Papers

The early stage of high-energy heavy-ion collisions undergoes transient dynamics, evolving non-perturbatively from a gluon-rich to a chemically equilibrated quark-gluon plasma. We develop an effective hydrodynamic approach that casts the microscopic quark equilibration dynamics as the relaxation evolution of an effective macroscopic bulk viscous pressure. The evolution of this effective bulk viscous pressure captures quark chemical equilibration and the breaking of conformal symmetry, thereby providing a smooth onset of the lattice QCD equation of state after a few fm/$c$ in the hydrodynamic evolution. We investigate phenomenological effects of this macroscopic description on final-state observables in $\mathrm{Pb}+\mathrm{Pb}$, $\mathrm{O}+\mathrm{O}$, and $\mathrm{p}+\mathrm{Pb}$ collisions at the Large Hadron Collider.

In the Minimal Supersymmetric Standard Model with heavy sfermions, a sub-hundred-GeV Bino-like neutralino can thermally achieve the observed dark matter abundance only through $h$- or $Z$-resonant annihilation. Since the couplings governing these resonances simultaneously determine the spin-independent and spin-dependent scattering off nucleons, reproducing the relic density imposes irreducible lower envelopes on the scattering cross sections. We evaluate these bounds including the complete one-loop corrections to these vertices, which enhance the direct-detection rates by up to $50\%$ and $30\%$, respectively, adopt the FLAG-2024 nucleon matrix elements with their most adverse $3\sigma$ shifts, and confront the predictions with a likelihood-based recast of the LZ data. We find that the LZ-2024 results exclude both resonant scenarios at conservative one-sided significances exceeding $5.9\sigma$ and $4.1\sigma$, respectively, irrespective of whether the neutralino constitutes all or only part of the dark matter, and independently of LHC electroweakino searches.

Paying particular attention to the different types of gluons, collinear, soft and Glauber, we argue that, in its standard formulation, the CGC does not contain the collinear sector required for a meaningful comparison with TMD factorization. The CGC Wilson lines usually identified as part of the proton matrix element should instead be interpreted as the equivalent of a soft factor. Restoring the missing collinear exchanges, we obtain a new definition of small-$x$ PDFs from an explicit calculation of the DIS cross section using CGC Feynman rules. The resulting expression can be cast in a form resembling TMD factorization without being equivalent to it. Finally, we discuss the evolution of these small-$x$ PDFs with respect to the rapidity cutoff $\Lambda$ and the Bjorken variable $x_b$.

Mediators coupled predominantly to the electron remain weakly constrained above the kinematic reach of the $B$~factories, a region that is difficult to access at hadron colliders and only partially covered by existing $e^+e^-$ data. We point out that the asymmetric $\mu^+e^-$ mode of the proposed $\mu$TRISTAN collider, operating at $\sqrt{s}=346$~GeV, is well suited to this window, and quantify its reach for two minimal realisations: an axion-like particle and a $Z'$ gauge boson, treated as effective interactions with the electron current. Both are radiated off the electron line and decay to an electron-positron pair, giving a common four-lepton signature whose Standard Model counterpart is under good control. A resonance search in the electron-positron invariant mass, performed for mediator masses between $5.5$ and $300$~GeV, yields projected $95\%$~CL sensitivities to couplings of order $10^{-5}$ at the light end of this range, improving on existing bounds by more than four orders of magnitude for the pseudoscalar and by up to two orders of magnitude for the vector, and providing the only constraint on the heaviest masses considered.

