Papers

Heavy Neutral Leptons are a class of hypothetical particle, motivated by simultaneously solving multiple of the standing issues of the Standard Model. In this work we investigate the decay structure of this type of particle in the hadronic picture for multi-body final states. We propose to link the resulting hadronic description to a partonic description in a seamless transition based on the hadron system's invariant mass. Beyond the impact on the total HNL lifetime, we will show that the multi-hadron channels emerging in this description can constitute interesting experimental signatures.

The Standard Model Effective Field Theory~(SMEFT) has attracted much attention as a model-independent way for probing new physical signals. In the SMEFT framework, $e^{-}p$ colliders can be used to study new interactions of gauge bosons, such as neutral Triple Gauge Couplings~(nTGCs). We study the signals and backgrounds of six different processes at the Future Circular Collider-hadron electron~(FCC-he) and propose different event selection strategies. The expected constraints on the coefficients of the dimension-8 operators for each process, as well as the combined constraints are obtained. The results show that the sensitivity of $e^{-}p$ colliders to nTGCs is similar to the current Large Hadron Collider~(LHC) experiments and is more competitive than that of Circular Electron Positron Collider~(CEPC) experiments.

The extended nuclear-recoil analysis of LUX-ZEPLIN (LZ) has reported one event compatible with a recoil energy near $248$ keV, motivating endothermic dark-matter scenarios with support at large recoil energy. We study a pseudo-Dirac electroweak-doublet dark-matter model embedded in a five-dimensional Dark-Dimension framework. The Standard Model and the vectorlike electroweak doublets are localized on the visible brane, while dark-number violation is communicated through a neutral bulk state. The resulting mass splitting is exponentially suppressed, $\delta=\delta_{\rm UV}e^{-2\pi MR}$, providing a geometric origin for the few-hundred-keV scale relevant to inelastic scattering. The neutral weak current is dominantly off diagonal, fixing the neutron-scale normalization at $\sigma_{\chi n}^{Z}\simeq1.86\times10^{-39}\,\mathrm{cm^2}$. Using a two-bin Poisson diagnostic of the extended LZ recoil window, we find a shallow minimum near $(m_\chi,\delta)\simeq(1.35~\TeV,366~\keV)$, while the thermally motivated point $(1.1~\TeV,360~\keV)$ lies only $\Delta\chi^2\simeq0.21$ higher. The same benchmark is kinematically inaccessible to light targets but remains open for xenon and tungsten, providing a characteristic multi-target test of the model. For CaWO$_4$ we obtain an integrated tungsten rate of $3.15\times10^{-2}$ events kg$^{-1}$ yr$^{-1}$ in the $95$–$150$ keV interval. These results connect the geometric origin of the pseudo-Dirac splitting with high-recoil direct-detection phenomenology.

We investigate a minimal realization of spontaneous leptogenesis in the type-II seesaw model, where the lepton and Higgs asymmetries are generated as decay and inverse-decay processes drive the plasma toward the displaced equilibrium dictated by a rotating Majoron background. We derive the complete set of Boltzmann equations governing the evolution of asymmetric particle densities and analytically and numerically identify the freeze-out and freeze-in regimes. The resulting asymmetries depend primarily on the triplet branching fractions and are nearly independent of the triplet mass. The asymmetry scales as the square root of the smaller branching fraction when either decay mode into leptons or Higgs fields is suppressed, reflecting the symmetry structure; the lepton number is conserved once either coupling is turned off. We also show that the Majoron background does not induce CP-asymmetric decay of the scalar triplet in the massless final state limit, and thus its impact is negligible. Our results establish spontaneous leptogenesis as a simple and robust alternative to thermal type-II leptogenesis that requires neither additional scalar triplets nor explicit CP-violating interactions.

