Papers

The Heavy Meson (Hymn) collaboration presents a new extraction of D meson fragmentation functions using experimental data from LEP and LHC. We focus particularly on kinematical regimes where perturbative QCD should be safely applicable to avoid contamination from higher-twist effects which could lead to an apparent process dependence of fragmentation functions. We account for the initial-state radiation and, as a novel ingredient, consider the prompt and non-prompt contributions separately. The analysis is carried out at next-to-leading order accuracy including uncertainty estimation based on Monte-Carlo replica technique. We disucss the exemplary case of $\mathrm{D}^0$ here and defer the results for $\mathrm{D}^\pm$ and $\mathrm{D}^{*,\pm}$ to a forthcoming publication.

A critical component of relativistic three-body scattering amplitudes is the one-particle exchange (OPE) process, wherein a single particle is exchanged between incoming and outgoing two-body subsystems. We present an improved, finite-sum expression for the partial-wave OPE that is valid for three massive, spinless particles in arbitrary angular momentum configurations. A collection of analytic and numerical checks demonstrate that our finite-sum expression reproduces the known properties of the partial-wave OPE, including its threshold scaling behavior and singularity structure. Compared with previous work, this result more efficiently handles the rapid proliferation of partial waves contributing to any total angular momentum $J$, enabling the construction of robust wavesets for three-body amplitude analyses.

In the nanohertz band, spatial correlations between pulsar timing residuals provide a key observable for characterizing stochastic gravitational-wave backgrounds and probing their polarization content. In torsionless Palatini spacetime, nonmetricity can generate two additional shear modes, referred to as the shear-$x$ and shear-$y$ modes. In this work, we investigate the pulsar timing response produced by the shear-induced motions of the emitting pulsar and the receiving Earth. Assuming that the electromagnetic field is minimally coupled to the physical metric and that the Earth and pulsar possess non-negligible effective hypermomentum responses, we derive the single-pulsar redshift, the frequency-domain two-point correlation function, and the corresponding spatial correlation. For a stationary and isotropic stochastic shear background, the normalized overlap reduction function (ORF) for distinct pulsars reduces in the short-wavelength limit to the pure dipolar form $\Gamma_{ab}^{\mathrm{sh}}(\zeta)=\cos\zeta$, where $\zeta$ is the angular separation between the two pulsars. The same dipolar correlation can also be produced by isotropic Solar System ephemeris errors, leading to a spatial degeneracy between the two signals. This degeneracy highlights the importance of information beyond the angular correlation for identifying Palatini shear signatures in PTA data.

We present a pedagogical showcase of BRST quantization for restoring symmetries in nuclear many-body systems as a reformulation and potential alternative to conventional projection methods. The formalism is illustrated using translational invariance for a simple system of two interacting masses in one dimension, but with an eye toward generalizing to more particles, higher dimensions, and other symmetries. We explain the considerations underlying particular choices within the BRST construction, and develop both Hamiltonian and path integral formulations to provide guidance for the variety of many-body and effective field theory contexts where gauge fixing for symmetry restoration might be useful. For the demonstration system we show how to diagonalize within the extended BRST phase space, how variation after projection is recovered for product reference states, how the corresponding gauge-fixed functional integral is constructed, and how collective zero modes are isolated and controlled. Throughout, we keep in mind extensions of BRST symmetry to various approximation schemes as a guide for consistent symmetry restoration.

The stabilization of the electroweak scale strongly motivates the search for new heavy resonances and top-partner states. We investigate the discovery potential of exotic resonances mediating the production of vector-like quarks at the High-Luminosity LHC ($\sqrt{s} = 13.6$ TeV), focusing on the $pp \to X \to t \bar{t}_p$ cascade decay. Using a model-independent Effective Field Theory approach, we classify the intermediate mediator $X$ by its spin (0 and 1) and color (singlet and octet) representations. Parton-level kinematics demonstrate that the normalized differential cross-section with respect to the transverse momentum provides a robust observable for spin discrimination. To address the experimental challenges of highly boosted, semi-resolved hadronic decays, we introduce a cut-flow strategy based on an inclusive four-jet invariant mass reconstruction, $M(4j)$. Because this standard approach remains sensitive to systematic uncertainties, we implement a Generalized BSM Tagger based on Deep Neural Networks (DNNs). By exploiting non-linear multi-jet correlations, the DNN achieves robust background rejection factors ranging from $\mathcal{O}(600)$ to $\mathcal{O}(1000)$ while preserving the underlying partonic signatures. Projecting to an integrated luminosity of $3000\text{ fb}^{-1}$, this combined strategy yields a projected statistical significance of $3.74\sigma$ for the dominant color-octet vector channel, establishing strong evidence potential and offering a robust phenomenological baseline for future HL-LHC searches.

