Dark matter (DM) environments around black holes (BHs) can influence their mergers through dynamical friction, causing gravitational wave (GW) dephasing during the inspiral phase. While this effect is well studied for collisionless dark matter (CDM), it remains unexplored for self-interacting dark matter (SIDM) due to the typically low DM density in SIDM halo cores. In this work, by considering BH mergers within SIDM spikes, which can arise from models with a massive force mediator, we show that the GWs emitted are dephased in a distinct manner. To incorporate the feedback of the BH orbital motion that can significantly modify the DM profiles, we use $N$-body simulations to analyze GW dephasing in binary BH inspirals within CDM and SIDM spikes. By tracking the binary’s motion in different DM environments, we show that the Laser Interferometer Space Antenna (LISA) can observe GW dephasing arising from SIDM spikes in particular scenarios. Our results indicate that these observations offer a possibility of distinguishing between binary-BH inspirals in different DM environments.

The conditions under which binary black hole (BBH) mergers embedded in active galactic nucleus (AGN) disks produce detectable optical counterparts remain poorly constrained observationally. We report multiepoch optical imaging and spectroscopic follow-up of S240413p, an O4 BBH candidate with 98% classification confidence and one of the smallest sky localizations reported to date ($\sim 61{\mathrm{deg}}^2$), obtained with the T80-South telescope through the S-PLUS Transient Extension Program (STEP). Our observations cover the 99% credible region across epochs that span $\sim 300\mathrm{days}$ postmerger. We prioritize AGN-hosted environments and identify two transient candidates, STEP2024gab/ZTF18acvgziq and STEP2024phe/ZTF19aaflhnr. Southern Astrophysical Research Telescope/Goodman spectroscopy and archival Dark Energy Spectroscopic Instrument spectra yield host supermassive black hole masses of $\log M_{\mathrm{SMBH}}/M_{\odot }=7.15\pm 0.05$ and $8.02\pm 0.04$. We compute predicted flare delay distributions for each host using a thermal radiation-driven outflow emission model and the spectroscopically derived host properties. Migration traps produced by thermal torques occur at $R_{\mathrm{BH}}/R_g\approx {10}^{4.2}$ and ${10}^{3.4}$ for the two hosts, with predicted flare delays spanning tens to several hundred days; our late epoch at $\sim 300\mathrm{days}$ coincides with both the peak of these distributions and the migration trap locations, while early epochs overlap only their tails. An independent five-dimensional detection efficiency analysis using BBH light curves and teglon confirms that $M_{\mathrm{SMBH}}\sim {10}^7–{10}^8{M}_{\odot }$ AGN environments at merger distances of $\sim 0.003–0.012\mathrm{pc}$ are the most favorable for detectable emission, a regime both candidate hosts occupy. We find no confirmed counterpart; a seasonal visibility gap leaves open the possibility that a flare occurred undetected, the merger may not have occurred within the AGN disk itself, or any emission may have been obscured by intrinsic AGN variability. These results demonstrate that long-baseline, AGN-prioritized monitoring is a necessary condition for accessing the highest-probability region of BBH merger parameter space and establish the need for physically informed follow-up strategies in the Rubin/Legacy Survey of Space and Time era.

High-frequency gravitational waves, particularly in the range $f\gtrsim {10}^{10}\mathrm{Hz}$, represent a compelling probe of physics beyond the Standard Model. Due to the absence of direct detection methods in this frequency regime, alternative strategies may be pursued. One promising approach involves the conversion of gravitons into photons in the presence of magnetic fields, a process known as the inverse Gertsenshtein effect. In this study, we explore such graviton-to-photon conversions occurring within the magnetic field environment of the M87 galaxy, utilizing realistic models for the galactic magnetic field and plasma density structure. We use the broadband electromagnetic spectrum of M87, ranging from millimeter to TeV gamma rays, to search for hidden contributions from graviton-photon conversions. In the well-constrained frequency range ${10}^{10}–{10}^{27}\mathrm{Hz}$, the lack of excess emission allows us to place improved bounds on the gravitational wave strain amplitude $h_c$ or on spectral energy density ${\mathrm{\Omega }}_{\mathrm{gw}}{h}^2$. We find that our results from M87 yield substantially stronger constraints compared to existing bounds derived from Milky Way magnetic field considerations, with improvements ranging from one to five orders of magnitude depending on the frequency band, thereby enhancing the prospects for probing high-frequency gravitational wave backgrounds through indirect electromagnetic signatures.

