Study of $J/\psi$ production in jets

The production of $J/\psi$ mesons in jets is studied in the forward region of proton-proton collisions using data collected with the LHCb detector at a center-of-mass energy of 13 TeV. The fraction of the jet transverse momentum carried by the $J/\psi$ meson, $z \equiv p_{\rm T}(J/\psi)/p_{\rm T}({\rm jet})$, is measured using jets with $p_{\rm T}({\rm jet})>20$ GeV in the pseudorapidity range $2.5<\eta({\rm jet})<4.0$. The observed $z$ distribution for $J/\psi$ mesons produced in $b$-hadron decays is consistent with expectations. However, the results for prompt $J/\psi$ production do not agree with predictions based on fixed-order non-relativistic QCD. This is the first measurement of the $p_{\rm T}$ fraction carried by prompt $J/\psi$ mesons in jets at any experiment.

Quarkonium production is often used as a probe of QCD phenomenology [20].In proton-lead (pPb) collisions, J/ψ production is used to study cold-nuclear-matter effects such as parton shadowing and nuclear absorption [21][22][23], while hadron melting in the quark-gluon plasma is investigated using J/ψ production in PbPb collisions [24][25][26].Double-J/ψ production is used to measure the effective cross section for double parton scattering [27][28][29][30][31], which is commonly assumed to be universal for all processes.If the prevailing picture of J/ψ meson production directly in parton-parton scattering is not valid, then many quarkonium-production results may need to be reinterpreted.
Another striking, yet untested, prediction of the direct-production paradigm is that J/ψ mesons are largely produced isolated, except for any soft gluonic radiation emitted by the cc state and potentially some particles from the underlying hadron-hadron collision.An alternative to the standard approach, which is also based on NRQCD, is the calculation of J/ψ meson production within jets using either analytic resummation [32] or the parton shower of a Monte Carlo event generator [33].Quarkonium production in the parton shower, which can explain the lack of observed polarization [34], predicts that J/ψ mesons are rarely produced in isolation.Consequently, it is of great interest to study the radiation produced in association with quarkonium states, e.g.J/ψ mesons in jets, to distinguish between these two different pictures of quarkonium production.
This Letter reports a study of J/ψ mesons produced in jets in the forward region of pp collisions.The fraction of the jet transverse momentum carried by the J/ψ meson, z(J/ψ ) ≡ p T (J/ψ )/p T (jet), is measured for J/ψ mesons produced promptly and for those produced in b-hadron decays.The data sample corresponds to an integrated luminosity of 1.4 fb −1 collected at a center-of-mass energy of √ s = 13 TeV with the LHCb detector in 2016.Only events containing exactly one reconstructed pp collision are used as these provide the best resolution on p T (jet).The analysis is performed using jets clustered with the anti-k T algorithm [35] using a distance parameter R = 0.5 and within the following kinematic fiducial region: jets are required to have p T (jet) > 20 GeV (c = 1 throughout this Letter) in the pseudorapidity range 2.5 < η(jet) < 4.0; J/ψ mesons, which are reconstructed using the J/ψ → µ + µ − decay, must satisfy 2.0 < η(J/ψ ) < 4.5; and muons are required to have p T (µ) > 0.5 GeV, p(µ) > 5 GeV, and 2.0 < η(µ) < 4.5.No requirements are placed on the multiplicity of jets per event or particles per jet, so that jets consisting of only a J/ψ candidate are allowed.This is the first measurement of z(J/ψ ) in prompt J/ψ production at any experiment.
The LHCb detector is a single-arm forward spectrometer covering the range 2 < η < 5, described in detail in Refs.[36,37].Simulated data samples are used to evaluate the muon reconstruction efficiency, the detector response for jet reconstruction, and to validate the analysis.In the simulation, pp collisions are generated using Pythia 8 [38] with a specific LHCb configuration [39].Decays of hadronic particles are described by EvtGen [40], in which final-state radiation is generated using Photos [41].The interaction of the generated particles with the detector, and its response, are implemented using the Geant4 toolkit [42] as described in Ref. [43].
