| Measurements of heavy quarkonium productions in proton-proton collisions provide important test for the theory of Quantum Chromodynamics(QCD),which describes the strong interactions between quarks and gluons.ψ(2S)is one of the cc quarkonia.It has no appreciable feed-down contributions from higher mass states,so its production cross-sections can be directly compared with QCD,making it an ideal laboratory for testing the theory.The Large Hadron Collider(LHC)at Conseil European Pour Recherches Nucleaires(CERN)is the world s largest and most powerful particle collider.The LHCb experiment is one of the four main experiments at the LHC.In this thesis,the differential production cross-sections of prompt and delayed(from b hadron decay)ψ(2S)in proton-proton collisions at a centre-of-mass energy((?))of 5 TeV are precisely measured through theψ(2S)→μ-μ+ decay channel in the kinematic range of transverse momentum pT<12 GeV/c and rapidity 2.0<y<4.5,using a data sample with the integrated luminosity of 8.11 pb-1 collected by the LHCb detector in November,2015.The integrated cross-sections of prompt ψ(2S)and ψ(2S)from b hadron decay within the whole measured kinematic range are:σ(prompt ψ(2S))=1.71±0.03(stat)±0.10(syst)μbσ(ψ(2S)fromb)=0.29±0.01(stat)±0.02(syst)μbThe experimental data are compared with the QCD theoretical calculations.A good agreement is observed between the Non-relativistic QCD(NRQCD)calculations and the measured prompt ψ(2S)cross-sections for pT>5 GeV,where NRQCD calculations are available.The FONLL perturbative QCD calculations are consistent with the measured cross-sections of ψ(2S)from b hadron decays within the whole measured kinematic range. |