arXiv subjects

Zhi-Wei Liu

Publications and source records attributed to Zhi-Wei Liu.

At least 19 recordsLinked to original sources

arXiv2026

Learning neural controllers for nonlinear systems from data

This article addresses the problem of designing neural feedback controllers for unknown nonlinear systems. We propose an indirect data-driven framework that uses offline data to identify the system dynamics, upon which a neural feedback controller and a neural Lyapunov function are jointly synthesized. Input constraints are enforced by integrating a hard-saturation structure into the controller architecture. Robust synthesis conditions are derived to account for data perturbations during identification. Formal stability is certified by combining SMT verification with local Lyapunov analysis near the equilibrium. Numerical examples validate the effectiveness of the proposed framework.

eess.SY↗

arXiv2026

Femtoscopic Correlation Functions in Density Operator Representation

Femtoscopic correlation functions (CFs) have been increasingly used to extract strong interactions between pairs of unstable particles, but their physical soundness has recently been questioned. To answer this, we formulate CFs at the operator level, with the observed subsystem described by a reduced density operator and subsequent dynamics absorbed into an effective measurement operator. The Koonin-Pratt form is recovered under four well-motivated reductions. The formulation makes explicit that the source-side and interaction-side representations must be consistently matched, and motivates an operational convention in which a measured reference correlation establishes a compatible source--interaction pairing that can be extended to other pairs for CF-to-CF predictions.

quant-ph↗

arXiv2026

Quantum interference effects enhanced in $π^+p$ femtoscopic correlation functions

We present a comprehensive analysis of the $π^+p$ femtoscopic correlation functions measured by the ALICE Collaboration in high-multiplicity $pp$ collisions at $\sqrt{s}=13$ TeV. Using the Koonin-Pratt formula with a Gaussian source and data-driven $πN$ partial-wave amplitudes, we account for the contributions from $π^+p$ scattering and $Δ(1232)^{++}$-decay, thereby successfully reproducing the measured data and their transverse-mass ($m_T$) dependence. The scattering contribution yields a peak near the relative momentum $k\approx140$ MeV/$c$, whereas the decay contribution peaks around $k\approx220$ MeV/$c$. The observed correlation peak results from a weighted sum of the two contributions, with $m_T$-dependent relative weights. We find that the 140 MeV/$c$ peak originates from quantum interference between the incident and scattered waves-a mechanism previously unnoticed in femtoscopic studies. This finding resolves the peak-shift puzzle in $π^+p$ correlations and provides a novel perspective for quantum interference effects in femtoscopy.

hep-ph↗

arXiv2026

Semiglobal Input-Delay Tolerance Algorithm for Distributed Nonconvex Optimization of Networked Nonlinear Systems

This paper studies a class of distributed optimization problems in networked nonlinear systems (NNSs) subject to input delays and consensus constraints. It introduces input-delay tolerant semiglobal convergence (IDTSC), meaning that for any prescribed compact initial set there exists an admissible delay bound under which the optimal solution is computed within consensus constraints and all node states converge to the solution. Building on a hierarchical design and input-to-state stability analysis, a new semiglobal input-delay tolerant (SIDT) algorithm is developed that practically achieves IDTSC for distributed optimization under the coupling between input delays and nonlinear dynamics. Further, by relaxing strict convexity requirements through the Polyak-Łojasiewicz condition, the SIDT algorithm broadens its applicability to nonconvex optimization. Finally, numerical experiments corroborate the theory on NNSs with input delays.

math.OC↗

arXiv2026

Revealing the nature of double-strangeness pentaquark states via femtoscopic correlation functions

