arXiv subjects

Shujun Zhao

Publications and source records attributed to Shujun Zhao.

16 recordsLinked to original sources

arXiv2026

Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics

We derive the necessary and sufficient conditions for nonlinear causality in viscous anisotropic hydrodynamics (VAH) within the approximation that neglects small correction terms. Relativistic hydrodynamics provides a successful description of the space-time evolution of the matter produced in relativistic heavy-ion collisions, yet the earliest stage at which a hydrodynamic description becomes valid remains an open question. VAH has been proposed as an extension of conventional viscous hydrodynamics (VH) that can accommodate the large pressure anisotropies of the early-time dynamics. However, in such far-from-equilibrium regimes, the nonlinear causality of the theory is not guaranteed. By analyzing the characteristic velocities of the VAH equations of motion, we derive a set of inequalities that ensures causal signal propagation in all directions. The resulting conditions take a remarkably simple form and admit a clear physical interpretation in terms of the characteristic modes of the anisotropic medium. These results establish the regime of validity of VAH and provide a foundation for its application to the early-time dynamics of relativistic heavy-ion collisions.

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arXiv2026

Diffusion and shear viscosity coefficients of hot isospin asymmetric strange hadronic matter using a chiral SU(3) model

We study the diffusion and shear viscosity coefficients of hot isospin asymmetric strange hadronic matter. The effects due to the baryon density, isospin, strangeness, and temperature on the nucleons and hyperons are studied within a chiral SU(3) model. The medium modifications of the baryons arise due to interactions with the mean scalar and vector fields within the model. The thermodynamic and transport properties are studied in the hot strange hadronic matter. The diffusion matrix associated with the multiple charges (baryon number, isospin, and strangeness), as well as the coefficient of shear viscosity, are computed from the Boltzmann equation using first-order Chapman--Enskog expansion within the relaxation time approximation. There are observed to be significant effects from the isospin asymmetry as well as the strangeness of the medium on the diffusion coefficients. The coefficient of shear viscosity, $\eta$ is observed to have a large enhancement in the presence of finite strangeness in the medium due to additional contributions from the hyperons. The effects due to isospin asymmetry on the shear viscosity coefficient is however observed to be marginal both in nuclear and hyperonic matter. The present study can be relevant for the experimental observables of asymmetric relativistic heavy-ion collisions, e.g., in the compressed baryonic matter (CBM) experiment at the FAIR facility at GSI as well as in the future J-PARC-HI program.

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arXiv2026

Forward hadron production in pp collisions at LHC energies from an event generator based on the color glass condensate framework

We investigate inclusive forward single-hadron production in high-energy proton--proton collisions using a CGC-inspired Monte Carlo event generator, MC-CGC. We carried out a systematic study of the sensitivity of the running-coupling Balitsky-Kovchegov (rcBK) evolution equation to its initial conditions by comparing three parameterizations: the McLerran-Venugopalan (MV) model and its two HERA DIS-constrained variants, MV$^\gamma$ and MV$^e$. Our results indicate that the current LHCb data favor the MV$^\gamma$ and MV$^e$ models, while the differences from the original MV model become more pronounced at higher transverse momentum and at mid-rapidity. As a complementary analysis, we also compared the dilute-dense (DHJ factorization) and dense-dense ($k_T$ factorization) frameworks. We found that the $k_T$ factorization framework provides a better description of the particle production spectra at mid-rapidity than the DHJ framework, where both the projectile and target are in the dense regime at LHC energies. Predictions for the FoCal measurements at ALICE, including the production of identified neutral mesons and jets, are also presented.

hep-ph↗

arXiv2026

Classification of Rational Functions of Degree Three over Finite Fields

We study rational functions over finite fields under PGL-equivalence. We say that $f, g \in \Bbb F_q(X)$ are \emph{equivalent} if there exist $\psi, \phi \in \Bbb F_q(X)$ of degree one such that $g = \psi \circ f \circ \phi$. Most properties of rational functions over finite fields as they appear in theory and applications are preserved under this equivalence. In a recent work, Mattarei and Pizzato classified rational functions of degree three over finite fields in even characteristic. In the present paper, we classify all rational functions of degree three over finite fields in odd characteristic. Our approach is based on careful analyses of the value frequencies and the ramification points of the degree three rational functions. The completion of our classification also relies on an explicit formula for the number of equivalence classes of degree three rational functions over finite fields recently obtained by the first author.

