Efficiency-corrected dimuon mass distributions for (left) $\sqrt{s}=7\,\mathrm{TeV}$ and (right) $\sqrt{s}=8\,\mathrm{TeV}$ samples in the region $3< p_{\mathrm T} <4 {\mathrm{\,GeV\!/}c} $, $3.0<y<3.5$. The thick dark yellow solid curves show the result of the fits, as described in the text. The three peaks, shown with thin magenta solid lines, correspond to the $\Upsilon\mathrm{(1S)}$ , $\Upsilon\mathrm{(2S)}$ and $\Upsilon\mathrm{(3S)}$ signals\,(left to right). The background component is indicated with a blue dashed line. To show the signal peaks clearly, the range of the dimuon mass shown is narrower than that used in the fit.

Double differential cross-sections $\dfrac{\mathrm{d}^2}{\mathrm{d} p_{\mathrm{T}}\,\mathrm{d} y}\upsigma^{\Upsilon\rightarrow \mu ^+\mu ^- }$ for (top) $\Upsilon\mathrm{(1S)}$ , (middle) $\Upsilon\mathrm{(2S)}$ and (bottom) $\Upsilon\mathrm{(3S)}$ at (left) $\sqrt{s}=7\,\mathrm{TeV}$ and (right) $\sqrt{s}=8\,\mathrm{TeV}$. The error bars indicate the sum in quadrature of the statistical and systematic uncertainties. The rapidity ranges $2.0<y<2.5$, $2.5<y<3.0$, $3.0<y<3.5$, $3.5<y<4.0$ and $4.0<y<4.5$ are shown with red filled circles, blue open squares, cyan downward triangles, magenta upward triangles and green diamonds, respectively. Some data points are displaced from the bin centres to improve visibility.

Differential cross-sections $\frac{\mathrm{d}}{\mathrm{d} p_{\mathrm T} }\upsigma^{\Upsilon\rightarrow \mu ^+\mu ^- }$ in the range $2.0<y<4.5$ for (red solid circles) $\Upsilon\mathrm{(1S)}$ , (blue open squares) $\Upsilon\mathrm{(2S)}$ and (green solid diamonds) $\Upsilon\mathrm{(3S)}$ mesons for (left) $\sqrt{s}=7\,\mathrm{TeV}$ and (right) $\sqrt{s}=8\,\mathrm{TeV}$ data. The curves show the fit results with the Tsallis function in the range $6< p_{\mathrm T} <30 {\mathrm{\,GeV\!/}c} $. The data points are positioned in the bins according to Eq.\,(6) in Ref. \cite{Lafferty:1994cj}.

Differential cross-sections $\frac{\mathrm{d}}{\mathrm{d} y}\upsigma^{\Upsilon\rightarrow \mu ^+\mu ^- }$ in the range $ p_{\mathrm T} <30 {\mathrm{\,GeV\!/}c} $ for (red solid circles) $\Upsilon\mathrm{(1S)}$ , (blue open squares) $\Upsilon\mathrm{(2S)}$ and (green solid diamonds) $\Upsilon\mathrm{(3S)}$ mesons for (left) $\sqrt{s}=7\,\mathrm{TeV}$ and (right) $\sqrt{s}=8\,\mathrm{TeV}$ data. Thick lines show fit results with the CO model predictions from Ref. \cite{ Kisslinger:2011fe,Kisslinger:2013mev,*Kisslinger:2014zga} in the region $2.5<y<4.0$, and dashed lines show the extrapolation to the full region $2.0<y<4.5$. The data points are positioned in the bins according to Eq.\,(6) in Ref. \cite{Lafferty:1994cj}.

Ratios of the differential cross-sections (left) $\frac{\mathrm{d}}{\mathrm{d} p_{\mathrm T} }\upsigma^{\Upsilon\rightarrow \mu ^+\mu ^- }$ and (right) $\frac{\mathrm{d}}{\mathrm{d} y}\upsigma^{\Upsilon\rightarrow \mu ^+\mu ^- }$ at $\sqrt{s}=8$ and $7\,\mathrm{TeV}$ for (red solid circles) $\Upsilon\mathrm{(1S)}$ , (blue open squares) $\Upsilon\mathrm{(2S)}$ and (green solid diamonds) $\Upsilon\mathrm{(3S)}$ . On the left hand plot, the results of the fit with a linear function are shown with straight thin red solid, blue dotted and green dashed lines. In the same plot, the nextdash-todash-leading order NRQCD theory predictions \cite{Han:2014kxa} are shown as a thick line. On the right hand plot, the curved red solid, blue dotted and greed dashed lines show the CO model predictions \cite{Kisslinger:2011fe,Kisslinger:2013mev,*Kisslinger:2014zga} with the normalisation fixed from the fits in Fig. ??? for $\Upsilon\mathrm{(1S)}$ , $\Upsilon\mathrm{(2S)}$ and $\Upsilon\mathrm{(3S)}$ mesons, respectively. Some data points are displaced from the bin centres to improve visibility.

