an external magnetic field. We show that the medium supports a persistent, conserved anomalous current carried by fermions. The current is determined by the axial chemical potential and suppressed by the Fermi velocity, in agreement with anomalous axial-current correlation functions. We finally discuss applications to axion physics, where axion dark matter acts as an effective axial chemical potential.

Motivated by the observed $KD^{(*)}$ molecular candidates $D_{s0}(2317)$ and $D_{s1}(2460)$, their bottom--strange counterparts, $K\bar{B}^{(*)}$ molecular states, are naturally expected, although not yet experimentally established. This discrepancy may reflect sizable heavy-quark flavor symmetry breaking, which introduces significant model uncertainties. Current studies of heavy-quark flavor symmetry breaking effects still exhibit strong parameter dependence, and further experimental input is required to constrain these effects, in particular regarding possible additional $K^{(*)}D^{(*)}$ and $K^{(*)}\bar{B}^{(*)}$ molecular states. In this work, we examine whether additional $K^{*}D^{(*)}$ molecular states can be identified among the observed $D_s$ resonances. Within the Gaussian expansion method, we solve the Schrödinger equation using $\sigma$, $\rho$, $\omega$, $\pi$, and $\eta$ exchange potentials, systematically including $S$-wave and higher partial waves. We find that $D_{s1}(2700)$ can be interpreted as a pure $P$-wave $DK^{*}$ molecule, while $D_{s1}(2860)$ and $D_{s3}(2860)$ are well described as $D^{*}K^{*}$ molecular states dominated by the $^{1}P_{1}$ and $^{5}P_{3}$ components, respectively. We also predict additional molecular states with various $J^{P}$ quantum numbers. These results provide a new description of the charmed--strange spectrum and a useful benchmark for heavy-quark flavor symmetry breaking effects.

The behavior of higher-order radiative corrections due to initial state radiation in processes of electron-positron annihilation is analyzed. Numerical results for energies of future colliders are presented. Uncertainties of the known results on these corrections are estimated. A modified scheme for simultaneous exponentiation of pure photonic and non-singlet pair corrections is presented. Matching of the exponentiated results with the existing analytic higher-order calculations is constructed. A new DIS-like subtraction scheme is discussed.

We investigate $J/\psi$ photoproduction off the proton, $\gamma p \to J/\psi p$, to elucidate the nonexistence of hidden-charm pentaquark signals reported by the GlueX and CLAS12 experiments. Within a coupled-channel rescattering mechanism, we employ the transition amplitudes from a previous coupled-channel analysis that dynamically generates the $P_{c\bar{c}}$ states. The kernel amplitudes for the transition to the $J/\psi N$ channel include both $t$-channel heavy-meson exchange and $u$-channel heavy-baryon exchange. We find that the rescattering contributions from the $\bar{D}^{(*)}\Sigma_c$ channels -- indispensable for the formation of the $P_{c\bar{c}}$ resonances -- are about one order of magnitude smaller than those from $\bar{D}^{(*)}\Lambda_c$, since $g_{\bar{D}^{(*)}N\Sigma_c}$ is roughly five times smaller than $g_{\bar{D}^{(*)}N\Lambda_c}$. Since the $P_{c\bar{c}}$ resonances couple to the $J/\psi N$ channel predominantly through the $\bar{D}^{(*)}\Sigma_c$ intermediate states, their suppression prevents the pentaquark signal from appearing in photoproduction. With only a single parameter controlling the overall normalization, the present work describes the GlueX and CLAS12 cross sections well. These results suggest that the null result from photoproduction need not be in conflict with the pentaquark signals observed by the LHCb Collaboration.

We study the non-leptonic weak decays of doubly charmed baryons (${\cal B}_{cc}$) into singly charmed baryons (${\cal B}_c$) and vector mesons ($V$), denoted as ${\cal B}_{cc}\to{\cal B}_{c}V$. The short-distance contributions are calculated within the naive factorization hypothesis, while the long-distance final-state interaction effects are modeled via hadronic triangle diagrams. Unlike previous approaches, which compute only the imaginary part using the Cutkosky cutting rule, we evaluate the complete loop integrals to obtain both the real and imaginary parts of the amplitudes. These provide the nontrivial strong phases essential for CP violation. The model parameters are determined using experimental data. With this improved calculation method, we predict the branching ratios and decay asymmetry parameters for various decay channels, as well as $CP$ violations for short-distance dominated and singly Cabibbo-suppressed channels. This strengthens our theoretical framework for future study of doubly charmed baryons. Certain decays, primarily driven by long-distance effects, have been calculated; their observation in future experiments could help clarify the role of final-state interactions in charm baryon decays. Therefore, our calculation of ${\cal B}_{cc}\to{\cal B}_{c}V$ provides crucial predictions for branching ratios, decay asymmetry parameters, and $CP$ violation, which are essential for guiding experimental study at LHCb.