math.NT↗

arXiv2025

Exploring the fluid behavior in p+p collisions at $\sqrt{s}=13 \mathrm{TeV}$ with viscous anisotropic hydrodynamics

The applicability of hydrodynamics in small collision systems remains controversial due to the small size and short lifetime of the system. In this letter, we employ viscous anisotropic hydrodynamics (VAH), which incorporates large pressure anisotropies, to study the collectivity in p+p collisions at $\sqrt{s}=13 \mathrm{TeV}$.VAH provides a good description for $v_{2}\{2\}$ and $v_{3}\{2\}$ over a wide range of multiplicities and correctly reproduces the experimentally observed negative $c_{2}\{4\}$. Traditional second-order viscous hydrodynamics (VH), on the other hand, can describe the measurements, in particular the negative $c_{2}\{4\}$, only with model parameters for which the bulk of the evolution is characterized by large values of the shear Knudsen number. It also can not capture the large longitudinal/transverse pressure anisotropy during the early evolution. These demonstrate the failure of traditional viscous hydrodynamics in small collision systems and establish viscous anisotropic hydrodynamics as a more reliable framework to describe the bulk evolution and the observed anisotropic flow in p-p collisions at the LHC.

nucl-th↗

arXiv2025

Nuclear Physics Confronts Relativistic Collisions Of Isobars

High-energy collisions involving the $A=96$ isobars $^{96}$Zr and $^{96}$Ru have been performed in 2018 at Brookhaven National Laboratory's Relativistic Heavy Ion Collider (RHIC) as a means to search for the chiral magnetic effect in QCD. This would manifest itself as specific deviations from unity in the ratio of observables taken between $^{96}$Zr+$^{96}$Zr and $^{96}$Ru+$^{96}$Ru collisions. Measurements of such ratios (released at the end of 2021) indeed reveal deviations from unity, but these are primarily caused by the two collided isobars having different radial profiles and intrinsic deformations. To make progress in understanding RHIC data, nuclear physicists across the energy spectrum gathered in Heidelberg in 2022 as part of an EMMI Rapid Reaction Task Force (RRTF) to address the following question. Does the combined effort of low-energy nuclear structure physics and high-energy heavy-ion physics enable us to understand the observations made in isobar collisions at RHIC?

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arXiv2025

On the Characteristic Polynomial of Linearized Polynomials

Let $k$ be a finite field, and $L$ be a $q$-linearized polynomial defined over $k$ of $q$-degree $r$ ($L=\sum^r_{i=0}a_iZ^{q^i}$, with $a_i\in k$). This paper provides an algorithm to compute a characteristic polynomial of $L$ over a large extension field $\mathbb F_{q^n}\supseteq k$. Our algorithm has computational complexity of $O(n(\log(n))^4)$ in terms of $\mathbb F_q$ operations with the implied constant depending only on $k$ and $r$. Up to logarithmic factors, and for linear maps represented by low degree polynomials, this provides a square root improvement over generic algorithms.

math.NT↗

arXiv2025

On a Conjecture About the Sum-Freedom of the Binary Multiplicative Inverse Function

A recent conjecture by C. Carlet on the sum-freedom of the binary multiplicative inverse function can be stated as follows: For each pair of positive integers $(n,k)$ with $3\le k\le n-3$, there is a $k$-dimensional $\Bbb F_2$-subspace $E$ of $\Bbb F_{2^n}$ such that $\sum_{0\ne\in E}1/u=0$. We confirm this conjecture when $n$ is not a prime.

math.NT↗

arXiv2025

A "breathing'' octupole $^{208}$Pb nucleus: resolving the elliptical-to-triangular azimuthal anisotropy puzzle in ultracentral relativistic heavy ion collisions

Relativistic heavy ion collisions provide a unique opportunity to probe the nuclear structure by taking an instantaneous snapshot of the colliding nuclei and converting it into momentum anisotropies of final emitted hadrons. A long-standing puzzle of too large a ratio of the elliptical-to-triangular ($v_{2}$-to-$v_{3}$) anisotropies in ultracentral $^{208}$Pb+$^{208}$Pb collisions at the Large Hadron Collider(LHC) cannot be solved simply by hydrodynamic simulations with initial conditions containing the spherical or certain deformed shape of $^{208}$Pb. In this Letter, using the iEBE-VISHNU relativistic viscous hydrodynamic hybrid model simulations with the Trento initial condition, we show that a dynamic octupole deformation--a shape-breathing of $^{208}$Pb --could potentially solve the $v_{2}$-to-$v_{3}$ puzzle and simultaneously describe the $v_3\{4\}$ data measured in experiment. Our results highlight the unique capability of capturing transient collective properties of nuclei on yoctosecond ($10^{-24}$~s) timescales, unfeasible with low-energy nuclear reactions.

