High density symmetry energy: A key to the solution of the hyperon puzzle

The recently developed nuclear effective interaction based on the so-called N3LO Skyrme pseudopotential is extended to include the hyperon-nucleon and hyperon-hyperon interactions by assuming the similar density, momentum, and isospin dependence as for the nucleon-nucleon interaction. The parameters in these interactions are determined from either experimental information if any or chiral effective field theory or lattice QCD calculations of the hyperon potentials in nuclear matter around nuclear saturation density $\rho_0$. We find that varying the high density behavior of the symmetry energy $E_{\rm sym}(\rho)$ can significantly change the critical density for hyperon appearance in the neutron stars and thus the maximum mass $M_{\rm TOV}$ of static hyperon stars. In particular, a symmetry energy which is soft around $2-3\rho_0$ but stiff above about $4\rho_0$, can lead to $M_{\rm TOV} \gtrsim 2M_\odot$ for hyperon stars and simultaneously be compatible with (1) the constraints on the equation of state of symmetric nuclear matter at suprasaturation densities obtained from flow data in heavy-ion collisions; (2) the microscopic calculations of the equation of state for pure neutron matter; (3) the star tidal deformability extracted from gravitational wave signal GW170817; (4) the mass-radius relations of PSR J0030+0451, PSR J0740+6620 and PSR J0437-4715 measured from NICER; (5) the observation of the unusually low mass and small radius in the central compact object of HESS J1731-347. Furthermore, the sound speed squared of the hyperon star matter naturally displays a strong peak structure around baryon density of $3-4\rho_0$, consistent with the model-independent analysis on the multimessenger data. Our results suggest that the high density symmetry energy could be a key to the solution of the hyperon puzzle in neutron star physics.