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The pT-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 D0→ 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 pT coverage and total uncertainties reduced by a factor ranging from 1.05 to 1.6, depending on pT, allowing for a more precise determination of their pT-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, fs/(fu + fd), 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.

Superfluidity and Bose-Einstein condensation are usually considered as two closely related phenomena. Indeed, in most macroscopic quantum systems, like liquid helium, ultracold atomic Bose gases, and exciton-polaritons, condensation and superfluidity occur in parallel. In photon Bose-Einstein condensates realized in the dye microcavity system, thermalization does not occur by direct interaction of the condensate particles as in the above described systems, i.e. photon-photon interactions, but by absorption and re-emission processes on the dye molecules, which act as a heat reservoir. Currently, there is no experimental evidence for superfluidity in the dye microcavity system, though effective photon interactions have been observed from thermo-optic effects in the dye medium. In this work, we theoretically investigate the implications of effective thermo-optic photon interactions, a temporally delayed and spatially non-local effect, on the photon condensate, and derive the resulting Bogoliubov excitation spectrum. The calculations suggest a linear photon dispersion at low momenta, fulfilling the Landau's criterion of superfluidity. We envision that the temporally delayed and long-range nature of the thermo-optic photon interaction offer perspectives for novel quantum fluid phenomena.