arXiv subjects

Lina Wu

Publications and source records attributed to Lina Wu.

At least 19 recordsLinked to original sources

arXiv2026

Blow up and Concentration without Quantization: sharp Harnack type inequalities

Motivated by the Onsager statistical mechanics description of turbulent Euler flows with point singularities, we refine the blow up analysis for sequences of solutions of a class of perturbed singular Liouville equations which share the phenomenon of "blow up and concentration without quantization". The problem is delicate because we are dealing with the exact threshold value above which one meets the well known "concentration without quantization" phenomenon, as recently pushed forward in [C.S. Lin, G. Tarantello, C. R. Math. Acad. Sci. Paris (2016)] and in [Y. Lee, C.S. Lin, G. Tarantello, W. Yang, Comm. PDE. (2017)]. First of all we need a new sharp Harnack type inequality for this particularly rich singular limit. However this is not enough, since the growth of the conformal factor inherited by the singularity prevents the use of classical quantization arguments. We solve also this issue with different strategies for "fast" and "slow" blow up, by a careful adaptation of arguments based on the Pohozaev identity, elliptic estimates and "Sup+CInf" inequalities in the same spirit of [C.C. Chen, C.S. Lin, Comm. An. Geom. (1998)].

math.AP↗

arXiv2026

Determining the Spin Density Matrix via Its Rank and Probing the Quantum Entanglement and Bell Non-Locality at the Lepton Colliders

Considering two-fermion $F_a F_b$ productions and decays via one scalar or photon exchange at the $e^+e^-$ collider, we show that the rank $r_{\rho}$ of spin density matrix $\rho$ is equal to the number of degrees of freedom of the mediator. For one generic scalar exchange, the spin density matrix is rank one for a pure state. With rank-one condition, we can determine the spin analyzing powers for $F_a$ and $F_b$ and their product if the CP symmetry is violated and conserved, respectively, and probe the CP violation. These results can be applied to the $\eta_c \to \Lambda {\bar \Lambda}$ at the BESIII experiment and the Higgs $\to \tau \tau $ at the LHC. For one photon exchange, the spin density matrix is rank two for a mixed state. Considering the $\Lambda \bar \Lambda $ productions and decays at the BESIII experiment as an example, we show that the spin analyzing powers for $F_a$ and $ F_b$ can be determined by the rank-two conditions in details. Therefore, we can reconstruct the spin density matrices, probe the quantum entanglement and Bell non-locality, and evade the no-go theorem. Furthermore, we conjecture that the $N\times N$ spin density matrix with $r_{\rho} \le N-2 $ can be reconstructed at the lepton colliders in general.

hep-ph↗

arXiv2026

Determining the Spin-Analyzing Powers via Invariants of the Spin Correlation Matrices and Probing the Bell Non-Locality at the Lepton Colliders

We consider the two-fermion $F_a F_b$ productions and decays via one mediator exchange at the $e^+e^-$ collider. With the assumption that the spin is defined via the Lorentz symmetry, or considering the implicit symmetry in the spin density matrix, we prove that the trace ${\rm Tr} [C]$ of the spin correlation matrix $C$ is an invariant quantity, and is invariant under basis rotations. Thus, for the exchanges of one mediator such as scalar and gauge boson, we can determine the product of the spin-analyzing powers for $F_a F_b$ via ${\rm Tr} [C]$, and reconstruct the spin correlation matrix. With the CHSH-Horodecki criterion, we can probe the Bell non-locality, and evade the no-go theorem. To be concrete, we study the Bell non-locality for the $\Lambda \bar \Lambda$ productions and decays at the BESIII experiment. In addition, the invariant ${\rm Tr} [C]$ is a new physics observable to probe the new physics beyond the Standard Model (SM) and study the SM precision measurements. Moreover, for the scalar exchanges, we discuss the general invariants of the spin correlation matrices and the related phenomenological consequences.

hep-ph↗

arXiv2026

Can Mirror Symmetry Challenge Local Realism? Probing Photon Entanglement from Positronium via Compton Scattering