In this work, we perform a systematic investigation of the $P$-wave $\Sigma_b K/\Lambda_b K^{*}/\Sigma_b K^{*}$ and $\Sigma_b\bar{K}/\Lambda_b\bar{K}^{*}/\Sigma_b\bar{K}^{*}$ systems for all possible $I(J^P)$ combinations. In contrast to our earlier study of the negative-parity sector [Eur. Phys. J. C 85, 1026 (2025)], the positive-parity sector is dominated by resonances. For the coupled-channel $I(J^P)=1/2(1/2^+)$ $\Sigma_b K/\Lambda_b K^*/\Sigma_b K^*$ system, we predict a narrow resonance above the $\Sigma_b K$ threshold. In the $I(J^P)=1/2(3/2^+)$ $\Lambda_b K^*/\Sigma_b K^*$ system, a molecular resonance candidate is found above the $\Lambda_b K^*$ threshold. For the higher-isospin $I=3/2$ sector, resonances are identified in the $\Sigma_b K^*$ subsystem for both $J^P=1/2^+$ and $3/2^+$ cases, though both states exhibit relatively compact sizes. We also extend our analysis to the $\Sigma_b\bar{K}/\Lambda_b\bar{K}^{*}/\Sigma_b\bar{K}^{*}$ systems, where a cutoff-sensitive resonance is found in the $I(J^P)=1/2(1/2^+)$ configuration. A broad molecular resonance candidate is found below the $\Sigma_b\bar{K}^*$ threshold in the $I(J^P)=1/2(3/2^+)$ system. We hope that these predictions provide useful guidance for future experimental searches for bottom-strange molecular pentaquarks by LHCb.

We investigate the in-medium modifications of the charge (electric) $G_C^{*}(Q^2)$, magnetic $G_M^{*}(Q^2)$, and quadrupole $G_Q^{*}(Q^2)$ form factors of the positively charged vector meson $K^{*+}$ in symmetric nuclear matter at zero temperature within the Schwinger proper-time Nambu-Jona-Lasinio (NJL) model. In this framework, both the nuclear medium effects and the electromagnetic structure of the $K^{*+}$ meson are described consistently in the NJL model at the quark level. We find that the charge, magnetic, and quadrupole form factors are suppressed with increasing nuclear density, indicating substantial in-medium modifications of the strange vector meson's internal structure. We further obtain a charge radius of $r_{K^{*+}}^{*}=0.74~\mathrm{fm}$ at normal nuclear density, which is slightly smaller than the corresponding value for the $\rho^{+}$ meson, $r_{\rho^{+}}^{*}\simeq0.75~\mathrm{fm}$.

We show that our previously proposed inelastic scalar dark matter (DM) model in gauged $U(1)_{B-L}$ symmetry naturally accounts for the $2.6\sigma$ high-energy recoil event recently reported by the LUX-ZEPLIN (LZ) collaboration. To satisfy the thermal relic abundance, TeV-scale scalar DM $S$ with $m_S \simeq m_{Z'}/2$ for resonant annihilation and the gauge coupling constant $g_{B-L} \sim 0.5$ are required, where $m_{Z^\prime}$ is the mass of $U(1)_{B-L}$ gauge boson $Z^{\prime}$. The resulting predicted DM-nucleon inelastic cross section of $\sigma_\mathrm{SI} \sim 10^{-45}$ cm${}^2$ is in excellent agreement with the LZ event. This scenario can be decisively tested for future collider searches for $Z^\prime$ boson resonance.

The LUX-ZEPLIN (LZ) Collaboration has reported a nuclear-recoil candidate at $E_R=248\pm23_{\rm stat}\pm23_{\rm sys}$ keV, with a maximum local significance of $3.4\sigma$ and a global significance of $2.6\sigma$. A prominent interpretation invokes heavy halo dark matter near an inelastic threshold and therefore depends sensitively on the poorly constrained high-speed tail of the Galactic velocity distribution. In this Letter, we propose a qualitatively different possibility based on light boosted dark matter (BDM), whose incident energy is determined primarily by the dark-sector mass spectrum. We consider multi-component scenarios in which the boosted state scatters elastically or inelastically off xenon nuclei. For elastic scattering, pseudoscalar-mediated momentum dependence suppresses low-energy recoils. Near-threshold endothermic scattering of a nearly monochromatic BDM flux can instead confine the signal between kinematically determined recoil endpoints, suppressing events in both the low- and high-energy sidebands. The upscattered state may furthermore decay invisibly within the dark sector, preserving a single-nuclear-recoil signature without requiring it to be detector-stable. We present representative benchmark spectra and discuss complementary tests using other target nuclei and large-volume liquid-scintillator experiments.

