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Abstract This paper presents the measurements of $$\pi ^{\pm }$$ π ± , $$\mathrm {K}^{\pm }$$ K ± , $$\text {p}$$ p and $$\overline{\mathrm{p}} $$ p ¯ transverse momentum ( $$p_{\text {T}}$$ p T ) spectra as a function of charged-particle multiplicity density in proton–proton (pp) collisions at $$\sqrt{s}\ =\ 13\ \text {TeV}$$ s = 13 TeV 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 $$p_{\text {T}}$$ p T 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 $$p_{\text {T}}$$ p T -differential particle ratios exhibit an evolution with multiplicity, similar to that observed in pp collisions at $$\sqrt{s}\ =\ 7\ \text {TeV}$$ s = 7 TeV , which is qualitatively described by some of the hydrodynamical and pQCD-inspired models discussed in this paper. Furthermore, the $$p_{\text {T}}$$ p T -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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