This study investigates photon entanglement generated from para-positronium decay by analyzing azimuthal correlations after the double Compton scattering with stationary electrons. We introduce a normalized correlation observable $\mathcal{O}_1 = \cos(2\phi_1 - 2\phi_2)/C_1$ to witness entanglement. In the absence of decoherence, $\langle\mathcal{O}_1\rangle = -1$, corresponding to a maximally entangled Bell state. With decoherence parameterized by $\rho$, the expectation becomes $-(1-\rho)$, allowing direct experimental quantification of coherence loss. A prior symmetry analysis of the Compton scattering process within the quantum field theory (QFT) is provided, which establishes the mirror-symmetric nature of the single-photon angular distribution. We further examine a local hidden-variable theory (LHVT) under the angular-momentum conservation. Imposing the mirror symmetry with respect to the plane defined by the photon spin and momentum leads to a non-negative LHVT prediction for $\langle \sin^2\theta_1 \sin^2\theta_2 \cos(2\phi_1-2\phi_2)\rangle$, contradicting the negative QFT prediction value for any $\rho < 1$. Thus, mirror symmetry serves as a novel criterion to exclude LHVT descriptions of the entangled state, whereas without preserving this symmetry, LHVTs can reproduce the correlations.

hep-ph↗

arXiv2026

Unveiling a Universal Formalism for Quantum Entanglement in Arbitrary Spin Decays

We present a comprehensive theoretical framework for probing quantum entanglement in the decay angular distributions of a spin-$S$ particle-antiparticle pair $A\bar{A}$, where each particle decays sequentially into a two-body final state, $A\to B+C$ and $\bar{A}\to\bar{B}+\bar{C}$, with $B(\bar{B})$ carrying spin $b$ and $C(\bar{C})$ being spinless. Starting from the most general polarized initial state, we derive the fully differential angular distribution $\mathcal{W}(\theta_1,\theta_2,\phi_1,\phi_2)$ and identify observables $\langle\cos(2S(\phi_1\mp\phi_2))\rangle$ whose expectation values directly depend on the entanglement-sensitive coefficients $\text{Re}\left(\alpha_{-S,\mp S}\alpha_{S,\pm S}^*\right)$ of the initial state. The proportionality factor $\mathcal{C}(S,b)$ in these relations is computed explicitly. For bosonic decays ($b=0,1,2,\ldots$), $\mathcal{C}(S,b)$ is universal and independent of decay dynamics; in particular, $\mathcal{C}(S,0)=1/2$ for any $S$, and $\mathcal{C}(1,1)=1/8$, matching known results for $W^+W^-$ decays. For fermionic decays ($b=\frac{1}{2},\frac{3}{2},\frac{5}{2}\ldots$), $\mathcal{C}(S,b)$ depends explicitly on the spin analysis powers $\alpha_{A/\bar{A}}$, making entanglement extraction more decay-dependent. We further demonstrate, within the context of $e^+e^-\to\gamma^*\to A\bar{A}$ production, how $\alpha_{A/\bar{A}}$ can be determined experimentally using specific angular observables restricted to the beam-axis region. Our results highlight the special role of bosonic decays in providing clean, model-independent tests of quantum entanglement at colliders, while outlining a pathway for entanglement measurement in fermionic cases through supplementary polarization information.

hep-ph↗

arXiv2026

Excluding Local Hidden Variables in $\Lambda\bar{\Lambda}$ Production: The Incompatibility with Angular-Momentum Conservation and CPT Invariance

We analyze spin entanglement in $\Lambda\bar{\Lambda}$ pairs produced in the decays of spin-zero particles, contrasting predictions from quantum field theory (QFT) with those of local hidden-variable theories (LHVTs). Using the self-analyzing weak decays $\Lambda \to p\pi^-$ and $\bar{\Lambda} \to \bar{p}\pi^+$, we derive the joint angular distributions within QFT. Our key findings are: For scalar production $h \to \Lambda\bar{\Lambda}$, no LHVT respecting locality and angular-momentum conservation can reproduce the QFT distribution. For pseudoscalar production $a \to \Lambda\bar{\Lambda}$, a CPT-symmetric LHVT is excluded by positivity constraints given the measured analyzing powers; however, if CPT symmetry is relaxed, an explicit LHVT construction -- with uniform hidden-variable measure and response functions satisfying $b_1 c_1 = 3\alpha_{\Lambda}\alpha_{\bar{\Lambda}}$ -- can match the QFT result. For the most general spin-zero decay $s\to \Lambda\bar{\Lambda}$ with arbitrary scalar-pseudoscalar mixing, we, under CPT invariance, identify the regions of parameter space where the QFT joint angular distribution does or does not admit an LHVT realization. These distinct signatures provide clear, experimentally testable criteria to discriminate between QFT and LHVT in $\Lambda\bar{\Lambda}$ systems across different production mechanisms.

hep-ph↗

arXiv2026

Onsager's Mean Field Theory of Vortex Flows with Singular Sources: Blow-Up and Concentration without Quantization

