Narrow Results

The parton distribution functions (PDFs) provide process-independent information about the quarks and gluons inside hadrons. Although the gluon PDF can be obtained from a global fit to experimental data, it is not constrained well in the large-$x$ region. Theoretical gluon-PDF studies are much fewer than those of the quark PDFs. In this work, we present the first lattice-QCD results that access the $x$-dependence of the gluon unpolarized PDF of the nucleon. The lattice calculation is carried out with nucleon momenta up to 2.16 GeV, lattice spacing $a\approx 0.12$ fm, and with valence pion masses of 310 and 690 MeV. We use reduced Ioffe-time distributions to cancel the renormalization and implement a one-loop perturbative pseudo-PDF gluon matching. We neglect mixing of the gluon operator with the quark singlet sector. Our matrix-element results in coordinate space are consistent with those obtained from the global PDF fits of CT18 NNLO and NNPDF3.1 NNLO. Our fitted gluon PDFs at both pion masses are consistent with global fits in the $x>0.3$ region.

We have studied the ground state bulk properties of magnesium isotopes using axially symmetric relativistic mean field formalism. The BCS pairing approach is employed to take care of the pairing correlation for the open shell nuclei. The contour plot of the nucleons distribution are analyzed at various parts of the nucleus, where clusters are located. The presence of an ¹⁶O core along bubble like α-particle(s) and few nucleons are found in the Mg isotopes.