# Measurement of the $\chi_b(3P)$ mass and of the relative rate of $\chi_{b1}(1P)$ and $\chi_{b2}(1P)$ production

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## Abstract

The production of $\chi_b$ mesons in proton-proton collisions is studied using a data sample collected by the LHCb detector, at centre-of-mass 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 $m(\chi_{b1}(3P))= 10515.7^{+2.2}_{-3.9}(stat) ^{+1.5}_{-2.1}(syst) MeV/c^2.$

## Figures and captions

 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 $\Upsilon{(1S)}$, dotted pink line for $\Upsilon{(2S)}$, dash-dotted green line for $\Upsilon{(3S)}$) 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. FitUps[..].pdf [49 KiB] HiDef png [236 KiB] Thumbnail [55 KiB] *.C file 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) $\chi _{ b }(1P)\rightarrow \Upsilon{(1S)} \gamma$, (b) $\chi _{ b }(2P)\rightarrow \Upsilon{(1S)} \gamma$, (c,e) $\chi _{ b }(3P)\rightarrow \Upsilon{(1S)} \gamma$ and (d,f) $\chi _{ b }(3P)\rightarrow \Upsilon{(2S)} \gamma$ channels. The result of the simultaneous fit to the $\chi _{ b }(3P)\rightarrow \Upsilon{(1S)} \gamma$ and $\chi _{ b }(3P)\rightarrow \Upsilon{(2S)} \gamma$ 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. Chib1P[..].pdf [25 KiB] HiDef png [338 KiB] Thumbnail [86 KiB] *.C file Chib2P[..].pdf [24 KiB] HiDef png [317 KiB] Thumbnail [91 KiB] *.C file Chib3P[..].pdf [25 KiB] HiDef png [337 KiB] Thumbnail [98 KiB] *.C file Chib3P[..].pdf [25 KiB] HiDef png [340 KiB] Thumbnail [98 KiB] *.C file Chib3P[..].pdf [26 KiB] HiDef png [359 KiB] Thumbnail [104 KiB] *.C file Chib3P[..].pdf [25 KiB] HiDef png [357 KiB] Thumbnail [105 KiB] *.C file 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 ${\mathrm{\,GeV\!/}c}$ , (b) 10--15 ${\mathrm{\,GeV\!/}c}$ and (c) 15--25 ${\mathrm{\,GeV\!/}c}$ . 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. Chib1P[..].pdf [23 KiB] HiDef png [344 KiB] Thumbnail [94 KiB] *.C file Chib1P[..].pdf [23 KiB] HiDef png [339 KiB] Thumbnail [90 KiB] *.C file Chib1P[..].pdf [22 KiB] HiDef png [324 KiB] Thumbnail [81 KiB] *.C file 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. Chibra[..].pdf [16 KiB] HiDef png [383 KiB] Thumbnail [97 KiB] *.C file sigmar[..].pdf [15 KiB] HiDef png [131 KiB] Thumbnail [46 KiB] *.C file Animated gif made out of all figures. PAPER-2014-040.gif Thumbnail

## Tables and captions

 Selection criteria for each $\chi _{ b }(nP)\rightarrow \Upsilon(mS)\gamma$ transition. SB indicates sideband. Table_1.pdf [47 KiB] HiDef png [64 KiB] Thumbnail [10 KiB] tex code Fitted values of the $\chi _{ b }(nP)$ $(n=1,2)$ masses (in ${\mathrm{\,MeV\!/}c^2}$ ) from the $\chi _{ b }(nP)\rightarrow \Upsilon{(1S)} \gamma$ transitions, compared to the world average values. The uncertainties are statistical only. Table_2.pdf [36 KiB] HiDef png [65 KiB] Thumbnail [11 KiB] tex code Fitted values of the $\chi _{ b }(3P)$ mass (in ${\mathrm{\,MeV\!/}c^2}$ ) 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 ($-3$ ${\mathrm{\,MeV\!/}c^2}$ and $-0.5$ ${\mathrm{\,MeV\!/}c^2}$ for the $\Upsilon{(1S)}$ and $\Upsilon{(2S)}$ transitions, respectively). The last row gives the total $\chi _{ b }$ yields. The uncertainties are statistical only. Table_3.pdf [50 KiB] HiDef png [65 KiB] Thumbnail [11 KiB] tex code Summary of the systematic uncertainties on the $\chi _{ b }(nP)$ ($n=1,2$) mass splitting and on the $\chi _{ b 1}(3P)$ mass in ${\mathrm{\,MeV\!/}c^2}$ . The last column refers to the simultaneous fit to the two transitions. Table_4.pdf [54 KiB] HiDef png [64 KiB] Thumbnail [11 KiB] tex code 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. Table_5.pdf [43 KiB] HiDef png [41 KiB] Thumbnail [7 KiB] tex code Summary of the systematic uncertainties on the $\chi _{ b }(1P)$ relative rates, expressed as fractions of the relative rate. Table_6.pdf [54 KiB] HiDef png [105 KiB] Thumbnail [17 KiB] tex code 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. Table_7.pdf [52 KiB] HiDef png [59 KiB] Thumbnail [10 KiB] tex code

Created on 23 February 2019.Citation count from INSPIRE on 23 February 2019.