Measurement of J / ψ production in association with a W ± boson with p p data at 8 TeV The ATLAS Collaboration

A measurement of the production of a prompt J / ψ meson in association with a W ± boson with W ± → µν and J / ψ → µ + µ − is presented for J / ψ transverse momenta in the range 8 . 5–150 GeV and rapidity | y J / ψ | < 2 . 1 using ATLAS data recorded in 2012 at the LHC. The data were taken at a proton–proton centre-of-mass energy of √ s = 8 TeV and correspond to an integrated luminosity of 20 . 3 fb − 1 . The ratio of the prompt J / ψ plus W ± cross-section to the inclusive W ± cross-section is presented as a diﬀerential measurement as a function of J / ψ transverse momenta and compared with theoretical predictions using diﬀerent double-parton-scattering cross-sections. This paper reports a measurement of the ratio of ﬁducial and inclusive cross-sections for associated prompt J / ψ + W ± production to the cross-section of inclusive W ± production in the same W ± kinematic region. The ﬁducial measurement for J / ψ + W ± is deﬁned in a restricted kinematic range for the muons from J / ψ decay, and is speciﬁc to the ATLAS detector, while the inclusive result is determined by correcting for the detector’s kinematic acceptance to muons. These cross-section ratios are presented for J / ψ transverse momenta in the range 8 . 5 < p T < 150 GeV and rapidities satisfying | y ( J / ψ )| < 2 . 1. The inclusive ratio is also quoted diﬀerentially as a function of the J / ψ transverse momentum.


Introduction
The associated production of prompt J/ψ mesons with W ± bosons provides a powerful probe of the production mechanism of charmonium in hadronic collisions, allowing tests of quantum chromodynamics (QCD) at the boundary between the perturbative and non-perturbative regimes. The ATLAS Collaboration has previously presented two analyses of J/ψ mesons produced in conjunction with vector bosons: the associated production of prompt J/ψ + W ± in √ s = 7 TeV data [1] and the production of prompt and non-prompt J/ψ + Z in √ s = 8 TeV data [2]. This paper presents a new measurement of the ratio of the cross-section for associated production of prompt J/ψ + W ± to the inclusive W ± production cross-section with W ± → µν and J/ψ → µ + µ + at a centre-of-mass energy of 8 TeV, exploiting a four-fold increase in integrated luminosity over the previous measurement [1]. The analysis strategy closely follows the methods of the earlier papers. Prompt production refers to a J/ψ meson that is not the product of a weak decay of a b-hadron while non-prompt production occurs when the J/ψ meson is produced at a secondary vertex, such as from a B meson decay. The J/ψ events that are produced from radiative decays of heavier charmonium states (such as χ c → γJ/ψ) are not distinguished from directly produced J/ψ mesons, as long as they are produced in the initial hard interaction.
Despite being studied for many decades [3][4][5][6][7][8][9], the production mechanism of J/ψ mesons in hadronic collisions is not fully understood. The main models for perturbative calculations of heavy quarkonium production (QQ) in hadronic collisions differ in whether the system is produced in a colour singlet (CS) state or a colour octet (CO) state [10][11][12][13][14]. The CS model requires two hard gluons in a colour singlet in the initial state, or one gluon splitting into QQ where one of the quarks radiates a hard gluon. The CO model followed by two software-based trigger levels that together reduced the accepted event rate to 400 Hz on average depending on the data-taking conditions during 2012 [19].

Event selection and reconstruction
The analysis uses 20.3 fb −1 of pp collision data at √ s = 8 TeV collected during 2012. Events were selected using a non-prescaled single-muon trigger that required at least one muon with |η| < 2.4, transverse momentum p T > 24 GeV, stable beams, and fully operational subdetectors.
The muon reconstruction begins by finding a track candidate independently in the inner tracking detector and the muon spectrometer. The momentum of the muon candidate is calculated by statistically combining the information from the two subsystems and correcting for parameterised energy loss in the calorimeter; these muon candidates are referred to as combined muons.
In some cases a track in the inner detector is identified as a muon if the extrapolated track is associated with at least one local track segment in the muon spectrometer. In such cases the information from the inner tracking detector alone is used to determine the momentum. For analyses studying low-mass objects, such as J/ψ mesons, the inclusion of these segment-tagged muons provides additional efficiency for reconstructing low-p T muons [20]. Table 1: Selection criteria for the inclusive W ± sample, where µ is the muon from the W ± boson decay.

