Invariant dimuon mass of the $\Upsilon$ candidates after the event selection requirements and before the $\Upsilon$ mass range requirement. The distribution is fitted with the sum (blue line) of a double-sided Crystal Ball function for each $\Upsilon$ state (dashed red line for $\Y1S$, dotted pink line for $\Y2S$, dash-dotted green line for $\Y3S$) and a second-order polynomial for the background (not shown). The hatched red bands show the signal regions and the hatched blue bands show the mass sidebands used for background studies.

Distribution of $m^*(\mu ^+ \mu ^- \gamma )\equiv m(\mu ^+ \mu ^- \gamma )-m(\mu ^+ \mu ^- )+m(\Upsilon)$ for $\chi _{ b }$ candidates with fit projections overlaid for (a) $\chi _{ b }(1P)\rightarrow \Y1S\gamma $, (b) $\chi _{ b }(2P)\rightarrow \Y1S\gamma $, (c,e) $\chi _{ b }(3P)\rightarrow \Y1S\gamma $ and (d,f) $\chi _{ b }(3P)\rightarrow \Y2S\gamma $ channels. The result of the simultaneous fit to the $\chi _{ b }(3P)\rightarrow \Y1S\gamma $ and $\chi _{ b }(3P)\rightarrow \Y2S\gamma $ mass distributions is shown in (e) and (f). The cyan dotted line shows the non-$\Upsilon$ background, the grey dashed line shows the combinatorial background, the red dashed line the $\chi_{b1}$ contribution, the green dash-dotted line the $\chi _{ b 2}$ contribution, and the blue full line the sum of all these contributions.

Distribution of $m^*(\mu ^+ \mu ^- \gamma )\equiv m(\mu ^+ \mu ^- \gamma )-m(\mu ^+ \mu ^- )+m(\Upsilon)$ for $\chi _{ b }(1P)$ candidates with fit projections overlaid for each of the three ranges in $p_{\rm T}^{\Upsilon}$ : (a) 5--10 $ {\mathrm{ Ge V /}c}$ , (b) 10--15 $ {\mathrm{ Ge V /}c}$ and (c) 15--25 $ {\mathrm{ Ge V /}c}$ . The cyan dotted line show the non-$\Upsilon$ background, the grey dashed line shows the combinatorial background, the red dashed line the $\chi_{b1}$ contribution, the green dash-dotted line the $\chi_{b2}$ contribution and the blue full line the sum of all these contributions.

Relative production cross-sections of $\chi_{b1}$ to $\chi_{b2}$ mesons as a function of $ p_{\rm T}^{\Upsilon} $. Panel (a) shows the comparison of this measurement (the hatched rectangles show the statistical uncertainties and the red crosses the total experimental uncertainty) to the LO NRQCD prediction [9] (green band), and to the LHCb $\chi _{ c }$ result (blue crosses), where the $p_{\rm T}$ axis has been scaled by $m(\chi _{ b })/m(\chi _{ c })=2.8$. Panel (b) compares this measurement (empty squares) to CMS results [31] (filled squares) and to the scaled LHCb $\chi _{ c }$ results (empty circles). The error bars are the total experimental uncertainties and do not include the uncertainties on the branching fractions.

Animated gif made out of all figures.

Selection criteria for each $\chi _{ b }(nP)\rightarrow \Upsilon(mS)\gamma $ transition. SB indicates sideband.

Fitted values of the $\chi _{ b }(nP)$ $(n=1,2)$ masses (in $ {\mathrm{ Me V /}c^2}$ ) from the $\chi _{ b }(nP)\rightarrow \Y1S\gamma $ transitions, compared to the world average values. The uncertainties are statistical only.

Fitted values of the $\chi _{ b }(3P)$ mass (in $ {\mathrm{ Me V /}c^2}$ ) for the $\chi _{ b }(3P)\rightarrow \Upsilon(mS)\gamma $ ($m=1,2$) transitions. The last column gives the result of the simultaneous fit to the two transitions. The values are corrected for the mass bias ($-3$ $ {\mathrm{ Me V /}c^2}$ and $-0.5$ $ {\mathrm{ Me V /}c^2}$ for the $\Y1S$ and $\Y2S$ transitions, respectively). The last row gives the total $\chi _{ b }$ yields. The uncertainties are statistical only.

Summary of the systematic uncertainties on the $\chi _{ b }(nP)$ ($n=1,2$) mass splitting and on the $\chi _{ b 1}(3P)$ mass in $ {\mathrm{ Me V /}c^2}$ . The last column refers to the simultaneous fit to the two transitions.

Relative rate of $\chi _{ b 1}(1P)$ and $\chi _{ b 2}(1P)$ production and ratio of total efficiency (in the three $p_{\rm T}^{\Upsilon}$ ranges). Uncertainties only refer to the statistical contributions.

Summary of the systematic uncertainties on the $\chi _{ b }(1P)$ relative rates, expressed as fractions of the relative rate.

Relative production cross section of $\chi_{b1}$ to $\chi_{b2}$ mesons for the $1P$ state for each $p_{\rm T}^{\Upsilon}$ bin. The first uncertainty is statistical, the second is the systematic uncertainty and the third is due to the uncertainty on the branching fractions.