The online event selection is performed by a trigger [44], which consists of a hardware stage using information from the calorimeter and muon systems, followed by a software stage, which performs the J/ψ candidate reconstruction.The hardware stage selects events with at least one dimuon candidate with p T (µ + )p T (µ − ) greater than a threshold that varied between 1.3 and 1.5 GeV during the 2016 data taking.In the software stage, two muon candidates with p T (µ) > 0.5 GeV are required to form a J/ψ candidate whose invariant mass is within 150 MeV of the known J/ψ mass [45].Additional selection criteria are applied offline to the J/ψ candidates: the tracks are required to satisfy stringent muon-identification criteria; and the muon and J/ψ candidates are required to be within the fiducial region of this analysis, where the detector is well understood.
A new data-taking scheme was introduced by LHCb in 2015 that enables offline-like performance in the online system.The alignment and calibration are performed in near real-time [46], and are available in the trigger reconstruction [47].Furthermore, an increase in the online CPU resources makes it possible to run the offline track reconstruction in the online system.This analysis is based on a data sample where all online-reconstructed particles in the event are stored, but most lower-level information is discarded, greatly reducing the event size.This data-storage strategy makes it possible to record all events containing a J/ψ candidate without placing any requirements on p T (J/ψ ), or on the displacement of the J/ψ decay from the primary vertex (PV).
Jet reconstruction is performed offline on this data sample by clustering the J/ψ candidates with charged and neutral particle-flow candidates [48], all reconstructed online, using the anti-k T clustering algorithm as implemented in FastJet [49].This is the first LHCb analysis to use online-reconstructed particles that were not involved in the trigger decision.The J/ψ candidates, rather than their component muons, are used in the clustering to prevent muons from a single J/ψ decay being clustered into separate jets.Reconstructed jets with p T (jet) > 15 GeV and 2.5 < η(jet) < 4.0 are kept for further analysis, where jets in the p T (jet) range 15-20 GeV are retained for use in unfolding the detector response.The η(jet) requirement, which is included in the fiducial region definition, ensures a nearly uniform resolution of 20-25% on the p T of the non-J/ψ component of the jet, with minimal p T dependence above 10 GeV.This is similar to the resolution achieved on data events [48] when using offline reconstruction for p T below 20 GeV, but worse at higher p T where the resolution in such events is about 15%.This degradation arises largely because calorimeter information not associated to particle-flow candidates is not stored in this data sample.
The jet momenta are not corrected for reconstruction bias.Instead, the effect of the detector response on the z(J/ψ ) distributions is removed using an unfolding procedure.This involves first determining the reconstructed J/ψ yields in bins of [z(J/ψ ), p T (jet)], then correcting them for detection efficiency.Bin migration, which occurs largely due to the resolution on the non-J/ψ component of the jet, is accounted for by unfolding the [z(J/ψ ), p T (jet)] distributions of corrected J/ψ yields using an iterative Bayesian procedure [50,51] (see the Supplemental Material to this Letter [52] for a detailed discussion of the unfolding).Finally, the unfolded [z(J/ψ ), p T (jet)] distributions are integrated for p T (jet) > 20 GeV to produce the measured z(J/ψ ) spectra.The binning scheme employs ten equal-width z(J/ψ ) bins, and three p T (jet) bins of 15-20, 20-30, and > 30 GeV.The yield of J/ψ → µ + µ − decays reconstructed in each [z(J/ψ ), p T (jet)] bin, which includes J/ψ mesons produced promptly and in b-hadron decays, is determined from an unbinned maximum likelihood fit to the corresponding dimuon invariant-mass distribution.The signal component is modeled as the sum of two Crystal Ball functions [53] that share all shape parameters except the width.The combinatorial background is described by an exponential function.Both the signal and background shapes are allowed to vary in each bin independently.An example of the invariant-mass distribution from one [z(J/ψ ), p T (jet)] bin is shown in Fig. 1 along with the fit result.The total J/ψ signal yield in the data sample is almost two million.
