Measurement of χc 1 and χc 2 production with √ s = 7 TeV pp collisions at ATLAS

The prompt and non-prompt production cross-sections for the χc1 and χc2 charmonium states are measured in pp collisions at √ s = 7TeV with the ATLAS detector at the LHC using 4.5 fb−1 of integrated luminosity. The χc states are reconstructed through the radiative decay χc → J/ψγ (with J/ψ → μ+μ−) where photons are reconstructed from γ → e+e− conversions. The production rate of the χc2 state relative to the χc1 state is measured for prompt and non-prompt χc as a function of J/ψ transverse momentum. The prompt χc cross-sections are combined with existing measurements of prompt J/ψ production to derive the fraction of prompt J/ψ produced in feed-down from χc decays. The fractions of χc1 and χc2 produced in b-hadron decays are also measured.


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Various aspects of the production of χ c states have been studied at the LHC [13][14][15][16] and at the Tevatron [17,18]; however, measurements of the absolute production crosssections for prompt χ c and studies of non-prompt χ c production have not been performed previously at the LHC.
This paper presents measurements of the inclusive production of the χ c1 and χ c2 states in pp collisions at a centre-of-mass energy √ s = 7 TeV at the LHC. The χ c states are reconstructed through the radiative decays χ cJ → J/ψ γ (with J/ψ → µ + µ − ), where the photon is reconstructed through its conversion into a positron-electron (e + e − ) pair. Photon conversions reconstructed in the ATLAS inner tracking detector offer the very good mass resolution needed to resolve the χ c1 and χ c2 states individually. The χ c0 production rate is not measured explicitly because the inclusive yield of χ c0 in the data sample used in this analysis is considered to be too small to perform a reliable measurement. The inclusive production of the χ c1 and χ c2 states is separated experimentally into prompt and non-prompt components and measured differentially in both χ c transverse momentum p χ c T and J/ψ transverse momentum p J/ψ T , within the rapidity region |y J/ψ | < 0.75. The results obtained as a function of p J/ψ T and p χ c T are presented within the regions 10 ≤ p J/ψ T < 30 GeV and 12 ≤ p χ c T < 30 GeV respectively. These new measurements are combined with existing measurements of inclusive J/ψ production [8] to determine the fraction of prompt J/ψ produced in feed-down from χ c decays. The ratio σ ( χ c2 ) /σ ( χ c1 ) is a useful theoretical quantity as it is sensitive to the presence of possible colour-octet contributions to χ c production [19]. This cross-section ratio is measured as a function of p J/ψ T for prompt χ c1 and χ c2 production. These measurements are compared to theoretical predictions and to the measurements by other experiments. The branching fraction B(B ± → χ c1 K ± ) is also measured with the same data sample and event selection.

The ATLAS detector, data and Monte Carlo samples
The ATLAS detector [20] is a general-purpose particle physics detector with a cylindrical geometry 1 with forward-backward symmetric coverage in pseudorapidity η. The detector consists of inner tracking detectors, calorimeters and a muon spectrometer, and has a three-level trigger system.
The inner tracking detector (ID) is composed of a silicon pixel detector, a semiconductor microstrip detector (SCT) and a transition radiation tracker, which together cover the pseudorapidity range |η| < 2.5. The ID directly surrounds the beam pipe and is immersed in a 2 T axial magnetic field generated by a superconducting solenoid. The calorimeter system surrounds the solenoid and consists of a highly granular liquid-argon electromagnetic calorimeter and an iron/scintillator tile hadronic calorimeter. The muon spectrometer (MS) surrounds the calorimeters and consists of three large air-core superconducting magnets JHEP07(2014)154 (each with eight coils), which generate a toroidal magnetic field. The MS is instrumented in three layers with precision detectors (monitored drift tubes and cathode strip chambers) that provide precision muon tracking covering |η| < 2.7 and fast trigger detectors (resistive plate chambers and thin gap chambers) covering the range |η| < 2.4.
The ATLAS trigger is a three-level system consisting of a level-1 trigger implemented in hardware and a software-based two-stage high level trigger (HLT). The data sample used in this analysis is collected with a dimuon trigger. The level-1 muon trigger system identifies regions of interest (RoI) by searching for coincidences between hits in different trigger detector layers within predefined geometrical windows enclosing the paths of muons with a given set of transverse momentum thresholds. The level-1 system also provides a rough measurement of muon position with a spatial granularity of ∆φ × ∆η ≈ 0.1 × 0.1. The level-1 RoI then serves as a seed for HLT algorithms that use higher precision MS and ID measurements to reconstruct muon trigger objects. The selection performed by the HLT algorithms is discussed in section 3.
The measurements presented in this paper are performed with a data sample corresponding to an integrated luminosity of 4.5 fb −1 collected during the 2011 LHC protonproton run at a centre-of-mass energy √ s = 7 TeV. The selected events were collected under stable LHC beam conditions with the detector in a fully operational state. Four Monte Carlo (MC) simulation samples are used to estimate the photon conversion reconstruction efficiency and to characterise the modelling of the χ c signal components used in the fitting procedure. The samples consist of simulated χ c1 → J/ψ γ → µ + µ − γ and χ c2 → J/ψ γ → µ + µ − γ decays produced either directly in pp interactions or through the process pp → bbX → χ c X ′ . All samples are generated with Pythia 6 [21] and use the ATLAS 2011 MC underlying event and hadronisation model tuning [22]. The response of the ATLAS detector is simulated using Geant4 [23,24]. The events are reconstructed using the same algorithms used to process the data. Each χ c event is overlaid with a number of minimum-bias pp events such that the overall distribution of additional pp interactions due to pile-up in data events is accurately described by the simulated samples.

