Study of χb meson production in p p collisions at √s=7 and 8TeV and observation of the decay χb(3P)→Υ(3S)γ

Eur. Phys. J. C (2014) 74:3092 DOI 10.1140/epjc/s10052-014-3092-z Regular Article - Experimental Physics Study of χbmeson production in pp collisions at √s=7and8TeV and observation of the decay χb(3P)→ϒ(3S)γ The LHCb Collaboration CERN, 1211 Geneva 23, Switzerland Received: 30 July 2014 / Accepted: 22 September 2014 / Published online: 8 October 2014 © CERN for the benefit of the LHCb collaboration 2014. This article is published with open access at Springerlink.com Abstract A study of χbmeson production at LHCb is performed on proton–proton collision data, corresponding to 3.0 fb−1of integrated luminosity collected at centre-of- mass energies √s= 7 and 8 TeV. The fraction of ϒ(nS) mesons originating from χbdecays is measured as a function of the ϒtransverse momentum in the rapidity range 2.0<yϒ<4.5. The radiative transition of the χb(3P) meson to ϒ(3S)is observed for the first time. The χb1 (3P) mass is determined to be mχb1 (3P)=10 511.3±1.7±2.5MeV/c2, where the first uncertainty is statistical and the second is systematic. 1 Introduction The production of quarkonia states in high-energy hadron collisions is described in the framework of non-relativistic quantum chromodynamics(NRQCD), as two-step process: a heavy quark–antiquark pair is first created perturbatively at short distances, then it evolves non-perturbatively into quarkonium at long distances. The NRQCD framework makes use of a combination of colour-singlet and colouroctet mechanisms [1–5]. Recent calculations [6–10] support the leading role of the colour-singlet mechanism. The comparison of experimental data for prompt production of S- wave quarkonia, e.g. J/ψor ϒ(1S)mesons, with theory predictions requires knowledge of feed-down contributions from P-wave quarkonia states, e.g. radiative χb→ϒγdecays. This contribution could significantly influence the interpretation of the measured polarization of S-wave vector quarkonia. In addition, measurements of the relative production rates of P-wave to S-wave quarkonia, as well as the tensor-to-vector ratios, provide valuable information on colour-octet matrix elements [10–12]. The production of P-wave charmonia, jointly referred to as χcstates, has been studied by the CDF [13], HERA-B [14], e-mail: Iv[email protected] LHCb [15–17], CMS [18], and ATLAS [19] collaborations; measurements involving χbstates have been performed by the CDF [20], ATLAS [21], CMS [22] and LHCb [23,24] experiments. This paper presents a measurement of the fractions of ϒmesons originating from radiative decays of χb mesons. Depending on the relative orientation of the quark spins, the χbstates can be either scalar, vector or tensor mesons, denoted by χbJ with total angular momentum J=0,1,2. The fractions of ϒ(nS)decays originating from χb(mP)decays, where n and m are radial quantum numbers of the bound states are defined as Rχb(mP) ϒ(nS)≡ σ(pp →χb1 (mP)X) σ(pp →ϒ(nS)X)×B1 + σ(pp →χb2 (mP)X) σ(pp →ϒ(nS)X)×B2,(1) where B1(2)denotes the branching fraction for the decay χb1(2)(mP)→ϒ(nS)γ. Possible contributions from χb0 (mP) →ϒ(nS)γdecays are neglected because of the small branching fraction for the corresponding radiative decays [25]. The results presented in this paper supersede earlier LHCb measurements [23,24]. In particular, the full data sample collected by LHCb at √s=7 and 8 TeV has been used and the measured fractions Rχb(mP) ϒ(nS)are reported for all six kinematically allowed transitions: χb(1P)→ϒ(1S)γ, χb(2P)→ϒ(1S)γ,χb(2P)→ϒ(2S)γ,χb(3P)→ ϒ(1S)γ,χb(3P)→ϒ(2S)γand χb(3P)→ϒ(3S)γin bins of transverse momentum of the ϒmesons in the rapidity range 2.0<y<4.5. The last transition, which is usually not considered in theory predictions, is observed for the first time. A precise measurement of the mass of the χb1 (3P)meson, which was recently observed by the ATLAS [21], D0 [26] and LHCb [24] collaborations, is also performed. 