The fraction of J/ψ mesons that originates from b-hadron decays is determined by fitting the distribution of the pseudo-decay-time t ≡ λ m(J/ψ )/p L (J/ψ ), where λ denotes the difference in position along the beam axis between the J/ψ decay and primary vertices, m(J/ψ ) is the known J/ψ mass [45], and p L (J/ψ ) is the component of the J/ψ momentum longitudinal to the beam axis.Only candidates with | t| < 10 ps, corresponding to about seven b-hadron lifetimes, and a mass consistent with the known J/ψ mass are used in these unbinned maximum likelihood fits.The t distribution from one [z(J/ψ ), p T (jet)] bin is shown in Fig. 2. The prompt-J/ψ component is modeled by a Dirac δ function, while the b-hadron component is modeled by an exponential decay function with a variable lifetime parameter; both are convolved with a double-Gaussian resolution function.A long and nearly symmetric tail in the t distribution arises due to J/ψ candidates produced in additional pp collisions that are not reconstructed.The shape of this component, the contribution of which is found to be O(0.1%) in all bins, is modeled by constructing the distribution with t calculated using J/ψ and PV candidates from different data events.Finally, the shape of the non-J/ψ component in each bin is parametrized using an empirical function obtained from a fit to the t distribution observed in the m(µ + µ − ) sidebands, while its normalization is fixed from the m(µ + µ − ) fit in the bin.The fraction of J/ψ mesons that are produced in b-hadron decays is determined to be in the range 20-60%, depending on [z(J/ψ ), p T (jet)] bin.
The J/ψ yields are corrected for detection efficiency by applying per-candidate weights of ε −1 tot , where ε tot is the total detection efficiency determined as the product of the reconstruction, selection, and trigger efficiencies.The use of per-candidate weights within a fiducial region where the efficiency is nonzero throughout produces accurate efficiencycorrected yields without requiring knowledge of the J/ψ → µ + µ − angular distribution or, equivalently, the J/ψ polarization.The weights, which are similar for nearly all candidates, are rarely greater than 5 and never greater than 20.Consequently, there is negligible impact on the statistical variance due to the use of weighted candidates, since the vast majority of events in each [z(J/ψ ), p T (jet)] bin contribute nearly equally.
The muon reconstruction efficiency is obtained from simulation in bins of [p(µ), η(µ)].Scale factors that correct for discrepancies between the data and simulation are determined using a data-driven tag-and-probe approach on an independent sample of J/ψ → µ + µ − decays [54].A small p T (J/ψ )-dependent correction is applied to the yields of J/ψ mesons produced in b-hadron decays to account for a drop in the efficiency at large b-hadron flight distances.Within the fiducial region of this analysis, the J/ψ reconstruction efficiency is on average about 90%.
The dominant contribution to the selection inefficiency is from the muon-identification performance, which is measured in bins of [p T (µ), η(µ)] using a highly pure calibration data sample of J/ψ → µ + µ − decays.The efficiency of selecting a reconstructed J/ψ candidate varies from 80% for z(J/ψ ) 0.1 to nearly 100% for z(J/ψ ) 0.5.The trigger efficiency is measured in bins of [ p T (µ + )p T (µ − ), η(J/ψ )] using a subset of this J/ψ calibration sample.Events selected by the hardware trigger independently of the J/ψ candidate, e.g.due to the presence of a high-p T hadron, are used to determine the trigger efficiency directly from the data.The fraction of J/ψ candidates in each [ p T (µ + )p T (µ − ), η(J/ψ )] bin that are selected by the dimuon hardware trigger gives the efficiency, which is about 40% on average for z(J/ψ ) 0.1 and 80% for z(J/ψ ) 0.5.
The effects of [z(J/ψ ), p T (jet)] bin migration, which are predominantly due to the detector response to the non-J/ψ component of the jet, are corrected for using an unfolding technique [50][51][52].The detector-response matrices for J/ψ mesons produced promptly and in b-hadron decays are dissimilar for two reasons: the p T -dependent particle multiplicities are different, and the undetected momentum carried by K 0 and Λ particles is, on average, larger for jets that contain a b-hadron decay.The p T (jet)-dependent mean and width of the reconstructed particle multiplicity distributions for jets in simulation are adjusted to match those observed in data.The detector response is studied using the p T -balance distribution of p T (jet)/p T (Z) in nearly back-to-back Z+jet events using the same data- The four-dimensional detector-response matrix for prompt J/ψ production.The shading represents the bin-to-bin migration probabilities ranging from (white) 0 to (black) 1, with the lightest shade of gray corresponding to a probability of 0.1-0.3%.Jets whose true p T (jet) is above 20 GeV but whose reconstructed p T (jet) is below 15 GeV, or vice versa, are included in the unfolding but not shown graphically.
driven technique as in Ref. [48].Small adjustments are applied to the p T (jet) scale and resolution in simulation to obtain the best agreement with data.The unfolding matrix for jets that contain a prompt J/ψ meson is shown in Fig. 3, while the corresponding matrix for b-hadron production is provided in the Supplemental Material [52].