We investigate short-range correlation (SRC) scaling of nuclear gluon modifications using nCTEQ SRC abundances and EPPS21 gluon distributions. Rescaling the EPPS21 central modifications by these abundances yields an approximately common curve for six nuclei from carbon to lead over $0.1\leq x\leq0.4$ at $Q^2=10$ and $100\,\mathrm{GeV}^2$. The SRC interpretation is supported by the broad agreement between the fitted abundances and high-momentum proton fractions from variational Monte Carlo calculations. Using an SRC proton fraction of approximately $20\%$ in carbon, the measured EMC-SRC correlation also gives a pure-SRC EMC slope of $1.94\pm0.12$, consistent with the nCTEQ estimate $2.02\pm0.20$. To test the connection between this scaling and SRC configurations, we propose recoil-tagged charm-production in deuteron deep-inelastic scattering (DIS), combining a backward high-momentum proton tag with a gluon-sensitive hard process. We formulate leading-power collinear factorization through an extended fracture function, which reduces within the plane-wave impulse approximation to a deuteron light-front spectral factor times a recoil-conditioned neutron gluon distribution. The tagged charm reduced cross section and its ratio to inclusive tagged DIS provide complementary observables for comparing gluon modifications in SRC-enriched configurations with the scaling inferred from inclusive nPDFs.

We study the mixing between a generic axion-like particle (ALP) and the light pseudoscalar mesons within chiral perturbation theory ($\chi$PT), and its consequences for low-energy scattering and decay processes. Starting from the most general ALP effective Lagrangian, we derive the ALP-meson kinetic and mass mixing induced at leading order in the ALP decay constant and isospin breaking for arbitrary ALP masses. As a result, we obtain the physical ALP mass to $\mathcal{O}(F^2/f_a^2)$, recovering the QCD-axion limit and finding that any ALP with a vanishing bare mass shares the QCD-axion mass. We provide a compact parameterization of every four-body amplitude involving pseudoscalar mesons and an arbitrary number of ALPs. As an illustration, we show the $K\bar{K}\to P^0a$ scattering. The framework applies for general ALP masses and couplings and consistently incorporates isospin breaking, essential for otherwise forbidden processes.

We study the pole mass for a heavy quark probe in the Gross–Neveu model, at the first non-trivial order in the $1/N$ expansion. We show that this mass suffers from a perturbative renormalon ambiguity structurally similar to the one in QCD. The exact large $N$ solution leads however to an explicit expression for the pole mass which can be decoded as a trans-series, and we find that non-perturbative corrections cure the renormalon ambiguity. We also calculate the self-energy of the heavy quark beyond perturbation theory by using the OPE method with condensates, and show that the results are in agreement with the large $N$ solution. The non-perturbative corrections to the pole mass turn out to be determined to a large extent by the condensate corrections to the self-energy. However, there is a class of corrections that has to be reorganized due to on-shell effects and cannot be obtained from the conventional condensate expansion. We discuss possible implications of this toy model for QCD.

Motivated by the recent HAL QCD lattice results on the $D$ - $D^*$ potential at nearly physical point $m_\pi=146.4$ MeV, we theoretically examine effects from the two-pion exchange in (semi-)long-range parts of the $DD^*$ system. We employ the framework of heavy-meson chiral perturbation theory with heavy-quark spin symmetry. The pion exchanges up to next-to-next-to-leading order (N$^2$LO) are taken into account. In order to separate the (semi-)long-range contributions, we apply the dispersion-relation method to one-loop diagrams. As a result, we find that the lattice data on the $D$ - $D^*$ potential in the regime of $0.5\, {\rm fm} \lesssim r$ is reproduced by adjusting the unknown $O(p^2)$ couplings. In particular, it turns out that contributions from isospin-independent N$^2$LO triangle diagrams play a central role in reproducing the lattice data of the form $V^{DD^*}\sim \left({\rm e}^{-m_\pi r}/r\right)^2$ in $1.0\, {\rm fm} \lesssim r\lesssim 2.0\, {\rm fm}$. We also present predictions of other $D^{(*)}$ - $D^{(*)}$ potentials, where the similar two-pion exchange tail is predicted. Our findings provide useful information on the (semi-)long-range regime of the $D$ - $D^*$ potential focusing on two-pion exchanges.

We present a lattice determination of the Bjorken sum rule via a Feynman-Hellmann calculation of the polarised forward Compton amplitude. We evaluate the lowest moment of the nucleon's polarised structure function, $g_1$, which we calculate over the range $0.5\lesssim Q^2 \lesssim 8$ GeV$^2$, covering both non-perturbative and perturbative regions. We compare our calculated moments with the Bjorken sum rule, and discuss implications for the calculation of higher-twist effects, as well as evaluations of $\alpha_s(Q^2)$ from hadronic quantities to complement phenomenological and other lattice methods.

