arXiv subjects

Jianlong Lu

Publications and source records attributed to Jianlong Lu.

14 recordsLinked to original sources

arXiv2026

The Type-I Seesaw as a Relativistic Fermionic Proximity Effect: Spectral Moments, EFT Consistency, and Sterile-Sector Reconstruction

We formulate the type-I seesaw as a relativistic fermionic proximity effect in the exact active-sector two-point kernel. Active neutrinos have no renormalizable gauge-invariant Majorana mass and couple by lepton-number-conserving Yukawa hybridization to a sterile Majorana pairing kernel. Integrating out the sterile fields gives a nonlocal Nambu-Gorkov embedding self-energy. In a sterile Takagi basis its anomalous and normal flavor responses are $\mathcal{A}(Q^2)=\sum_i M_i y_i y_i^T/(Q^2+M_i^2)$ and $\mathcal{B}(Q^2)=\sum_i y_i y_i^\dagger/(Q^2+M_i^2)$, respectively. Their low-energy expansions generate correlated lepton-number-violating and lepton-number-conserving moment towers. The leading moments reproduce the Weinberg coefficient and the dimension-six kinetic operator. Both towers share one sterile mass set; its positive normal support supplies a common annihilator, although anomalous residues can cancel at exact degeneracy. We prove normal block-Hankel positivity and positivity of a dimensionally rescaled mixed Nambu-Hankel sequence. The latter gives matrix Cauchy-Schwarz inequalities between lepton-number-conserving and lepton-number-violating data and can reveal paired directions hidden by a degenerate normal residue. Isolated nondegenerate pole residues satisfy an additional nonlinear compatibility identity. These results yield tree-level EFT consistency tests and a matrix-pencil reconstruction of visible pole and aggregate-residue data; selecting a unique ultraviolet Lagrangian requires additional information about sterile-basis multiplicities. An exact one-generation example distinguishes the static Schur-complement kernel from the physical Takagi pole mass. The proximity structure applies without a Fermi surface or condensate, and Nambu doubling introduces no new physical degrees of freedom.

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arXiv2026

When Similarity Is Interaction-Driven: Quantum Kernels for Regime-Sensitive Learning

Similarity in many decision systems is governed not by distance alone but by interactions among variables. In fraud and anomaly detection, small local perturbations can cross interaction-sensitive decision boundaries while leaving ambient distance almost unchanged. Motivated by this setting, we introduce a thin-slab interaction model and an interaction-driven quantum kernel constructed from entangled Pauli-string feature maps. The feature map explicitly encodes sparse high-order block interactions. We show that the resulting fidelity kernel is positive semidefinite, admits an exact block-factorized formulation, and induces a geometry sensitive to changes in interaction regime. Across balanced and imbalanced synthetic experiments spanning third-, fourth-, sixth-, and eighth-order interactions, the proposed kernel consistently outperforms linear, radial basis function, Laplacian, and polynomial kernels, as well as an engineered-interaction linear baseline supplied with the planted block products. On real fraud-detection benchmarks, it achieves the highest mean accuracy and F1 on Credit Card Fraud Detection and ranks second on IEEE-CIS Fraud Detection. These findings show that quantum-kernel performance depends on alignment between feature-map geometry and the underlying predictive structure, rather than on Hilbert-space dimension alone. Because the prescribed block-factorized kernel can also be evaluated exactly on a classical computer, the results establish predictive and representational value rather than computational quantum speedup.

quant-ph↗

arXiv2026

Operational quantum estimation theory for neutrino oscillations: identifiability, attainability, and spectral precision bounds

Quantum Fisher information (QFI) bounds state-encoded precision before measurement choice but does not establish identifiability, joint attainability, or detector sensitivity. We develop an operational framework for three-flavor oscillations that separates state, measurement, and reconstructed-event information. At fixed baseline, energy, source flavor, and matter profile, the propagated state is a pure qutrit, so its six-coordinate QFI has rank at most four. Resolved broadband components can restore rank because the aggregate kernel equals the intersection of their active kernels. We analyze joint attainability using quantum curvature, exact pure-state Holevo costs, and numerical primal-dual brackets, and propagate information through flavor projection, detector response, Poisson sampling, and nuisance profiling. An independent implementation of the public DUNE GLoBES configuration reproduces the reference spectra to relative error $3.87\times10^{-16}$ and the profiled likelihood curvature to $3.26\times10^{-6}$. Under the declared scaling and tolerance, its 264-bin event information has numerical rank six at all 176 documented physics points, whereas any four retained rule totals have rank at most four. The weakest record has effective rank five at the declared practical threshold. A conditional likelihood pilot also shows finite-grid overcoverage and dependence on the auxiliary-measurement ensemble. The framework identifies when local quantum or Fisher bounds do not support global experimental-sensitivity claims.