We are investigating the possibilities to directly detect the presence of heavy ions accelerated by supernova remnants (SNRs) reverse shocks. For this purpose we model the spectrum of 0.1–10 MeV gamma-ray emission produced by accelerated ejecta ions interacting with ambient protons. The resulting spectral lines are broad and have complex shapes due to the Doppler-broadening of anisotropic nuclear emission. We focus on young, historical Galactic SNRs; SN 1006, Tycho, Kepler, and Cassiopeia A. For each remnant, we compute total line fluxes and compare them with the projected sensitivities of future gamma-ray missions (e-ASTROGAM, COSI, and AMEGO). Our findings indicate that Cassiopeia A is the most promising candidate, for which we predict a peak intensity of $\sim {10}^{-11}\mathrm{erg}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}$ for the 6.13 MeV oxygen line. However, under realistic parameters, the flux maximum only marginally exceeds the e-ASTROGAM sensitivity threshold ($7\times {10}^{-12}\mathrm{erg}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}$), while lines from other species fall below detectability. Thus, only under favorable conditions—such as enhanced acceleration efficiency or a concave particle spectrum—could the oxygen line be detectable, making Cas A a key target for future MeV missions.

We present a set of numerical-relativity binary neutron star merger simulations incorporating muons and muonic reactions for two baseline baryonic equations-of-state. In order to investigate the possible impact of muons and muonic weak reactions, we treat neutrinos with a gray (energy-independent) truncated moments scheme and an implicit-explicit time integrator. Newly computed neutrino rates are employed within the full kinematics approach for a set of relevant reactions, and pair-processes are modeled via opacities computed using reaction kernels, that allow a consistent treatment of neutrino interaction rates. We find that equilibration between matter and radiation is successfully captured by a novel two timescales approach. Of astrophysical interest is the general agreement between our muonic and nonmuonic results regarding the remnant evolution, disk and outflow properties. Average electron fractions, asymptotic velocities and temperatures are different by less than $\sim 6\%$, while the main impact of muons is a reduction in ejecta masses by at most $\sim 17\%$. Therefore, based on our findings, accounting for the presence of muons and muonic reactions might result much less severe consequences regarding nucleosynthetic yields and electromagnetic counterparts than previously reported in the literature.

Quantum backreaction effects may quench Hawking evaporation through a “memory burden,” allowing primordial black holes (PBHs) with formation masses well below ${10}^{15}\mathrm{g}$ to survive to the present and contribute to the dark matter. We show that ultrahigh-energy cosmic rays (UHECRs) provide a powerful and previously unexplored probe of this scenario. We compute the proton and neutron emission from memory-burdened PBHs, including the Galactic-halo contribution and the extragalactic proton component, and confront it with the Pierre Auger Observatory proton spectrum and its EeV neutron limits from the Galactic plane. This yields new constraints on the PBH dark-matter fraction as a function of the PBH formation mass and the evaporation-suppression parameter $k$. For $k\gtrsim 3$ the nonobservation of ultrahigh-energy protons leads to bounds competitive with those from UHE gamma rays, while neutron limits remain comparable to high-energy neutrino constraints. Our results highlights the key role of multimessenger astronomy in constraining beyond-the-standard-model scenarios.