We present femtoscopy as a new way to search for saturated gluonic matter in inclusive photonuclear processes, such as inclusive ultraperipheral collisions at the Large Hadron Collider (LHC) and the inclusive photonuclear reactions at the Electron-Ion Collider (EIC). As the femtoscopic approaches are sensitive to the space-time structure of the particle emitting source, they are ideal in providing insights also about the initial stage of the collision, where the gluon distributions may impact the effective size of the dipole the quasireal photons oscillate into. This technique demonstrates its capabilities in isolating nuclear shadowing and gluon saturation effects. Finally, we show how a femtoscopic approach is highly sensitive to sub-fermi scale structures typically observed in ultraperipheral collisions, such as gluonic hot spots.

We revisited the singlet fermionic dark matter model in this work, where a Majorana fermion $\chi$ carrying $Z_4$ charge is assumed as the DM candidate. A new singlet scalar $S_0$ with a non-zero vacuum expectation value is also introduced to the SM so that $\chi$ can obtain mass after spontaneous symmetry breaking. We focus on the secluded DM region for the model, where interactions between DM and SM particles can be negligible. We have a new Higgs $h_2$ in the model, and the mixing angle of $h_2$ with the SM Higgs will play an important role in determining DM production, depending on the mass hierarchy between the new Higgs mass and the DM mass. We study DM relic density as a function of the model's four free parameters and estimate the viable parameter space under DM relic density constraint as well as direct detection constraint. We focus on the heavy DM mass region, and our analysis indicates that the mixing angle does not necessarily need to be very small in the secluded dark matter scenario, which offers potential for probing such models in future collider experiments.

One of the most important neutrino interactions is the Inverse Beta Decay (IBD). However, the IBD events typically carry no directional information in water Cherenkov detectors as the positron directions are mostly isotropic at low energies, such as those in supernova studies. As Gadolinium is being added to Super-Kamiokande, the improved neutron capture efficiency not only allows better background rejection, but the neutron capture information could potentially provide additional information that allows better event reconstruction. Due to neutron diffusion in water, event-by-event reconstruction is difficult. However, if the final neutron capture position is correlated with the initial neutrino momentum, it may be possible that neutrino directionality could be reconstructed statistically, with or without using the positron information. In this work, we use Geant4 to simulate neutron propagation in water. We show that in a wide range of neutrino energies from about 10 MeV to several hundred MeV, neutron capture information could statistically enhance the neutrino directionality, compared to positron-only inference, even with neutron diffusion considered. However, practical application of this technique depends crucially on detection effects, especially the vertex reconstruction resolutions. Our work therefore motivates developments of better reconstruction algorithms and techniques, as well as detector upgrades.

We use effective field theory to factorize production matrix elements that appear in the NRQCD framework for quarkonium cross sections. By applying a Hubbard-Stratonovich transformation and appropriate field redefinitions, we show that the soft and ultrasoft sectors of NRQCD can be decoupled from the heavy quark and antiquark fields in a hybrid vNRQCD/pNRQCD Lagrangian at leading order in the velocity power-counting. This enables us to re-factorize quarkonium production matrix elements in terms of matrix elements of color-singlet composite fields, which we can write as the wave-function at the origin, and state independent vacuum correlators of chromo-electric and chromo-magnetic gluon fields. This approach verifies powerful relationships between the LDMEs of different S-wave quarkonia originally derived using pNRQCD. Additionally, it allows us to derive new relationships for the production matrix elements used in the transverse momentum dependent factorization (TMD) framework, known as TMD soft transition functions, providing a much stronger set of constraints on these nonperturbative operators. This work significantly advances our understanding of quarkonium production, particularly in the TMD framework.