2 The LHCb detector and data samples The LHCb detector [27] is a single-arm forward spectrometer covering the pseudorapidity range 2 <η<5, 123 3092 Page 2 of 13 Eur. Phys. J. C (2014) 74:3092 designed for the study of heavy-flavoured particles. The detector includes a high-precision tracking system consisting of a silicon-strip vertex detector surrounding the interaction region, a large-area silicon-strip detector located upstream of a dipole magnet with a bending power of about 4 Tm, and three stations of silicon-strip detectors and straw drift tubes placed downstream of the magnet. The combined tracking system provides a momentum measurement with a relative uncertainty that varies from 0.4 % at low momentum to 0.6 % at 100 GeV/c, and an impact parameter measurement with a resolution of 20 μm for charged particles with large transverse momentum, pT. Different types of charged hadrons are distinguished using information from two ring-imaging Cherenkov detectors(RICH) [28]. Photon, electron and hadron candidates are identified by a calorimeter system consisting of scintillating-pad(SPD) and preshower(PS) detectors, an electromagnetic calorimeter(ECAL) and a hadronic calorimeter [29]. Muons are identified by a system composed of alternating layers of iron and multiwire proportional chambers [30]. The trigger [31] consists of a hardware stage, based on information from the calorimeter and muon systems, followed by a software stage, which applies a full event reconstruction. Candidate events used in this analysis must pass the hardware trigger, with the specific requirement that the product of the pTof two muon candidates be greater than (1.3GeV/c)2 and (1.6GeV/c)2for data collected at √s=7 and 8 TeV, respectively. The first stage of the software trigger selects candidate events with two well-reconstructed tracks with hits in the muon system, pTgreater than 500 MeV/cand momentum greater than 6 GeV/cfor each track. The two tracks are required to originate from a common vertex and to have an invariant mass greater than 2.7 GeV/c2. Events are required to pass a second software trigger stage, where the previous trigger decision is confirmed using improved track reconstruction algorithms, and the requirement that the invariant mass of the dimuon pair exceeds 4.7 GeV/c2is applied. The data samples used in this paper have been collected by the LHCb detector in pp collisions at √s=7 and 8 TeV with integrated luminosities of 1.0 fb−1and 2.0 fb−1, respectively. Simulated samples are used to determine signal efficiencies. In these samples, ϒand χbmesons are produced unpolarized. The effect of the unknown initial polarization on the efficiencies, and therefore on the results, is taken into account as a systematic uncertainty. In the simulation, pp collisions are generated using Pythia [32] with a specific LHCb configuration [33]. Decays of hadrons are described by EvtGen [34], in which final-state radiation is generated using Photos [35]. The interaction of the generated particles with the detector and its response are implemented using the Geant4 toolkit [36,37] as described in Ref. [38]. A comparison of the distributions of the relevant variables used in this analysis is performed on data and simulated samples, in order to assess the reliability of the simulation in computing signal efficiencies and good agreement is found. 