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A study is presented of central exclusive production of $\Upsilon(nS)$states, where the $\Upsilon(nS)$ resonances decay to the $\mu^+\mu^-$ finalstate, using $pp$ collision data recorded by the LHCb experiment. Thecross-section is measured in the rapidity range $2<y(\Upsilon)<4.5$ where themuons are reconstructed in the pseudorapidity range $2<\eta(\mu^\pm)<4.5$. Thedata sample corresponds to an integrated luminosity of 2.9 fb$^{-1}$ and wascollected at centre-of-mass energies of $7$ TeV and $8$ TeV. The measured$\Upsilon(1S)$ and $\Upsilon(2S)$ production cross-sections are\begin{eqnarray} \sigma(pp \to p\Upsilon(1S)p) &=& 9.0 \pm 2.1 \pm 1.7\textrm{pb and}\nonumber\\ \sigma(pp \to p\Upsilon(2S)p) &=& 1.3 \pm 0.8 \pm0.3\textrm{ pb},\nonumber \end{eqnarray} where the first uncertainties arestatistical and the second are systematic. The $\Upsilon(1S)$ cross-section isalso measured as a function of rapidity and is found to be in good agreementwith Standard Model predictions. An upper limit is set at 3.4 pb at the 95\%confidence level for the exclusive $\Upsilon(3S)$ production cross-section,including possible contamination from $\chi_b(3P)\to\Upsilon(3S)\gamma$ decays.

Measurement of the exclusive $\Upsilon$ production cross-section in $pp$ collisions at $\sqrt{s}=$7 TeV and 8 TeV