Systematic uncertainties on the z(J/ψ ) distributions apply to both the prompt and b-hadron production modes.Uncertainty on the J/ψ yields arises from the efficiency corrections and from possible mismodeling of the components in the invariant-mass and pseudo-decay-time fits.The uncertainty on each component of the total efficiency is assessed by repeating the data-driven efficiency studies on simulated events, where the difference between the true and efficiency-corrected J/ψ yields in bins of [p T (J/ψ ), η(J/ψ )] is used to determine the systematic uncertainty.The relative uncertainty on the reconstruction efficiency is determined to be 2%, which includes the unknown J/ψ polarization.The relative uncertainties on the trigger and selection efficiencies are in the ranges 2-5% and 0-2%, respectively, depending on [z(J/ψ ), p T (jet)] bin.
The uncertainty on the total J/ψ yield obtained from the invariant-mass fits (1%) is studied by replacing the nominal signal and background models with single Crystal Ball and quadratic functions, respectively.The relative uncertainty on the fraction of J/ψ mesons produced in b-hadron decays (1%) is determined by comparing the fit results obtained from simulated t distributions to the true fractions.Potential mismodeling of the non-J/ψ and wrong-PV components is found to contribute negligible uncertainty.The total relative uncertainty on the J/ψ yields is 3-6% depending on [z(J/ψ ), p T (jet)] bin, which corresponds to a bin-dependent absolute uncertainty on z(J/ψ ) of 0.001-0.005.
The uncertainty associated with the detector response to the non-J/ψ component of the jet is studied by building alternative unfolding matrices, where the p T scale and resolution are varied within the uncertainties obtained from the data-driven p T -balance study of Z+jet events.The data are unfolded using these alternative matrices, with the differences in the z(J/ψ ) distribution used to assign z(J/ψ )-dependent absolute uncertainties of 0.001-0.014.The p T (jet) and z(J/ψ ) spectra used to generate the unfolding matrices, along with the unfolding procedure itself, are also potential sources of uncertainty.These are studied by simulating data samples similar to the experimental data, then unfolding them using response matrices constructed from p T (jet) and z(J/ψ ) distributions that are different from those used to generate the samples.Based on these studies, an uncertainty of 0.01 is assigned to each z(J/ψ ) bin due to unfolding.Finally, the uncertainties due to the fragmentation model and due to the K 0 and Λ components of the jet are found to be negligible.The total absolute systematic uncertainty in each z(J/ψ ) bin, which dominates over the statistical one, is 0.010-0.015.
The measured normalized z(J/ψ ) distributions for J/ψ mesons produced promptly and for those produced in b-hadron decays are shown in Fig. 4 (the numerical values are provided in Ref. [52]).The b-hadron results are consistent with the Pythia 8 prediction [52,55], where the uncertainty shown is due to b-quark fragmentation [56,57] (other sources of uncertainty are ignored [52]).The prompt-J/ψ results do not agree with the leading-order (LO) NRQCD-based prediction as implemented in Pythia 8, which includes both color-octet and color-singlet mechanisms using long-distance matrix elements determined empirically [52].At small z(J/ψ ), Pythia 8 predicts that most of p T (jet) arises from a parton-parton scatter other than the one that produced the J/ψ meson.The dominant source of uncertainty on the prompt-J/ψ prediction at large z(J/ψ ) is due to the underlying event; however, since no rigorous method exists for determining this uncertainty, no uncertainty is assigned to the prediction.Given that the underlying event at LHCb is well described by Pythia 8, e.g., the energy flow is accurately predicted at the 5% level [58], the prompt-J/ψ results cannot be reconciled with this prediction.Furthermore, LO and partial next-to-leading-order (NLO*) calculations in both the color-singlet and color-octet models similarly fail to describe the data [52,59].
Prompt J/ψ mesons in data are observed to be much less isolated than predicted, which qualitatively agrees with the alternative picture of quarkonium production presented in Ref. [32] (after this Letter was submitted, Ref. [60] demonstrated quantitative agreement).
The lack of isolation observed for prompt J/ψ production may be related to the longstanding quarkonium polarization puzzle.If high-p T J/ψ mesons are predominantly produced within parton showers, rather than directly in parton-parton scattering, then the observed lack of both polarization and isolation could be explained [34].Future related measurements of J/ψ production in jets should help shed light on the nature of quarkonium production [61,62].
