Charm fragmentation fractions and cc̄ cross section in p$-$Pb collisions at √sNN=5.02 TeV

The total charm-quark production cross section per unit of rapidity dσ( cc̄)/dy, and the fragmentation fractions of charm quarks to different charm-hadron species f(c→ hc), are measured for the first time in p$-$Pb collisions at √sNN = 5.02 TeV at midrapidity ($-0.96<y<0.04$ in the centre-of-mass frame) using data collected by ALICE at the CERN LHC. The results are obtained based on all the available measurements of prompt production of ground-state charm-hadron species: D⁰, D⁺, Dₛ⁺, and J/ψ mesons, and Λc⁺ and Ξc⁰ baryons. The resulting cross section is $dσ({ cc̄})/dy =219.6 ± 6.3\;(stat.) {\;}-11.8+10.5\;(syst.) {\;}-2.9+7.6\;(extr.)± 5.4\;(BR)± 4.6\;(lumi.) ± 19.5\;(rapidity shape)+15.0\;(Ωc⁰)$ mb, which is consistent with a binary scaling of pQCD calculations from pp collisions. The measured fragmentation fractions are compatible with those measured in pp collisions at $√s = 5.02$ and $13$ TeV, showing an increase in the relative production rates of charm baryons with respect to charm mesons in pp and p$-$Pb collisions compared with ${e⁺e⁻}$ and ${e⁻p}$ collisions. The $p_T$-integrated nuclear modification factor of charm quarks, $R_pPb({ cc̄})= 0.91 ± 0.04\;{ (stat.)}{}+0.08-0.09\;{ (syst.)}{}+0.04-0.03\;{ (extr.)}{}± 0.03\;{ (lumi.)}$, is found to be consistent with unity and with theoretical predictions including nuclear modifications of the parton distribution functions.