In the present work, we investigate the molecular properties of the hidden charm pentaquark states $P_c$ and $P_{cs}$ with a coupled-channel framework that combines heavy quark spin symmetry and the local hidden gauge formalism. By solving the Bethe-Salpeter equation with the cutoff method, we obtain the pole trajectories, wave functions, and root-mean-square radii. For the hidden charm system, the full coupled-channel interactions respecting the heavy quark spin symmetry are essential to generate the $P_c$ states, which significantly affect the poles’ widths. The dominant bound channels are $\overline{D}{\mathrm{\Sigma }}_c$ and ${\overline{D}}^{*}{\mathrm{\Sigma }}_c$, which couple strongly to the lower decay channels. In contrast, for the hidden charm strange system, the full heavy quark spin symmetry treatment is not necessary, where the splitting pseudoscalar meson-baryon (PB) and vector meson-baryon (VB) sectors yield similar results. The main bound channels $\overline{D}{\mathrm{\Xi }}_c$ and ${\overline{D}}^{*}{\mathrm{\Xi }}_c$ couple strongly to ${\overline{D}}_s{\mathrm{\Lambda }}_c$ and ${\overline{D}}_s^{*}{\mathrm{\Lambda }}_c$, respectively, but weakly to the lower decay channels, different from the hidden charm case. The trajectories of the pole widths for the loosely bound channels $\overline{D}{\mathrm{\Xi }}_c^{\prime }$, ${\overline{D}}^{*}{\mathrm{\Xi }}_c^{\prime }$, and ${\overline{D}}^{*}{\mathrm{\Xi }}_c^{*}$ exhibit distinct behaviors. Notably, all the primary bound channels have similar binding energies in the single-channel interactions due to equally attractive potentials. Furthermore, we also calculate the wave functions and root-mean-square radii of the corresponding poles. The wave functions are localized within $0\sim 6\mathrm{fm}$ and vanish fast beyond 4 fm. The root-mean-square radii, evaluated by two consistent methods, typically lie between 0.5 and 2 fm, comparable to the characteristic scale of molecular states. The root-mean-square radii depend on the pole trajectories and differ among the full coupled-channel case, the split PB and VB sectors, and the single-channel interactions.

We analyze the radiative decays of the $1P$, $1D$, $2S$, and $2P{\mathrm{\Lambda }}_c$ and $1D$, $2S$, and $2P{\mathrm{\Xi }}_c$ charmed baryons, belonging to the flavor antitriplet (${\overline{\mathbf{3}}}_{\mathrm{F}}$), using the constituent quark model. We compute electromagnetic transitions from ground and $P$-wave states to ground states, as well as from second-shell states to both ground and $P$-wave final states. Electromagnetic decay widths are especially valuable for identifying resonances when multiple states share similar mass and total decay width. We give branching ratios of several electromagnetic decay widths that can confirm the assignment of the ${\mathrm{\Xi }}_c(3055)$ reported by LHCb. Likewise, we provide branching-ratio predictions that can help guide the assignment of the ${\mathrm{\Xi }}_c(3080)$ states, and discuss their possible interpretation either as $1D$ states with ${\mathbf{J}}^{\mathbf{P}}=5/2^{+}$ or as $2S$ states with ${\mathbf{J}}^{\mathbf{P}}=1/2^{+}$. For the first time, this work provides calculations of electromagnetic decays for $D_{\rho }$-wave states, $\rho -\lambda$ mixed configurations, and $\rho$-mode radially excited states in singly charmed baryons of the flavor antitriplet. Both experimental and model-dependent uncertainties are taken into account throughout our analysis.

We study oscillon/$I$-ball solutions in a real scalar version of the Friedberg-Lee-Sirlin model. Using the multiple-scale analysis, we derive the conditions for oscillon solutions and explore multifield oscillon configurations. In these configurations, the two fields form colocated oscillons that oscillate with frequencies set by their respective masses. These multifield oscillons can be viewed as a bound state of two oscillons due to attractive interactions between the fields. We confirm these analytical predictions through numerical lattice calculations. This work extends the standard picture of single-field oscillons and may be relevant for cosmological scenarios involving multiple interacting real scalar fields.

