arXiv subjects

Wei-jie Fu

Publications and source records attributed to Wei-jie Fu.

At least 19 recordsLinked to original sources

arXiv2026

Critical net-proton number fluctuations with hydrodynamics

We compute the net-proton number fluctuations and their ratios $C_2/C_1$, $C_3/C_2$ and $C_4/C_2$ on the hydrodynamic freeze-out hypersurface of particlization at nine collision energies, $\sqrt{s_{\mathrm{NN}}}=7.7-200$ GeV, based on the fluctuations obtained from the functional renormalization group (fRG) approach, where both the regular and the critical fluctuations arising from the critical end point (CEP) are included. The transverse momentum and rapidity acceptance windows as same as the experimental measurements, the isospin randomization for the proton number fluctuations, and the global baryon conservation effect are implemented in the calculations. The results are also compared with the baseline results without critical fluctuations. It is found that for the low-order cumulants, e.g., $C_2/C_1$ the difference between the critical and non-critical results is small, while the difference increases with the increasing order of cumulants in the region of low collision energy. A non-monotonic dependence on the collision energy is observed in $C_4/C_2$ with critical fluctuations, which is absent in the results without critical fluctuations.

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arXiv2026

Fierz-complete four-quark interactions and the QCD phase diagram

The dynamics of Fierz-complete four-quark interactions and its influence on the QCD phase diagram have been investigated within the functional renormalization group approach to QCD at finite temperature and densities. It is found that in the vacuum the pion and sigma channels play the overwhelmingly dominant role, and all the other channels are negligible. However, when it is near the critical end point (CEP), the magnitude of four-quark couplings in other channels increases sizably and they become more and more important. In comparison to the single scalar-pseudoscalar channel of four-quark interactions, the dynamics of Fierz-complete four-quark interactions increases a bit the curvature of the phase boundary, and moves the CEP to location of larger baryon chemical potential and smaller temperature.

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arXiv2026

Pion Distribution Amplitudes from Functional QCD

We present the first functional QCD calculation of the pion distribution amplitude (DA) using the large-momentum effective theory within the functional renormalisation group (fRG) approach. With only the strong coupling and current quark masses as inputs, we compute the quasi-DA from first-principles QCD correlation functions. By pushing the pion momentum up to $P_z = 4.5\ \mathrm{GeV}$, the quasi-DA becomes fully saturated, rendering the extrapolation errors to the light-cone limit negligible. The resulting second-order moment $\langle \xi^2 \rangle_\pi = 0.267$ is significantly smaller than existing lattice-LaMET determinations and lies in a range consistent with other nonperturbative approaches.

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arXiv2026

Functional renormalization group study of the jet quenching parameter near the QCD critical end point

We investigate the jet quenching parameter $\hat{q}$ in the QCD phase diagram within a QCD-assisted low-energy effective theory using the functional renormalization group (fRG). Following the formalism that relates $\hat{q}$ to the spectral functions of the chiral order-parameter field, we compute the $\sigma$ and $\pi$ meson contributions to $\hat{q}$ at finite temperature and baryon chemical potential from analytically continued mesonic two-point functions. We find that $\hat{q}$ receives appreciable contributions mainly above the chiral phase boundary and exhibits a pronounced enhancement at large baryon chemical potential as the chiral crossover sharpens toward the critical end point (CEP), a behavior consistent with the picture of partonic critical opalescence (PCO), a pronounced enhancement of jet transverse momentum broadening induced by the critical $\sigma$ field fluctuations.