Motivated by the Onsager statistical mechanics description of turbulent Euler flows with point singularities, we make a first step in the generalization of the mean field theory in [Caglioti, Lions, Marchioro, Pulvirenti; Comm. Math. Phys. (1995)]. On one side we prove the equivalence of statistical ensembles, on the other side we are bound to the analysis of a new blow up phenomenon, which we call "blow up and concentration without quantization", where the mass associated with the concentration is allowed to take values in a full interval of real numbers. This singular behavior may be regarded as lying between the classical blow up-concentration-quantization and the blow up without concentration phenomenon first proposed in [Lin, Tarantello; C.R. Math. Acad. Sci. Paris (2016)]. A careful analysis is needed to generalize known pointwise estimates in this non standard context, resulting in a complete description of the allowed asymptotic profiles.

math.AP↗

arXiv2026

A Harnack-type inequality for a perturbed singular Liouville Equation

Motivated by the Onsager statistical mechanics description of turbulent Euler flows with point singularities, we obtain a Harnack-type inequality for sequences of solutions of the following perturbed Liouville equation, \begin{equation}\nonumber -\Delta v_n=\left({\epsilon_n^2+|x|^2}\right)^{\alpha_n}V_n(x)e^{\displaystyle v_n} \qquad\text{in} \,\,\, \Omega, \end{equation} where $\epsilon_n\to0^+$, $\alpha_n\to\alpha_\infty\in(-1,1)$, $\Omega$ is a bounded domain in $\mathbb{R}^2$ containing the origin and $V_n$ satisfies, \begin{equation}\nonumber 0<a\leq V_n\leq b<+\infty, \,\, V_n\in C^{0}(\Omega), \,\,V_n\to V \,\, \text{locally uniformly in}\,\,{\Omega}. \end{equation}

math.AP↗

arXiv2026

A simple proof of the Uniqueness of blow-up solutions of mean field equations

For a regular mean field equation defined on a compact Riemann surface, an important work of Bartolucci-Jevnikar-Lee-Yang \cite{bart-4} proved a uniqueness theorem for blow-up solutions under non-degeneracy assumptions. However, the proof is highly nontrivial and challenging to read. In this article, we not only provide a simple proof for the regular equation but also extend our proof to the case of singular equations with negative singular poles. Our proof supplements what is not written in a recent outstanding work by Bartolucci-Yang-Zhang \cite{byz-1}.

math.AP↗

arXiv2025

Generalized Three-Family Supersymmetric Pati-Salam Models from Type IIA Intersecting D6-Branes

Generalizing three-family chiral fermion conditions to $I_{ac}=-(3+h)$ and $I_{ac'}=h$, with positive integer $h$, we extend the landscape of three-family ${\cal N}=1$ supersymmetric Pati-Salam models in a broader region. Differing from the former investigation with $I_{ac}=-3$ and $I_{ac'}=0$, we do not restrict that the $a$ stack of D6-branes must be parallel to the orientifold image of the $c$-stack along one of the three two-tori. In this investigation, without the simple parallel construction, we find four new classes of supersymmetric Pati-Salam models that are allowed by the extended three generation condition with $I_{ac}=3, I_{ac'}=-6$ and $I_{ac}=-1, I_{ac'}=-2$ through the intersections of $a$- and $c/c'$-branes. Moreover, with the $SU(2)_{L'}$ gauge coupling realized from $SU(2)_{L_1}\times SU(2)_{L_2}$ symmetry breaking, the canonical normalization requirement of the gauge kinetic term provides an alternative approach that can be imposed before the renormalization group equation evolution for $SU(2)_{L'}$ gauge coupling. This turns out to be an effective mechanism to realize the string-scale gauge coupling relation, especially for the new supersymmetric Pati-Salam models with large $g_b/g_a$ ratio. We show that this symmetry-breaking modified renormalization group evolution can highly suppress $g_b/g_a$, and finally realizes string-scale gauge coupling relations for the extended supersymmetric Pati-Salam models as well.

hep-th↗

arXiv2025

High-Quality Axion Models with the Anomalous $U(1)_X$ Gauge Symmetry

We propose the generic high-quality axion models with anomalous $U(1)_X$ gauge symmetry and vector-like particles. We briefly review the gauge anomaly cancellations via the Green-Schwarz mechanism, study the breaking of the $U(1)_X$ gauge symmetry, as well as derive the Nambu-Goldstone boson, Peccei-Quinn (PQ) axion, and axion decay constant in general. The high-dimensional operators, which break the $U(1)_{PQ}$ global symmetry, have dimension eleven or higher due to the anomalous $U(1)_X$ gauge symmetry, and thus the axion quality problem is solved. In particular, unlike the high-quality axion models with anomaly free $U(1)$ gauge symmetry, we only need to introduce two pairs of vector-like particles. To be concrete, we present three specific models with two pairs of vector-like particles. We show that gauge anomalies in all three models can be canceled via the Green-Schwarz mechanism. To achieve gauge coupling unification, we need to introduce additional vector-like particles only in Model I. We find that gauge coupling unification is achieved at the unification scale around $10^{16}$ GeV with a relative error of less than 1\%. Notably, gauge coupling unification in Model II is achieved naturally with the smallest relative error of 0.1\%.