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arXiv2025

Two Absolutely Irreducible Polynomials over $\Bbb F_2$ and Their Applications to a Conjecture by Carlet

Two polynomials $F_k(X_1,\dots,X_k)$ and $\Theta_k(X_1,\dots,X_k)$ over $\Bbb F_2$ arose from the study of a conjecture by C. Carlet about the sum-freedom of the multiplicative inverse function of $\Bbb F_{2^n}$. Both $F_k$ and $\Theta_k$ are homogeneous and symmetric with $\text{deg}\,F_k=2^k-2$ and $\text{deg}\,\Theta_k=2^{k-1}$. It is known that $F_k$ is absolutely irreducible for $k\ge 3$. Using the Lang-Weil bound and a curious connection between $F_k$ and $\Theta_k$, we show that $\Theta_k$ ($k\ge 3$) is also absolutely irreducible. This conclusion allows us to improve several existing results about Carlet's conjecture.

math.NT↗

arXiv2024

On Sum-Free Functions

A function from $\Bbb F_{2^n}$ to $\Bbb F_{2^n}$ is said to be {\em $k$th order sum-free} if the sum of its values over each $k$-dimensional $\Bbb F_2$-affine subspace of $\Bbb F_{2^n}$ is nonzero. This notion was recently introduced by C. Carlet as, among other things, a generalization of APN functions. At the center of this new topic is a conjecture about the sum-freedom of the multiplicative inverse function $f_{\text{\rm inv}}(x)=x^{-1}$ (with $0^{-1}$ defined to be $0$). It is known that $f_{\text{\rm inv}}$ is 2nd order (equivalently, $(n-2)$th order) sum-free if and only if $n$ is odd, and it is conjectured that for $3\le k\le n-3$, $f_{\text{\rm inv}}$ is never $k$th order sum-free. The conjecture has been confirmed for even $n$ but remains open for odd $n$. In the present paper, we show that the conjecture holds under each of the following conditions: (1) $n=13$; (2) $3\mid n$; (3) $5\mid n$; (4) the smallest prime divisor $l$ of $n$ satisfies $(l-1)(l+2)\le (n+1)/2$. We also determine the ``right'' $q$-ary generalization of the binary multiplicative inverse function $f_{\text{\rm inv}}$ in the context of sum-freedom. This $q$-ary generalization not only maintains most results for its binary version, but also exhibits some extraordinary phenomena that are not observed in the binary case.

math.NT↗

arXiv2024

Exploring the compactness of $α$ cluster in $^{16}$O nuclei with relativistic $^{16}$O+$^{16}$O collisions

Probing the $α$ cluster of $^{16}$O with the relativistic $^{16}$O+$^{16}$O collisions has raised great interest in the heavy ion community. However, the effects of the $α$ cluster on the soft hadron observables vary largely among different studies. In this paper, we explain the differences by the compactness of the $α$ cluster in oxygen, using iEBE-VISHNU hydrodynamic simulations with different initial state $α$ cluster configurations. We also find several observables, such as the intensive skewness of the $[p_{\rm T}]$ correlator $Γ_{p_{\rm T}}$, the harmonic flows $v_2\{2\}$, $v_2\{4\}$, $v_3\{2\}$, and the $v_n^2-δ[p_{\rm T}]$ correlations $ρ(v_{2}^{2}, [p_{\rm T}])$, $ρ(v_{3}^{2}, [p_{\rm T}])$ in $^{16}$O+$^{16}$O collisions are sensitive to the compactness of the $α$ cluster in the colliding nuclei, which can be used to constrain the configurations of $^{16}$O in the future. Our study serves as an important step toward the quantitative exploration of the $α$ cluster configuration in the light nuclei with relativistic heavy ion collisions.