Electrically neutral spin-1/2 fermions can interact via Yukawa or gauge couplings with electrically charged particles, leading to quantum-induced couplings between the neutral fermion and the photon. In this paper, we present general expressions for the diagonal and transition electromagnetic moments of Dirac and Majorana spin-1/2 fermions generated at the one-loop level. We also briefly discuss the implications of these results for several neutral spin-1/2 fermions of phenomenological interest, such as neutral components of $SU(2)_L$ multiplets (which are potential candidates for dark matter) or Standard Model neutrinos.

We investigate helicity effects in electron-positron pair production in circularly polarized electric fields with frequency chirping using the quantum-kinetic formalism for fermions. In particular, we calculate helicity-resolved momentum distributions and characterize the helicity imbalance through the helicity-asymmetry parameter for various electric-field configurations, including temporally asymmetric fields and dynamically assisted two-color fields with different frequency-chirping configurations. We find that right- and left-helicity electrons preferentially populate opposite momentum half-spaces along the out-of-plane momentum direction, leading to a pronounced helicity asymmetry in the produced electron distributions. For temporally asymmetric fields, frequency chirping substantially modifies the momentum distributions and can strongly enhance the helicity asymmetry, with the response depending sensitively on the pulse asymmetry parameter. For symmetric and elongated pulses, the helicity asymmetry approaches 100% at sufficiently large chirp strengths, whereas the compressed-pulse case exhibits a qualitatively different response with suppressed asymmetry at large chirp. For dynamically assisted fields, chirping the weak high-frequency component produces the strongest helicity response, reaching a maximum asymmetry of nearly 87% in the combined field, while chirping the strong field alone results in only a moderate asymmetry of about 12%-14%. Simultaneous chirping produces a large helicity imbalance together with substantial restructuring of the momentum spectrum, although its helicity response is weaker than that obtained by chirping the weak field alone. These results demonstrate that helicity-resolved momentum distributions provide additional information on the spin-dependent dynamics of Schwinger pair production beyond that contained in helicity-summed spectra.

In this work we estimate the first unknown QCD correction to the decay of the Higgs boson into gluons, $H\to gg$, in the heavy-top limit using Padé approximants built to the perturbative series and to its Borel transform. In the process, we also obtain estimates for the first unknown coefficients of the QCD $\beta$ function, of the QCD decoupling relation, and of the gluonium correlator. We also provide an updated prediction for the first unknown coefficient of $\Gamma(H\to b\bar{b})$. We determine the polynomial dependence of the perturbative coefficients on the number of quark flavors, $n_f$. We point out that the large-$n_f$ result for $H\to gg$ can be obtained from results for the gluonium correlator already available in the literature. The coefficient of the highest power of $n_f$ is then imposed as a constraint and is also used as a new test to discard unreliable approximants. The method is validated through the postdiction of the last known coefficient of the series. Our model-independent estimate for the yet unknown coefficient of order $\alpha_s^7$ of $\Gamma(H\to gg)$ is $-312\pm 15$ (in the $\overline{\mathrm{MS}}$ scheme with $\mu=m_H$, where $m_H$ is the Higgs mass). With our estimate the residual renormalization-scale dependence of $\Gamma(H\to gg)$ is reduced by a factor of almost 1.5.

We derive a family of sum rules for the tensor structure functions of targets with spin one or higher, rooted in exact Siegert relations. The mixed rank-two $TT$–$LT$ degeneracy combines amplitudes of opposite crossing parity and, under the superconvergence assumption, gives $\int_0^1\! d x\,[b_2(x,Q^2)-3b_4(x,Q^2)]=0$ in the Hoodbhoy–Jaffe–Manohar (HJM) basis. At large $Q^2$, the protected moment agrees with Detmold's target-mass-complete twist-two OPE; in the strict Bjorken projection, and if $b_4$ is neglected, it reduces to the Efremov–Teryaev (ET)-type condition $\int_0^1\! d x\,x\,b_1(x)=0$, whose measured-range footprint is consistent with the HERMES data. Two further rank-two combinations connect crossing-even amplitudes and determine the corresponding subtraction functions through weighted HJM moments. The protected combination can be isolated through separated tensor $LT$ and $TT$ responses, providing a direct experimental strategy for JLab and, ultimately, a future EIC.