hep-ph↗

arXiv2025

Bypassing Spin-Analyzing Power Dependence for Quantum Entanglement at Colliders: A Case Study of $\Lambda\bar{\Lambda}$

We study, as a concrete case study using the $\Lambda(\to p\pi^-)\bar{\Lambda}(\to \bar{p}\pi^+)$ system, whether quantum entanglement in fermion pairs produced at colliders can be certified solely using angular information from final-state decays, while remaining independent of the parity-violating decay parameters $\alpha_\Lambda$ and $\alpha_{\bar{\Lambda}}$. Building on a general decomposition of any angular observable in terms of Wigner d-functions, we show that the expectation value must take the form $\mathcal{O}_0+\mathcal{O}_1\alpha_\Lambda+\mathcal{O}_2\alpha_{\bar{\Lambda}}+\mathcal{O}_3\alpha_\Lambda\alpha_{\bar{\Lambda}}$, with coefficients $\mathcal{O}_i$ ($i=0,1,2,3$) linear in the spin-density matrix elements $\alpha_{k,j}\alpha^*_{m,n}$. We obtain the value ranges of observables over the general and separable spaces of $\alpha_{k,j}$, and demonstrate a sufficient entanglement condition for pure states, extending it to mixed states by convexity. In constructing an $\alpha_\Lambda$- and $\alpha_{\bar{\Lambda}}$-independent witness from angular observables alone, we find that there are obstacles to probe quantum entanglement via the inequality-type and ratio-type ways. In particular, for the ratio-type criterion ${\langle A\rangle}/{\langle B\rangle}$, the presence of zeros of $\langle B\rangle$ in both the general and separable spaces of $\alpha_{k,j}(k,j=\pm\frac{1}{2})$ results in identical value ranges of ${\langle A\rangle}/{\langle B\rangle}$ in the two spaces (covering the entire real line), thereby precluding any effective criterion. Finally, for this specific system, we present the successful constructions with additional spin information.

hep-ph↗

arXiv2025

Dark photon dark matter constraints at the Taiwan axion search experiment with haloscope

The dark photon is a well motivated candidate for the dark matter which comprises most of the mass of our visible Universe, leading to worldwide experimental and observational efforts towards its discovery. A primary tool in this search is the cavity haloscope, which facilitates resonantly enhanced conversion to photons from both dark photons and axions. In this context, limits from axion search experiments are often directly converted into dark photon constraints, without re-analyzing the original data. However, this rescaling may not fully capture all of the relevant physics due to various reasons. By re-examining data taken by the Taiwan Axion Search Experiment with Haloscope (TASEH) experiment, we derive a world-leading constraint on the dark photon parameter space, excluding $|\epsilon|\gtrsim2\times10^{-14}$ in the $19.46 - 19.84\,\mu$eV mass range, which exceeds the na{\"i}ve `rescaling limit' by roughly a factor of two. We emphasize that accounting for the scanning timing information is crucial for deriving limits for the polarized dark photon case. In the data, we also analyze a tentative signal excess with a local significance of 4.7$\sigma$ ($m_X \simeq 19.5\,\mu$eV) that persists in the absence of a magnetic field. While this excess mimics the behavior of a dark photon signal, it has been excluded by recent results from the HAYSTAC and ORGAN-Q experiments. This case study, nevertheless, highlights the risk of discarding valid dark photon signals when relying on axion-specific magnetic field vetoes.

hep-ex↗

arXiv2025

Infrared and Visible Image Fusion Based on Implicit Neural Representations

Infrared and visible light image fusion aims to combine the strengths of both modalities to generate images that are rich in information and fulfill visual or computational requirements. This paper proposes an image fusion method based on Implicit Neural Representations (INR), referred to as INRFuse. This method parameterizes a continuous function through a neural network to implicitly represent the multimodal information of the image, breaking through the traditional reliance on discrete pixels or explicit features. The normalized spatial coordinates of the infrared and visible light images serve as inputs, and multi-layer perceptrons is utilized to adaptively fuse the features of both modalities, resulting in the output of the fused image. By designing multiple loss functions, the method jointly optimizes the similarity between the fused image and the original images, effectively preserving the thermal radiation information of the infrared image while maintaining the texture details of the visible light image. Furthermore, the resolution-independent characteristic of INR allows for the direct fusion of images with varying resolutions and achieves super-resolution reconstruction through high-density coordinate queries. Experimental results indicate that INRFuse outperforms existing methods in both subjective visual quality and objective evaluation metrics, producing fused images with clear structures, natural details, and rich information without the necessity for a training dataset.