Event and χ c candidate selection
The selected events passed a dimuon trigger in which the HLT identified two oppositely charged muons, each with transverse momentum p T > 4 GeV. The HLT fits the two candidate muon tracks to a common vertex and a very loose requirement on the vertex χ 2 is imposed. Finally, a broad dimuon invariant mass cut (2.5 < m (µ + µ − ) < 4.0 GeV) is applied to select dimuon candidates consistent with J/ψ → µ + µ − decays. Each event passing the trigger selection is required to contain at least one reconstructed pp collision vertex formed from at least three reconstructed tracks with p T > 400 MeV.
In the offline analysis, muon candidates are formed from reconstructed ID tracks matched to tracks reconstructed in the MS. Each muon track is required to be reconstructed from at least six SCT hits and at least one pixel detector hit. For the low-p T muons (typically below 20 GeV) produced in J/ψ → µ + µ − decays, the track parameters measured in the ID provide more accurate measurements than the MS as they are not af-

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fected by muon energy loss in the calorimeters. Therefore, the ID measurements alone are used to reconstruct the momentum of muon candidates. Events are required to contain at least one pair of oppositely charged muons, each with transverse momentum p µ T > 4 GeV and |η µ | < 2.3 (the region where the trigger and reconstruction efficiencies are optimal). Each muon pair is fitted to a common vertex and a very loose vertex quality requirement (fully efficient for genuine J/ψ → µ + µ − decays) is imposed. The dimuon pair is considered a J/ψ → µ + µ − candidate if the invariant mass of the pair, calculated from the track parameters recalculated by the vertex fit, satisfies 2.95 < m (µ + µ − ) < 3.25 GeV. The event and J/ψ → µ + µ − candidate are retained for further analysis if the two muon candidates reconstructed offline are consistent with the objects reconstructed by the HLT (matched within ∆R = (∆φ) 2 + (∆η) 2 < 0.01). The rapidity of the J/ψ candidate reconstructed offline is required to satisfy |y J/ψ | < 0.75. This selection retains only the candidates reconstructed within the region of the detector with the optimal dimuon mass resolution, which is necessary to reliably resolve the individual χ cJ states.
Photon conversions are reconstructed from pairs of oppositely charged ID tracks whose helices touch when projected onto the transverse plane. Tracks must be reconstructed with transverse momentum p T > 400 MeV and |η| < 2.3 and contain at least six SCT hits. Track pairs consistent with the photon conversion hypothesis are fitted to a common vertex with their opening angle constrained to be zero. The vertex fit is required to converge with χ 2 per degree of freedom less than five. To reject fake conversions from π 0 → e + e − γ decays and other promptly produced track pairs, the radial displacement r of the reconstructed conversion vertex with respect to the z-axis is required to satisfy 40 < r < 150 mm. This fiducial region includes the three layers of silicon pixels in the ID, and so selects conversions occurring within these silicon pixel layers and their associated service structures. The efficiency for reconstructing converted photons from only ID tracks decreases significantly beyond the upper limit of 150 mm. In this analysis, no information from the calorimeters is used in the reconstruction of photon conversions. The reconstructed momentum of the converted photon is calculated from e + e − track parameters recalculated by the vertex fit with the invariant mass constrained to be zero. Reconstructed converted photons are required to have transverse momentum p γ T > 1.5 GeV and |η γ | < 2.0. Candidate χ c → J/ψ γ → µ + µ − γ decays are selected by associating a reconstructed photon conversion with a candidate J/ψ → µ + µ − decay. To reject combinations of J/ψ → µ + µ − decays and photons not consistent with a χ c decay, the impact parameter of the converted photon with respect to the dimuon vertex is required to be less than 5 mm. This requirement has a negligible inefficiency for genuine χ c decays.

Cross-section determination
The distribution of mass difference ∆m = m (µ + µ − γ) − m (µ + µ − ) is used to distinguish the χ c1 and χ c2 states. This distribution is used in place of the three-body invariant mass as some partial cancellation of contributions from the dimuon mass resolution is achieved, resulting in improved overall mass resolution. Non-prompt χ c candidates produced in the decays of b-hadrons can be distinguished experimentally from prompt χ c candidates  is sensitive to the p χ c T spectrum used as input to the simulation and must be calculated with an alternative approach. Acceptance corrections are derived for each measured p J/ψ T bin with the same simulation used to generate the acceptance maps, but with the χ c decays generated with a transverse momentum spectrum taken from a fitted parameterisation of the differential cross-sections measured as a function of p χ c T and presented in this paper.