We investigate the geometric structure of a Hermitian two-level mixing Hamiltonian motivated by neutral meson oscillations and its connections with qubit, fermionic, and topological descriptions. Mapping the Hamiltonian to an effective qubit representation, we analyze the geometric phase associated with cyclic parameter evolution on the Bloch sphere. Without identifying the complex mixing phase with a physical CP-violation observable, we interpret it as a CP-like geometric parameter controlling the azimuthal orientation of the Hamiltonian vector and its reversal under phase conjugation. Third-order Bargmann invariants constructed from the eigenstates yield an associated discrete phase whose dependence on the mixing parameters is examined alongside the continuous geometric construction. The cyclic evolution is also represented as a single-qubit $R_z$ phase operation and expressed through Majorana bilinears. Extending the construction to the momentum-dependent Bogoliubov-de Gennes Hamiltonian of the Kitaev chain, we relate momentum-space winding to the topological regimes and the quantized Berry (Zak) phase in the real-parameter model, while the corresponding Bargmann construction approaches the global phase in the continuum limit. Together, these results provide a geometric perspective connecting phase structure, qubit operations, fermionic representations, and momentum-space topology within related two-level Hamiltonians.

Using the Covariant Spectator Theory (CST), we calculate the dressed quark mass function and wave-function renormalization for the five quark flavors from up/down to bottom in both the spacelike and timelike regions of Minkowski space. The calculation employs a model dressed-gluon propagator fitted to lattice data in the spacelike region. The remaining free parameters of the quark self-energy are determined by fits to lattice results for the quark mass function including a constraint built into the wave-function renormalization. We perform these fits using lattice data from two different groups and find that the resulting mass predictions are within the range of the typical constituent masses used in quark models.

We develop a comprehensive Wilson-line formulation of quark Reggeization in QCD. Starting from a next-to-eikonal operator built from a semi-infinite Wilson line and a background-quark insertion, we identify an interpolating operator for the Reggeized quark and derive its nonlinear rapidity evolution using the background-field method. In the dilute regime, its positive-signature component exhibits Regge-pole evolution governed by the quark Regge trajectory, whereas the negative-signature sector displays mixing between quark and gluon degrees of freedom, in accordance with its known Regge-cut structure. In the planar limit, this mixing is suppressed, and Reggeization emerges without an explicit signature projection, recovering signature degeneracy. We illustrate the universality of the construction by extracting the same Reggeized-quark operator from a more general Wilson-line operator describing a gluon-to-quark transition. Furthermore, we extend the formalism to massive quarks, deriving a coordinate-space evolution kernel whose Fourier transform reproduces the massive-quark Regge trajectory. Finally, from the leading operator-mixing structure of the evolution equation and signature arguments, we show that the Reggeized-quark interpolating operator is expected to remain an eigenstate of the rapidity evolution up to next-to-leading logarithmic accuracy.