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arXiv2026

Kaon Distribution Amplitudes from Euclidean Functional QCD

We study the kaon quasi-distribution amplitude (quasi-DA) and distribution amplitude (DA) within the large-momentum effective theory (LaMET) combined with the first-principles functional QCD. Using quark correlation functions and the kaon Bethe-Salpeter amplitude in the Euclidean space from the 2+1 flavour functional QCD [1] as inputs, we obtain the kaon quasi DA in the large longitudinal momentum region with the contour deformation method [2] in the complex plane of momentum. By performing $1/P_z^2$ and $1/P_z^4$ order extrapolations of the kaon quasi-DA for the choices of the maximal longitudinal momentum $P_z^{\max}\in[2,2.5]$ GeV, we obtain a single-peaked and asymmetric kaon DA with the uncertainties arising from the extrapolation interval and ansatz. We find the first and second order moments of the kaon DA, $\langle ξ\rangle_K = 0.020(3)$ and $\langle ξ^2 \rangle_K = 0.253(12)$, respectively.

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arXiv2026

Solving Functional Renormalization Group Equations with Neural Networks

We employ deep neural networks to represent the field derivative of the scale-dependent effective potential in the functional renormalization group (fRG) framework for nonperturbative quantum field theory. By embedding the fRG flow equations directly into the loss function, the network parameters are determined so as to provide a continuous and differentiable representation of the scale- and field-dependent effective potential without relying on precomputed training data. Focusing on the $O(N)$ scalar field theory within the local potential approximation at finite temperature, we demonstrate that this neural network representation accurately captures the renormalization group flow across symmetric, broken, and critical regimes. A key ingredient is a decomposition of the representation into an analytically known large-$N$ contribution and a learned finite-$N$ correction, which efficiently mitigates numerical stiffness associated with convexity restoration in the broken phase. The physics-driven solutions show excellent agreement with established finite-difference and discontinuous Galerkin methods. We further apply the same strategy to the Wilson--Fisher fixed-point equation in three dimensions, illustrating that neural network representations provide a unified framework for both scale-dependent flows and fixed-point problems. For fixed points, the large-field asymptotic form alone can replace the exact large-$N$ reference, while a composite small- and large-field ansatz further improves accuracy, extending the method to problems without an analytically solvable limit. Our results indicate that physics-driven deep learning offers a robust and flexible numerical tool for functional renormalization group studies.

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arXiv2026

Strangeness neutrality and the QCD phase diagram

We map out the phase structure of $N_f=2+1$ flavour QCD at strangeness neutrality with functional QCD. We find a critical end point at $(T_{\rm CEP},μ_{B,{\rm CEP}})|_{n_S=0} = (92, 696)$\,MeV. The computation is done with the functional renormalisation group, and we systematically improve on previous works, hence reducing the systematic error significantly. Our results pass relevant QCD benchmarks: they agree well with and corroborate the QCD phase structure from functional QCD results at vanishing strangeness chemical potential. Moreover, they agree well with lattice QCD results at vanishing chemical potential. Specifically, the ratio of the second order curvature coefficient $κ_2$ agrees with that obtained from lattice computations, $κ_2(n_S=0)/κ_2(μ_S=0)=0.897(20)$.

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arXiv2025

Real-time evolution of critical modes in the QCD phase diagram

A QCD-assisted relaxation dynamic model for the critical mode of the critical end point (CEP) in the QCD phase diagram is developed, which allows us to investigate the critical slowing down effect quantitatively in the QCD phase diagram, especially in the proximity of the CEP, without any phenomenological parameters. The relaxation time from nonequilibrium to equilibrium in the QCD phase diagram is extracted from the Langevin simulations of the QCD-assisted relaxation dynamic model. It is found that in a narrow region along the phase boundary radiated from the CEP, the relaxation time is enhanced significantly. Outside this narrow region, the relaxation time drops drastically, which implies that the dynamic critical region is small in the QCD phase diagram. We also find that the effects of critical slowing down are mild on the chemical freeze-out curves.

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arXiv2025

Deuteron yields near the QCD phase transition

We investigate the influence of QCD phase transition and critical fluctuations of the critical end point (CEP) on the deuteron yield within the functional renormalization group (fRG) approach, by using the nucleon coalescence model and a low energy effective field theory of quarks and mesons. It is found that the two-point baryon density correlation function is enhanced in a narrow region radiated from the CEP along the phase boundary. The deuteron yield arising from the two-point baryon correlation is small compared to the leading-order contribution, which is attributed to the fact that in the regime of low collision energy, i.e., the region of large baryon chemical potential, the freeze-out curves deviate from the critical region, resulting in that the enhancement of the deuteron yield stemming from the critical fluctuations near the CEP is mild.