We formulate, within a fixed FSI-improved amplitude convention, a zero-locus diagnostic for the direct contact term in $\phi\to\pi^+\pi^-\pi^0$. The resonant $\rho\pi$ contribution is dressed channel by channel with the complex Omnès function, the direct term is multiplied by the averaged Omnès factor, and a real constant background is retained as a smooth residual amplitude. In this convention, $F^{\rm FSI}=R+c e^{i\delta_{\rm dir}}D$ with $c=g_{\phi3\pi}^{\rm eff}$, and the difference of two constrained invariant-mass gradients of the reduced Dalitz density gives a local quadratic identity for $c$ on the zero-contour. The construction provides a closure and stability diagnostic complementary to a global Dalitz-plot fit. For the benchmark input $g_{\phi3\pi}^{\rm eff}=-24.0~{\rm GeV}^{-3}$, we identify a numerically stable zero-contour branch around $M_{+0}=0.460\pm0.025~{\rm GeV}$ and $M_{+-}\le0.560~{\rm GeV}$, where the tight-contour median estimator reproduces $g_{\phi3\pi}^{\rm est}\simeq -24.0~{\rm GeV}^{-3}$, a closure recovery of the injected coupling within the chosen FSI-improved convention rather than an independent extraction. We further vary the mass-window selection of the branch. The median remains close to the injected value under shifts of the $M_{+0}$ window and moderate changes of its width, while the mean and standard deviation are more sensitive to outlier points near unstable quadratic branches. The method therefore identifies Dalitz-plane regions where the direct-term interference is locally well-conditioned and provides useful guidance for control-region choices and systematic variations in future global fits.

We investigate the electromagnetic (EM) properties of vector and axial-vector heavy-light hybrid mesons within the light cone QCD sum rules framework. These states are characterized by an explicit gluonic degree of freedom and are studied through interpolating currents corresponding to the $J^{P(C)}=1^{-(-)}$, $1^{+(-)}$, $1^{+(+)}$, and $1^{-(+)}$ hybrid configurations. By analyzing the correlation function in the presence of an external background photon and matching its hadronic and QCD representations, we derive the light cone sum rules for the magnetic dipole and electric quadrupole form factors and extract the corresponding electromagnetic moments at $Q^2=0$. The QCD side of the sum rules incorporates the perturbative photon emission contributions as well as the relevant non-perturbative effects described by photon distribution amplitudes (DAs). Numerical predictions are obtained for the charged $\bar b g u$, $b g\bar u$, $\bar c g d$, $c g\bar d$, $\bar c g s$, and $c g\bar s$ hybrid configurations. The calculated electromagnetic moments show variations among the different hybrid configurations. A more systematic pattern is observed for the electric quadrupole moments (EQMs): the results obtained from the $\mathcal J_\mu^1$ and $\mathcal J_\mu^3$ currents are generally close to each other, as are those obtained from $\mathcal J_\mu^2$ and $\mathcal J_\mu^4$, with the former pair generally yielding somewhat larger magnitudes. The magnetic dipole moments (MDMs), in contrast, do not necessarily exhibit the same systematic grouping, although they also show variations among the different currents and configurations. For the bottom-containing states...

The Low-Burnett-Kroll theorem (extended to non-abelian gauge theory) states that the tree-level emission amplitude of a soft gauge boson from an arbitrary hard process can be expressed in terms of the non-radiative amplitude including the next-to-soft term. Reformulating the soft theorem in the framework of an on-shell effective theory leads to a natural gauge-invariant split into an external and internal emission process to any order in the soft expansion. In this framework, we derive a compact expression for the all-order external emission amplitude expressed in terms of the non-radiative amplitude, and express the local emission amplitude through a single gauge-invariant operator at every order beyond the next-to-soft one. For scalar QCD, we compare the number of Lorentz- and $SU(3)$-invariant amplitudes for the radiative and non-radiative hard process with an arbitrary number of scalar quarks and antiquarks.

