Chiral Invariant Mass Constraints from HESS J1731–347 in an Extended Parity Doublet Model with Isovector Scalar Meson

The recent discovery of an extremely light and small central compact object (CCO) within the supernova remnant HESS J1731-347, with mass <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mo>.</mo><msubsup><mn>77</mn><mrow><mo>−</mo><mn>0.17</mn></mrow><mrow><mo>+</mo><mn>0.20</mn></mrow></msubsup><mspace width="4pt"></mspace><msub><mi>M</mi><mo>⊙</mo></msub></mrow></semantics></math></inline-formula> and radius <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>10</mn><mo>.</mo><msubsup><mn>4</mn><mrow><mo>−</mo><mn>0.78</mn></mrow><mrow><mo>+</mo><mn>0.86</mn></mrow></msubsup></mrow></semantics></math></inline-formula> km, is challenging our understanding of neutron stars. In this article, we identify it as an ultra-light neutron star (NS) and constrain the chiral invariant mass of nucleon <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>m</mi><mn>0</mn></msub></semantics></math></inline-formula> from the observational data of NS using an extended parity doublet model with the isovector scalar meson <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>a</mi><mn>0</mn></msub><mrow><mo>(</mo><mn>980</mn><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. We show that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mi>σ</mi></mrow></semantics></math></inline-formula> data from the HESS J1731-347 impose a very narrow constraint on the allowed values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>m</mi><mn>0</mn></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mn>0</mn></msub></semantics></math></inline-formula> in the crossover model: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>830</mn><mspace width="0.166667em"></mspace><mspace width="4.pt"></mspace><mi>MeV</mi><mo>≲</mo><msub><mi>m</mi><mn>0</mn></msub><mo>≲</mo><mn>900</mn><mspace width="0.166667em"></mspace><mspace width="4.pt"></mspace><mi>MeV</mi></mrow></semantics></math></inline-formula> for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>L</mi><mn>0</mn></msub><mo>=</mo><mn>40</mn></mrow></semantics></math></inline-formula> MeV, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>850</mn><mspace width="0.166667em"></mspace><mspace width="4.pt"></mspace><mi>MeV</mi><mo>≲</mo><msub><mi>m</mi><mn>0</mn></msub><mo>≲</mo><mn>890</mn><mspace width="0.166667em"></mspace><mspace width="4.pt"></mspace><mi>MeV</mi></mrow></semantics></math></inline-formula> for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>L</mi><mn>0</mn></msub><mo>=</mo><mn>45</mn></mrow></semantics></math></inline-formula> MeV. We also study the higher-order asymmertic matter properties such as the symmetry incompressibility <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>K</mi><mrow><mi>s</mi><mi>y</mi><mi>m</mi></mrow></msub></semantics></math></inline-formula> and the symmetry skewness <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>Q</mi><mrow><mi>s</mi><mi>y</mi><mi>m</mi></mrow></msub></semantics></math></inline-formula> in the presence of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>a</mi><mn>0</mn></msub></semantics></math></inline-formula> meson. We find that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>K</mi><mrow><mi>s</mi><mi>y</mi><mi>m</mi></mrow></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>Q</mi><mrow><mi>s</mi><mi>y</mi><mi>m</mi></mrow></msub></semantics></math></inline-formula> are very sensitive to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>m</mi><mn>0</mn></msub></semantics></math></inline-formula> in the presence of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>a</mi><mn>0</mn></msub></semantics></math></inline-formula> meson.