The differential cross-section for the inclusive
production of ψ(2S) mesons in pp collisions at √s = 7 TeV
has been measured with the LHCb detector. The data sample
corresponds to an integrated luminosity of 36 pb−1.
The ψ(2S) mesons are reconstructed in the decay channels
ψ(2S) → μ+μ− and ψ(2S) → J/ψπ+π−, with the
J/ψ meson decaying into two muons. Results are presented
both for promptly produced ψ(2S) mesons and for those
originating from b-hadron decays. In the kinematic range
pT(ψ(2S)) ≤ 16 GeV/c and 2 < y(ψ(2S)) ≤ 4.5 we measure
σprompt
ψ(2S)
= 1.44 ± 0.01 (stat) ± 0.12 (syst)
+0.20
−0.40 (pol) µb,
σb

ψ(2S)
= 0.25 ± 0.01 (stat) ± 0.02 (syst) µb,
where the last uncertainty on the prompt cross-section is due
to the unknown ψ(2S) polarization. Recent QCD calculations
are found to be in good agreement with our measurements.
Combining the present result with the LHCb J/ψ
measurements we determine the inclusive branching fraction
B

b → ψ(2S)X
=
2.73 ± 0.06 (stat) ± 0.16 (syst) ± 0.24 (BF)

× 10−3,
where the last uncertainty is due to the B(b → J/ψX),
B(J/ψ → μ+μ−) and B(ψ(2S) → e+e−) branching fraction
uncertainties.