nucl-th↗

arXiv2024

Determining the neutron skin thickness by relativistic semi-isobaric collisions

The neutron skin thickness of the benchmark nucleus $^{208}$Pb is crucial for our understanding of the equation of state of nuclear matter. In this paper, we discuss the effect of the neutron skin on the flow ratio observables in the semi-isobaric collisions $^{208}$Pb+$^{208}$Pb and $^{197}$Au+$^{197}$Au using iEBE-VISHNU hydrodynamic simulations. Our results suggest that $^{208}$Pb and $^{197}$Au should have the same magnitude of neutron skin thickness to describe the anisotropic flow ratios between the semi-isobaric systems. Our method provides an unconventional way to determine the neutron skin with the existing relativistic heavy ion collision data.

nucl-th↗

arXiv2024

Exploring the Nuclear Shape Phase Transition in Ultra-Relativistic $^{129}$Xe+$^{129}$Xe Collisions at the LHC

The shape phase transition for certain isotope or isotone chains, associated with the quantum phase transition of finite nuclei, is an intriguing phenomenon in nuclear physics. A notable case is the Xe isotope chain, where the structure transits from a $\gamma$-soft rotor to a spherical vibrator, with the second-order shape phase transition occurring in the vicinity of $^{128-130}$Xe. In this letter, we focus on investigating the $\gamma$-soft deformation of $^{129}$Xe associated with the second-order shape phase transition by constructing novel correlators for ultra-relativistic $^{129}$Xe+$^{129}$Xe collisions. In particular, our iEBE-VISHNU model calculations show that the $v_2^2-[p_T]$ correlation $\rho_{2}$ and the mean transverse momentum fluctuation $\Gamma_{p_T}$, which were previously interpreted as the evidence for the rigid triaxial deformation of $^{129}$Xe, can also be well explained by the $\gamma$-soft deformation of $^{129}$Xe. We also propose two novel correlators $\rho_{4,2}$ and $\rho_{2,4}$, which carry non-trivial higher-order correlations and show unique capabilities to distinguish between the $\gamma$-soft and the rigid triaxial deformation of $^{129}$Xe in $^{129}$Xe+$^{129}$Xe collisions at the LHC. The present study also provides a novel way to explore the second-order shape phase transition of finite nuclei with ultra-relativistic heavy ion collisions.

nucl-th↗

arXiv2023

Collective flow and the fluid behavior in p/d/$^3$He+Au collisions at $\sqrt{s_{NN}} = 200$ GeV

By varying the intrinsic initial geometry, the p/d/$^3$He+Au collisions at the Relativistic Heavy Ion Collider (RHIC) provide a unique opportunity to understand the collective behavior and probe the possible sub-nucleon fluctuations in small systems. In this paper, we employ the hybrid model iEBE-VISHNU with Trento initial conditions to study the collective flow and the fluid behavior in p/d/$^3$He+Au collisions. With fine-tuned parameters, iEBE-VISHNU can describe the $v_2(p_T)$ and $v_3(p_T)$ data from the PHENIX and STAR collaborations. However, for some certain parameter sets with initial sub-nucleon fluctuation, the hydrodynamic simulations have already beyond their limits with the average Knudsen number $\langle K_n \rangle$ obviously larger than one. Our calculations demonstrate that, for a meaningful evaluation of the fluid behavior in the small systems, model simulations should also pay attention to the validity range of hydrodynamics.

nucl-th↗

arXiv2023

Probing the nuclear deformation with three-particle asymmetric cumulant in RHIC isobar runs

$^{96}_{44}$Ru+$^{96}_{44}$Ru and $^{96}_{40}$Zr+$^{96}_{40}$Zr collisions at $\sqrt{s_{_{\rm NN}}}=200$ GeV provide unique opportunities to study the geometry and fluctuations raised from the deformation of the colliding nuclei. Using iEBE-VISHNU hybrid model, we predict ${\rm ac}_{2}\{3\}$ ratios between these two collision systems and demonstrate that the ratios of ${\rm ac}_{2}\{3\}$, as well as the ratios of the involving flow harmonics and event-plane correlations, are sensitive to quadrupole and octupole deformations, which could provide strong constrains on the shape differences between $^{96}$Ru and $^{96}$Zr. We also study the nonlinear response coefficients $χ_{4,22}$, which show insensitivity to the deformation effect.

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