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Context.In situ observations by the Parker Solar Probe (PSP) have revealed new properties of the proton velocity distributions (VDs), including hammerhead features that suggest a non-isotropic broadening of the beams. Aims.The present work proposes a very plausible explanation for the formation of hammerhead proton populations through the action of a proton firehose-like instability triggered by the proton beam. Methods.We investigated a self-generated firehose-like instability driven by the relative drift of ion populations using a simplified moment-based quasi-linear (QL) theory. While simpler and faster than advanced numerical simulations, this toy model provided rapid insights and concisely highlighted the role of plasma micro-instabilities in relaxing the observed anisotropies of particle VDs in the solar wind and space plasmas. Results.The QL theory proposed here shows that the resulting transverse waves are right-hand polarized and have two consequences on the protons: (i) They reduce the relative drift between the beam and the core, but above all, (ii) they induce a strong perpendicular temperature anisotropy specific to the observed hammerhead ion beam. Moreover, the long-run QL results suggest that these hammerhead distributions are rather transitory states that are still subject to relaxation mechanisms, in which instabilities such as the one discussed here are very likely involved. This foundational work motivates future detailed studies using advanced methods.