We propose a novel framework that simultaneously addresses the origin of Dirac neutrino masses and the nature of self-interacting dark matter (SIDM). The model is based on an $A_{4}$ modular symmetry to ensure the Diracness of neutrinos as well as the stability of the DM. The neutrino sector realizes a Dirac Inverse Seesaw mechanism where the smallness of the neutrino mass is governed by the vacuum expectation value (VEV) of a singlet scalar $\phi$. This same scalar couples to a vector-like fermion DM candidate, inducing a tiny Majorana mass splitting that renders the DM pseudo-Dirac and inelastic. Crucially, the scalar also acts as a light mediator for DM self-interactions, potentially solving the small-scale structure problems of Cold DM. In light of the recent 248 keV nuclear-recoil event, LZ230616, observed by LUX-ZEPLIN (LZ) DM direct detection experiment, we demonstrate that our inelastic SIDM parameter space naturally accommodates this signal via endothermic scattering kinematics. Furthermore, the spontaneous breaking of the dark parity required for this inelasticity produces a network of cosmological domain walls. We show that the explicit symmetry breaking needed to safely annihilate these walls generates a stochastic gravitational wave background. The non-holomorphic modular symmetry reduces the free parameters, correlating neutrino observables, addressing DM phenomenology, $\Delta N_{\rm eff}$, and gravitational-wave signatures.

The LUX-ZEPLIN (LZ) Collaboration has reported a $248$ keV nuclear-recoil candidate for which endothermic dark matter (DM) gives some of the largest local significances. We study Solar-capture constraints on three interpretations: a thermal Higgsino, a thermal pseudo-Dirac fermion with off-diagonal vector interactions, and neutron-philic endothermic spin-dependent scattering through $\mathcal{O}_4$. The canonical full-density thermal Higgsino is excluded: its LZ-preferred splitting near $0.38\,\mathrm{MeV}$ lies well below the splitting required to suppress Solar capture sufficiently to satisfy the IceCube upper limits on DM annihilation in the Sun, $\delta\gtrsim0.51$-$0.56\,\mathrm{MeV}$. For the pseudo-Dirac benchmark parameters that fit the LZ event, we find $C_\odot=1.53\times10^{20}\,\mathrm{s}^{-1}$, while two-state kinetics limits the fixed-orbit annihilation rate to $\Gamma_A\lesssim4.4\times10^{14}\,\mathrm{s}^{-1}$, about $1.7\times10^5$ below the IceCube upper limit for the $b\bar b$ channel. A semi-analytic treatment indicates that re-excitation cycles further cool the captured population, although a full phase-space calculation is required for its final distribution. For neutron-philic $\mathcal{O}_4$ scattering at $m_\chi=1$ TeV and $\delta=300$ keV, finite-temperature capture gives $C_\odot=3.98\times10^{17}\,\mathrm{s}^{-1}$, with nuclear-structure uncertainties giving an envelope $(1.77$-$9.72)\times10^{17}\,\mathrm{s}^{-1}$. Under the equilibrium assumption, the upper edge remains about a factor $154$ below the IceCube upper limit for the $b\bar b$ channel. We use $b\bar b$ only as a soft-hadronic proxy because an exact constraint requires the model-specific annihilation spectrum. Solar capture therefore excludes the thermal-Higgsino interpretation but not endothermic explanations generically.

The LZ collaboration has reported a nuclear-recoil excess near 248 keV with a global significance of $2.6\sigma$. Although halo dark matter with a magnetic dipole-dipole interaction and a TeV-scale mass provides the best fit to the excess among the interactions considered by LZ, it predicts a considerable number of events at lower recoil energies, where no excess is observed. We show that a boosted velocity distribution can alleviate this tension and provide a better fit to the LZ recoil spectrum. Moreover, the boost opens up the possibility of explaining the excess with much lighter dark matter, with masses down to the GeV scale. We demonstrate these features first in a model-independent analysis and then realize them in a concrete dark matter model, in which halo dark matter annihilates into on-shell mediators that subsequently decay into boosted dark-sector particles. Our results demonstrate that boosted dark sector particles provide a viable interpretation of the LZ excess.

The recent observation of an event with large recoil energy at LUX-ZEPLIN has found a possible explanation in terms of the inelastic scattering of a pseudo-Dirac particle like the Higgsino of the MSSM. For pseudo-Dirac dark matter, the mass splitting $\delta m$ is correlated with the mass of some heavier states. While rough dimensional considerations seem to indicate mass ranges of the heavy particles hopelessly out of reach even at future colliders, we point out that this is not the case in GUT-induced scenarios. Working with a specific model based on SU(6), we show that the experimentally favored $\delta m$ implies the presence of a $Z'$ gauge boson with a mass in the 10s of TeV. We derive the predicted $Z'$ signal in the dilepton channel and we confront it with the sensitivity of the FCC-$hh$ to $Z'$ resonances. We show that the $Z'$ falls squarely in reach of the early discovery potential of the FCC-$hh$.

