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### Abstract

Using a data sample corresponding to an integrated luminosity of 2.0 fb-1, collected by the LHCb experiment, the production of the.c(1S) state in proton-proton collisions at a centre-of-mass energy of v s = 13 TeVis studied in the rapidity range 2.0 < y < 4.5 and in the transverse momentum range 6.5 < pT < 14.0GeV. The cross-section for prompt production of.c(1S) mesons relative to that of the J/. meson is measured using the p p decay mode and is found to be s.c(1S)/sJ/. = 1.69 +/- 0.15 +/- 0.10 +/- 0.18. The quoted uncertainties are, in order, statistical, systematic and due to uncertainties on the branching fractions of the J/.. p p and.c. p p decays. The prompt.c(1S) production cross-section is determined to be s.c( 1S) = 1.26 +/- 0.11 +/- 0.08 +/- 0.14 mu b, where the last uncertainty includes that on the J/. meson cross-section. The ratio of the branching fractions of b-hadron decays to the.c(1S) and J/. states is measured to be Bb..c X /Bb. J/. X = 0.48 +/- 0.03 +/- 0.03 +/- 0.05, where the last uncertainty is due to those on the branching fractions of the J/.. p p and.c. p p decays. The difference between the J/. and.c(1S) masses is also determined to be 113.0 +/- 0.7 +/- 0.1MeV, which is the most precise single measurement of this quantity to date.