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The role of the magnetic field in the fragmentation process: the case of G14.225-0.506

B-fields are predicted to play a role in the formation of filamentary structures and their fragmentation process. We aim at investigating the role of the B-field in the process of core fragmentation toward the hub-filament systems in the IRDC G14.2, which present different fragmentation level. We performed observations of the thermal dust polarization at 350 μm using the CSO toward the hubs. We applied the polarization--intensity-gradient method to estimate the significance of the B-field over the G-force. The B-field in Hub-N shows a uniform structure along the E-W orientation, perpendicular to the major axis of the hub-filament system. The I-gradient in Hub-N displays a local minimum coinciding with the dust core MM1a detected with interferometric observations. The B-field orientation is perturbed when approaching the dust core. Hub-S shows 2 local minima, reflecting the bimodal distribution of the B-field. In Hub-N, both E and W of the hub-filament system, the I-gradient and the B-field are parallel whereas they tend to be perpendicular when penetrating the filaments and hub. The analysis of the δ- and Σ B-maps indicate that, the B-field cannot prevent the collapse, suggesting that the B-field is initially dragged by the infalling motion and aligned with it, or is channeling material toward the central ridge from both sides. Values of Σ B > 1 are found toward a N-S ridge encompassing the dust emission peak, indicating that in this region B-field dominates over G-force, or that with the current angular resolution we cannot resolve an hypothetical more complex structure. We estimated the B-field strength, the MtF ratio and the A-M number, and found differences between the 2 hubs. The different levels of fragmentation observed in these 2 hubs could arise from the differences in the B-field properties rather than from different intensity of the G-field.