We propose a $N=1$ supersymmetric $SU(6)$ theory with an intermediate $(SU(3)_C\times SU(3)_L\times U(1)_X)$ phase, in which common fields and operators relate the neutrinos, gauge mediation, unification, and symmetry-breaking sectors. The inverse-seesaw Dirac matrix is antisymmetric and thus has rank two, leaving one massless neutrino at leading order. The leading symmetry-allowed correction lifts this zero mode through its projection onto the left and right null vectors of the Dirac matrix, resulting in a quartic suppression by the ratio of the intermediate and ultraviolet scales. The complete unified messenger multiplets preserve the relative one-loop gauge-coupling crossing, while the supersymmetry-breaking spurion entering the messenger sector also determines the scale of lepton-number violation. The coupling governing (331) breaking fixes both the inflationary normalization and the radial mass in the broken vacuum. For the conditional heavy spectrum adopted in the threshold calculations, the gauge couplings remain perturbative. The physical scalar directions transverse to the inflaton are stable within the neutral $((\Phi,\bar\Phi,S))$ subspace. These results provide the analytical scale relations among the inverse seesaw, messenger sector, unified gauge evolution, and inflation, while keeping the assumptions associated with the ultraviolet Higgs and heavy-threshold sectors explicitly.

We investigate the 248~keV nuclear recoil excess reported by LUX-ZEPLIN (LZ) in a leptophobic inelastic dark matter framework, in which the mass splitting naturally suppresses low-energy recoils. We find two viable branches, including the endothermic solution with a high dark matter mass $m_\chi \gtrsim400$~GeV and the exothermic one with a mass of tens GeV. Remarkably, the exothermic dark matter scenario with $m_\chi\sim55$~GeV can simultaneously account for the LZ excess, the Galactic Center GeV gamma-ray excess, and the AMS-02 antiproton excess. The favored annihilation cross-section is slightly below the one required for the observed relic abundance, resulting in an overabundant relic in the minimal setup. An additional neutrino-portal mediator can provide the required depletion while leaving the gamma-ray and antiproton signals essentially unchanged. We further show that paleo-detectors provide a powerful probe of the inelastic interpretation, requiring exposures of $\sim10$ and $\sim100$~mg Gyr for the endothermic and exothermic scenarios, respectively.

We investigate the level shifts in protonium using the framework of non-relativistic effective field theory (NREFT). Our study is prompted by the PUMA collaboration's plans to probe the neutron-to-proton ratio in the nuclear density tail using antiprotonic atoms – a method for which light atoms provide an important benchmark. We calculate the corrections to the Deser-Goldberger-Baumann-Thirring formula for the complex level shift of S-wave states from the unitary cusp and Coulomb photon exchange. Structure dependent corrections enter at the next order. For higher-partial-wave states, they enter already at leading order. Using input from chiral NNbar interactions, we compare to other calculations and measurements from LEAR.

The recent LUX-ZEPLIN (LZ) search reported a nuclear-recoil event near $248~{\rm keV}$. Such a high-recoil event can be interpreted in terms of endothermic inelastic dark matter scattering, which typically requires a mass splitting of order a few hundred keV between the initial and final dark states. The inert doublet model (IDM) provides a natural realization of this scenario through the $Z$-mediated transition $H+N\to A+N$. In this work, we systematically examine whether this interpretation can be consistently realized in the IDM under the relevant theoretical constraints and existing experimental bounds. We perform a detailed profile-likelihood analysis of the LZ event, and find a viable high-mass IDM region with a profile best fit at $m_H=1080~{\rm GeV}$ and $m_A-m_H=369~{\rm keV}$.

