Measurements of the production of P-wave charmonium states through radiative decays at the ATLAS experiment

. The production cross sections of the χ c 1 and χ c 2 charmonium states are measured in pp collisions at √ s = 7 TeV using 4.5 fb − 1 of integrated luminosity recorded by the ATLAS detector at the LHC. The χ c states are reconstructed via the radiative decay χ c → J /ψ ( μ + μ − ) γ , where the photons are reconstructed using γ → e + e − conversion in the detector material. Di ﬀ erential production cross sections for prompt and non-prompt χ c 1 , 2 are presented, as well as the fraction of inclusive J /ψ produced by feed-down from the χ c states. The results are compared with a range of theoretical predictions. The branching fraction of B ( B + → χ c 1 K + ) is measured using the same dataset and χ c event selection.


Introduction
Quarkonium is a flavorless mesonic bound state of a quark and its anti-quark. The charmonium (cc) and bottomonium (bb) systems have been studied particularly deeply both experimentally and theoretically since the discoveries of the J/ψ and Υ mesons in the 1970s, and a variety of excited states has been found and investigated. Charmonium has a rich energy level spectrum reminiscent of positronium. The J/ψ is perhaps the most widely known state of charmonium, a 3 S 1 state of the bound cc quarks. Due to its relatively large branching ratio of decay into a lepton pair, it is a valuable tool not only for heavy quark studies, but is also a "standard candle" for understanding the detector performance due to the clean experimental signature.
The production of the cc pair is well understood in terms of Quantum Chromodynamics (QCD), since heavy quark masses are larger than QCD hadronization scale Λ QCD and perturbative calculations can be applied. On the other hand, the dynamics of the bound state are non-perturbative and it is a natural laboratory for precise tests of effective theories and lattice QCD, since it probes the interplay between the perturbative and non-perturbative regions of QCD -namely the evolution of the cc pair into a colourless bound state.
Many other aspects of quarkonium production remain a challenging problem for QCD [1]. The large mass of c and b quarks makes the non-relativistic model description possible. The effective theories -the Color Singlet (CS) model and the Color Octet (CO) model which emerged in the nonrelativistic QCD (NRQCD) were able to explain the transverse momentum (p T ) spectra of the 3 S 1 charmonium states observed at the Tevatron and the LHC. However, the polarization predictions of those models disagree with measurements [2]. Currently, no model is able to describe both production cross section and polarization, and therefore the experimental hadron spectroscopy has an essential role in understanding of QCD in the quarkonia regimes. The ATLAS detector at the LHC allows the study of such bound states in wide transverse momenta and rapidity regions.
Study of the χ c production is important, as it represents a significant feed-down fraction in radiative decays of χ cJ → J/ψγ. Furthermore, the relative production ratio such as σ(χ c2 )/σ(χ c1 ) is a sensitive measurement for disentangling the CO contributions to the prompt charmonium production mechanisms [4].

The ATLAS detector
ATLAS is a general purpose detector at the LHC optimized for high p T physics and instantaneous luminosity of 10 34 cm -2 s -1 with almost 4π coverage [5]. The ATLAS detector consists of an Inner Detector (ID) tracker, electromagnetic and hadronic calorimetry systems and a Muon Spectrometer (MS). The key sub-detectors for the study presented in this paper are the ID and the MS. The ID surrounds the interaction point and provides precise information for the reconstruction of charged particle tracks. It consists of a Pixel Detector, a semiconductor microstrip tracker (SCT) and a transition radiation tracker (TRT). For measurements of track momenta and particle charge, the ID is located in a 2 T magnetic field generated by a superconducting solenoid and covers the pseudorapidity region of |η| < 2.5 1 . The ID system is enclosed by the liquid-argon lead electromagnetic and the iron scintillator hadronic sampling calorimeters. The MS pseudorapidity coverage extends up to |η| < 2.7, covering a large phase space of the muon transverse momenta up to 1 TeV. Muons are reconstructed using the information provided by the MS and the ID.

Measurement of the χ cJ production
The measurement of the χ c1,2 differential production cross section is performed using the radiative decay channel χ cJ → J/ψγ. The measurement is performed in 5 bins of transverse momentum p T and one bin of rapidity |y J/ψ | < 0.75. The χ c0 cross section is not measured due to its small branching fraction to J/ψ and γ and difficult background situation. The measurements presented in this paper are performed using the 4.5 fb −1 collected by the ATLAS detector during the 2011 LHC run at a centre-of-mass energy √ s = 7 TeV. A full description of the measurements can be found in [6].