The direct detection (DD) of Higgsino-like dark matter (DM) through inelastic scattering processes may provide a promising avenue, along with the elastic scattering, when the mass splitting between the neutral Higgsino pairs is extremely tiny. The mass splitting can be reduced further by adopting the on-shell renormalization for the neutral and charged Higgsinos in the MSSM. Moreover, all the one-loop electroweak (EW) corrections to the three-point vertices for the neutralino(s)-Higgs interactions have been considered, while both elastic and inelastic DM-nucleon scattering cross-sections have been calculated primarily through Higgs exchange. Subsequently, the expected number of scattering events in the latest LUX-ZEPLIN (LZ) DD experiment are also computed. Our results highlight a few scenarios in which the inelastic component may exceed the corresponding elastic component, leading to enhanced direct detection scattering rates.

We study the spin-$1/2\to1/2$ semileptonic decays of singly charmed baryons ($\Lambda_c^+$, $\Xi_c^{0,+}$, and $\Omega_c^0$) into the light baryon octet within a relativistic three-quark model. The constituent quark masses and spatial wave functions are determined by the baryon mass spectrum. For the physical $\Xi_c$ states, the light flavor $\mathrm{SU}(3)$ breaking ($m_s > m_{u,d}$) naturally induces a coherent mixing between the flavor antitriplet and flavor sextet configurations, which is completely fixed by the mass eigenstates. Consequently, no adjustable parameters are introduced in calculating the weak transition amplitudes. Using these wave functions, we calculate the $c\to s,d$ helicity amplitudes with the Bakamjian–Thomas boost, including the spatial Jacobian and the Wigner rotations of the constituent spins. The branching fractions, $q^2$ distributions, longitudinal polarizations, and form factors are then obtained from these amplitudes. For the $\Lambda_c^+\to\Lambda\ell^+\nu_\ell$ and $\Lambda_c^+\to n\ell^+\nu_\ell$ modes, our branching fractions and form factors are in good agreement with the experimental data and Lattice QCD results. For $\Xi_c^0\to\Xi^-e^+\nu_e$, we obtain branch ratio $\mathcal B_{\ell} \simeq 4.0~\%$, which is consistent with recent Lattice QCD calculations but lies well above the current experimental average. Clarifying the origin of this discrepancy calls for further dedicated efforts from both experimental and theoretical sides. For the $\Omega_c^0\to\Xi^-\ell^+\nu_\ell$ decay, the spin-$1$ $ss$ spectator yields a positive longitudinal polarization of the final $\Xi^-$, in contrast to the negative polarizations in the predominantly antitriplet decay modes. Our predictions for the $q^2$ spectra, angular asymmetries, and final baryon polarizations may provide useful references for future measurements of singly charmed baryon semileptonic decays.

These lectures were presented at the 2026 QCD Masterclass in Saint-Jacut-de-la-mer, France. They supplement the published notes from the 2024 school with presentation of a few new topics that have become popular in recent years. These include event metrics, anomaly detection, scaling laws, the limits of classification performance, and regression that respects spacetime symmetries. Many of the presented results are known, but some new results are derived, especially related to anomaly detection. As was the case in those original notes, while all these problems are motivated from machine learning applied to QCD, no discussion of details of machine learning is presented in these notes. All results follow from application of fundamental principles of QCD. I begin these notes with an apology for humanist physics.

We report on the QCD calculations underlying a next-to-leading-order (NLO) QCD Laplace sum-rule analysis of the light tensor $(J^P = 2^+)$ hybrid meson mass and coupling. This article focuses on the calculation of the NLO perturbative and leading-log NLO non-perturbative contributions. The diagrammatic renormalization method is employed, and a renormalization-group approach is used to determine the leading-log NLO corrections to condensate contributions, including the dimension-six gluon condensate, whose renormalization we extend to $n_f$ quark flavors. The NLO contributions provide a systematically improved theoretical description of the light tensor hybrid correlation function, leading to more reliable determinations of its mass and coupling. The phenomenological implications of our results are discussed separately in these proceedings.