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

We present a lattice QCD calculation of the electric polarizability of the charged kaon using a four-point function approach, which is the Euclidean analog of low-energy Compton scattering. In the case of the charged kaon, the polarizability is separated into an elastic term, determined from the charge radius extracted via the kaon electromagnetic form factor, and an inelastic term obtained from the time-integrated difference of four-point correlation functions. Our study employs 500 configurations of Wilson quenched ${24}^3\times 48$ lattices, and we compute connected diagrams as a proof of principle. From this analysis we obtain a charged kaon electric polarizability of ${\alpha }_E=(1.682\pm 0.523)\times {10}^{-4}{\mathrm{fm}}^3$ and a squared charge radius $r_E^2=0.3303\pm 0.0028{\mathrm{fm}}^2$ after extrapolation to the physical pion mass. The quoted uncertainties include statistical errors and, for ${\alpha }_E$, the ${\mathit{q}}^2\to 0$ extrapolation; they do not include systematic effects from the quenched approximation, omitted disconnected diagrams, finite volume, or the single lattice spacing, which may be comparable in size. The results at the simulated masses should therefore be regarded as the primary outcome, with the physical-point values serving as an indicative extrapolation. The study demonstrates the applicability of the four-point function framework to strange mesons, extends previous four-point function polarizability studies, and provides a foundation for future calculations with increased statistics, dynamical fermions, and improved control of systematic uncertainties.

We investigate the $S$-wave ${\eta }_c{\eta }_c$ and $J/\psi J/\psi$ scattering in the $J^{PC}=(0,2{)}^{++}$ channels up to a center-of-mass energy of 6.6 GeV. The calculations are carried out at two unphysical pion masses, $m_{\pi }\approx 420\mathrm{MeV}$ and 250 MeV in $N_f=2$ lattice QCD. For each $m_{\pi }$, we extract the finite-volume energy levels on two lattices with an identical lattice spacing ($a\simeq 0.136\mathrm{fm}$) but different spatial volumes. Since the coupled-channel effects between the ${\eta }_c{\eta }_c$ and $J/\psi J/\psi$ channels are found to be negligible, we analyze the corresponding scattering properties using the single-channel L"uscher method. We find that the interactions in these dicharmonium systems are dominated by the quark rearrangement effect. In the $0^{++}$ channel, the near-threshold attraction in $J/\psi J/\psi$ and repulsion in ${\eta }_c{\eta }_c$ can be explained through the Fierz rearrangement. The attractive interaction in the ${}^1{S}_0$ $J/\psi J/\psi$ channel allows for the existence of a near-threshold scalar structure, which may correspond to the $X(6200)$. In the $2^{++}$ channel, while the ${}^5{S}_2$ $J/\psi J/\psi$ system exhibits a repulsive interaction near threshold, the scattering amplitude has a Castillejo-Dalitz-Dyson zero at $\sqrt{s}=6.45\mathrm{GeV}$ and a resonance pole at $\sqrt{s_R}=[6.543(10)-i0.548(34)/2]\mathrm{GeV}$ for $m_{\pi }\approx 420\mathrm{MeV}$, and $\sqrt{s_R}=[6.538(13)-i0.537(56)/2]\mathrm{GeV}$ for $m_{\pi }\approx 250\mathrm{MeV}$, where the uncertainties are statistical. This resonance may correspond to the $X(6600)$ (or $X(6400)$) reported by the ATLAS and CMS Collaborations. Our result supports its $2^{++}$ assignment, in agreement with the latest spin-parity determination by CMS. Despite the observed dominance of the quark rearrangement effect, the light-hadron dynamics underlying dicharmonium scattering need to be explored at lighter pion masses. Furthermore, since our lattices are coarse and the lattice volumes are small, the associated systematic uncertainties should be controlled in future studies using more sophisticated lattice setups.