W ± boson selection
At least one isolated muon that originates < 1 mm from primary vertex along z-axis p T (trigger muon) > 25 GeV |η µ | < 2.4 Missing transverse momentum > 20 GeV m T (W ± ) > 40 GeV |d 0 |/σ d 0 < 3 Table 2: Definition of the fiducial region for the J/ψ cross section measurement, where µ 1 is the highest-p T muon from the J/ψ decay, and µ 2 is the second-highest-p T muon from the J/ψ decay.
An inclusive W ± sample is defined by applying the W ± boson selections listed in Table 1. Candidate muons from W ± decays are required to be combined and to match the muon reconstructed by the trigger algorithm. The primary vertex is chosen as the reconstructed vertex with the highest Σp 2 T of associated tracks and must have, at minimum, three associated tracks with p T > 400 MeV.
Calorimetric and track isolation variables are defined by calculating the sum of transverse energy (E T ) deposits in the calorimeter cells and track p T respectively within a cone size ∆R = 0.3 around the muon direction. The energy deposited by the muon is subtracted from the calorimetric isolation variable, and only tracks compatible with originating from the primary vertex and with p T > 1 GeV (excluding the muon itself) are considered for the track isolation. A correction depending on the number of reconstructed vertices is made to the calorimetric isolation to account for additional energy deposits due to pile-up vertices.2 For the muon to be considered isolated, the two isolation variables defined above must both be less than 5% of the muon p T .
Transverse impact parameter significance is defined as |d 0 |/σ d 0 , where d 0 is the impact parameter, defined as the distance of closest approach of the muon trajectory to the primary vertex in the x y-plane and σ d 0 is the uncertainty on the impact parameter.
The W ± boson transverse mass is defined as where the variables φ µ and φ ν represent the azimuthal angles of the muon from the W ± boson decay and the missing transverse momentum E miss T respectively. The E miss T is calculated as the magnitude of the negative vector sum of the transverse momenta of calibrated electrons, photons, hadronically decaying τ-leptons, jets and muons, as well as additional low-momentum tracks that are associated with the primary vertex but are not associated with any other E miss T component [21].

W ± + J/ψ event selection
If an event has two additional muons then the J/ψ selections listed in Table 2 are also applied to define the associated J/ψ + W ± sample. The J/ψ candidates are required to have a vertex < 10 mm from the primary vertex along the z-axis and must be formed from either two combined muons or from one combined muon and one segment-tagged muon and at least one muon must have p T > 4 GeV. A vertex fit is performed to constrain the two muons to originate from a common point.
To distinguish prompt J/ψ candidates from those originating from b-hadron decay (non-prompt), the pseudo proper decay time is used: where ì L is the 2-D displacement vector of the J/ψ decay vertex from the primary event vertex, and ì p J/ψ T and m(µ + µ − ) are the transverse momentum and invariant mass of the J/ψ candidate, respectively. Prompt J/ψ candidates should have a pseudo proper decay time consistent with zero (within resolution).

Inclusive W ± sample
A signal sample of W ± → µν Monte Carlo (MC) was used to verify the overall modelling of the signal+background in the inclusive W ± sample. The backgrounds W ± → τν, Z → µµ, Z → ττ, diboson, tt and single top were also modelled with MC simulations. Most of the MC samples were generated using P -B [22][23][24] for the hard scatter and showered using either P 6 [25]   After accounting for all background events (which contribute an estimated 12% of the original yield with Z → µ + µ − and W ± → τ ± ν making up 80% of the background), a total W ± yield of (6.446 ± 0.035) × 10 7 events is found. The absolute luminosity scale is derived from beam-separation scans performed in November 2012. The uncertainty in the integrated luminosity is 1.9% [39].