We study $e^{+}e^{-} \to J/\psi+\eta_c+X$ at next-to-leading order (NLO) in $\alpha_s$ within the nonrelativistic QCD (NRQCD) framework to assess the color-octet (CO) mechanism at low energies. QCD corrections significantly enhance both color-singlet (CS) and CO leading-order results, with non-negligible QED-diagram contributions to the CS channel. At $\Upsilon(4S)$, CO terms increase the inclusive cross section by $20\%$–$30\%$, and the enhancement grows rapidly with $\sqrt{s}$, yielding an energy dependence distinct from CS predictions and providing a sensitive test of NRQCD. Including $\psi(2S)$ feed-down further amplifies the NRQCD prediction by about $40\%$ at $\Upsilon(4S)$. With Belle's reconstruction of $J/\psi \to \mu^+\mu^-$ and six $\eta_c$ decay channels, the process shows promising potential for observation.

We present a modular implementation of next-to-leading order (NLO) perturbative QCD (pQCD) thermodynamics with finite strange quark mass in the MUSES Calculation Engine, enabling reproducible connections between high-density QCD calculations and neutron star observables. Using this implementation, we investigate the interplay between flavor symmetry and physically motivated renormalization-scale prescriptions in cold, $\beta$-equilibrated quark matter. We compare prescriptions associated with the conserved-charge $BQS$, isospin $BI_3S$, and $SU(3)$ Cartan $BI_3Y$ bases, and show that their different symmetry properties at finite perturbative order can significantly affect the predicted flavor composition. In particular, while the $BQS$ and $BI_3Y$ prescriptions yield the same reduced $\beta$-equilibrated \eos{} for $\mu_S=0$, they can predict different flavor compositions, whereas the $BI_3S$ prescription generates additional contributions to the charge-neutrality condition and develops strong scale dependence at low chemical potentials. We then apply stability and causality constraints to investigate the effect of the strange quark mass on the neutron star \eos{}. In an exploratory benchmark at $\mu_B=2.4$~GeV and fixed fiducial renormalization scale, increasing the fixed strange quark mass from $m_s=0$ to $m_s=300$~MeV reduces the fraction of \eos{} in our prior that is incompatible with the pQCD constraint from 51% to 36% and qualitatively changes the region of \eos{} space that is selected, retaining greater support for stiffer behavior. These results motivate systematic studies of strange quark mass and renormalization-scale uncertainties in pQCD constraints. The MUSES implementation provides a modular framework for such extensions and for future higher-order calculations.

We investigate the UV viability of strongly first-order electroweak phase transitions (SFOEWPTs) in the Type-I two-Higgs-doublet model (2HDM), considering both the Normal and Inverted Scenarios (NS and IS). For each scenario, we scan $5\times10^6$ physical parameter points and determine the cutoff scale $\Lambda_{\rm c}$ through a two-loop renormalization-group analysis, where $\Lambda_{\rm c}$ is set by the first violation of perturbativity, tree-level unitarity, or vacuum stability. For one-step transitions, the SFOEWPT strength and high-scale UV validity exhibit a pronounced tension: the maximal transition strength $\xi_p$ decreases with increasing $\Lambda_{\rm c}$. Requiring $\Lambda_{\rm c}>10~\text{TeV}$ limits the transition strength to $\xi_p\lesssim2.7$ in the NS and $\xi_p\lesssim1.8$ in the IS, while requiring $\xi_p>1$ restricts the cutoff scale to $\Lambda_{\rm c}\lesssim O(10^6)~\text{GeV}$ in both scenarios. Multistep transitions exhibit qualitatively different behavior. Two-step SFOEWPTs, found in appreciable numbers only in the IS, can remain theoretically consistent up to $\Lambda_{\rm c}\sim O(10^{15})~\text{GeV}$ while reaching $\xi_p\simeq7$, without exhibiting the pronounced $\xi_p$-$\Lambda_{\rm c}$ anticorrelation characteristic of one-step transitions. Imposing UV validity also sharpens the phenomenologically viable parameter space. In particular, increasing the minimum allowed cutoff scale for two-step SFOEWPTs in the IS favors a light scalar spectrum and moderate $\tan\beta$, providing a promising target for current and future collider searches.