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arXiv2026

Testing a Flavor-Singlet Radial-Hybrid Interpretation of the $X(2370)$: Glueball Ambiguity and Discriminating Amplitude Measurements

The nature of the pseudoscalar $X(2370)$ remains unresolved: glueball, hybrid, conventional $q\bar q$, and mixed configurations are all viable at the level of present information. We test a flavor-singlet $J^{PC}=0^{-+}$ radial-hybrid interpretation using a channel-dependent one-node overlap surrogate at $m_X=2.359~\mathrm{GeV}$ and a separate flavor-singlet radiative production factor. The resulting decay template naturally suppresses $K^{*}\bar K$ and can be conditionally normalized to the measured width, although its dominant scalar and tensor channels remain model dependent. Reproducing the inferred central $J/\psi\to\gamma X$ rate requires an effective singlet-production amplitude about $4.4$ times the fixed-$V(0)$ continuation of the available $N_f=2$ lattice anchor. In a common-nuisance screening comparison, the hybrid-mixed-glueball integrated-score difference is $-1.29$, $+0.04$, and $+0.41$ for tight, baseline, and wide nuisance settings, respectively; these values constitute a conditional-score tie rather than a composition measurement. We identify coherent amplitudes in $f_0(980)\eta$, $a_0(980)\pi$, and $K_0^{*}(1430)\bar K$ as particularly informative. Under the stated proxy forecast covariance, including theory uncertainty for both templates, their joint separation is $\Delta\chi^2\simeq6.5$ from the shared glueball template and $\simeq7.6$ from the radial-$q\bar q$ surrogate. A flavor-singlet radial hybrid is therefore compatible with current data but remains indistinguishable from a mixed-glueball interpretation; a coherent amplitude analysis can test the competing decay patterns.

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arXiv2026

Exact Phenomenology of the Neutrino Cuboid: Normal Mass Ordering, the Tribimaximal Limit, and Cosmological Constraints

We investigate the exact phenomenology of a geometric neutrino cuboid defined by $m_1=m_0\sin\xi$, $m_2=m_0\cos\xi\sin\zeta$, and $m_3=m_0\cos\xi\cos\zeta$, whose cubic point corresponds to mass degeneracy and the tribimaximal values of the solar and atmospheric mixing angles. Imposing the mass-mixing alignment $\xi=\theta_{12}$ and $\zeta=\theta_{23}$, we derive closed-form consistency relations without relying on an expansion about the cubic limit. These relations show that the observed condition $\sin^2\theta_{12}<1/3$ selects normal mass ordering and, in the resulting normal-ordering regime, the physical condition $0<\Delta m_{21}^2/\Delta m_{31}^2<1$ requires $\theta_{23}$ to lie in the lower octant. Representative JUNO-based inputs give $\sin^2\theta_{23}\simeq0.440$, $(m_1,m_2,m_3)\simeq(0.0938,0.0942,0.1063)\mathrm{eV}$, and $\sum_i m_i\simeq0.294\mathrm{eV}$. We demonstrate that the first-order expansion around the tribimaximal point is numerically unstable for the solar-to-atmospheric mass-splitting ratio because of a leading-order cancellation. Present atmospheric-angle data yield only mild tension with exact alignment, whereas stringent neutrino-mass bounds in baseline $\Lambda$CDM cosmology strongly disfavor it; its viability under extended cosmological models remains model dependent. We finally formulate geometric alignment residuals as general null-test observables, providing a systematic framework for testing the neutrino cuboid with future oscillation and absolute-mass measurements.

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arXiv2026

Exact constraints on family-separated seesaw relations and their phenomenological consequences

Working at tree level and at a common renormalization scale, we examine the family-separated seesaw ansatz of Z.-z.~Xing, arXiv:2605.27049v2. For a fixed light-heavy pairing, imposing $m_iU_{\alpha i}U_{\beta i}+M_iR_{\alpha i}R_{\beta i}=0$ together with $UU^\dagger+RR^\dagger=\mathbf{1}$ yields the general exact solution $U=VD^{-1/2}$ and $R=iVE\,\operatorname{diag}\!\left(\sqrt{r_i/(1+r_i)}\right)$, where $r_i=m_i/M_i$, $D=\operatorname{diag}(1+r_i)$, $V$ is unitary, and $E=\operatorname{diag}(\eta_i)$ with $\eta_i=\pm1$. Consequently, $U^\dagger U$ and $R^\dagger R$ are diagonal, and distinct columns are exactly orthogonal. An exact unitary completion gives, in a convenient sterile basis, $M_R=D_N-D_\nu$ and $Y_\nu=(i/v)VE(D_\nu D_N)^{1/2}$, so that $Y_\nu^\dagger Y_\nu=D_\nu D_N/v^2$ is diagonal. In the canonical domain $M_i>m_i$, the singlet masses relevant to the unbroken-phase decay description are $\widehat{M}_i=M_i-m_i>0$, distinct from the broken-phase heavy eigenvalues $M_i$. Hence, at the scale of exact alignment, all standard unflavored and flavored nonresonant one-loop decay asymmetries vanish in the nondegenerate perturbative regime. For $m_i=0$, the paired Yukawa column and decay width vanish instead. The flavor-summed rephasing-invariant combination used in the proposed asymmetry also cancels identically, although individual CP-odd invariants may remain nonzero. Thus the proposed correlation between low-energy CP violation and these decay asymmetries does not follow from exact family separation. This result does not address radiative misalignment, resonant or coherent dynamics, or thermal and higher-loop sources. We also correct the proposed heavy-mass reconstruction formulas and clarify the implications for neutrinoless double-beta decay, Yukawa scaling, parameter counting, and light-heavy mass orderings.