Recent discoveries of exotic hadrons, which cannot be classified within the conventional quark model of $q \bar{q}$ mesons and $qqq$ baryons, strongly imply the existence of dynamically generated hadronic molecules. Some of these hadron-hadron interactions are accompanied by coupled-channel effects, which remain challenging to quantitatively determine. In this work, we demonstrate that femtoscopy provides a sensitive probe of such coupled-channel dynamics. We calculate correlation functions for the double-strangeness pentaquark candidates $P_{css}(4493)$ ($J^P=1/2^-$) and $P_{css}(4633)$ ($J^P=1/2^-$ or $3/2^-$), revealing clear signatures of the attractive interactions that can form bound states. The results are markedly different from those obtained in scenarios that neglect off-diagonal transitions, highlighting the importance of coupled-channel effects for understanding the structure of these hadrons.

hep-ph↗

arXiv2026

Probing the structure of the $D_{s 0}^*(2317)$ and $X(3872)$ states through correlation functions

Over the past 20 years, many new hadron states have been discovered, but understanding their nature remains a key experimental and theoretical challenge. Recent studies have established that hadron-hadron interactions primarily govern the generation of new hadronic states, with their spectroscopy serving as a powerful tool for probing these interactions and determining the corresponding compositeness. In this work, we study four scenarios to determine the $DK$ interaction by reproducing the mass of the $D_{s0}^*(2317)$, i.e., assuming the $D_{s0}^*(2317)$ as a $DK$ molecule, a mixture of a $DK$ molecule and a bare state, a $DK-D_sη$ molecule, and a mixture of a $DK-D_sη$ molecule and a bare state. Using the $D^{0}K^{+}$ interactions derived from these scenarios, we predict the $D^{0}K^{+}$ correlation functions. Our results demonstrate that the lineshape of the $D^{0}K^{+}$ correlation function is sensitive to the admixture effects from the coupled-channel $D^+K^0$ and the bare state. Furthermore, we find that the $D^{0}K^{+}$ correlation function can probe the position of the bare state, if such a QCD bare state exists. Using the shallow-bound state candidate $X(3872)$ as input, we study the $D^0\bar{D}^{*0}$ correlation functions. These functions are highly sensitive to short-range dynamics and bare-state admixtures, resulting in clearly distinguishable correlation-function line shapes across different values of compositeness.

hep-ph↗

arXiv2026

Learning to Sparsify Stochastic Linear Bandits

This paper addresses the problem of learning to sparsify stochastic linear bandits, where a decision-maker sequentially selects actions from a high-dimensional space subject to a sparsity constraint on the number of nonzero elements in the action vector. The key challenge lies in minimizing cumulative regret while tackling the potential NP-hardness of finding optimal sparse actions due to the inherent combinatorial structure of the problem. We propose an adaptively phased exploration and exploitation algorithmic framework, utilizing ordinary least squares for parameter learning and specialized subroutines for sparse action selection. When the action set is a Euclidean ball, optimal sparse actions can be efficiently computed, enabling us to establish a $\tilde{\mathcal{O}}(d\sqrt{T})$ regret, where $d$ is the dimension of the action vector and $T$ is the time horizon length. For general convex and compact action sets where finding optimal sparse actions is intractable, we employ a greedy subroutine. For general strongly convex action sets, we derive a $\tilde{\mathcal{O}}(d \sqrt{T})$ $α$-regret; for general compact sets lacking strong convexity, we establish a $\tilde{\mathcal{O}}(d T^{2/3})$ $α$-regret, where $α$ pertains to the approximation ratio of the greedy algorithm. Finally, we validate the performance of our algorithms using extensive experiments including an application to recommendation system.

cs.LG↗

arXiv2026

Solving the Inverse Source Problem in Femtoscopy with a Toy Model

Hadron-hadron interactions, as a non-perturbative effect, play a significant role in understanding phenomenological problems in particle physics. Femtoscopy is a powerful tool in heavy-ion collision experiments, enabling the extraction of hadron-hadron interactions via momentum-correlation functions (CFs). These CFs are generally factorized into a convolution of source functions and hadron-hadron wave functions, with the latter encoding information about hadron-hadron interactions. However, source functions remain ambiguous and are commonly approximated by a Gaussian form. Reconstructing source functions from experimental correlation data constitutes an ``inverse problem." To address it, we propose a toy model based on the Tikhonov regularization. Employing a square potential well of four distinct potential strengths, we calculate the CFs for inputs of a Gaussian source function and its hybrid form. The obtained CFs are subsequently used to reconstruct the source functions via the Tikhonov regularization. Our results demonstrate that the Gaussian source function can be successfully reconstructed, indicating the potential of this approach for extracting realistic source functions of hadron pairs of interest in the future.