Event selection
Collision events for this analysis are selected as follows. Two J/ψ candidate muons are required to have both ID and MS track segments and must be of opposite charges. In addition, they must pass the di-muon trigger with a p T threshold of 4 GeV. The ID tracks must satisfy quality requirements by having been reconstructed from at least one Pixel hit and at least six SCT hits, and are required to have originated from a primary vertex built from at least three tracks. The di-muon system invariant mass for the J/ψ candidate must fall within the 2.95 < m(μ − μ + )< 3.25 GeV window. In addition, the di-muon system must be within the central part of the ATLAS detector with rapidity |y (μ + μ − ) | < 0.75, since this central region of the detector has the smallest di-muon invariant mass resolution.
For the converted photons, two oppositely charged tracks are required with at least six hits in the SCT subdetector and with p T at least 400 MeV. In addition, the ID tracks must be reconstructed within |η| < 2.3. Track pairs consistent with the photon conversion hypothesis are fitted to a common vertex, which is required to converge with a χ 2 /N do f < 5. Reconstructed converted photon candidates must have p γ T > 1.5 GeV and must fall within the pseudorapidity range of |η γ | < 2. In addition, the conversion point must be within the Pixel Detector radius of 40 < r < 150 mm to reject fake conversions from π 0 → e + e − γ . An additional requirement on the 3-dimensional impact parameter a 0 < 5 mm is imposed on the J/ψ and γ candidates to ensure that they come from a common vertex.

The differential χ c1 and χ c2 cross section measurements
The P-wave charmonia are produced directly at the pp collision, emerge in a feed-down from the higher-energy charmonium states such as Ψ(2S ) and also result from decay of b-hadrons. The pseudoproper lifetime τ is the discriminating factor for the χ cJ production classes (prompt and non-prompt b-hadron cascade production), and is defined as: where L xy is the transverse flight length from the primary vertex defined as the one with highest p T of tracks and m PDG J/ψ is the world average invariant mass of the J/ψ. The prompt χ cJ candidates have τ compatible with 0. A simultaneous Δm -lifetime fit is performed to extract number of candidate events for prompt and non-prompt production, where the mass difference Δm = m(μ + μ − γ) -m(μ + μ − ) is used to discriminate between the χ c1 and χ c2 states. The Δm and lifetime distributions for the kinematic region of 10 ≤ p J/ψ T < 30 GeV and |y J/ψ | < 0.75 are shown in figure 1. The differential cross sections for the prompt and non-prompt χ c1 and χ c2 production in a given bin are calculated as ICNFP 2013 where L is the integrated sample luminosity and Δp χ cJ T represents the p T bin width. To recover the true number of χ cJ s, each reconstructed event is weighted by a factor which includes the detector kinematic acceptance, data-driven measurements of the trigger efficiency and the di-muon reconstruction efficiency. In addition, the photon conversion reconstruction efficiency is estimated using a Monte Carlo simulation. The measured cross section is shown in figure 2 for prompt χ c and in figure 3 for the non-prompt case. The cross-section results are also measured as a function of p J/ψ T .  The acceptance (and therefore the measured cross section) depends significantly on the production polarisation of the χ cJ system, which is not currently known for LHC conditions. The corresponding uncertainty is estimated by calculating the weighting factors for maximal polarisation scenarios and re-evaluating the cross section for each one. The zero-polarisation scenario is used for the central values of the cross section, and the variations around this are taken as a theoretical uncertainty. In the following plots, the error bars represent the total uncertainty of the measurement. The results show that in the case of prompt production (figure 2), the next-to-leading Order (NLO) NRQCD is in good agreement with the data, while the k T factorisation model grossly overestimates the measured production cross section, in contrast to the leading order (LO) CSM which predicts significantly lower cross sections, because the higher order corrections are probably large. In the case of non-prompt production, the Fixed Order Next-to-Leading Logarithm (FONLL) prediction is in general agreement with the data, with statistical uncertainties limiting the precision.