The production ratios $\mathscr{R}_{\mathrm{i,j}}$ for (top) $\Upsilon\mathrm{(2S)}$ to $\Upsilon\mathrm{(1S)}$ , (middle) $\Upsilon\mathrm{(3S)}$ to $\Upsilon\mathrm{(1S)}$ , and (bottom) $\Upsilon\mathrm{(3S)}$ to $\Upsilon\mathrm{(2S)}$ , measured with data collected at (left) $\sqrt{s}=7\,\mathrm{TeV}$ and (right) $\sqrt{s}=8\,\mathrm{TeV}$. The error bars indicate the sum in quadrature of the statistical and systematic uncertainties. The rapidity ranges $2.0< y<2.5$, $2.5\le y<3.0$, $3.0\le y<3.5$, $3.5\le y<4.0$ and $4.0\le y<4.5$ are shown with red circles, blue squares, cyan downward triangles, magenta upward triangles and green diamonds, respectively. Some data points are displaced from the bin centres to improve visibility.

The production ratios (red solid circles) $\mathscr{R}_{2,1}$, (blue open squares) $\mathscr{R}_{3,1}$ and (green solid diamonds) $\mathscr{R}_{3,2}$ for (left) $\sqrt{s}=7\,\mathrm{TeV}$ and (right) $\sqrt{s}=8\,\mathrm{TeV}$ data, integrated over the (top) $2.0<y<4.5$ region and (bottom) $ p_{\mathrm T} <30 {\mathrm{\,GeV\!/}c} $ region.

Animated gif made out of all figures.

Efficiency-corrected signal yields for data samples accumulated at $\sqrt{s} =7$ and $8\,\mathrm{TeV}$ summed over the full kinematic range $ p_{\mathrm T} <30 {\mathrm{\,GeV\!/}c} $, $2.0<y<4.5$. The uncertainties are statistical only.

Summary of relative systematic uncertainties (in %) for the differential production cross-sections, their ratios, integrated cross-sections and the ratios $\mathscr{R}_{8/7}$. The ranges indicate variations depending on the $( p_{\mathrm T} ,y)$ bin and the \Upsilon state.

Results of the fits to the transverse momentum spectra of \Upsilon mesons using the Tsallis function in the reduced range $6< p_{\mathrm T} <30 {\mathrm{\,GeV\!/}c} $.

The production cross-section $\upsigma^{\Upsilon\rightarrow \mu ^+\mu ^- }$ (in $\rm \,pb $) for \Upsilon mesons in the full kinematic range $ p_{\mathrm T} <30 {\mathrm{\,GeV\!/}c} $\,(left two columns), and reduced range $ p_{\mathrm T} <15 {\mathrm{\,GeV\!/}c} $\,(right two columns), for $2.0<y<4.5$. The first uncertainties are statistical and the second systematic.

The ratio of production cross-sections for \Upsilon mesons at $\sqrt{s}=8$ to that at $\sqrt{s}=7\,\mathrm{TeV}$ in the full kinematic range $ p_{\mathrm T} <30 {\mathrm{\,GeV\!/}c} $\,(left) and reduced range $ p_{\mathrm T} <15 {\mathrm{\,GeV\!/}c} $\,(right) for $2.0< y<4.5$. The first uncertainties are statistical and the second systematic.

The ratios $\mathscr{R}_{\mathrm{i,j}}$ in the full kinematic range $ p_{\mathrm T} <30 {\mathrm{\,GeV\!/}c} $ and in the reduced range $ p_{\mathrm T} <15 {\mathrm{\,GeV\!/}c} $ for $2.0< y<4.5$. The first uncertainties are statistical and the second systematic.

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