Origin of nucleon mass in the light of PSR J0614-3329 with quark-hadron crossover

The recent NICER observation of PSR J0614-3329, revealing the smallest reliably measured neutron star radius of $R=10.2{9}_{\ensuremath{-}0.86}^{+1.01}\text{ }\text{ }\mathrm{km}$ at mass $M=1.4{4}_{\ensuremath{-}0.07}^{+0.06}{M}_{\ensuremath{\bigodot}}$, provides an unprecedented constraint on the equation of state of dense matter. We investigate the implications of this measurement for the origin of nucleon mass within the parity doublet model framework, which naturally incorporates both chiral variant and chiral invariant mass components. We construct unified equations of state by employing the parity doublet model with isovector scalar meson ${a}_{0}(980)$ for hadronic matter up to twice nuclear saturation density, smoothly connected to a Nambu-Jona-Lasinio-type quark model at higher densities through a crossover transition. By systematically varying the chiral invariant mass ${m}_{0}$ and quark matter parameters, we determine which values simultaneously satisfy all current astrophysical constraints, including gravitational wave observations from GW170817, NICER measurements of several pulsars, and the existence of two-solar-mass neutron stars. The inclusion of PSR J0614-3329 dramatically refines the allowed range of the chiral invariant mass from the previous constraint of $580\text{ }\text{ }\mathrm{MeV}\ensuremath{\lesssim}{m}_{0}\ensuremath{\lesssim}860\text{ }\text{ }\mathrm{MeV}$ to $800\text{ }\text{ }\mathrm{MeV}\ensuremath{\lesssim}{m}_{0}\ensuremath{\lesssim}860\text{ }\text{ }\mathrm{MeV}$, raising the lower bound by approximately 220 MeV. This result indicates that the chiral invariant mass must constitute at least 85% of the nucleon mass, challenging the traditional picture of nucleon mass generation through spontaneous chiral symmetry breaking alone and highlighting the importance of gluon condensation and other nonchiral mechanisms.