Trigger efficiency
The dimuon trigger efficiency is determined from J/ψ → µ + µ − and Υ → µ + µ − decays in data using the method described in ref.
[26]. The dimuon trigger efficiency ǫ trig is defined as the efficiency with which the trigger system can select events that pass the full offline -8 -

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dimuon selection. The method factorises the total efficiency into three parts, where ǫ RoI is the efficiency with which the trigger system can identify a single muon with transverse momentum p µ T and charge-signed pseudorapidity q · η µ as an RoI. Charge-signed pseudorapidity is used to account for the charge asymmetry in single-muon triggering due to the toroidal magnetic field. The factor c µ + µ − is present to correct for inefficiencies associated with the dimuon selection of the trigger. These include vertexing and dimuon charge requirements and effects associated with the finite size of the muon RoI. The factor c µ + µ − and the single-muon efficiency ǫ RoI are determined using a sample of J/ψ → µ + µ − decays selected with a single-muon trigger with an 18 GeV transverse momentum threshold. The efficiency ǫ RoI is derived in two-dimensional bins of p µ T and q · η µ from the fraction of fitted J/ψ → µ + µ − decays that pass the high-p T single-muon trigger and that also pass the dimuon trigger selection (corrected for dimuon effects with c µ + µ − ). The average dimuon trigger efficiency for J/ψ → µ + µ − decays with 10 ≤ p J/ψ T < 30 GeV is between 50% to 60% for the fiducial region studied.

Muon reconstruction efficiency
The efficiency to reconstruct and identify both muons from the decay J/ψ → µ + µ − is described by the equation The quantity ǫ trk is the reconstruction efficiency for muon tracks subject to the ID track selection described in section 3 and is determined to be (99 ± 1)% over the full kinematic region studied [26]. The single-muon identification efficiency ǫ µ is derived from an analysis of a sample of J/ψ → µ + µ − decays in data, unbiased by any muon selection criteria as described in ref.
[26]. The muon identification efficiency reaches a plateau of around 98% for muons with p µ T > 8 GeV. The efficiency of the dimuon invariant mass requirement 2.95 < m (µ + µ − ) < 3.25 GeV discussed in section 3 is estimated to be (99.0 ± 0.5)% by performing fits to the m (µ + µ − ) distribution of an inclusive sample of J/ψ → µ + µ − decays reconstructed within the same fiducial region used in the analysis.

Photon conversion reconstruction efficiency
The total photon conversion reconstruction efficiency ǫ γ is determined from the MCsimulated χ c → J/ψ γ event samples described in section 2. The decay products in the simulated samples of radiative χ c decays are propagated through the ATLAS detector simulation. The description of the ID material distribution in the MC simulation samples is checked by comparing the distributions of various conversion observables (including conversion vertex fit χ 2 , vertex position and kinematic variables) measured in data and MC simulation. The distributions are found to agree well and no significant discrepancies are The total photon conversion reconstruction efficiency ǫ γ is factorised into two parts, where P conv is the probability that a photon converts within the fiducial region for conversions (40 < r < 150 mm) and ǫ conv is the converted-photon reconstruction efficiency. The conversion probability P conv is derived from the ratio of the number of generated photons from radiative χ c decays that convert in the fiducial region of the ID to the total number of photons from radiative χ c decays. The calculation of P conv is performed in bins of η γ to account for changes in the detector material traversed for photons of different pseudorapidity. No significant dependence of P conv on photon energy is observed for photons within the kinematic fiducial region (p γ T > 1.5 GeV). The conversion probability varies from around 7% to 11% within the fiducial region studied.
The reconstruction efficiency for converted photons, ǫ conv , is determined from the equation where N γ conv is the number of simulated photons from radiative χ c decays that convert in the fiducial region of the ID and N γ reco is the number of reconstructed photon conversions. This ratio is calculated in bins of p γ T and |η γ | (no significant asymmetry in photon pseudorapidity is observed) with a method that is verified to account correctly for experimental resolution in p γ T . The conversion reconstruction efficiency is around 15% at p γ T = 1.5 GeV and approaches a plateau of approximately 45% for p γ T > 5.0 GeV.

Extraction of corrected yields
Corrected χ cJ yields are extracted by performing a simultaneous fit to the mass difference ∆m = m (µ + µ − γ)−m (µ + µ − ) and pseudo-proper decay time τ distributions of weighted χ c candidates. Separate unbinned maximum likelihood fits are performed in bins of both J/ψ candidate transverse momentum p J/ψ T and χ c candidate transverse momentum p χ c T . The fits are performed within the χ c signal region of 0.2 < ∆m < 0.7 GeV and no restriction on τ is applied. The full probability density function (pdf) used to perform the fits has the form, where f sig is the fraction of χ c signal candidates determined by the fit, while F sig and F bkgd are pdfs that respectively model the signal and background components of the mass difference and pseudo-proper decay time distributions. The quantity δτ is the per-candidate uncertainty on the pseudo-proper decay time calculated from the covariance matrix of the vertex fit to the dimuon tracks. The distributions of the pseudo-proper decay time uncertainty δτ observed in the background (∆m < 0.3 GeV or ∆m > 0.48 GeV) and signal (background subtracted within 0.3 < ∆m < 0.48 GeV) regions are found to be consistent -10 -