In low-energy heavy-ion collisions, baryon stopping is an important process, in which protons from the initial colliding nuclei are stopped at mid-rapidity region. Quantifying such stopping can reveal information on the properties of the nuclear medium, such as net-baryon density. Though experimental measurement of net-proton rapidity spectra provides constraints, microscopic origin of such protons is not fully accessible. Transport model studies can therefore provide deeper insight into the microscopic origin of protons transported from initial nuclei, complementing experimental measurements. This article presents an investigation of baryon stopping in minimum-bias Au+Au collisions over a wide range of beam energies, $\sqrt{s_{NN}} = 2.4-17.3$ GeV ($E_{\rm lab} = 1.23A-158A$ GeV). Final-state protons are classified based on their origin by analyzing their interaction history in the UrQMD model. A significant fraction of transported protons at mid-rapidity originates from initial neutrons rather than initial protons, referred to as isospin-converted protons, and their contribution as a function of collision energy and centrality is quantified. Anisotropic flow coefficients of different proton categories are estimated and compared with experimental measurements. Furthermore, a comparison between the $\pi^{-}/\pi^{+}$ ratio and isospin conversion rate is performed. The latter is further compared with the $\alpha$ parameters of the Kitazawa-Asakawa formalism, revealing a significant deviation from the chemical equilibrium assumption $\alpha_N = \alpha_\pi$ below $\sqrt{s_{NN}} \lesssim$ 10~GeV. Finally, the saturation of the isospin conversion rate is found to coincide with the onset of nuclear transparency, demonstrating that isospin randomization and baryon stopping are coupled phenomena in hadronic transport across the NICA/FAIR energy range.

We propose a concrete theoretical framework for the double inverse seesaw mechanism within an alternative gauged $U(1)_{B-L}$ model, where the tiny neutrino masses emerge radiatively at the loop level in accordance with the 't Hooft naturalness criterion. By assigning non-universal $B-L$ charges of $(-4, -4, 5)$ to the right-handed neutrinos, we introduce vector-like fermions and two inert singlet scalars that circulate in the loop to generate the required mass terms. The spontaneous breaking of the $U(1)_{B-L}$ symmetry leaves a remnant $Z_2$ symmetry, which naturally stabilizes these new particles as dark matter (DM) candidates. We systematically investigate both fermionic and bosonic DM scenarios, assuming their interactions are predominantly mediated by the $B-L$ gauge boson ($Z'$). Our comprehensive analysis of the relic density, direct detection, and collider bounds reveals that the fermionic DM scenario is strongly favored. In contrast, the bosonic DM via the $Z'$ portal is severely constrained and largely ruled out by the latest direct detection experiments such as LZ, PandaX-4T, and XENONnT.

The dielectric function is central to describing many-body screening effects in dark matter (DM) direct detection with condensed matter targets. Current superconducting detector analyses employ the free-electron Lindhard dielectric function to model in-medium effects, an approximation whose validity in the superconducting state remains untested. We derive the electronic dielectric function for bulk superconductors within the Bardeen-Cooper-Schrieffer (BCS) framework, incorporating the full Bogoliubov quasiparticle coherence factors in the random-phase approximation. A systematic comparison with the Lindhard function for aluminum and tungsten silicide (WSi) reveals good agreement for energy depositions $\omega\gtrsim5\Delta$, establishing the Lindhard function as a robust approximation for superconducting DM detectors operating in this regime.