Separation of prompt and non-prompt J/ψ
The associated prompt J/ψ + W ± yield is measured using a two-dimensional unbinned maximum likelihood method to the J/ψ mass and pseudo proper decay time in the region 2.4 GeV < m(µ + µ − ) < 3.8 GeV and −2 ps < τ(µ + µ − ) < 10 ps. The pseudo proper decay time for the prompt signal is modelled as a double Gaussian distribution while a single-sided exponential function is used for the non-prompt signal. The prompt background component is modelled as a double-sided exponential function and the non-prompt background is the sum of a single-sided and a double-sided exponential function. The lifetime fit takes into account resolution effects by convolving the exponential functions with a Gaussian resolution function. The J/ψ mass distribution is modelled with a Gaussian distribution for both the prompt and non-prompt signal and a third-order polynomial is used for both the prompt and non-prompt combinatorial backgrounds. To improve the stability of the fit, the mean and width of the J/ψ mass distribution are fixed to the values derived from fitting a large inclusive J/ψ sample.
After the fit is performed, the sPlot tool [40] is used to extract per-event weights according to the parameters of the fit model. These weights are used to generate prompt signal distributions for other variables such as the W ± transverse mass, the J/ψ transverse momentum and the azimuthal opening angle between the W ± and the J/ψ.
The results of applying the two-dimensional mass and lifetime fit to the J/ψ candidate events are shown in Figure 1, giving prompt signal yields of 93 ± 14 (stat) for |y J/ψ | < 1 and 102 ± 17 (stat) for 1 < |y J/ψ | < 2.1. Two rapidity ranges are used to account for the difference in muon momentum resolution between the barrel and endcap regions of the detector.

W ± + J/ψ backgrounds
The same backgrounds considered for the inclusive W ± sample are used for the associated prompt J/ψ +W ± sample. In addition, background from B c → J/ψ µν is also considered. Using MC, the expected yields are found to be consistent with zero (3.7 +1.9 −3.4 events). A significant background arises from simultaneous production of a W ± and a J/ψ from different pp interactions in the same bunch crossing, where the two production vertices are not distinguished. The probability that, when a W ± is produced, a J/ψ is also produced nearby, can be estimated statistically. The average number of pile-up collisions occurring within 10 mm of a given interaction vertex is determined to be 2.3 ± 0.2 and is found by sampling the luminosity-weighted distribution of the mean number of inelastic interactions per proton-proton bunch crossing. This number is combined with the pp inelastic cross-section and the prompt J/ψ cross-section [2] to give an estimate of the pile-up contribution as a function of the p T and rapidity of the J/ψ in the associated production sample. The fraction of pile-up events is determined to be (10.5 ± 1.2)% of the candidate events.
The desired signal topology is prompt J/ψ + W ± , where the W ± boson decays to µ ± ν. Production of prompt J/ψ + W ± with a different decay of the W ± boson, or of prompt J/ψ + Z, are treated as backgrounds. Background from prompt J/ψ + W ± with W ± → τ ± ν is determined using MC. An inclusive MC sample of W ± → τ ± ν events is used to determine the probability of an event to pass the W ± → µ ± ν selection, yielding a background of (2.3 ± 0.1)% of the candidate events. Background from prompt J/ψ + Z events is calculated using the measured value of σ(pp → J/ψ + Z)/σ(pp → Z) in the 8 TeV ATLAS data [2]. This ratio is scaled by the probability of Z → µ + µ − and Z → τ + τ − to pass the W ± → µ ± ν selection in inclusive MC samples, giving a total background of (9.5 ± 0.5)% events. The J/ψ + Z background is subtracted as a constant fraction in the p T differential distribution since the measured ratio of