We develop a general framework for matching KSVZ-like ultraviolet completions featuring vector-like fermions and a spontaneously broken $\mathrm{U}(1)_{\mathrm{PQ}}$ symmetry onto the Standard Model Effective Field Theory and the low-energy axion-like particle effective theory. The framework applies to arbitrary vector-like fermion representations and PQ-charge assignments, and systematically captures the effective interactions generated in both sectors. We then perform a comprehensive phenomenological analysis of the resulting SMEFT operators, based on global fits to electroweak precision, Higgs, and flavor observables, obtaining robust bounds on the corresponding Wilson coefficients that are largely independent of the details of the ultraviolet realization. These constraints can subsequently be translated into the QCD axion and ALP parameter space, providing indirect probes of ALP couplings. We further investigate several representative examples of the interplay between the SMEFT and ALP sectors, illustrating how direct ALP searches and indirect precision and flavor observables provide complementary information on the same underlying dynamics. We find that, over large regions of parameter space, indirect constraints derived from the SMEFT analysis dominate over direct ALP probes, except in scenarios where the PQ-charge assignment permits mass mixing with Standard Model fermions. Overall, our results establish a unified framework for connecting ultraviolet completions, SMEFT analyses, and ALP searches, enabling both the interpretation of existing constraints and the exploration of future signals within a common theoretical setting.

In the Born-Oppenheimer approximation for QCD, the exotic hidden-charm tetraquark meson $\chi_{c1}(3872)$ is a near-threshold bound state in Born-Oppenheimer potentials associated with an isospin-0 adjoint meson. The $\chi_{c1}(3872)$ is the $1^{++}$ member of a heavy-quark spin-symmetry multiplet whose other members have $J^{PC}$ quantum numbers $0^{++}$, $1^{+-}$, and $2^{++}$. We introduce a simple model for the Born-Oppenheimer potentials that interpolates between the adjoint-meson potential at short distances and the triplet-meson-pair potential at large distances. We take into account the spin splittings of charm mesons nonperturbatively for the first time by solving the diabatic Schrödinger equation. We also take into account the spin splittings of the adjoint meson as well as a narrow avoided crossing with the quarkonium potential. We tune the energy of $\chi_{c1}(3872)$ to the $D^* \bar{D}$ threshold and then calculate the spin splittings of the other members of the multiplet and their decay widths into charm-meson pairs. We also calculate the energies and decay widths of the corresponding multiplet of hidden-bottom tetraquarks. These calculations provide a template for the quantitative analysis of all hidden-heavy hadrons using the Born-Oppenheimer approximation for QCD.

We study the next-to-leading order electroweak corrections to $e^+e^- \rightarrow W^+W^-$ from dimension-six two-fermion top-quark operators in the Standard Model Effective Field Theory. We compute analytical and numerical results for future electron-positron colliders, focusing on the proposed LEP3 and FCC-ee that will operate at centre-of-mass energies below the $t \bar{t}$ production threshold. We compare the indirect sensitivity arising from virtual corrections to $WW$ production to that from $ZH$ production, and to the current constraints from LEP and LHC data. We show that NLO corrections can provide competitive sensitivity to these operators. This work represents a first step towards the systematic computation of electroweak corrections to $W$-pair production at lepton colliders in the SMEFT, whose impact can then be properly assessed in global analyses.

We critically examine the expectation that in a fundamental quantum field theory, dimensionless couplings in the Lagrangian density should all be of order unity. We propose a measure to quantify the adherence of a theory to this: the spread (the ratio of the largest to the smallest of the magnitudes) of such dimensionless couplings, obtaining various closed-form results. If we take independent identically distributed (IID) couplings to parameterise our uncertainty on the values of the order unity couplings, ratios of couplings can be much larger than one might naively expect. For a theory with 20 IID unit normal couplings, the probability that the magnitude of the ratio of two of them is greater than 100 is 0.29, for example. Even when the IID couplings have exponentially suppressed tails, the distribution of ratios of order one couplings has fat power-law tails which grow with the number of independent couplings.

Neutrino evolution in dense astrophysical environments is typically described either within a quantum kinetic framework, which neglects the build-up of multi-body correlations, or through simplified many-body calculations that allow significant entanglement to develop. In this work, we compare these two approaches in a simple neutrino-gas configuration, with particular emphasis on the role of non-forward scattering processes. These effects are incorporated either through a collision term in the kinetic description, or by considering the full neutrino-neutrino many-body Hamiltonian. We highlight differences between the two descriptions in both their characteristic timescales and asymptotic behavior. Motivated by the natural suitability of quantum computing for many-body calculations, we further investigate the non-classicality of neutrino evolution, discussing Trotter error scaling, along with the associated costs of constructing quantum circuits in terms of entangling gates and non-Clifford gates. We find that the resources needed for neutrino many-body evolution are on the low end of typical high-energy physics problems and on the mid to high end with respect to quantum chemistry problems. For the full Hamiltonian, resource requirements increase relative to the truncated version. We emphasize the importance of efficient fermion-to-qubit encodings, which are essential for reducing the substantial computational resources required for such simulations.

