Measurement of $\Upsilon$ production in $pp$ collisions at $\sqrt{s} = 7$ TeV

The production of $\Upsilon(1S)$, $\Upsilon(2S)$ and $\Upsilon(3S)$ mesons in proton-proton collisions at the centre-of-mass energy of ${\sqrt{s}=7~{\rm TeV}}$ is studied with the LHCb detector. The analysis is based on a data sample of $25~{\rm pb}^{-1}$ collected at the Large Hadron Collider. The $\Upsilon$ mesons are reconstructed in the decay mode $\Upsilon\rightarrow \mu^+ \mu^-$ and the signal yields are extracted from a fit to the $\mu^+\mu^-$ invariant mass distributions. The differential production cross-sections times dimuon branching fractions are measured as a function of the $\Upsilon$ transverse momentum $p_{\rm T}$ and rapidity $y$, over the range $p_{\rm T}<15~{\rm GeV/c}$ and $2.0<y<4.5$. The cross-sections times branching fractions, integrated over these kinematic ranges, are measured to be \begin{eqnarray*}{} \sigma(pp\rightarrow \Upsilon(1S)\, X)\times{\mathcal{B}(\Upsilon(1S)\rightarrow\mu^+\mu^-)} = 2.29\phantom{0} \pm 0.01\phantom{0} \pm 0.10\phantom{0}\,\, _{-0.37}^{+0.19}~{\rm nb}, \\ \sigma(pp\rightarrow \Upsilon(2S)\, X)\times{\mathcal{B}(\Upsilon(2S)\rightarrow\mu^+\mu^-)} = 0.562 \pm 0.007 \pm 0.023\, _{-0.092}^{+0.048}~{\rm nb}, \\ \sigma(pp\rightarrow \Upsilon(3S)\, X)\times{\mathcal{B}(\Upsilon(3S)\rightarrow\mu^+\mu^-)} = 0.283 \pm 0.005 \pm 0.012 \,_{-0.048}^{+0.025}~{\rm nb}, \end{eqnarray*} where the first uncertainty is statistical, the second systematic and the third is due to the unknown polarisation of the three $\Upsilon$ states.