Hadronic decay channels can provide direct information on the momentum-space structure of confined quark systems. We investigate this possibility in the $\psi(4040)$–$\psi(4160)$ system using an instantaneous Bethe–Salpeter (BS) framework combined with a relativistic $^3P_0$ decay model. The BS solutions yield nearby bare $3\,^3S_1$ and $2\,^3D_1$ states at 4051 and 4110 MeV, respectively, whose opposite displacements from the physical vector states motivate an effective two-state level-repulsion description. By comparing the matched open-charm channels $D\bar D$, $D\bar D^*+{\rm c.c.}$, $D_s\bar D_s$, and $D_s\bar D_s^*+{\rm c.c.}$ with the same leading $P$-wave threshold behavior, we show that channel-dependent overlap kernels act as momentum-space nodal filters. At $M=4146$ MeV, the $PV/PP$ width ratio is 0.253 in the nonstrange sector but 1.63 in the strange sector, reversing the ordering expected from phase space alone. The momentum-resolved amplitudes reveal that different channels weight opposite sides of the same $2D$ nodal region differently, leading to distinct cancellation patterns and a common recoil condition, $P_f\simeq0.775$ GeV, for charge-resolved $D\bar D^*$ amplitude zeros. These results establish open-charm decays as a probe of momentum-space wave-function structures in heavy quarkonium.

We provide a detailed discussion for all kinematical configurations of the analytic continuation to negative values of initial-state on-shell energies used to generate interferences of scattering amplitudes from vacuum amplitudes in the Loop-Tree Duality. We also extend previous discussions on the matching of threshold singularities and introduce angular averaging as an efficient strategy to achieve a local cancellation when the matching of threshold singularities from vacuum amplitudes is constrained by flavour.

We develop a manifestly gauge and Lorentz invariant perturbative calculus to study the finite time and distance evolution of the electrically charged states created by Wilson-line-dressed scalar field operators in scalar quantum electrodynamics. By an Osterwalder-Schrader reflection and Euclidean gluing, the overlap of two dressed states is expressed as a Euclidean 2 point function of dressed operators, which is then evaluated in renormalized perturbation theory with a Stueckelberg photon mass as a gauge, BRST and Lorentz invariant infrared cutoff. This renders explicit and computable in closed form several structural features of the charged sector that have so far been accessible mainly through non-perturbative or algebraic arguments. We find that states dressed by non-parallel Wilson lines are “cloud orthogonal". Their overlap vanishes as a power of the infrared regulator, with an exponent that depends only on the angle between the two dressings and is an infrared analogue of the cusp anomalous dimension with the difference that it is one-loop exact whenever the charged matter is mass-gapped. Charged states are thereby superselected by the orientation of their dressing. Within a superselection sector the 2 point function is infrared finite but exhibits the infraparticle. The mass shell pole is replaced by the edge of a branch cut. As a result, the asymptotic spread of a dressed charge is a power law in proper time with a one-loop-exact computable exponent depending on the dressing and on the direction of motion. We show that although cloud orthogonality and the infraparticle are each extremely sensitive to fundamental infrared cutoffs, the infraparticle scaling law persists across a wide window of proper time.

We present a closed-form perturbative framework for two-flavour vacuum neutrino oscillations in the presence of a weak, flavour-blind Planck-scale mass correction generated by the dimension-five Weinberg operator of the Standard Model Effective Field Theory. The perturbative treatment is developed in direct structural analogy with approaches used to describe weak Earth-matter effects. We derive simple analytical expressions for the modification of the oscillation length, the oscillation phase, and the flavour-conversion probability, valid for arbitrary neutrino mixing and baseline lengths. Unlike matter-induced perturbations, the Planck-scale correction is constant along the neutrino trajectory. Consequently, its effect on the transition probability remains bounded and independent of the baseline at the amplitude level, while the associated modification of the effective mass-squared splitting produces a phase mismatch that increases linearly with propagation distance. We further present illustrative order-of-magnitude sensitivity projections for next-generation long-baseline and reactor neutrino experiments, including DUNE, Hyper-Kamiokande, and JUNO. Our results indicate that the accumulated phase drift provides a particularly promising observable for probing Planck-scale mass corrections and for distinguishing a possible quantum-gravity contribution from conventional matter-induced effects.

