This paper presents the measurements of $$\pi ^{\pm }$$π±, $$\mathrm {K}^{\pm }$$K±, $$\text {p}$$p and $$\overline{\mathrm{p}} $$p¯ transverse momentum ($$p_{\text {T}}$$pT) spectra as a function of charged-particle multiplicity density in proton–proton (pp) collisions at $$\sqrt{s}\ =\ 13\ \text {TeV}$$s=13TeV with the ALICE detector at the LHC. Such study allows us to isolate the center-of-mass energy dependence of light-flavour particle production. The measurements reported here cover a $$p_{\text {T}}$$pT range from 0.1 to 20 $$\text {GeV}/c$$GeV/c and are done in the rapidity interval $$|y|<0.5$$|y|<0.5. The $$p_{\text {T}}$$pT-differential particle ratios exhibit an evolution with multiplicity, similar to that observed in pp collisions at $$\sqrt{s}\ =\ 7\ \text {TeV}$$s=7TeV, which is qualitatively described by some of the hydrodynamical and pQCD-inspired models discussed in this paper. Furthermore, the $$p_{\text {T}}$$pT-integrated hadron-to-pion yield ratios measured in pp collisions at two different center-of-mass energies are consistent when compared at similar multiplicities. This also extends to strange and multi-strange hadrons, suggesting that, at LHC energies, particle hadrochemistry scales with particle multiplicity the same way under different collision energies and colliding systems.

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