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A bstract The p T -differential production cross sections of prompt and non-prompt (produced in beauty-hadron decays) D mesons were measured by the ALICE experiment at midrapidity ( | y | < 0 . 5) in proton-proton collisions at $$ \sqrt{s} $$ s = 5 . 02 TeV. The data sample used in the analysis corresponds to an integrated luminosity of (19 . 3 ± 0 . 4) nb − 1 . D mesons were reconstructed from their decays D 0 → K − π + , D + → K − π + π + , and $$ {\mathrm{D}}_{\mathrm{s}}^{+}\to \upphi {\uppi}^{+}\to {\mathrm{K}}^{-}{\mathrm{K}}^{+}{\uppi}^{+} $$ D s + → ϕ π + → K − K + π + and their charge conjugates. Compared to previous measurements in the same rapidity region, the cross sections of prompt D + and $$ {\mathrm{D}}_{\mathrm{s}}^{+} $$ D s + mesons have an extended p T coverage and total uncertainties reduced by a factor ranging from 1.05 to 1.6, depending on p T , allowing for a more precise determination of their p T -integrated cross sections. The results are well described by perturbative QCD calculations. The fragmentation fraction of heavy quarks to strange mesons divided by the one to non-strange mesons, f s / ( f u + f d ), is compatible for charm and beauty quarks and with previous measurements at different centre-of-mass energies and collision systems. The $$ \mathrm{b}\overline{\mathrm{b}} $$ b b ¯ production cross section per rapidity unit at midrapidity, estimated from non-prompt D-meson measurements, is $$ \mathrm{d}{\sigma}_{\mathrm{b}\overline{\mathrm{b}}}/\mathrm{d}y\left|{}_{\left|\mathrm{y}\right|<0.5}=34.5\pm 2.4{\left(\mathrm{stat}\right)}_{-2.9}^{+4.7}\left(\mathrm{tot}.\mathrm{syst}\right)\right. $$ d σ b b ¯ / d y y < 0.5 = 34.5 ± 2.4 stat − 2.9 + 4.7 tot . syst μb. It is compatible with previous measurements at the same centre-of-mass energy and with the cross section pre- dicted by perturbative QCD calculations.
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