In summary, the production of J/ψ mesons in jets is studied using pp-collision data collected by LHCb at √ s = 13 TeV in the fiducial region: p T (jet) > 20 GeV and 2.5 < η(jet) < 4.0; 2.0 < η(J/ψ ) < 4.5; and p T (µ) > 0.5 GeV, p(µ) > 5 GeV, and 2.0 < η(µ) < 4.5.The fraction of the jet p T carried by the J/ψ meson is measured for J/ψ mesons produced promptly and for those produced in b-hadron decays.The observed distribution for J/ψ mesons produced in b-hadron decays is consistent with the Pythia 8 prediction; however, the prompt-J/ψ results do not agree with predictions based on fixed-order NRQCD as implemented in Pythia 8.

Supplemental Material Unfolding
The unfolding is performed using an iterative Bayesian approach [50] as implemented in RooUnfold [51].The unfolding matrices for both the prompt and b-hadron-decay cases are sensitive to the z(J/ψ ) distributions used to construct them.In the initial unfolding step, both matrices are generated under the assumption of a uniform true z(J/ψ ) distribution.Three iterations of the unfolding technique are performed using these matrices, producing initial unfolded z(J/ψ ) distributions.Next, these unfolded z(J/ψ ) distributions are used to construct updated unfolding matrices, which are then used to perform three further iterations of the unfolding technique on the data, producing improved z(J/ψ ) distributions.This process is repeated one more time to obtain the final unfolded z(J/ψ ) distributions presented in the Letter; therefore, in total, 9 iterations of the unfolding technique are performed using 3 unfolding matrices for both prompt and b-hadron production.The procedure is terminated after three super-iterations for two reasons: it is found to converge, i.e. the differences between the input and output z(J/ψ ) distributions are O(0.001); and in studies performed on simulated data samples, no gain in accuracy is observed using additional iterations.The unfolding matrices for both prompt and b-hadron production used in the final super-iterations are shown in Fig. 3 in the Letter and in Fig. 5, respectively.

Theory Predictions
All Pythia 8 predictions are generated using Pythia 8.212 and EvtGen 1.04.Radiative J/ψ decays are handled by Photos using the PHOTOS VLL setting, while the standard EvtGen decay tables are used for all other decays.The production of prompt J/ψ mesons is simulated in Pythia 8 with the flag Charmonimum:all=on, while the production of J/ψ mesons from b-hadron decays is done with HardQCD:all=on.
Prompt J/ψ production in NRQCD is calculated using a summed expansion of Fock states.The leading term is color-singlet J/ψ production, while the sub-leading terms describe color-octet cc production in association with a gluon.Each term is factorized into a perturbatively calculated short-distance matrix element (SDME) and an empirically determined long-distance matrix element (LDME).Within Pythia 8, both the leading color-singlet 3 S states are used to calculate prompt J/ψ production.The unpolarized SDMEs for each state are calculated at tree level, while the LDMEs are taken from Ref. [56].Since the Pythia 8 SDMEs are LO, the corresponding LDMEs are taken from LO fits.Feed-down from higher mass charmonium states is included, also calculated with both color-singlet and color-octet contributions.
The Pythia 8 parton shower is applied to color-octet states, but not color-singlet states, where a quark-splitting kernel with twice the standard probability is used.After showering, all color-octet states are forced to decay isotropically into a color-singlet state with an associated soft gluon.The mass splitting for this decay is 200 MeV.Consequently, colorsinglet production in Pythia 8 is isolated, while color-octet production is accompanied by soft radiation which has only a small effect on z(J/ψ ).A larger effect comes from multi-parton interactions coincident with the J/ψ , shifting z(J/ψ ) to lower values.
In Fig. 4 of the Letter, the full LO NRQCD prediction is calculated using all pp collisions where a charmonium (cc) system is produced with pT (cc) > 2 GeV.The DPS contribution is calculated using pp collisions where both a cc and a dijet (jj) system are produced in separate parton-parton scatters, with pT (cc) > 2 GeV and pT (jj) > 10 GeV.Additionally, ∆R < 0.5 is required between the final-state J/ψ and a parton from the jj system.The SPS prediction is defined as the difference between the full and DPS calculations.The shape and normalization of the SPS contribution is validated against a full LO NRQCD prediction with pT (cc) > 10 GeV.Multi-parton interactions are included for all Pythia 8 calculations.