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within their uncertainties. Consequently, terms for the distribution of δτ factorise in the likelihood and are not included [28].
The signal pdf F sig is composed of several components, where the pdfs M J (∆m) model the χ cJ signal components of the ∆m distribution and T (N)P sig model the (non-)prompt χ c signal contributions to the pseudo-proper decay time distribution. The parameter f P sig is the fraction of the total χ c signal that is promptly produced, f (N)P 0 is the fraction of (non-)prompt signal identified as χ c0 and f (N)P 1 is the fraction of (non-)prompt signal (excluding χ c0 contributions) identified as χ c1 .
The χ c1 and χ c2 signal pdfs M 1,2 (∆m) are each described by a Crystal Ball (CB) function [29][30][31]. The CB function is characterised by a Gaussian core with a width σ i (associated with the pdf M i (∆m)) and a power law low-mass tail described by the parameter n. The transition between the core and tail is described by the threshold parameter α. The mass resolutions of prompt and non-prompt χ c are found to be consistent from MC simulation studies. The natural widths of the χ c1 and χ c2 states are sufficiently small (below 2 MeV [4]) relative to the detector mass resolution (around 10 MeV) that their effects can be neglected. The peak positions of both the χ c1 and χ c2 CB functions are fixed to the world average values of their respective masses [4] multiplied by a common scale factor κ. The factor κ is a free parameter in the fit and is present to account for electron energy losses that result in a small momentum scale shift. The fitted values are typically around κ = 0.98. The two parameters α and n of the CB functions are found to be consistent for both states and are fixed to values determined from fits to MC simulation samples. The resolution parameter σ 1 is determined by the fit with the constraint σ 2 = 1.07 × σ 1 applied, where the value of the scale factor is extracted from MC simulation studies. The χ c0 signal pdf, M 0 (∆m), is modelled by the sum of a CB function and a Gaussian pdf; all parameters describing the shape of the χ c0 signal are fixed to values determined from MC simulation (including a natural width of (10.3±0.6) MeV [4]), while the peak position of the χ c0 signal is a free parameter in the fit. The χ c0 peak is clearly visible in the ∆m distribution shown in figure 2. However, the χ c0 yield is not reported because the statistical significance of the signal is marginal when the data are fitted in separate bins of p J/ψ T and p χ c T . The pdfs T P sig and T NP sig describing the prompt and non-prompt χ c signal contributions to the pseudo-proper decay time distributions are modelled by a delta function δ (τ ) and an exponential function exp (−τ /τ sig ), where τ sig is a free parameter in the fit. Both χ c signal pseudo-proper decay time pdfs are convolved with the function R (τ ′ − τ, δτ ) describing the experimental resolution in pseudo-proper decay time. The resolution function R is described by a Gaussian function with a mean value of zero and width S · δτ where S is a scale factor that is determined by the fit, while δτ is the per-candidate uncertainty on the pseudo-proper decay time τ .

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The background pdf F bkgd is composed of two components, where M (N)P bkgd describes the (non-)prompt background contributions to the ∆m distribution and T (N)P bkgd describes the (non-)prompt background contributions to the pseudo-proper decay time distribution. The parameter f P bkgd is the fraction of the background that is promptly produced. The functions M (N)P bkgd are both modelled by the function where all four parameters (A, B, C and m 0 ) in the pdf are determined by the fit. The shape of the background pdf is motivated by studies with MC simulation samples and a sample of µ + µ − γ candidates in data with dimuon invariant masses in the sidebands of the J/ψ peak. The prompt and non-prompt background pdfs each use an independent set of four parameters. Endowing both background pdfs with an independent set of parameters is motivated by the observation that the shape of the background contribution to the ∆m distribution in data varies significantly as a function of pseudo-proper decay time. The pdf T P bkgd (τ, δτ ) is modelled with a delta function convolved with the pseudo-proper decay time resolution function R. The pdf T NP bkgd (τ, δτ ) consists of two components, where g bkgd determines the relative mixture of the single-and double-sided exponential components. The parameters τ bkgd and τ sym determine the shapes of the single-and doublesided exponential components, respectively. The result of the fit described above to the inclusive data sample with 10 ≤ p J/ψ T < 30 GeV is shown by the projections onto the mass difference and pseudo-proper decay time axes as shown in figure 2. The purity of the selected J/ψ candidates is around 90%, with no strong dependence on pseudo-proper decay time. A larger background contribution to the m (µ + µ − γ) − m (µ + µ − ) distribution, relative to the χ c signal, is observed for µ + µ − γ candidates with longer pseudo-proper decay times. This behaviour is consistent with the expectation from MC simulation and is due to the presence of additional charged particles and photons produced close to the dimuon system in the decays of b-hadrons.
Bin migrations in the measured p χ c T and p J/ψ T distributions are corrected with the method described in refs [8,26]. The approach involves fitting the measured p χ c T and p J/ψ T distributions with a smooth analytic function that is convolved with a resolution function determined from MC simulation. The ratio of the functions with and without convolution is used to deduce a correction factor for each measured bin in p χ c T and p J/ψ T . The average correction for the cross-sections measured as a function of p J/ψ T is 0.5%. Corrections to the cross-sections measured as a function of p χ c T are significantly larger, around 4% on average, due to an asymmetric experimental resolution in p χ c T caused by electron energy loss through bremsstrahlung.