Recent results from the DAMIC-M and PandaX collaborations have excluded the standard freeze-in production of dark matter for masses in the range $3~\mathrm{MeV} \lesssim m_\chi \lesssim 1~\mathrm{GeV}$ in the context of extensions of the Standard Model featuring an additional ultra-light $U(1)_{\rm X}$ gauge boson. In this work, we analyze the constraints induced by DAMIC-M and PandaX results on the reheating temperature in freeze-in models at stronger coupling, or when a non-thermal source (such as inflaton decay) comes into play. We identify viable scenarios in which the DM relic abundance is correctly reproduced while evading current experimental bounds on the electron-scattering cross section, $\overline{\sigma}_\mathrm{e}$. In particular, we show that for reheating temperatures below the electroweak scale, Boltzmann suppressed production can be compensated by stronger couplings, bringing freeze-in scenarios within present experimental reach. Finally, we study a hybrid scenario in which a small branching ratio of inflaton decay seeds a nonzero initial dark-matter abundance. We show that such contributions can significantly modify freeze-in predictions across broad regions of parameter space, offering an additional pathway for probing extremely feeble interactions.

Recent high-resolution imaging observations of strong lens systems reveal dense low-mass perturbers. We propose a soliton core, whose central density is boosted by a supermassive black hole (SMBH), in the fuzzy dark matter (FDM) model as an efficient perturber in strong gravitational lensing. The higher central density makes it less efficient in the tidal mass loss, and leads to the higher impact in gravitational lensing. We show that the mass profile of a $\sim 10^6M_\odot$ perturber in JVAS B1938+666, which does not resemble any known astronomical object, can be well explained by a soliton core in the FDM model with the mass of $4\times 10^{-21}$eV hosting an SMBH with the mass of $4\times 10^5M_\odot$. The high mass of the SMBH may be explained by several scenarios that predict heavy SMBH seeds such as the direct collapse black hole formation and primordial black holes.

Motivated in part by anomaly cancellation for integral charge spectra in chiral gauge theory, we study the symmetric locus in the ideal degree-three Prouhet-Tarry-Escott problem. A symmetric integer solution is one whose entries are paired about a common center $c\in \frac12\mathbb Z$. This symmetry reduces the problem to a sum-of-two-squares equation, $x^2+y^2=u^2+v^2$, in integer variables, subject to the appropriate parity conditions. Thus the problem is governed by representations as sums of two squares. For the full symmetric locus, let $N_{\mathrm{sym}}(H)$ denote the number of nontrivial symmetric integer solutions of height at most $H$, counted with unordered multiset conventions and summed over the admissible centers. Then \begin{align*} N_{\mathrm{sym}}(H) = \frac{4\log 2}{3\pi^2}H^3\log H+O(H^3). \end{align*} The logarithmic enhancement comes from the second moment of the sum-of-two-squares representation function. In particular, the symmetric locus is larger than one would expect from the naive $H^3$ degree-weighted box-counting scale alone. This asymptotic identifies a large arithmetically structured subfamily of the ideal degree-three solution space, and suggests that paired anomaly-free integral charge spectra reflect a fundamental number-theoretic structure.

We introduce SPADE (SPlit And Delay Embeddings), an autoregressive transformer for sequences whose tokens carry multiple features. Rather than embedding these features jointly, SPADE embeds them independently. Delaying each feature stream relative to the previous one allows intra-token correlations to be learned by the standard self-attention mechanism. Applied to point-cloud calorimeter shower generation in the highly granular ILD detector, SPADE is competitive with the state of the art AllShowers model on photon showers, and substantially outperforms its VQ-VAE-based predecessor OmniJet-$\alpha_C$. The mechanism is applicable to any generative task with multi-feature tokens, enabling LLM-style pretraining workflows for higher-dimensional data.

Although measurements of the Cosmic Microwave Background (CMB) are consistent with a nearly scale-invariant primordial spectrum of adiabatic perturbations, in which the energy densities of different components (radiation, baryons, and dark matter) fluctuate proportionally, there could also exist isocurvature perturbations, in which density fluctuations of the individual components differ from the adiabatic mode. Cold dark matter isocurvature (CDI) perturbations with a variety of spectral tilts generated in pre-inflationary axion models provide one such example. In this article, we present the most updated constraints on these axion CDI perturbations using the latest CMB anisotropy measurements from Planck, the Atacama Cosmology Telescope (ACT), and the South Pole Telescope (SPT). We study both fixed spectral indices with values ranging from red- to blue-tilted spectra as well as the case with a free index. We find that the constraint on the spectral index gets moderately improved with the combined datasets compared to Planck alone, while the bounds on the isocurvature amplitudes for the fixed spectral indices we consider do not get tighter. We also discuss the theoretical implications of our constraints, in particular for models giving rise to blue-tilted spectra.