Detector effects and acceptance corrections
The efficiency for reconstructing muons varies depending on the p T of the muon, with efficiencies of 65% for 3 GeV muons increasing to a plateau efficiency of 99% for muons above 10 GeV. The nominal relative momentum resolution for muons is < 3.5% up to transverse momenta p T ∼ 200 GeV [41]. To correct the measurements for reconstruction efficiency, a per-event weight is computed using muon efficiency measurements extracted from large inclusive J/ψ → µ + µ − and Z → µ + µ − data samples and applied as a function of the pseudorapidity and p T of each muon from the J/ψ decay. In addition, a per-event weight is applied to correct the J/ψ rate for muons that fall outside the detector acceptance. Although inclusive J/ψ spin-alignment measurements find a near isotropic distribution [42-44], this may not apply to the spin-alignment of J/ψ mesons produced in association with a W boson, due to the different relative contributions of the J/ψ production modes. Consequently, a variety of extreme polarisation states of the J/ψ are considered for the acceptance correction. The method for accounting for the muon reconstruction efficiency and acceptance is discussed in detail in Ref. [2].
After correcting for the J/ψ daughter muon efficiency and acceptance, ratios of cross-sections for associated prompt J/ψ + W ± production to inclusive W ± production are measured in a single W ± → µ ± ν fiducial region defined as |η µ | < 2.4, p T (µ ± ) > 25 GeV and p T (ν) > 20 GeV both differentially in p J/ψ T and also integrated over p J/ψ T . These measurements will be discussed in Section 6. Using MC, the efficiency for reconstructing inclusive W ± → µν is found to depend linearly on the p T of the W ± boson (p W T ). A linear correlation is also found between the values of p J/ψ T and p W T for the associated production sample in data. These two effects lead to a correction to the differential cross-section ratio based on the p T of the prompt J/ψ candidate. To apply the correction, the average p J/ψ T is determined for each bin in the differential distribution; this gives a corresponding value for the average p W T and hence the average efficiency for that bin. The efficiency for the inclusive W ± sample is held constant at its average value, giving efficiency corrections from 0.93 ± 0.02 at low p J/ψ T to 0.78 ± 0.04 in the highest p J/ψ T bin.

Double parton scattering
The measured yield of prompt J/ψ + W ± includes contributions from SPS and DPS processes. The DPS contribution can be estimated using the effective cross-section (σ eff ) measured by the ATLAS Collaboration, as well as the double-differential cross-section for pp → J/ψ prompt production (σ J/ψ ) [2]. Based on the assumptions that the two hard scatters are uncorrelated, the probability that a J/ψ is produced by a second hard process in an event containing a W ± boson is given by where σ i j J/ψ is the cross-section for J/ψ production in the appropriate p T (i) and rapidity ( j) interval and σ eff is the effective transverse overlap area of the interacting partons. Since σ eff may not be process-independent, it is unclear which value of σ eff to use for prompt J/ψ + W ± production, so two different values are considered: σ eff = 15 ± 3(stat.) +5 −3 (sys.) mb from W ± + 2-jet events [45] and σ eff = 6.3 ± 1.6(stat.) ± 1.0(sys.) mb from prompt J/ψ pair production [46]. These two values of σ eff are chosen since they are the two ATLAS measurements closest to the J/ψ + W ± final state. The latter value is close to those inferred in Refs. [47,48] from the earlier ATLAS measurements of J/ψ + W ± and J/ψ + Z production [1, 2]. With these assumptions, it is estimated that between (31 +9 −12 )% (σ eff = 15 mb) and (75 ± 23)% (σ eff = 6.3 mb) of the inclusive signal yield is due to DPS interactions, where the uncertainties in the inclusive W ± yield, the J/ψ cross-section and σ eff are propagated to the DPS fraction.
The distribution of the azimuthal opening angle ∆φ(J/ψ, W ± ) between the directions of the J/ψ and W ± is sensitive to the contributions of SPS and DPS. The DPS component should not have a preferred ∆φ value, while the SPS events are expected to peak at ∆φ ≈ π due to momentum conservation. The estimated DPS yield can be validated with data, assuming that the low ∆φ(J/ψ, W ± ) is exclusively due to DPS interactions. Figure 2 shows the measured ∆φ distribution with the estimated DPS contribution using the two different values of σ eff . Both values of σ eff are consistent with the data at low ∆φ. The normalized ∆φ distributions with and without correcting for efficiency and acceptance are consistent with each other within the statistical uncertainties   Figure 2: The sPlot-weighted opening angle ∆φ(J/ψ, W ± ) for prompt J/ψ +W ± candidates, uncorrected for efficiency or acceptance, compared with the sum of the expected pileup and DPS contributions. The data is not corrected for J/ψ + V backgrounds which contribute ∼10% and have a shape similar to the overall distribution. The DPS contribution is shown for the two values of σ eff = 15 mb and σ eff = 6.3 mb, as described in the text. The peak at ∆φ π is assumed to come primarily from SPS events.