Systematic uncertainties
The relevant sources of systematic uncertainty on the prompt and non-prompt χ c1 and χ c2 cross-section measurements have been identified and their effects are discussed and quantified below. MC and data control samples used to derive the efficiencies. The corresponding uncertainty in the χ c yields is quantified by repeatedly varying the values of the efficiencies within their statistical uncertainties by a random amount and recalculating the weights used to extract the corrected χ c yields. The systematic uncertainty is estimated from the RMS of the distribution of the average weight in each p χ c T and p J/ψ T bin.
Conversion probability. The conversion probability P conv derived using MC simulation samples is sensitive to the modelling of the ID material distribution in the ATLAS detector simulation. As discussed in section 4.4, the description of the ID material distribution in MC simulation is found to agree with the distribution observed in data [27]. The uncertainties in the modelling of the mass distribution are used to define an alternative ATLAS detector model with a larger amount of material in the conversion fiducial region. Samples of χ c → J/ψ γ events are generated with both the nominal and the alternative detector model, using the same method as described in ref. [32]. The difference in the simulated conversion probabilities is taken as an estimate of the corresponding systematic uncertainty.
Converted-photon reconstruction efficiency. The converted-photon reconstruction efficiency ǫ conv derived using MC simulation samples is sensitive to any potential differences in the behaviour of the photon conversion reconstruction algorithm in data and simulation. These effects are studied by comparing several sensitive distributions (including conversion vertex position, vertex fit quality and e + e − track hits) of a sample of photon conversions in data and simulation. The systematic uncertainty in ǫ conv due to residual simulation mismodelling effects is estimated to be ±9%. The systematic uncertainty on the determination of ǫ conv due to potential residual mismodelling of bin migrations in p γ T is estimated to be ±5% from several self consistency tests performed with MC simulation samples.
Acceptance. The per-candidate acceptance correction for the measurements binned in p χ c T is calculated from the reconstructed value of p χ c T for each χ c candidate. This reconstructed value of p χ c T is scaled by around +0.5% to avoid an over-correction due to the asymmetric experimental resolution in p χ c T . The correction procedure is verified with simulation studies and has a systematic uncertainty of ±2%. The acceptance corrections for the measurements binned in p J/ψ T are sensitive to the p χ c T distribution used as an input to the acceptance simulation. This sensitivity is studied by varying the analytic function used to fit the measured p χ c T distribution. The systematic uncertainty in the acceptance corrections due to the fitted parametrisation of the measured p χ c T distributions is estimated to be between 4-8%, depending on the individual χ cJ yield. The systematic uncertainty in the acceptance correction, due to the unknown χ c spin-alignment, is evaluated by comparing the acceptance calculated assuming isotropic decay angular distributions to that calculated with the angular distributions corresponding to the spin-alignment scenarios shown in table 1. This comparison is used to derive an uncertainty envelope associated with the unknown χ c spin-alignment. The spin-alignment envelope is treated as a separate uncertainty and is discussed in more detail in section 6.    T . Each pseudo-data sample is fitted with the nominal fit model and five alternative fit models that include a variety of alterations as discussed below.
• Each of the fixed α and n parameters in the χ c1 and χ c2 signal CB functions is individually released to be determined by the fit.
• The scaling of the χ c1 and χ c2 ∆m resolution parameters σ 1 and σ 2 is removed and both parameters are independently determined by the fit.
• The fit is repeated with the χ c0 signal component of the pdf removed. This test is motivated by the fact that the χ c0 signal is insignificant in some of the p T bins studied.
• An alternative background pdf (with four free parameters) for the mass difference distribution is tested.
The systematic uncertainty due to the fit model is then estimated from the mean of the distribution of the relative changes in the yield between the nominal and alternative models. The systematic uncertainty due to the fit model for the prompt and non-prompt crosssection ratios and non-prompt fractions is evaluated in the same way to ensure correlations between the signal components in the evaluation of the systematic uncertainty are taken into account.
Integrated luminosity. The uncertainty in the integrated luminosity of the data sample used is estimated to be 1.8%. The methods used to determine this uncertainty are described in detail in ref. [33]. This systematic uncertainty does not affect the cross-section ratios or non-prompt fractions.
-   The individual sources of systematic uncertainty are summarised in tables 2 and 3. The largest sources of systematic uncertainty are associated with the photon conversion reconstruction efficiency, the fit model and the acceptance. The individual sources of systematic uncertainty studied are not strongly correlated and the total systematic uncertainty on the measurements is obtained by adding the individual systematic uncertainties in quadrature. These uncertainties are generally much smaller than the uncertainty associated with the unknown χ c spin-alignment.

Results and interpretation
The differential cross-sections of prompt and non-prompt χ c1 and χ c2 production are measured in bins of p J/ψ T and p χ c T within the rapidity region |y J/ψ | < 0.75. The results measured as a function of p J/ψ T and p χ c T are presented within the regions 10 ≤ p J/ψ T < 30 GeV and 12 ≤ p χ c T < 30 GeV, respectively. The measurements of the prompt production of χ c1 and χ c2 as a function of p J/ψ T are combined with existing measurements [8] of prompt J/ψ production to determine the fraction of prompt J/ψ produced in χ c decays. The production rate of χ c2 relative to χ c1 is measured for prompt and non-prompt χ c as a function of p J/ψ T . The fractions of χ c1 and χ c2 produced in the decays of b-hadrons are also presented as a function of p χ c T . While the prompt and non-prompt χ c1 and χ c2 yields are necessarily extracted from separate fits, statistical correlations between the yields are taken into account in the calculation of the statistical uncertainties on the cross-section ratios and non-prompt fractions. Tabulated results for all of the measurements are included in appendix A.
The spin-alignment of the χ c mesons produced at the LHC is unknown. All measurements are corrected for detector acceptance assuming isotropic angular distributions for the -16 -