We study the structure of the $X(3915)$ meson in a quark model and explore how its production in heavy ion collisions depends on its internal structure. We first analyze the $X(3915)$ as a $c\overline{c}s\overline{s}$ state and solve the Hamiltonian with color-spin interactions within the quark model. We find that the ground state of the $c\overline{c}s\overline{s}$ with total spin 0 obtained from the quark model analysis favors a separated $D_s{\overline{D}}_s$ state. To probe its structure further, we study its production in relativistic heavy ion collisions for various proposed configurations. We calculate the transverse momentum distributions and yields for the $X(3915)$ assuming its structure to be either a charmonium, a tetraquark, or a hadronic molecular state. We argue that, by measuring the transverse momentum distributions and yields of the $X(3915)$ produced in heavy ion collisions, one can identify the structure of the $X(3915)$.

Although heavy-quark symmetry implies a $B_1\overline{B}$ molecular partner of the $D_1\overline{D}$ molecule, no such state has been observed experimentally to date. In this work, we propose that the experimentally observed $\mathrm{\Upsilon }(11020)$ may be a candidate for such a molecular state, although it may also contain a $B_1{\overline{B}}^{*}$ component. To explore whether the $\mathrm{\Upsilon }(11020)$ can be interpreted as an $S$-wave $B_1\overline{B}–B_1{\overline{B}}^{*}$ molecule, we calculate its strong decay widths within this molecular scenario using the compositeness condition and effective Lagrangians. The coupling of the $\mathrm{\Upsilon }(11020)$ to its constituents $B_1$ and ${\overline{B}}^{(*)}$ is determined by fitting the available experimental data on $\mathrm{\Upsilon }(11020)\to e^{+}{e}^{-}$ and $\mathrm{\Upsilon }(11020)\to {\chi }_{bJ}\pi \pi \pi$ decays. With the extracted coupling, we compute the partial decay widths of the $\mathrm{\Upsilon }(11020)$ into $B_{(s)}^{(*)}{\overline{B}}_{(s)}^{(*)}$, $\pi \pi \mathrm{\Upsilon }(nS)$, $\pi \pi h_b(nP)$, and $\pi \pi \pi {\chi }_{b1}$ via hadronic loops, as well as the three-body $B^{*}\pi {\overline{B}}^{(*)}$ decays via tree-level diagrams. Our results suggest that the $\mathrm{\Upsilon }(11020)$ can indeed be interpreted as an $S$-wave $B_1\overline{B}–B_1{\overline{B}}^{*}$ molecule with a dominant $B_1\overline{B}$ component, whose main decay channel is $B_s^{*}{\overline{B}}^{*}$. Moreover, the partial widths for $\mathrm{\Upsilon }(11020)\to \pi \pi \mathrm{\Upsilon }(nS)$ and $\mathrm{\Upsilon }(11020)\to \pi \pi h_b(nP)$ are found to be only a few eV. In contrast, the widths for $\mathrm{\Upsilon }(11020)\to \pi \pi \pi {\chi }_{bJ}$ are considerably larger, with $\pi \pi \pi {\chi }_{b1}$ reaching up to 0.167 MeV, while the yet-unobserved $\pi \pi \pi {\chi }_{b0}$ channel could be as large as 0.754 keV. These distinctive decay patterns could serve as experimental signatures of the molecular nature of the $\mathrm{\Upsilon }(11020)$, and their confirmation would provide a test of the applicability of heavy-quark symmetry.