The fraction of the prompt J/ψ produced in χ c decays
The measurements of the prompt χ c1,2 production cross section are combined with existing measurements of the prompt J/ψ production [7] to estimate the fraction of J/ψs which are produced in the χ c decays. The results are presented in bins of p T . The measurements show that around 20-30% of J/ψ mesons are produced in the χ c feed-down. This result is compatible with the LHCb measurements in the overlapping region of the p T spectra. The results are shown in figure 4. The NLO NRQCD predictions describe the measurement with a good agreement.

The χ cJ relative cross sections
The ratio of the prompt cross sections of χ c2 and χ c1 (figure 5, left) are compared against predictions from CS and NLO NRQCD CO calculations. The NLO NRQCD is in general agreement with the data for lower p T range, while the LO CSM systematically underestimates the measurement. On the other hand, the non-prompt cross section ratio (shown in figure 5, right) is in principle predicted by the relative branching fractions, and it is in good agreement with the CDF data in the p T spectrum overlap range.

The fractions of χ c1 and χ c2 produced in the decays of b-hadrons
The inclusive χ c production (shown in figure 6) is dominated by the prompt processes unlike the J/ψ, where the feed-down from b-hadron decays is substantial.

ICNFP 2013
00082-p.5 Figure 5. (left)The production cross section of the prompt χ c2 relative to the prompt χ c1 measured as a function of p J/ψ T . The measurements are compared to the predictions of NLO NRQCD, LO CSM and to the measurement from CMS [9]. (right) The production cross section of the non-prompt χ c2 relative to the non-prompt χ c1 measured as a function of p J/ψ T . The measurement from CDF [10] is also shown. The factors B 1 and B 2 on both plots represent the branching ratios B J = B J (χ cJ → J/ψγ) [6].

Measurement of the B ± → χ c1 K ± branching fraction
The branching fraction B(B ± → χ c1 K ± ) is measured using the B ± → J/ψK ± decay as a reference. The final states are identical except for a photon, which allows the direct test of the Monte Carlo-derived photon conversion efficiency corrections, used in the previous measurements presented in this paper. The branching ratio is measured using the relation: where A is the factor which corrects for the different detector acceptances of the two decay channels, N B χ c1 and N B J/ψ are the fitted signal yields for the χ c1 decay channel and the reference channel. The χ c1 and J/ψ event selection criteria are kept as close to the inclusive χ c measurements as possible. Both decays are reconstructed within the kinematic region of 10 < p J/ψ T < 30 GeV and |y J/ψ | < 0.75.

EPJ Web of Conferences
00082-p.6 The candidate events in both channels are weighted to correct for the trigger efficiency, muon reconstruction efficiency and in the case of the B ± → χ c1 K ± also for the conversion probability and reconstruction efficiency using the same corrections derived for the inclusive χ c production measurement. The fit results are shown in figure 7. The measured branching fraction is (B ± → χ c1 K ± )=(4.8 ± 0.6(stat.) ± 0.6(syst.)) × 10 −4 . This value is in good agreement with the current world average value of (4.79 ± 0.23) × 10 −4 [3], strongly suggesting that the simulation-derived photon conversion probabilities used in the measurements of the χ cJ production cross sections are valid. The cross sections for both prompt and non-prompt χ c1 and χ c2 production are measured in pp collisions at the centre-of-mass energy of 7 TeV with the ATLAS detector at the LHC. The production rate of the χ c2 state relative to the χ c1 state is measured for both prompt and non-prompt production as a function of J/ψ transverse momentum. The measurements of the prompt χ cJ are combined with existing ATLAS measurements of the prompt J/ψ production to obtain the fraction of the prompt J/ψ produced in the feed-down from χ cJ decays. The fractions of χ c1 and χ c2 produced in the decays of b-hadrons are also presented as functions of transverse momentum. The measurements of the prompt χ cJ production are compared to the theoretical predictions of the NLO NRQCD CO model, the k T factorisation approach and the CS model. The NRQCD CO predictions are found to be in general agreement with the measurements. The k T factorisation approach predicts larger cross section than the measurement, while the LO CSM prediction significantly underestimates the data. The measurements of the non-prompt χ cJ production are found to be consistent with the FONLL predictions. The branching ratio B(B ± → χ c1 K ± ) = (4.8 ± 0.6(stat.) ± 0.6(syst.)) × 10 −4 is also measured using the same dataset and χ cJ event selection. The measured value is found to be in good agreement with the world average and provides a confirmation of the conversion reconstruction efficiencies derived from the simulation.