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arXiv2025

$D_N$-Orthogonal Freedom in the Canonical Seesaw: Flavor Invariants and Physical Non-Equivalence of F-Classes

We study basis-independent structures in the Type-I seesaw mechanism for light Majorana neutrinos, assuming the canonical scenario with three heavy right-handed (sterile) neutrinos. Let $m_ν$ denote the $3\times3$ mass matrix of light neutrinos, obtained at tree level from heavy Majorana singlets with diagonal mass matrix $D_N = \mathrm{diag}(M_1,M_2,M_3)$ and Dirac matrix $m_D$. We show that all right-actions $F$ on the seesaw matrix that leave $m_ν$ unchanged form the group $G = D_N^{1/2} O(3,\mathbb{C}) D_N^{-1/2}$. While oscillation data determine the PMNS matrix $U_{\rm PMNS}$ and the mass-squared splittings, they do not fix the $F$-class within $G$. We classify basis-invariant quantities into those that are class-blind (e.g.\ $\detη$) and class-sensitive (e.g. $\mathrm{Tr}\,η$, $\mathrm{Tr}\,η^2$, an alignment measure, and CP-odd traces relevant to leptogenesis), where $η$ denotes the non-unitarity matrix of the light sector. We provide explicit formulas and both high-scale and GeV-scale benchmark examples that illustrate these invariant fingerprints and their scaling with $D_N$. This converts the degeneracy at fixed $m_ν$ into measurable, basis-invariant fingerprints.

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arXiv2025

Transformer-Based Neural Quantum Digital Twins for Many-Body Spectral Reconstruction and Adaptive Quantum-Annealing Schedule Design

We introduce Transformer-based Neural Quantum Digital Twins (Tx-NQDTs) to reconstruct the low-energy spectral evolution of many-body quantum systems along quantum-annealing paths, including ground- and first-excited-state energies, spectral gaps, and transition matrix elements, at efficient computational cost. Tx-NQDTs employ a graph-informed Transformer neural network trained to estimate the spectral information needed for annealing-schedule design. We integrate these estimates with an adaptive schedule-construction procedure guided by first-order adiabatic perturbation theory (FOAPT), which is used as a closed-system spectral diagnostic to allocate annealing time near predicted spectral bottlenecks. Experiments on a D-Wave quantum annealer ($N=10,15,20$ logical variables, with schedules represented by up to 12 control points) show that Tx-NQDT-informed schedules can improve empirical ground-state success probabilities relative to the default $20\,\mu\mathrm{s}$ linear schedule under the tested hardware conditions. The proposed schedules achieve success probabilities $2.2$--$11.7$ percentage points higher across the reported easy and hard subsets and outperform the default baseline in 44 of 60 cases. The results demonstrate the feasibility of using learned logical spectral information to automatically generate adaptive quantum-annealing schedules for practical hardware experiments.

quant-ph↗

arXiv2022

Comment on "Flavor invariants and renormalization-group equations in the leptonic sector with massive Majorana neutrinos"

Recently in [JHEP 09 (2021) 053], Wang et al. discussed the polynomial ring formed by flavor invariants in the leptonic sector with massive Majorana neutrinos. They have explicitly constructed the finite generating sets of the polynomial rings for both two-generation scenario and three-generation scenario. However, Wang et al.'s claim of the finiteness of the generating sets of the polynomial rings and their calculation by the approach of Hilbert series with generalized Molien-Weyl formula are both based on their assertion that the unitary group ${\rm U}(n,\mathbb{C})$ is reductive, which is unfortunately incorrect. The property of being reductive is only applicable to linear algebraic groups. And it is well-known that the unitary group ${\rm U}(n,\mathbb{C})$ is not even a linear algebraic group. In this paper, we point out the above issue and provide a solution to fill in the accompanying logical gaps in [JHEP 09 (2021) 053]. Some important results from the theory of linear algebraic group, the invariant theory of square matrices and group theory are needed in the analysis. We also clarify some somewhat misleading or vague statements in [JHEP 09 (2021) 053] about the scope of flavor invariants. Note that, although built from incorrect assertion, Wang et al.'s calculation results in [JHEP 09 (2021) 053] are nonetheless correct, which is ultimately because the ring of invariants of ${\rm U}(n,\mathbb{C})$ is isomorphic to that of ${\rm GL}(n,\mathbb{C})$ which is itself reductive.