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decay of the χ c states. The total uncertainty in the measurements due to this assumption is obtained by comparing the acceptance calculated with the extreme χ c spin-alignment scenarios discussed in section 4.1 to the central value, calculated with the isotropic scenario. The maximum uncertainty due to spin-alignment effects averaged over each measurement bin is shown in tables 2 and 3 and for each measurement bin in the tabulated results in appendix A. The uncertainty due to spin-alignment effects is not included in the total systematic uncertainty. Factors that can be used to scale the central cross-section values to any of the individual spin-alignment scenarios studied are also provided in table 13 of appendix A.

Differential cross-sections
Differential cross-sections for prompt χ c1 and χ c2 production are measured as a function of both p J/ψ T and p χ c T within the region |y J/ψ | < 0.75. These results are corrected for acceptance assuming isotropic decay angular distributions for the χ c1 and χ c2 states and are shown in figures 3 and 4. The position along the p T axis of each of the data points shown in these figures is adjusted to reflect the average value of the transverse momentum, p J/ψ T or p χ c T , for the χ c candidates within that p T bin, after all acceptance and efficiency corrections have been applied. The measurements are compared with the predictions of next-to-leading-order (NLO) non-relativistic QCD (NRQCD) [19,34,35], the k T factorisation approach [36,37] and leading-order (LO) colour-singlet model (CSM) [38] calculations. The NRQCD factorisation approach separates the perturbative production of a heavy quark pair (in a colour-singlet or -octet state) from the non-perturbative evolution of a heavy quark pair into a quarkonium state [1]. The long-distance effects are described by matrix elements that are determined by fitting experimental data [2]. For the predictions shown, the NRQCD long-distance matrix elements are extracted from measurements of J/ψ and ψ(2S) production at the Tevatron as described in ref. [35]. In the CSM, heavy quark pairs are produced directly in a colour-singlet state (described by perturbative QCD) and a potential model is used to describe the formation of the bound state [39][40][41][42]. In the high p T region studied, gg → χ cJ g processes constitute the dominant contribution to the CSM prediction. The k T factorisation approach convolves a partonic cross-section from the CSM with an un-integrated gluon distribution that depends on both longitudinal and transverse momentum (as opposed to the collinear approximation, which neglects parton transverse momentum) to calculate the hadronic cross-section. The shaded uncertainty bands of the NRQCD and CSM predictions are derived from factorisation and renormalisation scale uncertainties, and the NRQCD uncertainty also includes a contribution from the extraction of NRQCD long distance matrix elements from data. Good agreement between the NRQCD calculation and the measurements is observed. The k T factorisation approach predicts a cross-section significantly in excess of the measurement while the LO CSM prediction significantly underestimates the data. This suggests that higher-order corrections or colour-octet contributions to the cross-sections not included in either prediction may be numerically important.
Differential cross-sections are also measured for non-prompt χ c1 and χ c2 production as functions of both p decay angular distributions. The results are shown in figure 5 and are compared to the fixed order next-to-leading-logarithm (FONLL) prediction for b-hadron production [6,7]. These predictions are combined with measured momentum distributions of χ c1 and χ c2 in the B ±/0 rest frame for inclusive B → χ c X decays [43]. This prediction is scaled assuming all b-quarks hadronise into B ±/0 mesons. (1.3 ± 0.4) × 10 −3 are used [4]. The shaded uncertainty band on the FONLL predictions represents the theoretical uncertainty due to factorisation and renormalisation scales, quark masses and parton distribution functions combined with the uncertainty on the branching fractions used to scale the predictions. The measurements generally agree with the FONLL predictions, though the data tend to lie slightly below the predictions at high p T .

Fraction of prompt J/ψ produced in χ c decays
The prompt χ c1 and χ c2 cross-sections are summed to provide their total contribution to the prompt J/ψ cross-section for each p an independent data sample (recorded during the 2010 LHC run) and that the systematic uncertainties on the experimental efficiencies are evaluated using different methods and are all dominated by statistical effects. This provides a measurement of the fraction, Rχ c , of J/ψ produced in feed-down from χ c decays, neglecting the small contribution from radiative χ c0 decays, as a function of p J/ψ T . The measurements are shown in figure 6 and are compared to the predictions of NLO NRQCD and the LHCb measurement within the range 2.0 < y J/ψ < 4.5 [15]. The results show that between 20% and 30% of prompt J/ψ are produced in χ c feed-down at high J/ψ transverse momentum. Motivated by recent measurements [44,45], the spin-alignment envelope for this fraction given in table 9 in appendix A is calculated assuming no overall spin-alignment for promptly produced J/ψ.