3 Event selection and signal extraction This analysis proceeds through the reconstruction of ϒ(nS) candidates via their dimuon decays and their subsequent pairing with a photon candidate to reconstruct χb→ϒγdecays. The ϒcandidates are selected from pairs of oppositely charged tracks identified as muons and originating from a common vertex. The muons are required to have pTlarger than 1 GeV/c. Good track quality is ensured by requiring aχ2per degree of freedom, χ2/ndf, of the track fit to be less than 4 [39]. A multivariate estimator, based on information from the tracking, muon and RICH systems, as well as compatibility with the hypothesis of a minimum ionizing particle in the calorimeter system [40–42], is used to improve the muon identification purity. The identification efficiency for muons from ϒ→μ+μ−decays rises from 75 % to 98 % as the transverse momentum of the muon increases from 1 GeV/cto 3 GeV/c. A good quality of the two-prong common vertex is ensured by requiring the pvalue of the common vertex fit to be greater than 0.5 %. To improve the dimuon mass resolution and to suppress combinatorial background from muons originating in semileptonic decays of heavy-flavoured hadrons, the dimuon vertex is refitted using the position of the reconstructed pp collision vertex as an additional constraint [43]. The p-value for this fit is required to be larger than 0.05 %. When several collision vertices are reconstructed in the event, the one closest to the dimuon vertex is used. The invariant mass distributions for selected dimuon candidates in the kinematic range of transverse momentum 6 < pμ+μ− T<40 GeV/cand rapidity 2.0<yμ+μ−<4.5are showninFig.1for data collected at √s=7 and 8 TeV. Three clear peaks are visible, corresponding to the ϒ(1S),ϒ(2S) and ϒ(3S)signals(low-mass to high-mass). The yields of the ϒ(nS)signals are determined using an extended maximum likelihood fit to the unbinned dimuon mass distributions. The fit function is parameterised as the sum of three signal components and combinatorial background. Each ϒsignal has been modelled with a modified Gaussian function with power-law tails on both sides. The combinatorial background is modelled with an exponential function. The tail parameters of the signal functions are fixed using simulated events, whereas the mean and resolution are allowed to vary in the fit. The fit results are superimposed in Fig. 1and fitted signal yields are summarized in Table 1. The peak positions and mass resolutions are found to be in good agreement for the data collected at √s=7 and 8 TeV, 123 Eur. Phys. J. C (2014) 74:3092 Page 3 of 13 3092 91011 0 5000 10000 15000 20000 25000 30000 35000 40000 Candidates/(12 MeV/c2) m µ + µ − [GeV/c 2 ] LHCb √s=7 TeV 91011 0 10000 20000 30000 40000 50000 60000 70000 80000 90000 LHCb √s= 8 TeV m µ + µ − [GeV/c 2 ] Candidates/(12 MeV/c2) Fig. 1 Invariant mass distributions for selected dimuon candidates in the kinematic range 6 <pμ+μ− T<40 GeV/cand 2.0<yμ+μ−<4.5 for (left) data collected at √s=7 TeV and (right) 8 TeV. The three peaks on each plot correspond to the ϒ(1S),ϒ(2S)and ϒ(3S)signals(low-mass to high-mass). The result of the fit, described in the text, is illustrated with a red solid line, while the background component is shown with a blue dashed line Table 1 Yields of ϒ(nS)mesons, determined by fitting the dimuon invariant mass in the range 6 <pμ+μ− T<40 GeV/cand 2.0< yμ+μ−<4.5, for data collected at √s=7 and 8 TeV. Only statistical