Further SPS calculations have been performed using HelacOnia [59] for color-singlet 3S (1) 1 and color-octet 3S (8) 1 J/ψ production at LO and NLO*, which includes real but not virtual corrections.The HelacOnia calculations are performed with pT (cc) > 10 GeV and interfaced with the Pythia 8 parton shower.Because of technical limitations, multiparton interactions are not included.The LO HelacOnia predictions are consistent with equivalent Pythia 8 predictions.In Fig. 6 the LO and NLO* HelacOnia predictions are compared to the LO Pythia 8 predictions with multi-parton interactions.
Production of J/ψ mesons from b-hadron decays primarily depends on b-quark fragmentation.A systematic analysis of the fragmentation in Pythia, specifically of the Bowler parameter r b , was performed in the Z2 * tune by CMS [57] using Pythia 6.The r b parameter was found to be to 0.591 +0.216  −0.274 , where the uncertainty corresponds to one standard deviation.In the present analysis, Pythia 8 with the Monash tune [55] is used for theory predictions and so the r b uncertainty from the Z2 * tune is assigned to the  The z(J/ψ ) distribution for J/ψ mesons from b-hadron decays is also sensitive to the amount of g → b b splitting and the soft underlying event.The nominal Pythia 8 prediction includes both gluon splitting and the soft underlying event.Figure 6 compares the nominal prediction to a prediction without gluon splitting (HardQCD:hardbbbar=on) and a prediction without the underlying event (PartonLevel:MPI=off).Neglecting either of these effects can result in a z(J/ψ ) spectrum considerably harder than the nominal prediction.Although the uncertainties on these effects are neglected in this analysis, their sizes suggest that the associated uncertainties are not small; thus, the overall theory error on z(J/ψ ) is probably underestimated.However, this would not change the conclusion: data and theory are consistent for J/ψ mesons produced in b-hadron decays.z(J/ψ ) 0.0-0.1 0.1-0.20.2-0.30.3-0.40.4-0.5 0.5-0.6 0.6-0.7 0.7-0.80.8-0.90.9-1.00.0-0.1.00 −0.17 −0.16 −0.22 −0.12 −0.10 0.5-0.6 1.00 0.52 0.14 −0.06 −0.07 0.6-0.7 1.00 0.14 −0.05 −0.07 0.7-0.81.00 −0.07 −0.09 0.8-0.91.00 −0.11 0.9-1.01.00

Figure 1 :
Figure 1: Example dimuon invariant-mass distribution with the fit result superimposed from the bin [0.4 < z(J/ψ ) < 0.5, 20 < p T (jet) < 30 GeV].The signal is modeled as the sum of two Crystal Ball functions, while the background is described by an exponential function.

Figure 2 :
Figure 2: Example pseudo-decay-time distribution from the same bin as in Fig. 1 with the fit result superimposed.The right plot shows the [−0.2, 1] ps region on a linear scale.
Figure3: The four-dimensional detector-response matrix for prompt J/ψ production.The shading represents the bin-to-bin migration probabilities ranging from (white) 0 to (black) 1, with the lightest shade of gray corresponding to a probability of 0.1-0.3%.Jets whose true p T (jet) is above 20 GeV but whose reconstructed p T (jet) is below 15 GeV, or vice versa, are included in the unfolding but not shown graphically.

Figure 4 :
Figure 4: Measured normalized z(J/ψ ) distributions for J/ψ mesons produced (left) promptly and (right) in b-hadron decays, compared to predictions obtained from Pythia 8.The statistical uncertainties are negligible.The (DPS) double and (SPS) single parton scattering contributions to the prompt prediction are also shown (the DPS effective cross section in Pythia 8 is 31 mb).

Figure 5 :
Figure 5: Analog to Fig. 3 in the Letter for J/ψ mesons produced in b-hadron decays.

Figure 6 :
Figure 6: (top) Prompt-J/ψ calculations of z(J/ψ ) for color-singlet and color-octet production, with and without multi-parton interactions (MPI), i.e. the soft underlying event (the left plot is a log-scale version of the right).(bottom) Nominal z(J/ψ ) prediction for J/ψ mesons produced in b-hadron decays, compared to predictions (solid line) without gluon splitting and (dashed line) without MPI.

Table 3 :
Correlation matrix for J/ψ production in b-hadron decays.