We study linear gravitational perturbations and the corresponding quasinormal-mode spectra of electrically and magnetically charged black holes in the presence of higher-order corrections to the Einstein-Hilbert action. In particular, we consider a four-derivative interaction that couples the Riemann tensor to the electromagnetic field strength in the unique (Horndeski) combination that preserves second-order equations of motion. We provide a comprehensive analysis of the stability conditions. We numerically confirm the absence of exponentially growing modes throughout the physically admissible region of parameter space where the theory remains free of pathologies. We then investigate in detail the properties of the quasinormal-mode spectra and identify several distinctive features induced by the higher-order interaction.

The LZ experiment has recently reported a $248$ keV nuclear recoil event in a region where backgrounds are expected to be low. A pure higgsino scattering inelastically through a $Z$-boson is an exciting possible interpretation of this event, but at the mass required for thermal freeze-out to account for all dark matter, $m_\chi = 1.1$ TeV, it predicts several events in the empty high-energy sideband corresponding to $E_R\gtrsim350$ keV and is further excluded by searches for high energy neutrinos coming from the Sun by the IceCube detector. We fit the higgsino mass scale and neutral state mass splitting, $m_\chi$ and $\delta$, to the event and the empty sideband. We additionally recompute solar capture bounds as a function of $m_\chi$. The LZ data alone are best fit at low mass, $m_\chi \approx (240,\,450)$ GeV, but is excluded by solar capture. The parameter space most consistent with the event, the empty sideband and the solar capture bound is $m_\chi \approx (10^5,\,10^6) $ GeV with $\delta \approx (330,\,480)$ keV, with some dependence on DM halo modeling. Such a higgsino must be produced by some other method than standard freeze-out; this can be achieved by freezing-out during a period of early matter domination which ends by reheating the universe to temperature $T_{\rm RH}\approx 1$ TeV. We give a simple proof of concept model which does this via a Kim-Nilles mechanism and therefore connects to the origin of the Higgsino mass scale and solves the strong CP problem.

Interactions induced by dark matter particles which couple bilinearly to standard model particles through quantum fluctuations were termed quantum dark forces by Brax, Fichet, and Pignol, who constrained the mass and couplings of dark scalar, dark vector, and dark fermion bilinear exchange between nucleons. We extend their results to derive new constraints on quantum dark forces from bilinear scalar exchange between neutrons and electrons

Protons and neutrons differ dramatically in their electromagnetic sizes, but are bound by the strong (color) force and have nearly identical masses, like two twin states of the same “nucleon". To reveal the overall spatial extent, it must be examined through the strong interaction rather than electromagnetism. The $J/\psi$ particle, a compact color-charge dipole of a charm quark and antiquark, provides an ideal probe. Recent high-precision measurements of near-threshold $J/\psi$ production at Jefferson Lab offer a more precise glimpse of the proton's gluonic spatial structure. Combining these data with recent quark-sector results, we extract the distribution of the color field underlying mass generation in the nucleon and find it extends beyond both charge and mass distributions, revealing the nucleon's overall strong-interaction spatial extent of $0.94\pm 0.09$ fm.

We propose Bell tests for collider decays using independently sampled analysis axes as settings and detector regions to assign binary or null outcomes. We show that a Bell violation requires postselection, opening a loophole. However, under measurement independence and operational equivalence of acceptance events across settings, any local model exploiting the loophole must be nonclassical in the sense of measurement contextuality. We derive a Bell inequality violated by singlet correlations when the effective spin-analyzing powers are sufficiently high. Its violation then witnesses Bell nonlocality or measurement contextuality.

Triangular loop signals appear frequently in cosmological collider models but their analytical forms remain unknown due to multiple technical challenges. Here, we determine for the first time the leading analytical cosmological collider signals generated by a massive scalar triangle loop in inflationary bispectrum and trispectrum. Combining a directional cutting rule with partial Mellin-Barnes representations, we obtain both the local and nonlocal trispectrum signals in a soft limit and derive the leading signal in the squeezed bispectrum. Remarkably, all these signals are reproduced by the corresponding bubble diagram with a single effective pinched coupling. Signals beyond leading order and cases with arbitrary internal masses, spins, and interactions can be generated within the same framework. Our approach also provides a systematic route to extracting analytical loop signals from general cosmological correlators.

