Upsilon production cross section in $pp$ collisions at $\sqrt{s}=7\mathrm{TeV}$

The ${\rm Y}\left(1S\right)$, ${\rm Y}\left(2S\right)$, and ${\rm Y}\left(3S\right)$ production cross sections in proton-proton collisions at $\sqrt{s}=7\mathrm{TeV}$ are measured using a data sample collected with the CMS detector at the LHC, corresponding to an integrated luminosity of $3.1\pm 0.3{\mathrm{pb}}^{-1}$. Integrated over the rapidity range $|y|<2$, we find the product of the ${\rm Y}\left(1S\right)$ production cross section and branching fraction to dimuons to be $\sigma (pp\to {\rm Y}(1S\left)X\right)·\mathcal{B}\left({\rm Y}\right(1S)\to {\mu }^{+}{\mu }^{-})=7.37\pm {0.13}_{-0.42}^{+0.61}\pm 0.81\mathrm{nb}$, where the first uncertainty is statistical, the second is systematic, and the third is associated with the estimation of the integrated luminosity of the data sample. This cross section is obtained assuming unpolarized ${\rm Y}\left(1S\right)$ production. With the assumption of fully transverse or fully longitudinal production polarization, the measured cross section changes by about 20%. We also report the measurement of the ${\rm Y}\left(1S\right)$, ${\rm Y}\left(2S\right)$, and ${\rm Y}\left(3S\right)$ differential cross sections as a function of transverse momentum and rapidity.

Figure 1

The dimuon invariant-mass distribution in the vicinity of the ${\rm Y}\left(nS\right)$ resonances for the full rapidity covered by the analysis (top) and for the subset of events where the pseudorapidity of each muon satisfies $|{\eta }^{\mu }|<1$ (bottom). The solid line shows the result of a fit to the invariant-mass distribution before accounting for acceptance and efficiency, with the dashed line denoting the background component. Details of the fit are described in Sec. 6.

Figure 2

(Top) Unpolarized ${\rm Y}\left(1S\right)$ acceptance as a function of $p_{\mathrm{T}}$ and $y$; (bottom) the unpolarized ${\rm Y}\left(1S\right)$, ${\rm Y}\left(2S\right)$, and ${\rm Y}\left(3S\right)$ acceptances integrated over rapidity as a function of $p_{\mathrm{T}}$.

Figure 3

Single-muon identification efficiencies as a function of $p_{\mathrm{T}}^{\mu }$ for six $|{\eta }^{\mu }|$ regions, measured from data using $J/\psi$ T&P (closed circles). The efficiencies determined with ${\rm Y}$ MC truth (triangles), $J/\psi$ MC truth (open circles), and $J/\psi$ MC T&P (squares), used in the evaluation of systematic uncertainties, are also shown.

Figure 4

Single-muon trigger efficiencies as a function of $p_{\mathrm{T}}^{\mu }$ for six $|{\eta }^{\mu }|$ regions, measured from data using $J/\psi$ T&P (closed circles). The efficiencies determined with ${\rm Y}$ MC truth (triangles), $J/\psi$ MC truth (open circles), and $J/\psi$ MC T&P (squares), used in the evaluation of systematic uncertainties, are also shown.

Figure 5

Fit to the dimuon invariant-mass distribution in the specified $p_{\mathrm{T}}$ regions for $|y|<2$, before accounting for acceptance and efficiency. The solid line shows the result of the fit described in the text, with the dashed line representing the background component.

Figure 6

(Top) Fit to the dimuon invariant-mass distribution in the range $2<p_{\mathrm{T}}<5\mathrm{GeV}/c$ for $|y|<1$. (bottom) Fit to the ${\rm Y}\left(1S\right)$-acceptance and efficiency weighted dimuon distribution in the range $2<p_{\mathrm{T}}<5\mathrm{GeV}/c$ for $|y|<1$.

Figure 7

${\rm Y}\left(nS\right)$ differential cross sections in the rapidity interval $|y|<2$ (top left), and in the rapidity intervals $|y|<1$ and $1<|y|<2$ for the ${\rm Y}\left(1S\right)$ (top right), ${\rm Y}\left(2S\right)$ (bottom left) and ${\rm Y}\left(3S\right)$ (bottom right). The uncertainties on the points represent the sum of the statistical and systematic uncertainties added in quadrature, excluding the uncertainty on the integrated luminosity (11%).

Figure 8

(Left) Differential ${\rm Y}\left(1S\right)$ cross section as a function of rapidity in the transverse-momentum range $p_{\mathrm{T}}<30\mathrm{GeV}/c$ (data points) and normalized PYTHIA prediction (line). The uncertainties on the points represent the sum of the statistical and systematic uncertainties added in quadrature, excluding the uncertainty on the integrated luminosity (11%). (Right) Cross section ratios for ${\rm Y}\left(nS\right)$ states as a function of $p_{\mathrm{T}}$ in the rapidity range $|y|<2$.

Figure 9

Differential cross sections of the ${\rm Y}\left(nS\right)$ as a function of $p_{\mathrm{T}}$ in the rapidity range $|y|<2$, and comparison to the PYTHIA predictions normalized to the measured $p_{\mathrm{T}}$-integrated cross sections; ${\rm Y}\left(1S\right)$ (left), ${\rm Y}\left(2S\right)$ (middle), and ${\rm Y}\left(3S\right)$ (right). The theory prediction is shown in the form of a continuous spectrum (curve) and integrated in the same $p_{\mathrm{T}}$ bins as employed in the measurement (horizontal lines). The PYTHIA curve is used to calculate the abscissa of the data points [28]. The uncertainties on the points represent the sum of the statistical and systematic uncertainties added in quadrature, excluding the uncertainty on the integrated luminosity (11%).

Figure 10

Comparison of the CMS differential ${\rm Y}\left(nS\right)$ cross sections as a function of $p_{\mathrm{T}}$, normalized by ${\sigma }_{\mathrm{TOT}}=\sum _{}^{}(d\sigma /d{p}_{\mathrm{T}})\Delta p_{\mathrm{T}}$, to previous measurements; ${\rm Y}\left(1S\right)$ (left), ${\rm Y}\left(2S\right)$ (middle), and ${\rm Y}\left(3S\right)$ (right).