hep-ph↗

arXiv2021

(Reply to)$^{\textbf{2}}$ "Comment on 'Flavor invariants and renormalization-group equations in the leptonic sector with massive Majorana neutrinos' "

We respectfully reply to Wang et al.'s reply to our comment to their [JHEP $\textbf{09}$ (2021) 053]. Some more subtleties and details are discussed for hopefully better clarification and understanding, especially about the conditions in Hilbert's finiteness theorem. We also disprove Wang et al.'s incorrect assertion in their reply [arXiv:2110.13865 [hep-ph]] that there is an isomorphism between ${\rm U}(n,\mathbb{C})$ and ${\rm GL}(n,\mathbb{C})$. We give two proofs for our argument. One proof is in the context of Lie group for arbitrary positive integer $n$, and the other proof is in the context of abstract group for $n=3$ which can also be generalized to $n\geq 3$. In order to better illustrate the intrinsic differences between a compact Lie group and its complexification, we choose ${\rm SU}(n,\mathbb{C})$ and ${\rm SL}(n,\mathbb{C})$ as a pair of examples and give two proofs for the generally non-isomorphic relation between them. One proof is in the context of Lie group for integers $n\geq 2$, and the other proof is in the context of abstract group for $n=3$ which can again be generalized to $n\geq 3$.

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arXiv2021

Comment on: "Geometric phase of neutrinos: differences between Dirac and Majorana neutrinos" [Phys. Lett. B 780, 216 (2018)]

In [Phys. Lett. B 780, 216 (2018)], Capolupo et al. calculate the noncyclic geometric phases associated with neutrino flavor transitions in the two-neutrino scenario, and claim that the results depend on the choice of representations of neutrino mixing matrix thus can be use to distinguish between Dirac and Majorana neutrinos. In this paper, we show that their calculation is flawed due to incorrect application of the definition of noncyclic geometric phase and the omission of one term in Wolfenstein effective Hamiltonian. Their results are neither gauge invariant nor lepton field rephasing invariant. We present an alternative calculation, which is solely in order to demonstrate that the Majorana CP-violating phase enters the geometric phase essentially by lepton field rephasing transformation. We point out that the seemingly nontrivial dependence of geometric phase on Majorana CP-violating phase presented in [Phys. Lett. B 780, 216 (2018)] is unphysical and thus unmeasurable.

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arXiv2020

A Higgs Doublet + Higgs Singlet Scheme with Negative Kinetic Term for Neutrino Mass Generation

In this paper, we propose a scheme for neutrino mass generation. A Higgs singlet is introduced in the Standard Model of particle physics (SM). All of this new singlet and the charged and neutral Higgs fields in the original Higgs doublet are assumed to have nonzero vacuum expectation values (VEVs). The normal hierarchy of neutrino masses is evidently preferred in our scheme. The neutrino masses are explicitly calculated.

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arXiv2020

Why Neutrino Masses Cannot Arise from Nonzero VEV of Charged Higgs Field in the Only Higgs Doublet

A scheme of neutrino mass generation is proposed by [arXiv:2003.12069], in which the small nonzero neutrino masses come from nonzero vacuum expectation value (VEV) of the charged Higgs field in the Higgs doublet in the Standard Model of particle physics (SM). However, the introduction of nonzero VEV for the charged Higgs field implies broken ${\rm U}(1)$ symmetry in the electroweak theory, which leads to non-conservation of electric charge and nonzero mass of photon. By comparing the predicted ratio of VEVs of charged Higgs field and neutral Higgs field in [1] with the ratio constrained by the present experimental upper bound of photon mass, we show that this scheme does not work.

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arXiv2020

Neutrino Masses and Noncyclic Geometric Phase of Entangled Charged Lepton-Neutrino Pair in External Magnetic Field

In this paper, we consider a pair of entangled charged lepton-neutrino embedded in a constant magnetic field, which can be produced in the purely leptonic decay of charged pseudoscalar mesons. Particles with nonzero magnetic dipole moment will precess in the present of external magnetic field and induce a nontrivial noncyclic geometric phase. The dependence of this geometric phase on neutrino mass can be used to determine the Dirac/Majorana nature of massive neutrinos.

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