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### Abstract

The cross-sections of.(2S) meson production in proton-proton collisions at v s = 13 TeV are measured with a data sample collected by the LHCb detector corresponding to an integrated luminosity of 275 pb-1. The production cross-sections for prompt.(2S) mesons and those for.(2S) mesons from b-hadron decays (.(2S)-from-b) are determined as functions of the transverse momentum, pT, and the rapidity, y, of the.(2S) meson in the kinematic range 2 < pT < 20 GeV/c and 2.0 < y < 4.5. The production cross-sections integrated over this kinematic region are s(prompt.(2S), 13 TeV) = 1.430 +/- 0.005 (stat) +/- 0.099 (syst) mu b, s(.(2S)-from-b, 13 TeV) = 0.426 +/- 0.002 (stat) +/- 0.030 (syst) mu b. A new measurement of.(2S) production cross-sections in pp collisions at v s = 7 TeV is also performed using data collected in 2011, corresponding to an integrated luminosity of 614 pb-1. The integrated production cross-sections in the kinematic range 3.5 < pT < 14 GeV/c and 2.0 < y < 4.5 are s(prompt.(2S), 7 TeV) = 0.471 +/- 0.001 (stat) +/- 0.025 (syst) mu b, s(.(2S)-from-b, 7 TeV) = 0.126 +/- 0.001 (stat) +/- 0.008 (syst) mu b. All results show reasonable agreement with theoretical calculations.