The increasing diversity of high performance computing systems makes separate, architecture specific implementations of lattice gauge theory algorithms costly to maintain. We present kwqft, a performance portable Kokkos implementation of Wilson pure gauge Monte Carlo simulation for $\mathrm{SU}(N)$ Yang-Mills theory in an arbitrary number of space-time dimensions. The gauge group order $N$ and the dimension $D$ are compile time parameters. A single source targets the Serial, OpenMP, CUDA, HIP, and SYCL execution spaces, with MPI halo exchange overlapped with interior updates. The implementation reproduces the exact two-dimensional plaquette and published three and four dimensional values for gauge groups up to $\mathrm{SU}(17)$. On an NVIDIA A100 the Kokkos CUDA backend is competitive with a native CUDA code, SIMD acceleration improves the OpenMP path on Armv9 processors, and a large scale speedup is demonstrated for an $\mathrm{SU}(4)$ lattice on the LineShine supercomputer, currently ranked first on the TOP500 list.

A nuclear recoil measures dark matter (DM) scattering on nucleons, but usually cannot reveal the nature of the halo DM. An interchange of the ground and excited states of the DM can preserve an inelastic recoil spectrum while changing ground-state annihilation by several orders of magnitude. Solar neutrinos can then provide information that nuclear recoils leave unresolved. Motivated by the high-energy LUX-ZEPLIN candidate, we investigate a possible way to resolve the composition of singlino-Higgsino DM in the next-to-minimal supersymmetric standard model (NMSSM) by using nuclear recoils and solar neutrinos. Our analysis identifies solar-compatible singlino ground states and Higgsino ground states with weak inelastic transitions, whereas Higgsino-pair inelastic LZ fits predict excessive solar signals. An elastic Higgsino scattering alternative can suppress solar capture by closing the inelastic transition. Recoil spectra, solar evolution and target complementarity can therefore probe distinct aspects of the singlino-Higgsino DM composition, with residual degeneracies set by annihilation, halo and detector assumptions.

We study Standard Model Effective Field Theory (SMEFT) extensions in portal-mediated scattering processes from the perspective of quantum entanglement. Quantum information metrics maintain phase-sensitive spin and momentum correlations, whereas conventional collider and direct detection observables mainly depend on unpolarized cross-sections and event rates, which often suppress dimension-six interference terms or average over internal degrees of freedom. We assess linear and Von Neumann entropy fluctuations induced by higher-dimensional operator insertions by building final-state density matrices using helicity amplitudes. By avoiding conventional kinematic degeneracies, our formulation shows that entanglement measures capture interference contributions linearly in $1/\Lambda^2$, offering improved sensitivity to new physics scales. A theoretical framework for SMEFT Wilson coefficients is established by this information-theoretic method, creating new opportunities for accurate tests of fundamental interactions in high-energy and astroparticle physics.

Cosmic birefringence, the rotation of the polarization plane of CMB photons, provides an intriguing probe of physics beyond the Standard Model. In this paper, we investigate a vector Chern-Simons coupling between the neutrino current and photons as a possible origin of isotropic cosmic birefringence. Firstly, we perform the first analysis of anisotropic cosmic birefringence induced by the neutrino current. We find that the anisotropic signal sourced by lepton-number isocurvature fluctuations can be important on large scales, whereas on small scales, the anisotropic signal induced by gravitational effects becomes dominant comparing with the axion-like particle (ALP) scenario. Secondly, we show that a large lepton asymmetry generated through the Affleck-Dine mechanism can successfully account for the observed isotropic birefringence, and discuss its possible connection to the recently reported low helium-4 abundances in Subaru EMPRESS and Atacama Cosmology Telescope (ACT).