Systematic uncertainties
Almost all systematic uncertainties associated with the reconstruction of the W ± boson and the integrated luminosity cancel out in the ratio of the two processes J/ψ + W ± and inclusive W ± production in the same fiducial region. The remaining relevant systematic uncertainties are discussed below.
The choice of functions used to fit the mass and pseudo proper decay time is a source of systematic uncertainty. Three alternative models for the mass fit are studied: introducing a ψ(2S) mass peak into the fit model, letting the mean of the J/ψ mass peak float, and using exponential functions to model the background. The maximum difference between the nominal model yield and the yields from the alternative fit models is taken as a systematic uncertainty. Alternative pseudo proper decay time models are studied, but are not found to make a significant difference to the prompt J/ψ yield.
The reconstruction efficiencies used for the muons from J/ψ decay are derived from data as a function of p T and η as discussed in the previous section. A systematic uncertainty is determined by randomly varying the efficiency in each p T -η interval 100 times using a Gaussian distribution of width equal to the uncertainty in the efficiency in that interval. The RMS spread of the extracted yield is taken as the systematic uncertainty. The uncertainty due to the pile-up background estimation is also considered.
The J/ψ vertex is required to be within 10 mm of the primary vertex along the z-axis, which can affect the pseudo proper decay time distribution. The impact of this is determined by taking the difference in yields between the nominal value of 10 mm and a value of 20 mm, after correcting for pileup contributions, and including it as a systematic uncertainty.
The uncertainty on the fractional background from prompt J/ψ + W ± with W → τ ± ν is determined by propagating the statistical and systematic uncertainties on the numbers of selected W ± → τ ± ν and W ± → µ ± ν events in the inclusive MC samples. The background correction for prompt J/ψ + Z contamination incorporates the uncertainties on the selected Z → µ + µ − , Z → τ + τ − and W ± → µ ± ν events in the same way, and combines this with the full uncertainty (statistical and systematic) from the σ(pp → prompt J/ψ + Z)/σ(pp → Z) measurement [2].
The uncertainty on the difference in the reconstruction efficiency between the inclusive W ± sample and the prompt J/ψ + W ± sample takes into account the spread of p J/ψ T in each bin and the uncertainties in the linear fits for the reconstruction efficiency as a function of p W T and for p W T versus p J/ψ T . A nominal uniform spin-alignment is used; however, five different spin-alignment scenarios are considered, following the procedure adopted and described in detail Ref. [2], leading to a systematic uncertainty due to the unknown spin-alignment. A summary of the systematic uncertainties is given in Table 3.

Results
After applying the selections described above to the data, the signal extraction and cross-section ratio measurement is performed in the range of J/ψ transverse momentum 8.5-150 GeV and in two J/ψ rapidity intervals, |y J/ψ | < 1 (central) and 1 < |y J/ψ | < 2.1 (forward). Results are extracted in the two rapidity regions (due to the different dimuon mass resolution) and also combined into a single rapidity range.
The final prompt J/ψ + W ± signal yields after the application of the J/ψ acceptance and muon efficiency weights are 222 ± 37(stat) for the central region and 195 ± 33(stat) for the forward region, where the estimated pile-up contributions are removed.
The total cross-section ratio is calculated for three different measurement types: fiducial, inclusive and DPS-subtracted. The explanation of each of these methods follows, and the corresponding cross-section results are presented below and in Tables 4 and 5.