Matter fields localized around black holes can produce small secondary bumps in the effective potentials governing black-hole perturbations, potentially leading to quasinormal-mode spectral instabilities and late-time echoes. Considering physically motivated models of anisotropic fluids surrounding a spherically symmetric black hole, we show that the appearance of such a secondary bump is accompanied by either singular matter profiles or divergent characteristic speeds in the fluid. These features indicate that the corresponding matter configurations are unphysical. We further demonstrate that a secondary bump in the effective potential does not necessarily imply the existence of additional light rings in the spacetime.

We initiate the study of two-to-two scattering amplitudes involving two distinct scalar particles in $d = 4$ spacetime dimensions using the primal S-matrix bootstrap. We impose a $\mathbb{Z}_2 \times \mathbb{Z}_2$ global symmetry under which the two particles are the lightest ones carrying charges $(-,+)$ and $(+,-)$, guaranteeing their absolute stability and absence of triangular anomalous thresholds. For unequal masses, the presence of a pseudo-physical cut whose discontinuity is not directly constrained by physical unitarity qualitatively changes the bootstrap problem. We find several observables to be unbounded, while others obey non-trivial one-sided bounds or become bounded once another observable is fixed. In the equal-mass limit, where the pseudo-physical region disappears, two-sided bounds are recovered. As a proof of concept, we show that supplying information about the pseudo-physical discontinuity through an Omnès parametrisation also restores boundedness. Our results provide a starting point for future studies of physical processes such as pion-kaon and pion-nucleon scattering.

The entangling power of a unitary operator acting on a bipartite Hilbert space measures the entanglement it generates from product states, averaged over the inputs. A finite-dimensional unitary has a spectral decomposition $U=\sum_{a=1}^{n}e^{i\theta_a}P_a$, where $e^{i\theta_a}$ are the eigenvalues, $P_a$ the corresponding eigen-projectors, and $n$ is the number of distinct eigenvalues. After removing an overall phase, the entangling power is a function on the $(n-1)$-torus of relative eigenphases at fixed spectral projectors. We prove that this function is stationary at all $2^{n-1}$ points on the torus where every relative phase is $0$ or $\pi$, which we define as corners. Up to an overall phase, $U$ at each corner is a generalized reflection $R=\mathbb{I}-2Q$ satisfying $R^2=\mathbb{I}$, where $Q$ is the sum of spectral projectors whose relative phase is $\pi$. At the corner the entangling power is expressed in terms of seven local-unitary invariants of $Q$. A unitary gate $U$ can be realized as a corner of some projector family if and only if $U^2\propto\mathbb{I}$, a condition satisfied by many Clifford and non-Clifford gates. We illustrate the theorem with two-qubit gates, $SU(N)$ channel decompositions, and two-site spin chains, obtaining examples of minima, maxima, and saddle points. In addition, a corner that is a saddle point on the full phase torus can appear as a local maximum or minimum along different time-evolution trajectories.

The mass ratios of the quarks and charged leptons follow a simple pattern. The logarithmic generation steps come in a two to one ratio, a note to its octave, and the ordering is mirrored between the up-down and down-lepton comparisons. The pattern, read as charge counting on a $Z_N$ clock, is realized at level four and at no level that is not a multiple of four, which motivates modular level four and the finite group $S_4$, with the generations in the triplet at $T$ charges $(3,1,0)$ and the mirror in the sign singlet. The charged-lepton mass ratios lie on a theta-dressed lattice at $0.02\%$, which sets the base $\varepsilon=0.18664$, taken as $14/75$, and the harmonic modulus $\tau=1.0685i$. Five postulates in the weight one-half theta constants, identified on the same data, reproduce the six quark masses from three lepton masses and the electroweak scale. Two more and one empirical relation for $|V_{td}|$ close the CKM matrix, giving $|V_{us}|=\sqrt{m_d/m_s}=0.2255$, $|V_{cb}|=0.04197$, $|V_{ub}|=0.003721$, and $\delta=1.138$ against the measured $1.139\pm0.023$, with no continuous parameter. The unitarity triangle follows, with apex $(0.161,0.348)$ against the measured $(0.161\pm0.010,0.347\pm0.010)$, and $J=3.11\times10^{-5}$ against $(3.09\pm0.07)\times10^{-5}$. The same structure carries the neutrinos. A single theta insertion gives $\sin\theta_{13}=\theta_2(\tau)m_2/m_3$, which holds at $0.7\sigma$ on the 207-day JUNO data, and the harmonic condition completes a normal-ordered spectrum with $m_1=0.25$~meV, $\Sigma m_\nu=0.0589$~eV, a CP-conserving phase $\delta_{CP}=\pi$, and effective Majorana masses quantized at $1.3$ to $3.9$~meV. The ultraviolet completion belongs to the magnetized torus class, with Pati–Salam the natural gauge embedding.

