We investigate the dissociative ionization of 1,3-butadiene (${\mathrm{C}}_4{\mathrm{H}}_6$) induced by 1-MeV/u ${\mathrm{C}}^{4+}$ ions using a cold-target recoil-ion momentum spectroscopy, with a specific focus on the three-body channels involving ${\mathrm{H}}_2{}^{+}$ formation. With triplet-ion coincidence measurement, the dissociation channels ${{\mathrm{H}}_2}^{+} + {\mathrm{CH}}_2{}^{+} + {\mathrm{C}}_3{\mathrm{H}}_2{}^{+}$ and ${\mathrm{H}}_2{}^{+} + {\mathrm{CH}}_3{}^{+} + {\mathrm{C}}_3{\mathrm{H}}^{+}$ are directly identified, whereas the ${{\mathrm{H}}_2}^{+} + {\mathrm{C}}_2{\mathrm{H}}^{+} + {\mathrm{C}}_2{\mathrm{H}}_3{}^{+}$ and ${{\mathrm{H}}_2}^{+} + {\mathrm{C}}_2{{\mathrm{H}}_2}^{+} + {\mathrm{C}}_2{\mathrm{H}}_2{}^{+}$ channels are not well separated in the time-of-flight correlation map. These two three-body channels are disentangled by analyzing the correlation between kinetic energy release versus dissociation angle. Using Dalitz plots, Newton diagrams, and the native frame method, the sequential pathways with ${\mathrm{H}}_2{}^{+}$ emitted first are identified for all four channels. In addition, the ${{\mathrm{H}}_2}^{+} + {\mathrm{CH}}_2{}^{+} + {\mathrm{C}}_3{{\mathrm{H}}_2}^{+}$ channel exhibits a sequential pathway with ${\mathrm{CH}}_2{}^{+}$ emitted first, whereas the ${\mathrm{H}}_2{}^{+} + {\mathrm{C}}_2\mathrm{H}{}^{+} + {\mathrm{C}}_2{\mathrm{H}}_3{}^{+}$ channel also proceeds via a concerted mechanism. $Ab initio$ potential-energy surface calculations are performed to illuminate the intrinsic state and hydrogen-site selectivity governing ${\mathrm{H}}_2{}^{+}$ formation. These results provide insight into the mechanisms and dynamics of ${\mathrm{H}}_2{}^{+}$ formation in the three-body fragmentation processes of hydrocarbon molecules.

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• Atomic & molecular collisions