Fiducial, inclusive and DPS-subtracted cross-section ratio measurements
Due to the restrictive η and p T selection applied to the muons from the J/ψ, a fiducial measurement is made that is independent of the unknown J/ψ spin-alignment or the effects of the J/ψ acceptance corrections (see Table 2) and is given by where N eff (J/ψ + W ± ) is the background-subtracted yield of W ± + prompt J/ψ events after corrections for the J/ψ muon reconstruction efficiencies, N(W ± ) is the background-subtracted yield of inclusive W ± events and N fid pile-up is the expected number of pile-up background events in the fiducial J/ψ acceptance. It has been verified that the efficiency to reconstruct a W ± is the same for the inclusive W ± sample and for the associated J/ψ + W ± sample. The result is where the first uncertainty is statistical and the second is systematic.
The fully corrected inclusive production cross-section ratio, which accounts for the unknown J/ψ spin-alignment and the J/ψ acceptance, is given by where N eff+acc (J/ψ + W ± ) is the background subtracted yield of prompt J/ψ + W ± events after J/ψ acceptance corrections and efficiency corrections for the J/ψ decay muons, and N pile-up is the expected number of pile-up events in the full range of J/ψ decay phase space. The result is where the first uncertainty is statistical, the second systematic and the third is from the spin-alignment uncertainty.
Additional measurements are made by subtracting the estimated DPS contribution in each rapidity and p T interval from the inclusive cross-section ratio. and R DPSsub where the first uncertainty is statistical, the second systematic and the third is from the spin-alignment uncertainty. A comparison is made with J/ψ + W ± theory predictions, extended from the original predictions at a centre-of-mass energy of 7 TeV [13] to the fiducial region of this analysis at 8 TeV by the same authors. The predictions use a colour-octet long-distance matrix element (CO LDME) model for J/ψ production, the parameters of which are extracted by simultaneously fitting the differential cross-section and spin alignment of prompt J/ψ production at the Tevatron [14]. These theoretical calculations include only SPS production. They are normalised to the W ± boson production cross-section, calculated at next-to-next-to-leading order using the FEWZ program [49] and corrected for the ATLAS W ± selection requirements in Table 1 (5.511 nb). The predicted ratio is (0.428 ± 0.017) × 10 −6 [50,51]. value ± (stat) ± (syst) value ± (stat) ± (syst) ± (spin) |y J/ψ | < 1.0 2.85 ± 0.52 ± 0.44 ± 0.96 2.40 ± 0.47 ± 0.40 ± 0.68 Table 5: The DPS-subtracted differential cross-section ratio in two regions of y J/ψ for two different values of σ eff .

Differential production cross-section measurements
The inclusive differential cross-section ratio, dR incl J/ψ+W ± /dp T , is measured for |y J/ψ | < 2.1 in six J/ψ transverse momentum intervals across the entire range of 8.5 < p J/ψ T < 150 GeV, as shown in Table 6 and Figure 3. These measurements are compared with the SPS theoretical values provided by the CO model in conjuction with the estimated DPS contribution. For σ eff = 15 mb, this combined prediction consistently underestimates the measurement in all p T intervals, while for σ eff = 6.3 mb, the summed SPS and DPS contribution underestimates the measurement in the higher p T intervals, possibly because colour-singlet processes are not included in the prediction. Table 6: The measured inclusive (SPS+DPS) cross-section ratio dR incl J/ψ+W ± /dp T for prompt J/ψ for |y J/ψ | < 2.1. The estimated DPS contributions in each interval are listed for two possible values of σ eff .    Figure 3: The inclusive (SPS+DPS) differential cross-section ratio measurements and theory predictions presented in six p J/ψ T regions for |y J/ψ | < 2.1. NLO colour-octet SPS predictions are shown, with LDMEs extracted from the differential cross-section and spin alignment of prompt J/ψ mesons at the Tevatron [13,14]. The DPS contribution is estimated using (a) σ eff = 15 +5.8 −4.2 mb and (b) σ eff = 6.3 ± 1.9 mb and the method discussed in the text. The data points are identical in the two plots.

Conclusion
The ratio of the associated prompt J/ψ plus W ± production cross-section to the inclusive W ± boson production cross-section in the same fiducial region is measured using 20.3 fb −1 of proton-proton collisions recorded by the ATLAS detector at the LHC, at a centre-of-mass energy of 8 TeV. The result is presented initially for muons from J/ψ decay in the fiducial volume of the ATLAS detector and then corrected for the kinematic acceptance of the muons in the fiducial region. This correction factor depends on the spin-alignment state of the J/ψ produced in association with a W ± boson, which may differ from the spin alignment observed in inclusive J/ψ production. Measurements of the azimuthal angle between the W ± boson and J/ψ meson suggest that single-and double-parton-scattering contributions are both present in data. The measured prompt J/ψ + W ± production rates are compared with a theoretical prediction at NLO for colour-octet prompt production processes. Due to uncertainty in the value of the effective double-parton-scattering cross-section σ eff , two different values are used for comparisons of theoretical predictions with data. A smaller value of σ eff brings the predicted cross-section ratio closer to the measured value; however, neither value of σ eff is able to correctly model the J/ψ p T dependence, possibly because colour-singlet processes are not included in the prediction.           [49] C. Anastasiou, L. J. Dixon, K. Melnikov and F. Petriello, High precision QCD at hadron colliders: Electroweak gauge boson rapidity distributions at next-to-next-to leading order, Phys. Rev. D 69 (2004) 094008, arXiv: hep-ph/0312266.