We present initial-state corrections to $e^+\,e^-\to\mu^+\,\mu^-\,\gamma$ at next-to-next-to-leading-order in QED for several experimentally motivated scenarios up to a few GeV. We include photonic as well as vacuum-polarisation corrections into the Monte Carlo framework McMule that allows for the calculation of arbitrary infrared-safe observables. For the total cross sections, the corrections are typically below the percent level, but they can be locally larger in distributions. The vacuum-polarisation corrections are of similar size and must not be neglected, in particular for larger centre-of-mass energies.

We present a holographic model of QCD to study the strong coupling constant $\alpha_s$ from the low-energy region to the high-energy regime. The approach uses a double-dilaton background, which breaks conformal and chiral symmetries, while large-$N_c$ corrections are incorporated to connect the holographic description with perturbative QCD. The model leads to an infrared fixed point and provides a smooth transition to the pQCD running. The resulting background also produces linear Regge trajectories for scalar, vector, and tensor states in reasonable agreement with experimental data.

We propose a simple scenario of boson-fermion atomic dark matter, in which the dark matter abundance originates from a primordial particle-antiparticle asymmetry. The dark sector consists of a complex scalar and a Dirac fermion carrying opposite charges under an unbroken U(1)$_D$ gauge symmetry. Their asymmetries are generated non-thermally through the CP-violating decays of heavy Majorana fermions produced by inflaton decay, in close analogy with non-thermal leptogenesis in the visible sector. The symmetric components efficiently annihilate into massless dark photons, while the surviving scalar and fermion populations cannot annihilate with each other and instead recombine into neutral boson-fermion dark atoms. Remarkably, the same interactions responsible for generating the primordial asymmetry induce atom-antiatom oscillations after recombination, so that the present-day dark matter can be approximately symmetric despite its asymmetric origin. Residual ionized components or sufficiently extended dark atoms can also give rise to appreciable dark-matter self-interactions, potentially leaving observable imprints on the formation and structure of dark matter halos and offering complementary cosmological and astrophysical probes of the dark sector. The massless dark photon survives as dark radiation, yielding a characteristic contribution $\Delta N_{\rm eff}\simeq0.05-0.07$ for the thermal history considered here. This prediction lies within the reach of future precision CMB observations, providing a direct cosmological test of the scenario.

We study a two-component dark matter scenario comprising a stable pseudo-Nambu-Goldstone boson (pNGB) and its nearly degenerate long-lived quasi-pNGB partner. An approximate scalar symmetry relates their masses and suppresses the tree-level Higgs-mediated elastic scattering of the excited state through the small mass splitting. Their coupled thermal evolution yields comparable relic populations, while requiring the observed total abundance fixes the dark scalar symmetry-breaking scale and hence the dark gauge coupling. At the studied benchmark, an excited fraction of approximately one half survives under the adopted evolution assumptions. The quasi-pNGB excited state can therefore produce exothermic nuclear recoils despite a suppressed tree-level elastic signal. As an application, we examine the high-energy LUX-ZEPLIN event. For relic compatible parameters, the recoil normalization fixes the kinetic mixing, allowing this interpretation to be tested by independent mediator searches.

Cosmological first-order phase transitions can generate curvature perturbations through inhomogeneous quantum tunneling, as studied previously on superhorizon scales. In this work, we for the first time conduct three-dimensional lattice simulations that incorporate scalar metric perturbations and radiation perturbations, covering a range from bubble wall scales to super-horizon scales. We obtain the precise scalar perturbation power spectrum and the probability density function of energy density perturbations. Furthermore, we simulate the gravitational-wave energy spectra generated by each source during the first-order phase transition, including the scalar field itself, scalar metric perturbations, and the energy density and velocity perturbations of radiation. For gravitational waves, the contribution from other sources can exceed $1/3$ of that from the scalar field at superhorizon scales. Additionally, we compare the effects of different values of the transition strength and rate on the results. This paper provides more accurate numerical results for research aimed at detecting or constraining first-order phase transitions via gravitational waves and curvature perturbations.