uncertainties are shown Signal yield √s=7TeV √s=8TeV Nϒ(1S)326 300 ±638 747 610 ±969 Nϒ(2S)100 620 ±395 229 950 ±576 Nϒ(3S)57 613 ±312 129 450 ±459 and in agreement with the known ϒ(nS)masses [25] and the resolutions expected from simulated samples. Muon pairs with invariant mass in the intervals 9310 < mμ+μ−<9600 MeV/c2, 9860<mμ+μ−<10 155 MeV/c2 and 10 220 <mμ+μ−<10 520 MeV/c2areusedasϒ(1S), ϒ(2S)and ϒ(3S)candidates, respectively, when reconstructing χbparticles. The selected ϒcandidates are combined with photons reconstructed using the electromagnetic calorimeter and identified using a likelihood-based estimator, constructed from variables that rely on calorimeter and tracking information [16,29,44,45]. Candidate photon clusters must not be associated with the position of any reconstructed track extrapolated to the calorimeter. The photon selection is further refined by using information from the PS and SPD detectors. The photon transverse energy is required to be greater than 600 MeV. The χbsignals are searched for in the invariant mass of ϒγcombinations. To improve the ϒ(nS)γmass resolution and to remove any residual bias, the corrected mass mϒ(nS)γ≡mμ+μ−γ−(mμ+μ−−mϒ(nS))(2) is used, where mϒ(nS)is the known mass of the ϒ(nS)meson [25]. The resolution improves by a factor between two and four with respect to the one obtained by simply computing the invariant mass of the ϒγpair. The distributions of the corrected masses mϒ(nS)γare shown in Fig. 2for ϒ(1S),ϒ(2S) and ϒ(3S)candidates in the transverse momentum ranges 14 <pϒ(1S) T<40 GeV/c,18<pϒ(2S) T<40 GeV/cand 24 <pϒ(3S) T<40 GeV/c. The yields of χb(mP)mesons are determined from an extended maximum likelihood fit to the unbinned mϒ(nS)γ distributions. The fit model consists of the sum of signal components for all kinematically allowed χb(mP)→ ϒ(nS)γdecays and combinatorial background. Neglecting a possible contribution due to χb0 (mP)→ϒ(nS)γdecays, the signal from each χb(mP)multiplet is parameterised as the sum of two overlapping Crystal Ball(CB) functions [46] with high-mass tails. The peak positions are separated by the known mass-splitting between the tensor and vector states in the χb(1P)and χb(2P)multiplets [25]. For the χb(3P)multiplet the expected splitting of 10.5MeV/c2[47,48] is used. The tail parameters of the CB functions and the resolutions are fixed to the values determined using simulated samples. The yield fractions Nχb2 /Nχb1 of the tensor and vector states in each χb(mP)multiplet are assumed to be equal to 0.5 according to expectations from Refs. [11,47]. For the χb(1P) and χb(2P)cases, this choice agrees with direct measurements of the relative productions of χb2 (1P)/ χb1 (1P)and χb2 (2P)/ χb1 (2P)[22,49]. This assumption is necessary for the determination of signal yields, since the χb1 and χb2 states cannot be resolved given the limited invariant mass resolution for the ϒ(nS)γsystem. The impact of this assumption is quantified as a systematic uncertainty. With this parameterisation for the twelve χbsignal components, the free parameters are the three masses of the χb1 states and the six overall yields of χb1 and χb2 signals. The com- 123 3092 Page 4 of 13 Eur. Phys. J. C (2014) 74:3092 10 10.5 0 200 400 600 800 1000 1200 Candidates/(20 MeV/c 2 ) Candidates/(20 MeV/c 2 ) Candidates/(10 MeV/c 2 ) Candidates/(20 MeV/c 2 ) Candidates/(20 MeV/c 2 ) Candidates/(10 MeV/c 2 ) mΥ(1S)γ LHCb √s= 7 TeV 10 10.5 0 500 1000 1500 2000 2500 3000 mΥ(1S)γ 10.2 10.4 10.6 10.8 11 0 50 100 150 200 250 300 mΥ(2S)γ 10.2 10.4 10.6 10.8 11 0 100 200 300 400 500 600 700 mΥ(2S)γ 10.5 10.6 10.7 0 5 10 