spin configurations, is ideal laboratory for QCD tests. It’s like a hydrogen atom in QCD. Measured mass Mass from theory States with parallel quark spins (S=1): S-wave Υ state. P-wave χb states, composed by 3 spin states χb(0,1,2) . Υ can be readily produced in the radiactive decays of χb. χb (3P) state recently observed by ATLAS, D0 and LHCb. Study of χb production: 1 Measurement for Υ(NS) (N=1, 2, 3) cross sections in χb decays as a function of pT (NΥ) 2 Measurement of χb(0,1,2) (3P) mass. 2/34
originating from χb(1P) in pp collisions at √ s =7 TeV ”, arXiv:1209.0282, L = 32 pb−1 ”Observation of the χb(3P) state at LHCb in pp collisions at √ s =7 TeV ”, LHCb-CONF-2012-020, L = 0.9 fb−1. 3/34
σ(Υ) = Nχb→Υγ NΥ × Υ χb→Υγ = Nχb→Υγ NΥ × 1 reco γ Calculate for each Υ(nS), n = 1, 2, 3 and χb(mP), m = 1, 2, 3 Get N from fits: NΥ from m(µ+µ−) and Nχb→Υγ from [m(µ+µ−γ) − m(µ+µ−)] (for better resolution) Compute efficiency from Monte-Carlo simulation 4/34
40 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 0 10 20 30 40 0 20 40 60 80 100 120 140 3 10 × 0 10 20 30 40 0 5000 10000 15000 20000 25000 30000 35000 40000 Events pT (Υ) [ GeV/c] Υ(3S) Events pT (Υ) [ GeV/c] Υ(1S) Events pT (Υ) [ GeV/c] Υ(2S) √ s =7 TeV √ s =8 TeV √ s =7 TeV √ s =8 TeV √ s =7 TeV √ s =8 TeV Yields normalized by bin width. As expected, yields for 2012 are twice larger than for 2011 due to luminosity difference. 9/34
0 500 1000 1500 2000 2500 -4 -2 0 2 4 10 10.5 0 200 400 600 800 1000 -4 -2 0 2 4 Candidates/(20 MeV/c2) m µ+µ−γ − m µ+µ− + 9.4603 GeV/c2 √ s = 8 TeV pT (Υ (1S)) > 14 GeV/c Candidates/(20 MeV/c2) m µ+µ−γ − m µ+µ− + 9.4603 GeV/c2 √ s = 7 TeV pT (Υ (1S)) > 14 GeV/c 6 Crystal Ball functions for each of χb1,2(1, 2, 3P) signal (exclude the study of χb0 due to its low branching ratio) Product of exponential and linear combination of basic Bernstein polinomials for combinatorial background. 11/34
15 20 25 30 9.87 9.875 9.88 9.885 9.89 9.895 9.9 9.905 9.91 9.915 √ s =7 TeV, √ s =8 TeV √ s =7 TeV, √ s =8 TeV χb1(1P) mass GeV/c2 pT (Υ) [ GeV/c] The major cause of χb1(1P) mass floating in 10 MeV/c range can be the unknown fraction between Nχb1 and Nχb2 yields (λ parameter). We have only theoretical prediction for λ value . In this study the mass of χb1(1P) was fixed to 9892 MeV/c2. 13/34
25 30 35 40 10.235 10.24 10.245 10.25 10.255 10.26 √ s =7 TeV, √ s =8 TeV χb1(2P) mass GeV/c2 pT (Υ) [ GeV/c] In this study the mass of χb1(2P) was fixed to 10249 MeV/c2. 17/34
35 40 0 10 20 30 40 50 60 70 80 20 25 30 35 40 0 2 4 6 8 10 12 14 Events pΥ(2S) T [ GeV/c] χb(2P) Events pΥ(2S) T [ GeV/c] χb(3P) √ s =7 TeV √ s =8 TeV √ s =7 TeV √ s =8 TeV Yields normilized by bin width. 18/34
(10,507±2 MeV/c2) is consistent with the mass measured in another study with converted photons (10,509±3.0 MeV/c2). Summary The b (3P) states can be resolved with more statistics! b (3P) mass measurement using b (3P) (1S)ee : • m(b1 (3P) )=10509.5 3.0(stat) +5.3 -2.9 (syst) MeV/c2 • ATLAS measured b1 and b2 mass barycenter for m=12 and r12 =1 : m(b (3P) )= 10530 5(stat) 9(syst) MeV/c2 difference with this result~ 1.3 • D0: m(b (3P) )=10551 14(stat) 17(syst) MeV/c2 b (1P) mass splitting: m12 = 18.6 0.7(stat) 0.2 (syst) MeV/c2 In agreement with PDG value: m12 =19.4 0.6 (?) MeV/c2 b1,2 (1P) relative production cross section: in agreement with c and theory but statistically limited 23/24 21/34
