Parton distribution functions of the proton in a hot isospin-asymmetric nuclear medium and finite nuclei
When a nucleon is bound in a nucleus, its quark distributions are modified, and the change in the spin-dependent distributions can differ in size from that in the spin-independent ones. We compute the unpolarized $f_1(x)$, helicity $g_1(x)$, and transversity $h_1(x)$ distributions of the $u$ and $d$ quarks in a proton immersed in hot and isospin-asymmetric nuclear matter. The proton is described in the diquark spectator model, with the medium effects entering through the effective quark, diquark, and proton masses computed using the chiral SU(3) quark mean field (CQMF) model. The axial and tensor charges are obtained for baryon densities up to saturation density and temperatures $T = 0$ and $0.1$ GeV, in both symmetric nuclear matter and pure neutron matter. The distributions are then carried to $^{40}$Ca, $^{56}$Fe, $^{197}$Au, and $^{208}$Pb at zero temperature through the local density approximation. In symmetric matter at saturation density and zero temperature, the peaks of the three $u$ quark distributions move toward larger $x$ and fall least for the unpolarized distribution and most for the transversity distribution, so the spin-dependent $u$ quark distributions are modified more strongly. Between vacuum and saturation density, the axial charge of the proton drops from $1.28$ to $0.844$, and the tensor charge of the $u$ quark decreases while that of the $d$ quark grows in magnitude. At the center of each nucleus, the axial charge of the proton rises from $0.699$ in $^{40}$Ca to $0.817$ in $^{208}$Pb as the central baryon density decreases, which suggests that the modification at the center follows the central density rather than the mass number.