This paper proposes a novel mechanism based on the instantaneous Bethe-Salpeter (Salpeter) equation for investigating wave function mixing in vector mesons such as $\psi (3770)$. Conventional theories typically treat $\psi (3770)$ as a $2S-1D$ mixed state; however, considering only tensor forces or relativistic corrections alone often leads to mixing angles that are too small and inconsistent with experimental data. Phenomenological $2S-1D$ mixing requires experimental data as input to determine the mixing angles, resulting in limited theoretical studies on states like $\mathrm{\Upsilon }(1D,2D)$ in the absence of experimental data. To more accurately describe $S-D$ mixing and its relativistic effects, this paper systematically compares four relativistic wave function representations (${\phi }_1$, ${\phi }_2$, ${\phi }_3$, and ${\phi }_4$) by solving the Salpeter equation and calculates the mass spectra and dileptonic decay widths of charmonium and bottomonium. The study finds that the wave function representation ${\phi }_2$ can simultaneously reproduce the experimental data of both charmonium and bottomonium well. Further analysis reveals that, in addition to $S-D$ mixing, the wave functions of vector mesons contain a non-negligible $P$-wave component, meaning they are $S-P-D$ mixed states. We predict the mixing angles for bottomonium $\mathrm{\Upsilon }(1D)$ and $\mathrm{\Upsilon }(2D)$ to be $(1.78_{-0.25}^{+0.32})°$ and $(5.44_{-0.76}^{+1.10})°$, with dileptonic decay widths of ${2.29}_{-0.69}^{+0.86}\mathrm{eV}$ and ${10.5}_{-3.1}^{+4.2}\mathrm{eV}$, respectively.

Using a dataset of $7.33{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ annihilation data collected with the BESIII detector at center-of-mass energies from 4.128 to 4.226 GeV, we report an updated measurement of the branching fraction of $D_s^{+}\to {\tau }^{+}{\nu }_{\tau }$ via four ${\tau }^{+}$ decay modes: ${\tau }^{+}\to e^{+}{\nu }_e{\overline{\nu }}_{\tau }$, ${\mu }^{+}{\nu }_{\mu }{\overline{\nu }}_{\tau }$, ${\pi }^{+}{\overline{\nu }}_{\tau }$, and ${\pi }^{+}{\pi }^0{\overline{\nu }}_{\tau }$. The branching fraction is determined to be $\mathcal{B}(D_s^{+}\to {\tau }^{+}{\nu }_{\tau })=(5.37\pm 0.08_{\mathrm{stat}}\pm 0.06_{\mathrm{syst}})\%$. The product of the modulus of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cs}|$ and the $D_s^{+}$ decay constant $f_{D_s^{+}}$ is measured to be $f_{D_s^{+}}|V_{cs}|=(248.2\pm {1.9}_{\mathrm{stat}}\pm {1.4}_{\mathrm{syst}}\pm {0.6}_{\text{input}}\pm {0.8}_{\mathrm{EM}})\mathrm{MeV}$. Both the branching fraction and the product $f_{D_s^{+}}|V_{cs}|$ are the most precise results yet obtained. Then, taking $f_{D_s^{+}}$ from lattice quantum chromodynamics calculations results in $|V_{cs}|=0.993\pm 0.008_{\mathrm{stat}}\pm 0.006_{\mathrm{syst}}\pm 0.003_{\text{input}}\pm 0.003_{\mathrm{EM}}$. Conversely, one finds $f_{D_s^{+}}=(255.0\pm {1.9}_{\mathrm{stat}}\pm {1.4}_{\mathrm{syst}}\pm {0.6}_{\text{input}}\pm {0.8}_{\mathrm{EM}})\mathrm{MeV}$ when taking $|V_{cs}|$ from the CKMfitter group as an input. Combining with the world average value of $D_s^{+}\to {\mu }^{+}{\nu }_{\mu }$, the ratio of the branching fractions between $D_s^{+}\to {\tau }^{+}{\nu }_{\tau }$ and $D_s^{+}\to {\mu }^{+}{\nu }_{\mu }$ is estimated to be $10.04\pm 0.29$, which is consistent with the Standard Model prediction of lepton flavor universality.