By defining notions of similarity between collider events, metrics give rise to event manifolds with nontrivial geometric structure. Understanding these structures and their relation to the underlying physics remains largely unexplored, partly due to the challenge of systematically comparing spaces endowed with distinct metrics. We introduce the multi-reference relative representation (M3R) framework, which provides a unified coordinate system for analyzing different spaces on equal footing. Applying M3R to three physically motivated event metrics—the phase space, spectral 2-Wasserstein, and energy-flow 2-Wasserstein metrics—we study individual event manifolds and the decision boundaries separating different physical processes. We find that these metrics resolve distinct yet partially shared structures, while intra- and inter-manifold geometries exhibit qualitatively different properties. Combining multiple metrics further reveals complementary information that can be exploited within a unified representation. More broadly, M3R provides a general language for comparing and composing different notions of event similarity, opening a path toward a systematic geometric description of collider event space.

Supercooled first-order phase transitions provide an attractive framework for generating observable gravitational waves (GWs), but the accompanying entropy injection dilutes any pre-existing baryon asymmetry, motivating baryogenesis during or after the phase transition. Cold baryogenesis offers a promising mechanism in which bubble collisions generate Higgs winding configurations and the Chern-Simons number through out-of-equilibrium dynamics. In the present study, we perform three-dimensional lattice simulations of a two-field model where the scalar field responsible for the phase transition is separated from the Higgs sector. Using realistic initial conditions obtained from bounce solutions, we follow the bubble expansion and collisions and study the generation of Chern-Simons number. It is found that efficient Chern-Simons production persists even for strongly non-degenerate potentials with large latent heat, which are favorable for enhancing GW signals. We also estimate the resulting baryon asymmetry using the simulated Chern-Simons dynamics and an effective CP-violating operator. Our results demonstrate that cold baryogenesis remains viable in the strongly supercooled regime, providing an important step toward establishing baryogenesis from cosmological first-order phase transitions.

Rapid advances in AI have opened a new era for physics, enabling unprecedented capabilities in research and discovery. However, these advances also bring challenges in verifying, trusting, and reusing the results they so rapidly produce. Formalization is a necessary part of the solution to these challenges. In this paper, as well as giving an overview of the role of AI and formalization in physics, we make the case that: (1) formalization is an essential layer for AI-driven discoveries in both computational and theoretical physics; (2) AI is lowering the barrier to, and increasing the efficiency of, formalization in physics, though it remains weaker at choosing definitions and designing libraries than at writing proofs; (3) the speed AI brings to formalization in physics currently comes at the cost of trust, credit, and community; (4) shared, community-reviewed formal libraries such as Physlib should be central in making progress in this field, both as a trusted, reusable foundation for physics results and as the environment in which AI systems can reason about physics; (5) formalizing physics raises challenges beyond those in mathematics, most importantly that a checked proof does not establish that its definitions faithfully capture the intended physics. We also give our perspectives on near-term and long-term directions in these areas.

Nearby compact gamma-ray sources can move appreciably during the Fermi-LAT mission and thus evade searches that assume a stationary sky. Compact dark matter halos, dark matter spikes around primordial black holes (PBH), and evaporating PBH provide potential examples. We perform a novel all-sky search for steady point sources moving at 0.25 deg/yr-0.8deg/yr in ten years of 1-100 GeV Fermi-LAT data. For a transverse speed of 200 km/s, this angular range probes distances of roughly $3.0\times10^3$ AU to $9.7\times10^3$ AU. We find 577 candidate tracks, consistent with $533\pm27.0$ tracks in time-scrambled skies. We place a model-independent 90% upper limit of 80.8 recovered signal tracks. At peak calibrated sensitivity, this corresponds to fewer than 123 steady, full-sky sources with an incident $E^{-2}$ photon spectrum. We give the calibrated detection efficiency of the search to steady point sources and use it to derive illustrative constraints on both evaporating PBHs and PBHs surrounded by annihilating dark matter halos.