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arXiv2025

Toward precise $\xi$ gauge fixing for the lattice QCD

Lattice QCD provides a first-principles framework for solving Quantum Chromodynamics (QCD). However, its application to off-shell partons has been largely restricted to the Landau gauge, as achieving high-precision $\xi$-gauge fixing on the lattice poses significant challenges. Motivated by a universal power-law dependence of off-shell parton matrix elements on gauge-fixing precision in the Landau gauge, we propose an empirical precision extrapolation method to approximate high-precision $\xi$-gauge fixing. By properly defining the bare gauge coupling and then the effective $\xi$, we validate our $\xi$-gauge fixing procedure by successfully reproducing the $\xi$-dependent RI/MOM renormalization constants for local quark bilinear operators at 0.3\% level, up to $\xi \sim 1$.

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arXiv2025

Density functional theory of renormalization group in nuclear matter

The density functional renormalization group (density-fRG) is proposed to investigate the density fluctuations within the functional renormalization group approach, which allows us to quantify the medium effect and study physics of high densities. This method is applied to the nucleon-meson effective field theory, also known as the Walecka model, to study the properties of nuclear matter at high baryon densities. It is found that both the attractive and repulsive nucleon meson interactions are screened by the high density medium, which results in a stiffer equation of state (EoS) of nuclear matter in the regime of $ρ_0 \lesssim ρ\lesssim 2.5 ρ_0$, then a softer EoS when $ρ\gtrsim 2.5 ρ_0$. Here $ρ_0$ denotes the saturation baryon density of symmetric nuclear matter. Furthermore, a new phenomenon called the locking of Fermi surface is found. In the locking of Fermi surface the effective energy of quasi-nucleon is always close to the Fermi surface, which are both running with the renormalization group scale.

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arXiv2025

Fluctuations and correlations of quark spin in hot and dense QCD matter

In this work, we examine the impact of QCD phase transitions on the quark spin fluctuations and correlations. We propose the quark-antiquark correlation, which relates to the vector meson spin alignment and the $Λ-\barΛ$ correlation, can be used as a novel probe of the critical end point (CEP) in the QCD phase diagram. Using the Nambu-Jona-Lanisio model, we qualitatively study the properties of quark-antiquark spin correlations. Our findings reveal a peak structure near the CEP of the chiral phase transition, which may serve as an experimental signature of the CEP and account for the non-monotonic behavior of $ϕ$ meson alignment at low collision energies observed recently in experiments.

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arXiv2025

Soft modes in hot QCD matter

The chiral crossover of QCD at finite temperature and vanishing baryon density turns into a second order phase transition if lighter than physical quark masses are considered. If this transition occurs sufficiently close to the physical point, its universal critical behaviour would largely control the physics of the QCD phase transition. We quantify the size of this region in QCD using functional approaches, both Dyson-Schwinger equations and the functional renormalisation group. The latter allows us to study both critical and non-critical effects on equal footing, facilitating a precise determination of the scaling regime. We find that the physical point is far away from the critical region. Importantly, we show that the physics of the chiral crossover is dominated by soft modes even far beyond the critical region. While scaling functions determine all thermodynamic properties of the system in the critical region, the order parameter potential is the relevant quantity away from it. We compute this potential in QCD using the functional renormalisation group and Dyson-Schwinger equations and provide a simple parametrisation for phenomenological applications.

