Fraction of $\chi_c$ decays in prompt $J/\psi$ production measured in pPb collisions at $\sqrt{s_{NN}}=8.16$ TeV

The fraction of $\chi_{c1}$ and $\chi_{c2}$ decays in the prompt $J/\psi$ yield, $F_{\chi c}=\sigma_{\chi_c \to J/\psi}/\sigma_{J/\psi}$, is measured by the LHCb detector in pPb collisions at $\sqrt{s_{NN}}=8.16$ TeV. The study covers the forward ($1.5<y^*<4.0$) and backward ($-5.0<y^*<-2.5$) rapidity regions, where $y^*$ is the $J/\psi$ rapidity in the nucleon-nucleon center-of-mass system. Forward and backward rapidity samples correspond to integrated luminosities of 13.6 $\pm$ 0.3 nb$^{-1}$ and 20.8 $\pm$ 0.5 nb$^{-1}$, respectively. The result is presented as a function of the $J/\psi$ transverse momentum $p_{T,J/\psi}$ in the range 1$<p_{T, J/\psi}<20$ GeV/$c$. The $F_{\chi c}$ fraction at forward rapidity is compatible with the LHCb measurement performed in $pp$ collisions at $\sqrt{s}=7$ TeV, whereas the result at backward rapidity is 2.4 $\sigma$ larger than in the forward region for $1<p_{T, J/\psi}<3$ GeV/$c$. The increase of $F_{\chi c}$ at low $p_{T, J/\psi}$ at backward rapidity is compatible with the suppression of the $\psi$(2S) contribution to the prompt $J/\psi$ yield. The lack of in-medium dissociation of $\chi_c$ states observed in this study sets an upper limit of 180 MeV on the free energy available in these pPb collisions to dissociate or inhibit charmonium state formation.

Heavy ion collisions in the relativistic regime provide an opportunity to release quarks and gluons from hadrons and form a hot and dense quark-gluon plasma (QGP), the same state of matter theorized to exist microseconds after the Big Bang and to compose the core of neutron stars [1].While there are many indications of QGP formation in nucleus-nucleus collisions at RHIC and the LHC, its formation in small systems such as proton-nucleus collisions is not firmly established.The observation of collective particle flow in pPb collisions at the LHC, and pA and dA collisions at RHIC, suggests the existence of QGP droplets in these collisions (see for example [2]), but a lack of other signatures prevents a conclusion.Quarkonium states have a broad range of binding energies [3] of the same order of magnitude as the freeze-out temperature, the minimum temperature needed to form a QGP [4][5][6].The spectrum of quarkonium states that survive nucleus collisions is a powerful tool to determine the free energy and temperature reached by the initial stage of heavy ion collisions.However, a quarkonium state can also be broken by its interaction with comoving particles if the particle multiplicity is high enough, as observed in the nucleus-going direction in proton-and deuteron-nucleus collisions [7].The nuclear modification factor, defined as the ratio between the particle yield per nucleon interaction measured in heavy ion and pp collisions, is the most commonly used observable to quantify nuclear effects.The spin-1 ground-state charmonium meson J/ψ, with a binding energy of 640 MeV, has a nuclear modification factor similar to the open charm meson D 0 at forward and backward rapidity ranges in pPb collisions [8].This observation indicates that the nuclear modification factor observed in J/ψ yields in these collisions can be attributed solely to nuclear modification of parton densities before the formation of the cc pair.The charmonium state ψ(2S), with a binding energy of 50 MeV, has a suppression stronger than the J/ψ state at backward rapidity in p(d)A collisions at RHIC [9] and the LHC [10][11][12], indicating that this weakly bound state is also suppressed by final-state nuclear effects.
