Neutron star matter based on a parity doublet model including the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mn>980</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> meson
Yuk Kei Kong, Takuya Minamikawa, Masayasu Harada
Abstract
We study the effect of the isovector-scalar meson ${a}_{0}$(980) on the properties of nuclear matter and the neutron star (NS) matter by constructing a parity doublet model with including the ${a}_{0}$ meson based on the chiral SU(2)${}_{L}\ifmmode\times\else\texttimes\fi{}{\text{SU}(2)}_{R}$ symmetry. We also include the $\ensuremath{\omega}\ensuremath{-}\ensuremath{\rho}$ mixing contribution to adjust the slope parameter at the saturation. We find that, when the chiral invariant mass of nucleon ${m}_{0}$ is smaller than about 800 MeV, the existence of ${a}_{0}$(980) enlarges the symmetry energy by strengthening the repulsive $\ensuremath{\rho}$ meson coupling. On the other hand, for large ${m}_{0}$ where the Yukawa coupling of ${a}_{0}$(980) to nucleon is small, the symmetry energy is reduced by the effect of $\ensuremath{\omega}\ensuremath{-}\ensuremath{\rho}$ mixing. We then construct the equation of state (EoS) of a neutron star matter to obtain the mass-radius relation of NS. We find that, in most choices of ${m}_{0}$, the existence of ${a}_{0}$(980) stiffens the EoS and makes the radius of NS larger. We then constrain the chiral invariant mass of nucleon from the observational data of NS, and find that $580\phantom{\rule{0.16em}{0ex}}\phantom{\rule{4.pt}{0ex}}\text{MeV}\ensuremath{\lesssim}{m}_{0}\ensuremath{\lesssim}860\phantom{\rule{0.16em}{0ex}}\phantom{\rule{4.pt}{0ex}}\text{MeV}$ for ${L}_{0}=57.7$ MeV.