Using a sample of $e^{+}{e}^{-}$ annihilation data corresponding to an integrated luminosity of $4.4{\mathrm{fb}}^{-1}$ collected with the BESIII detector at the BEPCII collider and produced at center-of-mass energies from 4600 to 4698 MeV, an amplitude analysis is performed of the singly Cabibbo-suppressed decay ${\mathrm{\Lambda }}_c^{+}\to p{K}^{+}{K}^{-}$. The branching fractions of ${\mathrm{\Lambda }}_c^{+}\to p\varphi (1020)$, $p{f}_0(980)$, $\mathrm{\Lambda }(1405)K^{+}$, and $\mathrm{\Lambda }(1670)K^{+}$ are measured, where the latter two modes are decays that are observed for the first time. At the same time, with the detection efficiency based on the results of the amplitude analysis, the branching fraction of ${\mathrm{\Lambda }}_c^{+}\to p{K}^{+}{K}^{-}$ is updated to be $(9.94\pm 0.65_{\mathrm{stat}}\pm 0.50_{\mathrm{syst}})\times {10}^{-4}$, which is consistent with the current world average value within one standard deviation. The result supersedes the previous BESIII measurement with precision improved by approximately a factor of 1.5.

We propose that Feynman integral reduction is controlled by solutions of the Landau equations. We study integral relations with prescribed propagator powers using syzygy methods and discuss how syzygies can be expressed as a sum over components of the Landau singularity locus. This leads to a determinantal approach to solving the syzygy problem, giving rise to highly compact and physically transparent solutions. We demonstrate the method in applications to planar two-loop five-point integrals relevant for the $pp\to t\overline{t}H$ process. Our results suggest an efficient method of Feynman integral reduction and provide a novel physical perspective on the problem.

We propose a gauge-symmetry origin of a rank-two Dirac neutrino mass matrix that enforces one exactly massless neutrino, while being consistent with the oscillation data, as well as cosmological constraints. The mechanism relies on a minimal dark $SU(2{)}_D$ gauge symmetry under which one right-handed neutrinolike Weyl fermion is charged, thereby forbidding its Standard Model Yukawa coupling. Quantum consistency then fixes the minimal dark-sector completion: Cancellation of the Witten anomaly requires a second fermionic $SU(2{)}_D$ doublet, while a discrete $Z_4$ symmetry that forbids Majorana masses allows the two dark doublets to form a vectorlike pair. This anomaly-free completion gives rise to a secluded, confining dark sector that can contain a potential dark matter candidate, linking the protected neutrino texture to dark infrared dynamics.

A modified version of loop quantum cosmology model, the so-called mLQC-I, motivated by Thiemann’s regularization of the Hamiltonian constraint, leads to the resolution of the big bang singularity and a bounce in the isotropic setting, where either the pre- or postbounce epoch is necessarily characterized by an emergent Planckian de Sitter phase. In this work we explore the Planckian physics of this mLQC-I prescription for the Bianchi-I spacetimes. We show that, as in the isotropic model, there exists an emergent de Sitter phase which naturally dampens anisotropic shear and removes cosmic hair. However, this isotropization comes at a steep price: although a macroscopic postbounce regime is achieved, the universe does not become classical. As is well known from the Kasner solution, the classical evolution of a contracting Bianchi-I universe toward the singularity can in general be either point- or cigarlike. However, cigarlike evolution is prevalent unless the matter content dominates over the anisotropic shear. For a class of physically admissible initial conditions corresponding to cigarlike evolution, we further demonstrate that this isotropization mechanism is nongeneric. These results clarify and reinterpret recent claims by Gan et al. [Phys. Rev. Lett. 136, 251501 (2026)] that, in anisotropic mLQC-I, quantum gravity effects generically damp anisotropic shear in a manner independent of initial conditions and matter content, and that this damping arises from a novel quantum gravity effect. Our work explains the origin of this mechanism and its limitations in the mLQC-I model.