The production of $\chi_b$ mesons in protonproton collisions is studied using a data sample collected by the LHCb detector, at centreofmass energies of $\sqrt{s}=7$ and $8$ TeV and corresponding to an integrated luminosity of 3.0 fb$^{1}$. The $\chi_b$ mesons are identified through their decays to $\Upsilon(1S)\gamma$ and $\Upsilon(2S)\gamma$ using photons that converted to $e^+e^$ pairs in the detector. The relative prompt production rate of $\chi_{b1}(1P)$ and $\chi_{b2}(1P)$ mesons is measured as a function of the $\Upsilon(1S)$ transverse momentum in the $\chi_b$ rapidity range $2.0<y<4.5$. A precise measurement of the $\chi_b(3P)$ mass is also performed. Assuming a mass splitting between the $\chi_{b1}(3P)$ and the $\chi_{b2}(3P)$ states of 10.5 MeV/$c^2$, the measured mass of the $\chi_{b1}(3P)$ meson is $ m(\chi_{b1}(3P))= 10515.7^{+2.2}_{3.9}(stat) ^{+1.5}_{2.1}(syst) MeV/c^2.$
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 doublesided Crystal Ball function for each $\Upsilon$ state (dashed red line for $\Y1S$, dotted pink line for $\Y2S$, dashdotted green line for $\Y3S$) and a secondorder 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. 
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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 dashdotted line the $\chi _{ b 2}$ contribution, and the blue full line the sum of all these contributions. 
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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) 510 $ {\mathrm{ Ge V /}c}$ , (b) 1015 $ {\mathrm{ Ge V /}c}$ and (c) 1525 $ {\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 dashdotted line the $\chi_{b2}$ contribution and the blue full line the sum of all these contributions. 
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Relative production crosssections 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. 
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Animated gif made out of all figures. 
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Selection criteria for each $\chi _{ b }(nP)\rightarrow \Upsilon(mS)\gamma $ transition. SB indicates sideband. 
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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. 
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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. 
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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. 
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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. 
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Summary of the systematic uncertainties on the $\chi _{ b }(1P)$ relative rates, expressed as fractions of the relative rate. 
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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. 
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Created on 19 February 2021.