Cross-section ratios
The production rates of χ c2 relative to χ c1 are measured for prompt and non-prompt χ c as a function of p J/ψ T . The ratio of the prompt cross-sections is shown in figure 7. The measurements are compared to the NLO NRQCD and CSM predictions and to the measurements of CMS within the range |y J/ψ | < 1.0 [16]. The NLO NRQCD prediction is in generally good agreement with the measurements, particularly at lower p J/ψ T values. The cross-section ratio predicted by the CSM is consistently lower than the measurements. The ratio of the non-prompt cross-sections is shown in figure 8 and is compared to the measurement of CDF in pp collisions at √ s = 1.96 TeV and for p J/ψ T > 10 GeV [18].  The production cross-section of non-prompt χ c2 relative to non-prompt χ c1 , B ( χ c2 → J/ψ γ) σ ( χ c2 ) /B ( χ c1 → J/ψ γ) σ ( χ c1 ), measured as a function of p J/ψ T . The measurement from CDF [18] is also shown. The error bars represent the total uncertainty on the measurement, assuming isotropic decay angular distributions. The factors B 1 and B 2 denote the branching fractions B 1 = B ( χ c1 → J/ψ γ) and B 2 = B ( χ c2 → J/ψ γ), respectively.

Non-prompt fractions
The prompt and non-prompt χ c1 and χ c2 cross-sections are used to calculate the fractions of inclusive χ c1 and χ c2 produced in the decays of b-hadrons, f non−prompt . The non-prompt fraction is measured as a function of p χ c T and is shown in figure 9. The combined nonprompt fraction is observed to increase as a function of p χ c T , as is observed in the J/ψ and ψ(2S) systems. However, the inclusive production of χ c1 and χ c2 is dominated by prompt production in the kinematic region measured, contrary to what is observed in the J/ψ and ψ(2S) systems for the same high-p T region, where the inclusive cross-sections contain a larger component of feed-down from b-hadron decays [8,9].
The branching fraction B (B ± → χ c1 K ± ) is measured using the decay B ± → J/ψK ± as a reference channel (with χ c1 → J/ψ γ and J/ψ → µ + µ − for both channels). The final states of both channels are identical apart from the photon.
The branching fraction B (B ± → χ c1 K ± ) is measured from where A B is a factor to correct for the different detector acceptances of the two decays, and N B χ c1 and N B J/ψ are the corrected yields for the signal and reference decay channels respectively. The current world-average values are used for the branching fractions: B (B ± → J/ψK ± ) = (1.016 ± 0.033) × 10 −3 and B ( χ c1 → J/ψ γ) = 0.344 ± 0.015 [4]. Both decays are reconstructed within the region 10 ≤ p J/ψ T < 30 GeV and |y J/ψ | < 0.75.

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The branching fraction B (B ± → χ c1 K ± ) is measured using the same data sample and efficiency corrections used in the inclusive χ c production measurements. The χ c1 and J/ψ candidate selections (with the photon being reconstructed from conversions) and fiducial region are kept as close to the inclusive χ c measurement as possible.

Selection of B ± decays
The selection of candidate B ± → χ c1 K ± and B ± → J/ψK ± decays begins by searching for χ c and J/ψ candidates using the selection criteria described in the inclusive χ c measurement. Charged particles with tracks consistent with originating from the µ + µ − vertex are assigned the charged kaon mass and the µ + µ − K ± vertex is fitted. The candidate charged kaon track is required to contain at least one silicon pixel hit and at least six SCT hits, transverse momentum p T > 3 GeV and pseudorapidity |η| < 2.5. Candidates with a vertex fit quality χ 2 per degree of freedom < 6 are retained. The L xy of the J/ψ → µ + µ − candidate (as defined in section 4) is required to be greater than 0.3 mm to reject promptly produced J/ψ mesons. This cut rejects over 99% of the prompt J/ψ background and retains around 87% of the B ± signal. Candidate B ± → χ c1 K ± → µ + µ − γK ± decays are required to have 0.32 < m (µ + µ − γ) − m (µ + µ − ) < 0.43 GeV to select χ c1 decays and 4.65 < m (µ + µ − K ± ) − m (µ + µ − ) + m J/ψ < 5.2 GeV to reject backgrounds from B ± → J/ψK ± decays.