hep-ph↗

arXiv2026

Off-shell Chiral Dynamics in the $Λ(1405)$ Resonance and $K^-p$ Femtoscopic Correlations

We present the first systematic investigation of the $S=-1$ meson--baryon interaction within a fully off-shell covariant unitarized chiral effective field theory framework up to next-to-leading order. In particular, we perform a detailed comparison with the widely used on-shell approximation. We find that the resulting scattering observables are very similar, thereby confirming the validity of key results obtained within the on-shell scheme. A notable advantage of the off-shell treatment, however, is the absence of unphysical left-hand cuts induced by the on-shell approximation. Employing the off-shell amplitudes, we compute the femtoscopic correlation functions for $K^-p$ and $π^\pmΣ^\mp$ pairs. The $K^-p$ correlation functions are found to be consistent with previously published results based on the on-shell approximation, with marginal differences attributed to slight variations in the descriptions of the scattering data. The $π^\pmΣ^\mp$ correlation functions are predicted for the first time, and are expected to provide valuable constraints on the nature of the $Λ(1405)$ resonance and the coupled-channel chiral dynamics of the $K^-p$ system.

nucl-th↗

arXiv2026

$Λ_c N$ correlation functions with leading-order covariant chiral interactions

The $Λ_c p$ momentum correlation functions are investigated using $Λ_c N$ interactions derived within the covariant chiral effective field theory. Our analysis reveals that the interaction is weakly attractive in the spin-singlet ${}^1S_0$ channel. In contrast, the ${}^3S_1$ channel exhibits a pronounced sensitivity to coupled-channel effects, i.e., the inclusion of $S$--$D$ mixing results in a repulsive $Λ_c p$ interaction; its absence leads to a weakly attractive one. Consequently, the spin-averaged correlation function -- dominated by the triplet state weight -- exhibits repulsive behavior when the $S$-- $D$ mixing is present. Furthermore, the source size dependence of the correlation functions is examined, demonstrating that the resulting variations remain experimentally resolvable within the precision of current femtoscopic measurements. A systematic comparison with non-relativistic chiral effective field theory and phenomenological models yields distinct discrepancies in the femtoscopic correlation functions. These findings underscore the capacity of femtoscopy to discriminate between different theoretical descriptions of the $Λ_c N$ interaction and provide useful references for upcoming experimental data.

hep-ph↗

arXiv2026

$DD^*$ correlation functions in deciphering the nature of $T_{cc}(3875)^+$

Understanding near-threshold strong interactions is essential for disentangling hadronic molecules and compact multiquark states in heavy-flavor spectroscopy. In this context, the doubly charmed tetraquark candidate $T_{cc}(3875)^+$ serves as a critical benchmark because it lies very close to the $D^*$-$D$ thresholds. Motivated by the interaction ambiguity reported recently [\href{https://doi.org/10.1103/kd4s-9rzr}{Phys.Rev.D 113, L031505 (2026)}], we evaluate the $D^*$-$D$ scattering lengths and femtoscopic correlation functions for the molecular and molecule-compact admixture assignments of the $T_{cc}(3875)^+$. We show that, although these scenarios yield similar invariant-mass line shapes, their corresponding femtoscopic correlation functions differ markedly and remain clearly distinguishable for typical particle-emitting sources created at the LHC. Our results indicate that femtoscopy can serve as a sensitive and complementary probe of the near-threshold dynamics of $T_{cc}(3875)^+$, providing vital theoretical references for future LHC femtoscopy measurements.

hep-ph↗

arXiv2026

Recent developments and applications of the relativistic chiral nuclear force

The nuclear force is central to our understanding of complex nuclear phenomena and to the applications of nuclear techniques. The nonperturbative nature of the low-energy strong interaction and the color confinement have made an ab initio understanding of the nuclear force a challenge for almost a century since the pioneering work of Yukawa. Since 1990, chiral effective field theory (ChEFT) has become the de facto standard for describing nuclear interactions--most prior studies employed heavy-baryon chiral perturbation theory. Only recently, there have been successful attempts to construct a chiral nuclear force employing covariant baryon chiral perturbation theory. In this work, we review recent developments and applications of relativistic chiral nuclear forces. We first elaborate on the necessity of relativistic/covariant theories, then present the construction of the first high-precision relativistic chiral nuclear force up to next-to-next-to-leading order (NNLO), and discuss the ongoing progress in higher-order nucleon-nucleon (NN) and $nd$ scattering, as well as their applications in nuclear matter, finite nuclei, and hypernuclear systems. Finally, we summarize the achievements and outline the future outlook of this research field.

nucl-th↗

arXiv2025

$J/ψΛ$ femtoscopy and the nature of $P_{ψs}^Λ(4338)$

Over the past two decades, numerous exotic hadron states have been discovered, yet their underlying nature remains unclear. It is widely acknowledged that understanding hadron-hadron interactions is essential to unraveling their properties. Hadron spectroscopy is a powerful tool for this endeavor, providing rich experimental data that can shed light on exotic systems. Recently, the LHCb experiment analyzed the process $B^{-} \rightarrow J/ψΛ\bar{p}$ and observed a narrow peak in the $J/ψΛ$ invariant mass spectrum, regarding it as a candidate for a pentaquark. In this work, we extract the coupled-channel $J / ψΛ-\bar{D} Ξ_c-\bar{D}_s Λ_c$ potential based on the $J/ψΛ$ invariant mass spectrum. Our results indicate the existence of a bound state below the $\bar{D} Ξ_c$ mass threshold, corresponding to the experimentally measured state $P_{cs}(4338)$. Furthermore, we predict the scattering lengths and momentum correlation functions for the $J/ψΛ$ and $\bar{D}Ξ_c$ channels, which serve as theoretical references for future femtoscopy experiments.

hep-ph↗

arXiv2025

Online Convex Optimization with Memory and Limited Predictions

This paper addresses an online convex optimization problem where the cost function at each step depends on a history of past decisions (i.e., memory), and the decision maker has access to limited predictions of future cost values within a finite window. The goal is to design an algorithm that minimizes the dynamic regret against the optimal sequence of decisions in hindsight. To this end, we propose a novel predictive algorithm and establish strong theoretical guarantees for its performance. We show that the algorithm's dynamic regret decays exponentially with the length of the prediction window. Our algorithm comprises two general subroutines of independent interest. The first subroutine solves online convex optimization with memory and bandit feedback, achieving a $\sqrt{TV_T}$-dynamic regret, where $V_T$ measures the variation of the optimal decision sequence. The second is a zeroth-order method that attains a linear convergence rate for general convex optimization, matching the best achievable rate of first-order methods. The key to our algorithm is a novel truncated Gaussian smoothing technique when querying the decision points to obtain the predictions. We validate our theoretical results with numerical experiments.

math.OC↗

arXiv2025

Probing the di-$J/Ψ$ interaction and the nature of $X(6200)$ with femtoscopic correlation functions

Recent re-analyses of the di-$J/Ψ$ invariant mass spectra reveal a state near the di-$J/Ψ$ threshold, referred to as the $X(6200)$. Yet the nature of this near-threshold pole--whether it is a resonant, bound, or virtual state--remains unresolved due to our limited understanding of the di-$J/Ψ$ interaction. To address this question, we predict the di-$J/Ψ$ and $J/ΨΨ(2S)$ femtoscopic correlation functions based on the Koonin-Pratt formula with a Gaussian source and the coupled-channel dynamics. Our results show that the di-$J/Ψ$ correlation function exhibits distinctly different behaviors in each scenario, especially for small source sizes ($R\sim1$ fm), providing a clear experimental observable to distinguish the nature of $X(6200)$. These distinguishing features persist even when quantum statistical effects and coupled-channel dynamics are included and show negligible sensitivity to off-shell ambiguities. Given the high $J/Ψ$ production rates and clean detection channels at the LHC, we hope that these discoveries will stimulate further experimental studies and help clarify the nature of double-vector-charmonium interactions and the nonperturbative dynamics of fully-heavy tetraquark systems.