cs.CV↗

arXiv2025

Quantum Entanglement Theory and Its Generic Searches in High Energy Physics

We propose a new formalism for quantum entanglement (QE), and study its generic searches at the colliders. For a general quantum system with $N$ particles, we show that the quantum space (the total spin polarization parameter space) is complex projective space, and the classical space (the spin polarization parameter space for classical theory) is the cartesian product of the complex projective spaces. Thus, the quantum entanglement space is the difference of these two spaces. For the $ff$, $AA$, $Af$, $fff$, and $ffA$ systems, we propose their discriminants $Δ_i$. The corresponding classical spaces are the discriminant locus $Δ=0$ for $ff$ system, and intersections of the discriminant loci $Δ_i=0$ for $AA$, $Af$, $fff$, and $ffA$ systems in the quantum space. In particular, for two fermion $ff$ system, we prove that our discriminant criterion is equivalent to the original Peres-Horodecki criterion and the CHSH criterion. And thus our quantum entanglement space is indeed Bell non-local. With the collider searches, we can reconstruct the discriminants from various measurements, and probe the quantum entanglement spaces via a fundamental approach at exact level. In addition, for the specific approach, we present a comprehensive framework to detect quantum entanglement in high-energy multi-particle systems, spanning fermion pairs ($t\bar{t}$, $τ^{+}τ^{-}$), bosonic pairs ($W^{-}W^{+}$), and hybrid or three-body systems ($W^{-}t$, $ttt$, $t\bar{t}W^{-}$), by diverse observables through angular correlations in decay products. These results establish model-independent methodologies for probing QE across collider experiments, bridging quantum information principles with high-energy phenomenology, while offering novel pathways to explore exotic particles and quantum properties in multi-particle systems.

hep-ph↗

arXiv2024

A complementary result on a singular mean field equation with a sign-changing potential function

In this note, we study the singular mean field equation defined on a Riemann surface with a sign-changing potential function. We prove if some singular sources happen to be placed on the zero-level curve of the potential function, a priori estimate can still be obtained. As a consequence of this estimate, existence and multiplicity results can still be obtained based on the topology of the manifold.

math.AP↗

arXiv2024

Development of generic no-scale inflation

We develop generalized no-scale supergravity models of inflation, and then study the corresponding cosmological predictions as well as the formation of primordial black holes (PBHs) and scalar-induced gravitational waves (SIGWs). With a new parameter $0<a\leq 1$, the generalized no-scale supergravity provides the continuous connections among the generic no-scale supergravity from string theory compactifications. The resulting prediction of the CMB, spectrum index $n_s$, and tensor-to-scalar ratio $r$ can be highly consistent with the latest Planck/BICEP/Keck Array observations. Notably, the models with $a\neq 1$ give a smaller ratio $r\leq 10^{-3}$, which is flexible even under the anticipated tighter observational constraints at the future experiments. Additionally, these models have the potential to generate a broad-band stochastic gravitational wave background, and thus explain the NANOGrav 15yr signal. Furthermore, they predict the formation of PBHs with various mass scales, which could account for a significant portion of dark matter relic density in the Universe.

gr-qc↗

arXiv2024

Dark photon constraints from a 7.139 GHz cavity haloscope experiment

The dark photon is a promising candidate for the dark matter which comprises most of the matter in our visible Universe. Via kinetic mixing with the Standard Model it can also be resonantly converted to photons in an electromagnetic cavity, offering novel experimental possibilities for the discovery and study of dark matter. We report the results of a pathfinder dark photon dark matter cavity search experiment performed at Hunan Normal University and the Institute of Physics, Chinese Academy of Sciences, representing the first stage of the APEX (Axion and dark Photon EXperiment) program. Finding no statistically significant excess, we place an upper limit on the kinetic mixing parameter $|χ|<3.7\times 10^{-13}$ around $m_A\simeq 29.5$ $μ$eV at 90% confidence level. This result exceeds other constraints on dark photon dark matter in this frequency range by roughly an order of magnitude.

hep-ex↗