Abstract The TOTEM collaboration at the CERN LHC has measured the differential cross-section of elastic proton–proton scattering at $$\sqrt{s} = 8\,\mathrm{TeV}$$ s = 8 TeV in the squared four-momentum transfer range $$0.2\,\mathrm{GeV^{2}}< |t| < 1.9\,\mathrm{GeV^{2}}$$ 0.2 GeV 2 < | t | < 1.9 GeV 2 . This interval includes the structure with a diffractive minimum (“dip”) and a secondary maximum (“bump”) that has also been observed at all other LHC energies, where measurements were made. A detailed characterisation of this structure for $$\sqrt{s} = 8\,\mathrm{TeV}$$ s = 8 TeV yields the positions, $$|t|_{\mathrm{dip}} = (0.521 \pm 0.007)\,\mathrm{GeV^2}$$ | t | dip = ( 0.521 ± 0.007 ) GeV 2 and $$|t|_{\mathrm{bump}} = (0.695 \pm 0.026)\,\mathrm{GeV^2}$$ | t | bump = ( 0.695 ± 0.026 ) GeV 2 , as well as the cross-section values, $$\left. {\mathrm{d}\sigma /\mathrm{d}t}\right| _{\mathrm{dip}} = (15.1 \pm 2.5)\,\mathrm{{\mu b/GeV^2}}$$ d σ / d t dip = ( 15.1 ± 2.5 ) μ b / GeV 2 and $$\left. {\mathrm{d}\sigma /\mathrm{d}t}\right| _{\mathrm{bump}} = (29.7 \pm 1.8)\,\mathrm{{\mu b/GeV^2}}$$ d σ / d t bump = ( 29.7 ± 1.8 ) μ b / GeV 2 , for the dip and the bump, respectively.