2025MNRAS.539.3493G

L328 core has three sub-cores S1, S2, and S3, among which the sub-core S2 contains L328-IRS, a Very Low Luminosity Object, which shows a CO bipolar outflow. Earlier investigations of L328 mapped cloud/envelope (parsec-scale) magnetic fields (B-fields). In this work, we used JCMT/POL-2 submillimeter (sub-mm) polarization measurements at 850 $\mu$m to map core-scale B-fields in L328. The B-fields were found to be ordered and well-connected from cloud to core-scales, i.e., from parsec- to sub-parsec-scale. The connection in B-field geometry is shown using $Planck$ dust polarization maps to trace large-scale B-fields, optical and near-infrared polarization observations to trace B-fields in the cloud and envelope, and 850 $\mu$m polarization mapping core-scale field geometry. The core-scale B-field strength, estimated using the modified Davis-Chandrasekhar-Fermi relation, was found to be 50.5 $\pm$ 9.8 $\mu$G, which is $\sim$2.5 times higher than the envelope B-field strength found in previous studies. This indicates that B-fields are getting stronger on smaller (sub-parsec) scales. The mass-to-flux ratio of 1.1 $\pm$ 0.2 suggests that the core is magnetically transcritical. The energy budget in the L328 core was also estimated, revealing that the gravitational, magnetic, and non-thermal kinetic energies were comparable with each other, while thermal energy was significantly lower.