These lecture notes are intended as a coherent introduction to conformal field theory in general, and composite operators in particular, through a semiclassical framework for computing scaling dimensions, with emphasis on operators of the form $\phi^n$. In doing so, they aim to fill a gap in the literature and to help decode some of the relevant concepts. The physical idea is that at large $n$ an (heavy) operator creates a highly occupied state. Through the state-operator correspondence, this state lives on the cylinder $\mathbb{R}\times S^{d-1}$, and its scaling dimension is the corresponding energy of the theory on the cylinder. The notes are organized as a self-contained route from conformal symmetry to semiclassical dynamics. Part I reviews the conformal group, primary operators, radial quantization, the state-operator correspondence, and operator mixing. Part II builds the semiclassical framework, first in the free scalar theory, where the dimension of $\phi^n$ is recovered in three independent ways, and then through the double-scaling limit, the action variable, and Bohr-Sommerfeld quantization. Part III develops the general machinery of periodic saddles, Floquet theory, fluctuation determinants, the Gel'fand-Yaglom method, and the Gutzwiller trace formula. Part IV applies the framework to the $O(N)$ $\phi^4$ theory in $d=4-\epsilon$ at the Wilson-Fisher fixed point, deriving the classical elliptic solution, the Lamé fluctuation spectrum, the zero modes, and the one-loop contribution to the large-$n$ scaling dimensions. Beyond the explicit computation, the notes emphasize the role of composite operators as probes of collective sectors of quantum field theory, with extensions to gauge theories, conformal windows, and asymptotically safe field theories.

The Electron-Ion Collider (EIC) will enable a series of measurements at unprecedented energies and luminosities, providing new opportunities to investigate the microscopic structure of nucleons and nuclei at small $x_B$. Exclusive processes such as Deeply Virtual Compton Scattering (DVCS) offer unique access to the three-dimensional structure of hadrons through Generalized Parton Distributions (GPDs), while polarized electron and ion beams further enable detailed studies of spin-dependent structure. A model for coherent DVCS on polarized $^3$Heis developed and applied to simulations of for $9\times166$-GeV $e^3$He collisions at the EIC. Using this framework, the statistical precision achievable is estimated for measurements of beam-spin asymmetries and for the extraction of the Compton Form Factors (CFFs) $\mathcal H_{^3\mathrm{He}}$ and $\tilde{\mathcal H}_{^3\mathrm{He}}$. Early EIC data are found to enable precise differential measurements of the unpolarized CFF $\mathcal H_{^3\mathrm{He}}$ and to provide significant constraints on its real and imaginary components. By contrast, meaningful constraints on the polarized CFF $\tilde{\mathcal H}_{^3\mathrm{He}}$ require substantially larger integrated luminosities. The kinematics of the recoil $^3$He nucleus are also examined, and the far-forward detector capabilities at the EIC required to tag the intact nucleus and perform fully exclusive measurements of coherent nuclear DVCS are discussed.

WIMP scattering from 40Ar is investigated using a self-consistent Skyrme Hartree-Fock-Bogoliubov (HFB) approach. Nuclear form factors relevant to dark matter direct detection are calculated from the resulting one-body density matrix elements and compared with shell-model predictions. Good agreement is found for the spin-independent response, while significant differences are observed for the spin-orbit response due to variations in single-particle occupancies. The effects of particle-number projection are shown to be small for 40Ar. These results demonstrate the sensitivity of certain dark matter response channels to the underlying nuclear structure model and establish a framework for extending mean-field calculations to nuclei beyond the reach of large-scale shell-model studies.

We study the effects of dimension-four and dimension-six nonminimal Higgs couplings to the Ricci scalar $R$ in the $R^2$-Higgs inflation model in light of the recent ACT and SPT observations. We show that the dimension-six operators $|\Phi|^2 R^2$ and $|\Phi|^4 R$ can accommodate the enhanced scalar spectral index $n_s$ preferred by the combined CMB+BAO analyses. Using a doubly covariant formalism, we find that the same region of parameter space that explains the observed value of $n_s$ can also induce rapid preheating through the production of the Goldstone modes. If thermalization proceeds efficiently through this preheating mechanism, it may help match the inflationary scale with the CMB reference scale.