15 20 25 30 35 40 mΥ(3S)γ 10.5 10.6 10.7 0 10 20 30 40 50 60 70 80 90 mΥ(3S)γ [GeV/c2] [GeV/c2] [GeV/c2] [GeV/c2] [GeV/c2] [GeV/c2] LHCb √s= 8 TeV LHCb √s= 8 TeV LHCb √s= 8 TeV LHCb √s= 7 TeV LHCb √s= 7 TeV Fig. 2 Distributions of the corrected mass mϒ(nS)γfor the selected χbcandidates (black points) decaying into (top row) ϒ(1S), (middle row) ϒ(2S)and (bottom row) ϒ(3S), in the transverse momentum ranges given in the text, for (left) √s=7 TeV and (right) 8 TeV data. Each plot shows also the result of the fit (solid red curve), including the background (dotted blue curve) and the signal (dashed green and magenta curves) contributions. The magenta dashed curve corresponds to the χb1 signal and the green dashed curve to the χb2 signal binatorial background is parameterised as the product of an exponential and polynomial functions up to the fourth order. The fit results are superimposed on Fig. 2and the signal yields are summarized in Table 2. To perform a precise measurement of the χb1 (3P)mass, the data samples collected at √s=7 and 8 TeV are combined. A fit to the combined sample of χb(3P)→ϒ(3S)γ decays gives mχb1 (3P)=10 511.3±1.7MeV/c2, where the uncertainty is statistical only. For the determination of the χbsignal yields in pϒ Tbins, the masses of the χb1 states in the fits are fixed to the values obtained in the fits to the full pTranges. For each pϒ T bin the fractions Rχb(mP) ϒ(nS), defined by Eq. (1), are calculated separately for √s=7 and 8 TeV data samples as Table 2 Signal yields resulting from fits to the corrected mass mϒ(nS)γ distributions in the transverse momentum ranges 14 <pϒ(1S) T< 40 GeV/c,18<pϒ(2S) T<40 GeV/cand 24 <pϒ(3S) T<40 GeV/c. Only statistical uncertainties are shown Decay mode √s=7TeV √s=8TeV Nχb(1P)→ϒ(1S)γ1908 ±71 4608 ±115 Nχb(2P)→ϒ(1S)γ390 ±41 904 ±68 Nχb(3P)→ϒ(1S)γ133 ±31 196 ±50 Nχb(2P)→ϒ(2S)γ265 ±30 660 ±46 Nχb(3P)→ϒ(2S)γ48 ±17 73 ±26 Nχb(3P)→ϒ(3S)γ56 ±12 126 ±20 Rχb(mP) ϒ(nS)=Nχb(mP) Nϒ(nS)×εϒ(nS) εχb(mP) ,(3) 123 Eur. Phys. J. C (2014) 74:3092 Page 5 of 13 3092 where εχb(mP)and εϒ(nS)denote the total efficiencies, and Nχb(mP)and Nϒ(nS)are the fitted yields for the χb(mP) and ϒ(nS)states for the respective pϒ Tbin. The ratio of the efficiencies εχb(mP)and εϒ(nS)is largely determined by the reconstruction efficiency for photons from χbdecays. It is close to 25 % for χbmesons with transverse momentum larger than 20 GeV/c, and it drops to approximately 10 % for the lowest pTconsidered in this analysis. The dominant sources of inefficiency are the geometrical acceptance of the electromagnetic calorimeter, photon conversions in the detector material, the accidental overlap of clusters in the ECAL and the selection requirement on the photon transverse energy. The measurements are performed in six bins of pϒ(1S) Tin the range 6 <pϒ(1S) T<40 GeV/c, five bins of pϒ(2S) Tin the range 18 <pϒ(2S) T<40 GeV/cand two bins of pϒ(3S) Tin the range 24 <pϒ(3S) T<40 GeV/c. 4 Systematic uncertainties The systematic uncertainties on the fractions Rχb(mP) ϒ(nS), calculated using Eq. (3), are related to the determination of the signal yields and the evaluation of the efficiency ratios. The main contributions to the former are due to fit modelling, whereas the photon reconstruction efficiency and the knowledge of the initial state polarization dominate the uncertainty on the ratios of efficiencies εχb(mP)/εϒ(nS). The contributions due to other effects largely cancel in these ratios. Based on studies from Refs. [23,50–52] the systematic uncertainty associated with the ϒsignal yields determination is taken to be 0.7 % for all pϒ Tbins. In the χbfit model several sources of uncertainty are taken into account. The yield ratio N(χb2)/N(χb1), which is fixed in the fit to be 0.5 as predicted by theory, is varied from 0.3 to 1.0. These limits are obtained by following the prescription of Ref. [11], where the experimentally measured cross-section ratio of χcmesons is rescaled to predict the corresponding ratio for χbmesons. The ratio of cross-sections is then converted to a ratio of yields by taking into account the χb1 and χb2 radiative branching fractions and reconstruction efficiencies. For the χb(1P)and the χb(2P)mesons, the variation obtained agrees within uncertainties with the direct measurements of relative productions of χb2 (1P)and χb1 (1P)mesons and χb2 (2P)and χb1 (2P)mesons [49]. The corresponding systematic uncertainty on Rχb(mP) ϒ(nS)varies between 0.1 % and 15 % across pϒ Tbins. The systematic uncertainty due to a slight dependence of the mass fit results on pϒ Tis estimated by taking the minimum and the maximum values of the χb1 masses, repeating the fit and taking the maximum difference in the yields. The assigned uncertainty varies between 0.3 % and 20 % for various pϒ Tbins. The smaller values cor- Table 3 Summary of the relative systematic uncertainties for the fractions Rχb(mP) ϒ(nS) Source Uncertainty (%) ϒfit model 0.7 χbfit model χb1 /χb2 ratio 0.1–15 χb1 mass variation 0.3–20 χbmass resolution 2.0–12 Background model 2.0–10 mχb2 (3P)−mχb1 (3P)0.1–2 γreconstruction 3.0 χbpolarization 0.9–9 Table 4 Summary of systematic uncertainties for mχb1 (3P) Source Uncertainty (MeV/c2) χbfit model χbmass resolution 0.8 Background model 0.3 mχb2 (3P)−mχb1 (3P)0.4 χb1 /χb2 ratio 2.0 ECAL energy scale 1.0 ϒ(3S)mass uncertainty 0.5 responds to the low-Q transitions: χb(1P)→ϒ(1S)γ, χb(2P)→ϒ(2S)γand χb(3P)→ϒ(3S)γ. To assess the systematic uncertainty related to possible mismodelling of the mass resolution, the mass resolution is varied by ±10 % around the values obtained using simulated samples, and the difference between the obtained Rχb(mP) ϒ(nS)is treated as the corresponding systematic uncertainty. The maximum deviation in the results obtained from varying by ±1 the order of the polynomial function used in the fit model to describe the combinatorial background, is assigned as the systematic uncertainty associated with the background parameterisation. For the χb(3P)case, a systematic uncertainty stems from the assumption on the mass splitting between χb2 (3P) and χb1 (3P)states. This parameter is varied in the range between 9 and 12 MeV/c2. The obtained uncertainty for Rχb(3P) ϒ(3S)is found to be much smaller than the one obtained for Rχb(3P) ϒ(1S)and Rχb(3P) ϒ(2S). The assigned uncertainty on Rχb(3P) ϒ(nS) varies between 0.1 % and 2 %. The uncertainty due to possible imperfections in the simulation in the determination of the photon reconstruction efficiency is studied by comparing the relative yields between data and simulation for B+→J/ψK∗+ and B+→ J/ψK+decays, where the K∗+ meson is reconstructed using the K+π0final state [23,45,53–55]. According to these studies, a systematic uncertainty of 3 % is assigned for 123 3092 Page 6 of 13 Eur. Phys. J. C (2014) 74:3092 Fig. 3 Fractions Rχb(mP) ϒ(nS)as functions of pϒ T. Points with blue open (red solid) symbols correspond to data collected at √s=7(8)TeV, respectively. For better visualization the data points are slightly displaced from the bin centres. The inner error bars represent statistical uncertainties, while the outer error bars indicate statistical and systematic uncertainties added in quadrature photons in the