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arXiv2025

High-order fluctuations of temperature in hot QCD matter

A new thermodynamic state function is introduced to describe the thermodynamics relevant for the mean transverse momentum fluctuations of charged particles in heavy-ion collisions, which allows us to compute the temperature fluctuations of different orders in hot quantum chromodynamics (QCD) matter for the first time. Consequently, it is found that the temperature fluctuations are suppressed remarkably as the system transitions from the hadron resonance gas (HRG) to the quark-gluon plasma (QGP) with increasing temperature or baryon chemical potential, alongside a negative skewness. This is attributed to the general fact that the heat capacity of QCD matter increases significantly in QGP in comparison to that in HRG. These predictions provide a candidate observable to discover the thermodynamic temperature fluctuations in upcoming heavy-ion collision experiments, which also paves a novel way to study QCD thermodynamics and QCD phase diagram through measurements of the mean transverse momentum fluctuations of charged particles.

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arXiv2025

Universality of pseudo-Goldstone damping near critical points

Real-time dynamics of strongly correlated systems, in particular its critical dynamics near phase transitions, have been always on the cutting edge of studies in diverse fields of physics, e.g., high energy physics, condensed matter, holography, etc. In this work, we investigate the critical damping of collective modes associated with spontaneous breaking of approximate symmetries, which are called pseudo-Goldstone modes, in strongly correlated systems. Using the Schwinger-Keldysh field theory, we find a universal pseudo-Goldstone damping via the critical O($N$) model that has never been found before by other approaches. Different from the conventional damping found in holography and hydrodynamics, the new one is controlled by critical fluctuations, hence is invisible in mean-field systems or strongly correlated systems with classical gravity duals. Since the critical damping depends solely on the universalities of the critical point, irrespective of the microscopic details, our conclusion should be applicable to a wide class of interacting systems.

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arXiv2025

Quasi parton distributions of pions at large longitudinal momentum

In this paper, we develop an approach to calculate the valence-quark quasi parton distribution amplitude (quasi-PDA) and quasi parton distribution function (quasi-PDF) for the pion with a large longitudinal momentum with the functional renormalization group (fRG). This is demonstrated in a low energy effective theory (LEFT) with four-quark scatterings. In the study of the complex structure of quasi-PDA, we introduce a deformed integration contour in the calculations of quasi-PDA or quasi-PDF, which allows us to obtain correct integrals for all momentum fractions. It is found that the pion light-front PDA extrapolated from quasi-PDA based on the large momentum effective theory (LaMET) in the LEFT is comparable with lattice QCD and Dyson-Schwinger equation. This work paves the way to study the PDA and PDF within the fRG approach to first-principles QCD.

hep-ph↗

arXiv2025

Four-quark scatterings in QCD III

We study the full infrared dynamics of 2+1 flavour QCD with the functional renormalisation group approach. We resolve self-consistently the glue dynamics as well as the dynamics of chiral symmetry breaking. The computation hosts no phenomenological parameter or external input. The only ultraviolet input parameters are the physical ones in QCD: the light and strange quark masses. They are adjusted to the physical ratios of the pion and kaon masses, divided by the pion decay constant. The results for other observables of current first-principles computations are in quantitative agreement with the physical ones. This work completes the series of papers, initiated and furthered in [1,2], on dynamical chiral symmetry breaking and the emergence of mesonic bound states within the functional renormalisation group. As a first application we discuss the formation of light mesonic bound states. Amongst other applications such as the phase structure of QCD, the current work paves the way for studying QCD parton distribution functions within the functional renormalisation group approach to first-principles QCD.

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arXiv2024

The QCD moat regime and its real-time properties

Dense QCD matter may exhibit crystalline phases. Their existence is reflected in a moat regime, where mesonic correlations feature spatial modulations. We study the realtime properties of pions at finite temperature and density in QCD in order to elucidate the nature of this regime. We show that the moat regime arises from particle-hole-like fluctuations near the Fermi surface. This gives rise to a characteristic peak in the spectral function of the pion at nonzero \emph{spacelike} momentum. This peak can be interpreted as a new quasi particle, the moaton. In addition, our framework also allows us to directly test the stability of the homogeneous chiral phase against the formation of an inhomogeneous condensate in QCD. We find that the formation of such a phase is highly unlikely for baryon chemical potentials $μ_B \leq 630$\,MeV.

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