We present a novel model for inelastic dark matter in a simple extension of the Standard Model (SM) with a local $U(1)'$ baryon flavor symmetry, such as $U(1)_{B_i-B_j}$ with $i\neq j$. In this framework, we realize a realistic flavor structure for the mixing Yukawa couplings due to higher dimensional operators or renormalizable couplings between the SM quarks and extra vector-like quarks that are anomaly-free by themselves. We regard a Dirac singlet fermion as being dark matter and obtaining a small mass splitting for inelastic dark matter, only after the $U(1)'$ symmetry is broken spontaneously. We show that there is a consistent parameter space for explaining both the LZ nuclear recoil event and the correct relic density for dark matter and the existing collider and indirect detection bounds are satisfied at the same time. In this case, we predict a relatively light $Z'$ boson with $10-20\,{\rm GeV}$ mass and a weak gauge coupling, suggesting a dedicated search at colliders. The future data with higher recoil energies at direct detection experiments will play a decisive role of discriminating between the scenarios of light and heavy dark matter.

The single 248-keV nuclear-recoil candidate reported by LZ is reproduced by dark matter that downscatters, with the relic in the excited state of a pseudo-Dirac pair and a splitting \delta\simeq-350\keV. Every interpretation so far advanced is endothermic and places the splitting within a few percent of the xenon kinematic ceiling, so that the predicted count changes from zero to 143 times its central value as the halo escape speed runs from 500 to 600 km/s. The downscattering branch has no threshold speed; the same variation changes its count by 0.3 %. The ratio of counts below 70 keV to those above is 0.011, so the null standard search follows from the kinematics. A weak-strength coupling overproduces the event by 8.9\times10^{5}, so the mediator is a dark-sector one, and longevity of the relic excited state requires |\delta|<2m_e. Solving the coupled Boltzmann system removes the one free normalization. Rotating to the eigenchannels of the off-diagonal potential gives \sigma_0=(\pi/k^2)\sin^2(\delta_+-\delta_-), whose phase difference is 0.03 to 1.3 rad, so the Born rate exceeds the s-wave unitarity bound where it is used. One event then requires \sigma_p\simeq2\times10^{-42} cm^2 and a kinetic mixing \epsilon\simeq1\times10^{-6} at m_{A'}=1\GeV, with beam-dump coverage below 0.6\GeV pushing the mediator above that value. The ground state upscatters endothermically through the same operator, which excludes |\delta|\lesssim300 keV and makes the published endothermic reading the small-splitting limit of one model. The decisive test is argon, whose first form-factor zero lies at 695 keV against 94.6 keV for xenon; argon yields 4 to 6 events per tonne-year near 250 keV, where the endothermic reading is forbidden at any exposure.

The Georgi-Machacek model is a promising new physics scenario with isospin-triplet scalar fields, whose effects can qualitatively change the nature of the electroweak phase transition compared with the Standard Model. We examine the electroweak phase transition in this model by using the thermally resummed one-loop effective potential. We also incorporate effects of custodial symmetry breaking due to radiative corrections by evolving the couplings and classical fields according to the renormalization group equations. We identify viable parameter regions by Bayesian analysis using theoretical requirements and the latest experimental bounds. We then investigate the electroweak phase transition in the resulting parameter regions and discuss its phenomenological implications, such as Higgs boson decays into neutral gauge bosons, di-Higgs production at high-energy colliders, and stochastic gravitational waves associated with a first-order electroweak phase transition. We find that parameter points for the strong first-order electroweak phase transition can be verified by these observables at next-generation experiments.

This is an electronic version of the open source book "Quantum Theory of Angular Momentum" by D. A. Varshalovich, A. N. Moskalev, V. K. Khersonskii, original copyright o̧pyright} 1988 by World Scientific Publishing Co. Pte. Ltd, with the CC-BY 4.0 open source ebook funded by SCOAP. We have made appropriate modifications for the modern age–such as python-based symbolic manipulators to replace algebraic and numeric the tables. The new version contains a number of small modification, even though it is close to the original, with additional indices, hyperlinking, redrawing of figures. There has been a substantial check of the results presented, supported by the use of AI, even though all mistakes are the author's responsibility. All material is available from the book's github site (https://github.com/nwalet/Varshalovich/), where new updated versions will also be presented.