kinematical range considered in this analysis. This uncertainty is dominated by the knowledge of the ratio of the branching fractions for B+→J/ψK∗+ and B+→J/ψK+decays. Another source of systematic uncertainty is associated with the unknown polarization of χband ϒstates. The polarization of ϒmesons for pϒ T>10 GeV/cand in the central rapidity region |yϒ|<1.2 has been found to be small by the CMS collaboration [56]. Therefore in this paper we assume zero polarization of ϒmesons and no systematic uncertainty is assigned due to this effect. The systematic uncertainty related to the unknown polarization of χbmesons was estimated following Refs. [14,17]. For each pϒ Tbin, the ratios of efficiencies εχb1 /εϒand εχb2 /εϒare recomputed using various possible polarizations scenarios for χb1 and χb2 mesons. The maximum deviation of the efficiency ratio with respect to the one obtained with unpolarized production of χb1 and χb2 states is taken as the systematic uncertainty. The assigned uncertainty on Rχb(mP) ϒ(nS)varies between 0.9 % and 9 % for various pϒ Tbins. Systematic uncertainties due to external experimental inputs, e.g. the ϒmass or the mass splitting of χb(1P)and χb(2P)multiplets, are negligible. The systematic uncertainties on the Rχb(mP) ϒ(nS)measurements are summarized in Table 3. Systematic uncertainties on the measurement of the χb1 (3P)mass are due to the ECAL energy scale, the fit model and the ϒ(3S)mass [25]. The first of these is studied by comparing the reconstructed invariant mass of photons in π0→γγ decays with the known mass of the neutral pion [57–59], which gives an uncertainty of 1.0 MeV/c2 in χb(3P)→ϒ(3S)γdecays. The effects of possible mismodelling of the mass resolution and background models are found to be 0.8 MeV/c2and 0.3 MeV/c2, respectively. Other significant contributions to the systematic uncertainty are related to the assumptions on N(χb2)/N(χb1), and to the mass splitting between χbmultiplet components. The effect of the unknown value for the masssplitting is tested by varying mχb2 (3P)−mχb1 (3P)in the fit in a range between 9 and 12 MeV/c2, preferred by theory [47,48]; the obtained deviation of 0.4 MeV/c2is assigned 123 Eur. Phys. J. C (2014) 74:3092 Page 7 of 13 3092 Table 5 Fractions Rχb(mP) ϒ(nS)in bins of pϒ T, measured for data collected at √s=7TeV. The first block corresponds to Rχb(mP) ϒ(1S), the second to Rχb(mP) ϒ(2S) and the third to Rχb(mP) ϒ(3S).The first uncertainty is statistical and the second systematic pϒ T(GeV/c)Rχb(1P) ϒ(nS)Rχb(2P) ϒ(nS)Rχb(3P) ϒ(nS) ϒ(1S)6–8 14.8±1.2±1.33.3±0.6±0.2 8–10 17.2±1.0±1.45.2±0.6±0.3 10–14 21.3±0.8±1.44.0±0.5±0.31.7±0.5±0.1 14–18 24.4±1.3±1.25.2±0.8±0.41.8±0.6±0.2 18–22 27.2±2.1±2.15.5±1.0+0.4 −1.01.9±0.7±0.3 22–40 29.2±2.5±1.76.0±1.2+0.4 −0.72.9±1.0±0.4 ϒ(2S)18–20 31 ±6±4 20–22 30 ±9±3 22–24 33 ±10 ±5 24–28 28 ±9±3 28–40 29 ±8±3 18–40 4.4±1.6±0.5 ϒ(3S)24–29 44 ±12 ±10 29–40 36 ±14 ±8 Table 6 Fractions Rχb(mP) ϒ(nS)in bins of pϒ T, measured for data collected at √s=8TeV. The first block corresponds to Rχb(mP) ϒ(1S), the second to Rχb(mP) ϒ(2S) and the third to Rχb(mP) ϒ(3S).The first uncertainty is statistical and the second systematic pϒ T(GeV/c)Rχb(1P) ϒ(nS)Rχb(2P) ϒ(nS)Rχb(3P) ϒ(nS) ϒ(1S)6–8 15.5±0.9±1.32.8±0.5±0.2 8–10 18.5±0.7±1.54.6±0.4±0.3 10–14 23.2±0.6±1.43.0±0.4±0.21.4±0.4±0.1 14–18 24.2±0.9±1.25.0±0.5±0.31.2±0.4±0.1 18–22 26.0±1.4±1.24.0±0.7±0.30.9±0.5±0.1 22–40 28.5±1.8±2.17.6±1.0±0.62.1±0.5+0.7 −0.2 ϒ(2S)18–20 31 ±4±4 20–22 30 ±5±3 22–24 30 ±6±3 24–28 37 ±5+4 −8 28–40 28 ±5±3 18–40 2.7±1.0±0.3 ϒ(3S)24–29 34 ±8±7 29–40 40 ±9+5 −14 as the corresponding systematic