Phenomenologically similar sign-switching dark-energy histories need not have comparable scalar-field realizations. We reconstruct minimally coupled scalars with fixed kinetic sign for three prescribed histories: the error-function model (ECDM), the compact smooth-step model (SSCDM), and the ladder-like model (L$\Lambda$CDM). Continuous negative-to-positive density crossings select the phantom branch. ECDM yields a smooth on-shell potential at every finite redshift; its equation-of-state pole at the density zero is only a ratio singularity. Exact SSCDM has a regular trajectory but a $C^1$, non-$C^2$ endpoint potential, $V-V_e\propto|\phi-\phi_e|^{4/3}$. Its non-Lipschitz force permits delayed departures from frozen plateaus, so the reconstructed potential and plateau data do not uniquely generate the prescribed history. The exact Ladder requires distributional kinetic stress and has no ordinary classical realization in the adopted one-field action. In conditional synthetic comparisons, the sigmoid–Gaussian family ranks highest for ECDM and the generalized axion-like family for SSCDM, although the fitted axion exponents $n<1/2$ imply a divergent endpoint force. Representative regular forward solutions exhibit negative-to-positive scalar-density crossings, with the potential zero preceding the density zero. In a closure test, unretuned evolution of the top-ranked ECDM template tracks the target approximately, $\max|\Delta\widetilde\Omega_\phi|\simeq0.16$. Closure fails structurally for compact SSCDM: no potential with a locally Lipschitz force can reproduce its exact finite-duration frozen plateaus from exactly frozen initial data. Field-map existence, invertibility, and endpoint regularity must be assessed before interpreting a phenomenological history as scalar dynamics. The phantom action is used only as a homogeneous effective proxy.

Neutron stars (NSs) provide a unique laboratory for testing gravity in the strong-field regime and for searching for deviations from General Relativity (GR). In this work, we investigate the effects of Energy-Momentum Squared Gravity (EMSG) on NS structure and examine whether its signatures can be identified from observable stellar properties using supervised machine learning (ML). We solve the modified Tolman-Oppenheimer-Volkoff equations for approximately $10^{4}$ nuclear equations of state (EOSs) for EMSG coupling parameters $\alpha=\{-5.01,-2.50,0,+2.50,+5.01\}\times10^{-38}\,\mathrm{erg}^{-1}\mathrm{cm}^{3}$, and calculate the gravitational mass $M$, radius $R$, dimensionless tidal deformability $\Lambda$, and fundamental $f$-mode oscillation frequency for each stellar configuration. Imposing observational constraints on $M$, $R$, and $\Lambda$, we split our datasets into train and test sets, and we employ Random Forest (RF), K-Nearest Neighbors (KNN), Support Vector Machine (SVM), Logistic Regression (LR), and Gaussian Naive Bayes (GNB) to classify the representative sectors $\alpha=\{-5.01,0,+5.01\}\times10^{-38}\,\mathrm{erg}^{-1}\mathrm{cm}^{3}$ using $(M, R,\Lambda,f)$. The RF classifier performs best, achieving an accuracy of approximately $99.85\%$ with precision, recall, and F1-scores exceeding $99.8\%$, while KNN also achieves accuracy above $99\%$. The nearly diagonal confusion matrices demonstrate that the observationally viable NS configurations associated with different EMSG sectors remain highly separable in the multidimensional observable space. Our results show that NS observables retain robust signatures of EMSG even after observational filtering, establishing ML-assisted NS observations as a promising complementary approach for probing modified gravity with current and future multi-messenger observations.

