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Constraints on the symmetry energy and its associated parameters from nuclei to neutron stars

The symmetry energy obtained with the effective Skyrme energy density functional is related to the values of isoscalar effective mass and isovector effective mass, which is also indirectly related to the incompressibility of symmetric nuclear matter. In this work, we analyze the values of symmetry energy and its related nuclear matter parameters in five-dimensional parameter space by describing the heavy ion collision data, such as isospin diffusion data at 35 MeV/u and 50 MeV/u, neutron skin of $^{208}$Pb, and tidal deformability and maximum mass of neutron star. We obtain the parameter sets which can describe the isospin diffusion, neutron skin, tidal deformability and maximum mass of neutron star, and give the incompressibility $K_0$=250.23$\pm$20.16 MeV, symmetry energy coefficient $S_0$=31.35$\pm$2.08 MeV, the slope of symmetry energy $L$=59.57$\pm$10.06 MeV, isoscalar effective mass $m_s^*/m$=0.75$\pm$0.05 and quantity related to effective mass splitting $f_I$=0.005$\pm$0.170. At two times normal density, the symmetry energy we obtained is in 35-55 MeV. To reduce the large uncertainties of $f_I$, more critical works in heavy ion collisions at different beam energies are needed.