A recent ALICE measurement reports a finite strangeness enhancement in the toward-leading region of high-multiplicity proton-proton collisions. In this work, the trigger transverse momentum, $p_{\rm T}^{\rm trigg}$, dependence is investigated using ${\rm K}^{0}_{\rm S}$ and $\Xi^{\pm}$ production in PYTHIA8, with and without color ropes, and EPOS-LHC. For $3 < p_{\rm T}^{\rm trigg} < 15$~GeV/$c$, EPOS-LHC and PYTHIA8 with color ropes exhibit a multiplicity-dependent increase of the toward-leading $\Xi^{\pm}/{\rm K}^{0}_{\rm S}$ ratio, while the rope-free PYTHIA8 baseline shows a weaker dependence. With increasing trigger momentum, the enhancement is strongly suppressed in EPOS-LHC for $p_{\rm T}^{\rm trigg}\gtrsim10$~GeV/$c$, whereas it remains approximately unchanged in PYTHIA8 with color ropes. This contrasting behavior is consistent with a reduced core contribution in EPOS-LHC and a local string-overlap mechanism in PYTHIA8 with color ropes. The trigger transverse momentum thus provides a model-sensitive probe of the mechanisms contributing to the apparent strangeness enhancement in the jet-like region of the pp collisions.

We nonperturbatively construct a gauge-invariant measure for overlap fermions on four-dimensional Euclidean lattices in a class of nonabelian chiral gauge theories that includes the Standard Model. On admissible gauge fields, comparing chiral projectors at successive lattice spacings yields an exponentially local current and establishes the global properties needed for Lüscher's reconstruction of a smooth, gauge-invariant fermion measure. This provides a candidate nonperturbative lattice definition of the Standard Model.

We present a resonance-aware extension of electroweak Sudakov-logarithm reweighting in MadGraph5_aMC@NLO for NLO QCD-matched and FxFx multijet-merged event samples. The method identifies the hard production process underlying each event and evaluates its electroweak Sudakov correction while accounting for the spin correlations between unstable particles and their decay products. Photonic logarithms are removed from the virtual weight to avoid overlap with QED shower evolution. We validate the method in FxFx-merged $Z$+jets production and fully leptonic $W^+W^-$ production. The reweighting yields the expected growing weak suppression in high-energy tails and is stable under variations of the clustering and merging parameters. In $W^+W^-$ production, the density-matrix and spin-summed prescriptions are statistically compatible for the observables studied, indicating only a small additional helicity dependence of the Sudakov correction in this channel. The method provides a practical virtual weak-Sudakov approximation for matched and merged simulations, but does not constitute an exact NLO electroweak calculation.

We investigate the prospects for detecting invisible dark photons in charged kaon decays through the two-pion channel $K^+\to\pi^+\pi^0\,\gamma_D$ and the one-pion radiative decay $K^+\to\pi^+\gamma\,\gamma_D$, where $\gamma$ and $\gamma_D$ denote the ordinary photon and dark photon, respectively. The former decay was previously proposed as a golden channel for massless dark photon searches at NA62, while here we introduce the radiative process as a complementary probe and extend both analyses to massive dark photons. The three-body modes are particularly relevant at low dark photon masses, where the two-body decay $K^+\to\pi^+\, \gamma_D$ becomes strongly suppressed and vanishes in the massless limit. For massless dark photons, renormalizable interactions induced by kinetic mixing are absent, and the dominant contribution arises from the effective non-renormalizable flavor-changing quark interaction $s\to d\, \gamma_D$ mediated by a dimension-five magnetic-dipole operator. This is also true for massive dark photons. Their kinetic mixing contributes negligibly to these channels, after considering the existing bounds on the mixing parameter. Only the same flavor changing magnetic-dipole operator as in the massless case is relevant. Using the chiral quark model, we estimate the relevant hadronic matrix elements of the dipole operator and account for constraints from $K^+\to\pi^+\,X$, where $X$ denotes resonant missing energy, $K^+\to\pi^+\nu\bar\nu$, and $K^0\!\!-\!\bar{K}^0$ mixing. Based on these calculations, we determine the allowed branching ratios for these decay modes and the sensitivities required at NA62 and future charged-kaon facilities.