Calculation of A B
The acceptance correction factor A B is defined as the number of B ± → J/ψK ± decays relative to the number of B ± → χ c1 K ± decays that fall within their respective fiducial regions. The correction is derived from a large sample of generator-level MC simulation events that uses a fitted parameterisation of the ATLAS measurement of the B ± differential cross-section [46] (in the B ± → J/ψK ± mode) as an input. The simulation generates B ± → J/ψK ± and B ± → χ c1 K ± decays according to the measured spectrum. The angular distributions of the B ± decay products are generated with helicity equal to zero for the charmonium state in the rest frame of the B ± meson. This calculation gives A B = 2.30 ± 0.08 where the uncertainty is derived from the uncertainty in the fitted parameterisation of the measured B ± cross-section. The difference in the values of A B calculated with the nominal and alternative fit parameterisations is taken as an estimate of the systematic uncertainty. Candidate B ± → χ c1 K ± and B ± → J/ψK ± decays are weighted to correct for trigger efficiency, muon reconstruction efficiency and (for B ± → χ c1 K ± decays) conversion probability and converted-photon reconstruction efficiency using the same corrections derived for the inclusive χ c production measurement. Corrections are applied only for effects that are known not to fully cancel in the ratio N B χ c1 /N B J/ψ . Trigger and muon reconstruction efficiencies are corrected since not all J/ψ → µ + µ − decays in the fiducial region studied fall within the efficiency plateau. Since the data are only partially corrected, the weighted yields are not representative of the true yields of B ± mesons one would expect from the JHEP07(2014)154 data sample and fiducial region used. The corrected yields N B χ c1 and N B J/ψ are extracted from unbinned maximum likelihood fits to the m (µ + µ − γK ± ) − m (µ + µ − γ) + mχ c1 and m (µ + µ − K ± ) − m (µ + µ − ) + m J/ψ distributions of selected B ± decay candidates, where m J/ψ and mχ c1 are the world-average values for the masses of the J/ψ and χ c1 states [4].
The mass distribution for candidate B ± → χ c1 K ± decays is fitted with a B ± signal modelled by a Gaussian pdf where both the mean value and width are free parameters in the fit. The background distribution is modelled with a template derived from MC simulation of inclusive pp → bbX decays generated by Pythia 6 [21] and processed with the detector simulation. The Gaussian kernel estimation [47] procedure is applied to the background template from MC simulation to form a non-analytic background pdf. The mass distribution for candidate B ± → J/ψK ± decays is modelled with a double-Gaussian signal pdf where the mean value (common to both Gaussian pdfs), both width parameters and the relative normalisation of both components are determined by the fit. The background contribution to the B ± → J/ψK ± mass distribution from B ± → χ c1,2 K ± and B ±/0 → J/ψ (Kπ) ±/0 decays (where only the J/ψ and charged kaon are reconstructed) is modelled by the sum of a Gaussian and a complementary error function [46]. The background contribution from B ± → J/ψπ ± decays where the kaon mass is wrongly assigned to the pion track is modelled with a CB function [46].
The results of the fits to the mass distributions of candidate B ± → χ c1 K ± and B ± → J/ψK ± decays are shown in figure 10.

Systematic uncertainties
Several sources of systematic uncertainty on the measurement are considered. The systematic uncertainties due to the efficiency corrections (trigger, conversion probability, and muon and conversion reconstruction) are quantified with the same methods used in the inclusive χ c measurement. Several variations in both fit models are also tested to estimate the systematic uncertainty on N B χ c1 /N B J/ψ due to the fit models. The systematic uncertainty is taken as the maximum deviation of any single combination of alternative fit results from the average. The systematic uncertainty on A B due to the fitted parameterisation of the B ± cross-section is also propagated into an uncertainty on B (B ± → χ c1 K ± ). Table 4 shows a summary of the individual sources of systematic uncertainty considered.

Result
The measured branching fraction is B(B ± → χ c1 K ± ) = (4.9 ± 0.9 (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 [4] (dominated by measurements from Belle [48] and BaBar [49]), and supports the estimate of the conversion reconstruction efficiencies at the level of 19% (the total fractional uncertainty on the measurement, neglecting conversion-related systematic uncertainties). The precision of this measurement is significantly better than previous measurements from hadron collider experiments [4].

Conclusion
The cross-sections for prompt and non-prompt χ c1 and χ c2 production have been measured  -photon reconstruction efficiency  10  Conversion probability  4  Muon reconstruction efficiency  1  Trigger efficiency  1  Acceptance  3  Fit model  6  Statistical  18  Systematic  13  Total  22   Table 4. Sources of systematic uncertainty on the measurement of B(B ± → χ c1 K ± ). measurements of prompt J/ψ production to derive the fraction of prompt J/ψ produced in feed-down from χ c decays. The fractions of χ c1 and χ c2 produced in the decays of b-hadrons are also presented as functions of p χ c T . The measurements of prompt χ c production are compared to the theoretical predictions of NLO NRQCD, the k T factorisation approach and the Colour Singlet Model. The NRQCD predictions generally agree well with the data. The k T factorisation approach predicts a cross-section significantly in excess of the measurement while the CSM prediction significantly underestimates the data. This suggests that higher-order corrections or colour-octet contributions to the cross-sections not included in either prediction may be numerically important. The measurements of non-prompt χ c production generally agree well with predictions based upon the FONLL approach.
The branching fraction B(B ± → χ c1 K ± ) = (4.9 ± 0.9 (stat.) ± 0.6 (syst.)) × 10 −4 is also measured with the same dataset and χ c event selection. The measured value agrees well with the world average and supports the estimate of the conversion reconstruction efficiencies derived from simulation.

A Tabulated results
The following tables show the results presented in section 6. Statistical and systematic uncertainties are shown for each measurement along with the uncertainty envelope associated with the unknown χ c spin alignment.  Table 5. Differential cross-section for prompt χ c1 and χ c2 production, measured in bins of p  Table 6. Differential cross-section for non-prompt χ c1 and χ c2 production, measured in bins of p  Table 7. Differential cross-section for prompt χ c1 and χ c2 production, measured in bins of p χ c T .
-29 -JHEP07(2014)154   Table 9. Fraction of prompt J/ψ produced in feed-down from χ c decays as a function of p J/ψ T . The spin alignment envelope assumes that prompt J/ψ are produced unpolarised and represents the maximum uncertainty in the result due to the unknown χ c spin alignment.  Table 10. Production rate of prompt χ c2 relative to prompt χ c1 , measured in bins of p  Table 11. Production rate of non-prompt χ c2 relative to non-prompt χ c1 , measured in bins of p

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Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
[8] ATLAS collaboration, Measurement of the differential cross-sections of inclusive, prompt and non-prompt J/ψ production in proton-proton collisions at -33 -