decays have the same shape) 0 0.5 1 1.5 2 0 500 1000 1500 2000 2500 Candidates mµ+µ−γ − mµ+µ− GeV/c2 Monte-Carlo events in the flat left band are fitted as background in the model for real data. So efficiency needs to be calculated with χb mc-true events fitted by Crystal Ball function and some background which fits this band. Υ events are measured by counting mc-true events. 22/34
30 40 0 10 20 30 40 50 60 Υ(1S) fraction, % pΥ(1S) T [ GeV/c] χb(1P) → Υ(1S)γ √ s =7 TeV √ s =8 TeV √ s =7 TeV (2010) 10 20 30 40 0 2 4 6 8 10 12 14 Υ(1S) fraction, % pΥ(1S) T [ GeV/c] χb(2P) → Υ(1S)γ √ s =7 TeV √ s =8 TeV 10 20 30 40 0 1 2 3 4 5 6 7 8 9 Υ(1S) fraction, % pΥ(1S) T [ GeV/c] χb(3P) → Υ(1S)γ √ s =7 TeV √ s =8 TeV 20 25 30 35 40 0 10 20 30 40 50 60 Υ(2S) fraction, % pΥ(2S) T [ GeV/c] χb(2P) → Υ(2S)γ √ s =7 TeV √ s =8 TeV 20 25 30 35 40 0 5 10 15 20 25 Υ(2S) fraction, % pΥ(2S) T [ GeV/c] χb(3P) → Υ(2S)γ √ s =7 TeV √ s =8 TeV For χb(1P) decay the fraction is consistent with the previous results. About 40% of Υ come from χb, with a mild transverse momentum dependence. χb(3P) fraction in Υ(3S) decay is 34 ± 7 % for 24 < pΥ(3S) T < 40 GeV/c. 26/34
3P) → Υ(2S)γ decays Uncertainty due to the χb1(2P) mass variation in the pΥ(2S) T range is estimated by using the observed minimum and maximum values. Υ(2S) transverse momentum intervals 18 < pT < 25 GeV/c 25 < pT < 40 GeV/c m(χb1(2P)) / Change (%) Nχb(2P) Nχb(3P) Nχb(2P) Nχb(3P) 10.245 GeV/c2 (min mχb1(2P) ) 4 4 -2 19 10.255 GeV/c2 (max mχb1(2P) ) 3 2 8 -11 Maximum uncertainty on the yields is 8% and 19% for Nχb(2P) and Nχb(3P), respectively. 30/34
MC where chib particles are unpolarized. To evaluate systematic effects due to the unknown polarization of chib, MC events are reweighted as described in HERA-B Collaboration, I. Abt et al., Production of the Charmonium States χc1 and χc2 in Proton Nucleus Interactions at s = 41.6-GeV, arXiv:0807.2167 and LHCb collaboration, R. Aaij et al.,Measurement of the cross-section ratio σ(χc2 )/σ(χc1 ) for prompt χc production at √ s = 7 TeV, arXiv:1202.1080 For each simulated event in the unpolarised sample, a weight is calculated from the distribution of the following angles in the various polarisation hypotheses compared to the unpolarised distribution. ΘΥ angle between the directions of the µ+ in the Υ rest frame and the Υ in the χb rest frame. Θχb angle between the directions of the Υ in the χb rest frame and χb in the lab frame. φ angle between the Υ decay plane in the χb rest frame and the plane formed by χb direction in the lab frame and the direction of the Υ in the χb rest frame. Two hypotheses for χb1 state (w0, w1) and three hypotheses for χb2 (w0, w1, w2). 32/34
decays. About 40% of Υ come from χb, with mild dependence on Υ transverse momentum. Measured mass of χb(3P) is 10507±2 MeV/c2, consistent with another determination which uses converted photons. An LHCb internal note documenting this study has been written. The analysis is currently under internal review and will be the subject of an LHCb publication. 34/34