hep-ph↗

arXiv2025

Fast Distributed Algorithm for Aggregative Games in Malicious Environment

This paper addresses the distributed Nash Equilibrium seeking problem for aggregative games, where legitimate players' decisions are affected by potential malicious players. To describe players' behavior, we introduce a novel heterogeneous trustworthiness probabilistic framework by employing stochastic trust observations. To mitigate the waste of communication and gradient computation, we utilize a compressible unbalanced network information matrix and a multi-round communication mechanism to develop a fast Nash equilibrium seeking algorithm for aggregative games with unbalanced directed networks. By integrating the multi-round communication mechanism and a trustworthiness broadcast mechanism, we embed our fast convergence algorithm into the heterogeneous trustworthiness probabilistic framework, yielding a resilient fast Nash equilibrium seeking algorithm. Theoretical analysis confirms the convergence of the algorithm. Comparative simulations verify the accuracy of our fast convergence algorithm, and validation simulations verify the resilience of the algorithm.

eess.SY↗

arXiv2025

Traces of the $X(3960)$ state in the femtoscopic $D_s^+ D_s^- $ correlations

The femtoscopic $ D_s^+D_s^-$ correlations are investigated to predict the signature of the not-yet-established $X(3960)$ state reported by the LHCb Collaboration, in three scenarios: resonant, virtual, or bound. In the last two scenarios, it might also be identified as the state $X(3930)$. The formalism employed to generate this structure dynamically is based on the Bethe-Salpeter equation with a general $S$-wave potential. We investigate how the relevant properties and observables characterizing this state--such as the pole position, scattering length, and effective range--might be affected by variations in the model parameters. The amplitudes encoding the distinct interpretations of the $X(3960)$ state are then used as input to calculate the femtoscopic correlation function of the $D_s^+ D_s^- $ pair, which is analyzed and discussed.

hep-ph↗

arXiv2025

Chiral Evolution and Femtoscopic Signatures of the $K_1(1270)$ Resonance

We present a comprehensive study of the axial-vector resonance $K_1(1270)$ within the unitarized chiral perturbation theory, focusing on its two-pole structure and manifestation in femtoscopic observables. By considering the dominant $ρK$ and $K^*π$ coupled channels, we reproduce the well-established double-pole structure and trace the chiral evolution of both poles as functions of the pion mass, using the vector-meson mass trajectories fitted to lattice-QCD data and experimental values. The lower pole, dominantly coupled to $K^*π$, evolves from an above-threshold resonance to a virtual or bound state with increasing pion mass. In comparison, the higher pole, dominantly coupled to $ρK$, moves downward in energy, reflecting the strengthening of the chiral attraction. The influence of the finite vector-meson widths is systematically examined, showing that their inclusion smooths the pole trajectories without altering their qualitative behavior. Furthermore, femtoscopic CFs are calculated for all relevant vector-pseudoscalar channels in both charged sectors. The results exhibit distinct resonance and bound-state features consistent with the two-pole dynamics. The weak impact of higher channels, such as $ω\bar{K}$, $\bar{K}^*η$, and $ϕ\bar{K}$, confirms that the simplified two-channel treatment captures the essential dynamics of the $K_1(1270)$ resonance. This study demonstrates that combining chiral extrapolation and femtoscopic correlation analyses provides a powerful and complementary framework for connecting lattice-QCD calculations, chiral effective theory, and experimental measurements, offering new insights into the molecular nature and chiral origin of the $K_1(1270)$ resonance.

hep-ph↗