Within the framework of the lattice Boltzmann-Uehling-Uhlenbeck transport model, we present a systematic study of proton anisotropic flow observables measured by the HADES collaboration, by utilizing the recently developed density-, momentum- and isospin-dependent N5LO Skyrme pseudopotential. In particular, we investigate the impacts of the momentum dependence of nucleon mean-field potentials, the stiffness of symmetric nuclear matter (SNM) EOS, the high-density behaviors of the symmetry energy and the in-medium modification of nucleon-nucleon elastic cross sections on proton v₁, v₂, v₃, and v₄ in Au+Au collisions at s₍₍ = 2. 4\, GeV. Our results show that the proton anisotropic flows are strongly sensitive to the momentum dependence of nucleon mean-field potential as well as the incompressibility coefficient K₀ of SNM. In addition, the transverse momentum dependence of the proton v₂ exhibits a modest sensitivity to the higher-order skewness coefficient J₀ and kurtosis coefficient I₀ of SNM as well as the momentum dependence of the symmetry potential, while the transverse momentum dependence of the proton v₁ is shown to modestly depend on the in-medium modification of nucleon-nucleon elastic cross sections. Moreover, the high-density symmetry energy seems to have limited effects on the proton anisotropic flows. These findings highlight the necessity of considering the momentum dependence of nucleon mean-field potentials including the symmetry potential, the higher-order characteristic parameters of SNM EOS beyond K₀, and the in-medium modification of nucleon-nucleon elastic cross sections, in future Bayesian transport model analyses on proton anisotropic flows in heavy-ion collisions at HADES energies, thereby to extract information on nuclear matter EOS as well as the associated underlying nuclear effective interactions.
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