uncertainty. The χb1 (3P) mass exhibits a linear dependence on the assumed fraction of χb1 decays and varies from 10 509 to 10 513 MeV/c2, when the χb2 /χb1 yield ratio changes from 0.3 to 1.0. The determination of the χb1 (3P)mass is further checked using the large χb(1P)→ϒ(1S)γsignal, where the measured χb1 (1P)mass agrees with the known χb1 (1P)mass [25]to better than 0.5 MeV/c, separately for √s=7 and 8 TeV data. No additional systematic uncertainty is assigned. The systematic uncertainties on the χb1 (3P)mass measurement are summarized in Table 4. 5 Results and conclusion The measured fractions Rχb(mP) ϒ(nS)are presented in Fig. 3and Tables 5and 6. The results are dominated by the statistical uncertainties, and show no dependence on the pp collision energy. A measurement of the Rχb(3P) ϒ(3S)fraction is performed for the first time. The large value of this fraction impacts the interpretation of experimental data on ϒproduction and polarization. When data on ϒproduction and polarization are compared with theory predictions, as well as when different theory predictions are compared among themselves, it is often implicitly assumed that the fraction of ϒ(3S)mesons produced by feed down from higher states is small. The large measured value of Rχb(3P) ϒ(3S)indicates that these assumptions need to be revisited. In conclusion, the fractions of ϒmesons originating from χbradiative decays are measured using a data sample collected by LHCb at centre-of-mass energies of 7 and 8 TeV, as a function of the ϒtransverse momentum in the kinematic range 2.0<yϒ<4.5. The results presented in this paper 123 3092 Page 8 of 13 Eur. Phys. J. C (2014) 74:3092 supersede previous LHCb measurements [23] by increasing the statistical precision and exploiting more decay modes and higher transverse momentum regions. The measurement of the ϒ(3S)production fraction due to radiative χb(3P) decays is performed for the first time. Assuming the mass splitting mχb2 (3P)−mχb1 (3P)= 10.5MeV/c2, the mass of χb1 (3P)state is measured to be mχb1 (3P)=10 511.3±1.7±2.5MeV/c2, where the first uncertainty is statistical and the second systematic. This result is compatible and significantly more precise than the event yield average mass of χb1 (3P)and χb2 (3P)states of 10 530 ±5±17 MeV/c2and 10 551 ± 14 ±17 MeV/c2, reported by the ATLAS [21] and D0 [26] experiments, respectively. Acknowledgments We thank K.-T. Chao, H. Han, V. G. Kartvelishvili, J.-P. Lansberg A. K. Likhoded, A. V. Luchinsky, S. V. Poslavsky and H.-S. Shao for inspiring and fruitful discussions on P-wave bottomonia production. We express our gratitude to our colleagues in the CERN accelerator departments for the excellent performance of the LHC. We thank the technical and administrative staff at the LHCb institutes. We acknowledge support from CERN and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC (China); CNRS/IN2P3 (France); BMBF, DFG, HGF and MPG (Germany); SFI (Ireland); INFN (Italy); FOM and NWO (The Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MinES and FANO (Russia); MinECo (Spain); SNSF and SER (Switzerland); NASU (Ukraine); STFC (United Kingdom); NSF (USA). The Tier1 computing centres are supported by IN2P3 (France), KIT and BMBF (Germany), INFN (Italy), NWO and SURF (The Netherlands), PIC (Spain), GridPP (United Kingdom). We are indebted to the communities behind the multiple open source software packages on which we depend. We are also thankful for the computing resources and the access to software R&D tools provided by Yandex LLC (Russia). 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