We construct a minimal Majorana singlet-vector-like-doublet model for the single nuclear-recoil-like event reported by LZ near 248 keV. At the splitting inferred from the recoil energy, an electroweak-strength $Z$ transition predicts thousands of events; singlet-doublet mixing suppresses the rate without moving the recoil spectrum. Fixed-coupling interpretations instead require a larger splitting in the extreme halo tail, but solar gravitational acceleration removes this suppression, while the larger splitting shifts recoils toward LZ's empty high-energy sideband. In our model the same mixing suppresses solar capture and annihilation, while the small mass gap required for coannihilation weakens Higgs-mediated cooling, allowing the captured population to remain extended and out of equilibrium. Imposing the relic abundance and normalizing the rate to one event leaves a two-dimensional mass-splitting parameter space. A thermalized population gives the conservative IceCube limit $\delta=$300-301 keV; with our nonthermal cooling ansatz and elastic scattering treated at tree level, the nominal limit is $\delta=$331-341 keV near the 730-733 GeV relic-density endpoint, which is also favored by the recoil spectrum. We outline a gauged $U(1)_N$ origin for the parity and splitting and a candidate $R$-symmetric supersymmetric embedding.

The recent result by the LUX-ZEPLIN (LZ) experiment of a single nuclear-recoil event at $248\,\mathrm{keV}$ suggests an interpretation in terms of inelastic scattering between dark matter (DM) and the xenon target. The widely considered thermal Higgsino DM with $m_{\chi}\sim$~TeV and mass splitting $\delta \sim 350$~keV is essentially excluded as it would be captured efficiently by the Sun, with a resulting neutrino flux from its annihilation in excess of the IceCube limit, and expected recoils above the LZ nominal search window, where none were seen. However we argue that although these tensions apply to a Higgsino with constrained cross section, they need not apply to the broader set of inelastic candidates that alternative solutions to the hierarchy problem might suggest. We show that a new massive gauge boson, $Z'$ with a candidate DM sector and Majorana mass splitting of order $\sim 10^{-7}$ of the Dirac mass, evades current constraints. We propose an inelastic dark matter (iDM) candidate that can arise naturally in a Randall-Sundrum warped extra-dimensional model. The DM candidate involves a vector-like fermion confined to the TeV brane and a bulk field. The brane Lagrangian contains Dirac mass terms that are also naturally exponentially suppressed. The left-handed component of the bulk field has a Majorana mass with origin on the UV brane, while the interaction with Standard Model nucleons is mediated by a massive dark Kaluza-Klein (KK) gauge boson whose mass is also automatically in the right range. We propose a concrete model of thermal DM with $m_{\chi}\sim$~TeV in an RS geometry with warp factor $\pi kR\simeq 31.7$ and the $Z'$ a KK mode with natural TeV-ish scale mass in which the ratio of neutrino to quark coupling is also natural, giving a mass splitting of $\delta \sim 300$~keV, and show how it could explain the LZ signal while being consistent with existing constraints.

We investigate a minimal extension of the SM consisting of a $\mathbb{Z}_3$-stabilized complex scalar dark matter (CSDM) candidate, a down-type vector-like quark (VLQ), and a charged vector-like lepton (VLL). The additional vector-like fermions not only enable the CSDM to reproduce the observed relic abundance beyond the Higgs-resonance region through semi-annihilation and co-annihilation processes, but also induce correlated signatures across flavor, electroweak precision, dark matter, and collider observables. We perform a comprehensive one-loop analysis of neutral meson mixing, rare meson decays, charged lepton flavor violation, anomalous magnetic moments of charged leptons, and $Z$-pole observables. We find that neutral meson mixing and rare meson decays provide the dominant constraints on the VLQ sector, while charged lepton flavor-violating processes strongly restrict the VLL Yukawa couplings. Current direct-detection limits require Higgs-DM coupling $\lambda_{\Phi H} \lesssim5\times10^{-3}$ and the VLQ Yukawa coupling $\mathtt{y}_d \lesssim 0.05$ for TeV-scale VLQ masses, whereas present indirect-detection searches impose no additional constraints. Combining all flavor, electroweak precision, dark matter, and collider constraints, we identify viable parameter regions with CSDM masses above approximately $1.0~\rm TeV$ and VLQ masses above about $1.5~\rm TeV$. We also find that the LHC can exclude VLQs (VLLs) with masses up to approximately $1.6~(0.38)$ TeV, depending on the CSDM mass, at the $2\sigma$ confidence level. The HL-LHC can further probe an extended region of the parameter space, with discovery prospects at the $3\sigma$ level. Finally, we demonstrate the complementarity of flavor, dark matter, and collider searches in probing this framework.