Additional constraints on the free local energy produced in pA collisions, which would dissociate or prevent charmonium state formation, can be provided by the χ c1 and χ c2 states.These have binding energies of 220 and 180 MeV, respectively.The P-wave charmonium states χ cn are mainly reconstructed from the radiative decay χ cn → J/ψγ with branching ratios 1.4%, 34% and 19% for n = 0, 1 and 2 [13].The production of χ c0 mesons is rarely studied in this decay mode, due to its small branching ratio.Measurements of χ c production typically require high detection efficiency for low-energy photons, and effective discrimination against the overwhelming π 0 decay sources producing large combinatorial backgrounds in the J/ψγ mass distribution.For these reasons, χ c measurements in heavy ion collisions are rare.There are two χ c measurements in nucleus collisions: (i) HERA-B measured the fraction of χ c decays in J/ψ production in proton on C and W targets at √ s NN = 41.6 GeV [14], showing no dependence on the target material and (ii) PHENIX measured the χ c /J/ψ fraction in dAu collisions at √ s NN = 200 GeV [15], consistent with measurements in pp collisions at the same energy within the large statistical uncertainty.The identified χ c1 and χ c2 yields measured by the LHCb collaboration in pPb collisions at √ s NN = 8.16 TeV are consistent [16], although with large uncertainties given the difficulty in resolving the mass peaks.This Letter reports, for the first time at the LHC, the fraction F χc→J/ψ of χ c → (J/ψ → µ + µ − )γ decays in prompt J/ψ →µ + µ − yields.The measurement is made in eight p T,J/ψ ranges over 1 < p T,J/ψ < 20 GeV/c in pPb collisions at √ s NN = 8.16 TeV at forward (1.5 < y * < 4.0) and backward (−5.0 < y * < −2.5) rapidities, where y * is the J/ψ rapidity in the nucleon-nucleon center-of-mass system.Prompt J/ψ mesons are produced directly in the hadronization process (direct contribution) or via decays of higher-mass charmonium states (feeddown contribution).The measured χ c yield is the sum of the χ c1 and χ c2 yields, which minimizes the uncertainties related to the separation of these states.The fraction F χc→J/ψ is obtained by where N χc→J/ψγ and N J/ψ are the prompt χ c →J/ψ γ and J/ψ yields, and ε χc/J/ψ is the fraction of χ c →J/ψ γ decays which are detected in the LHCb acceptance relative to the decays where only the J/ψ is detected.The LHCb detector is a single-arm forward spectrometer described in Refs.[17,18].The silicon-strip vertex detector (VELO) surrounding the interaction region allows the determination of the position of the collision point, the primary vertex (PV).Charged particle tracks are determined by the combination of hits in the VELO, a large-area siliconstrip detector located upstream of a dipole magnet with a bending power of about 4 Tm, and three stations of silicon-strip detectors and straw drift tubes (OT) placed downstream of the magnet.Muons are identified by a system composed of alternating layers of iron and multiwire proportional chambers behind electromagnetic and hadronic calorimeters.Photons are identified by the calorimeter system [19] consisting of a scintillating pad detector (SPD), a preshower system (PS), an electromagnetic (ECAL) calorimeter, and a hadronic (HCAL) calorimeter.The SPD and PS are designed to discriminate between signals from photons and electrons, while the ECAL and HCAL provide the energy measurement and identification of photons and neutral hadrons.The relative energy resolution of the ECAL is 8%/ √ E + 0.9%, where E is in GeV.This analysis is based on data acquired during the 2016 LHC heavy-ion run, where the LHCb experiment recorded proton and 208 Pb ion collisions at a center-of-mass energy per nucleon pair of √ s NN = 8.16 TeV.The forward (positive) rapidity sample is collected in collisions where the proton follows the direction from the VELO to the muon detectors, namely pPb collisions, corresponding to an integrated luminosity of 13.6 ± 0.3 nb −1 .The backward (negative) rapidity sample is obtained with a reverse beam direction, Pbp collisions, with 20.8 ± 0.5 nb −1 integrated luminosity.
The online event selection used in this analysis is performed by a trigger system consisting of a hardware stage that selects events containing at least one muon candidate, and two software trigger stages in which events with two tracks identified as muons with p T > 500 MeV/c are selected.The muon pair is required to have an invariant mass within 150 MeV/c 2 of the known J/ψ mass [13].In the offline selection, muons are identified by a neural network algorithm.The muon also must satisfy the momentum requirements p T > 600 MeV/c, p > 8 GeV/c, and be in the LHCb pseudorapidity range 2 < η < 5.The J/ψ candidate is selected by requiring the muon pair invariant mass to be within 80 MeV/c 2 of its known mass and its transverse momentum p T,J/ψ must be larger than 1 GeV/c.The J/ψ candidate must be consistent with originating from the collision point.
Photons are identified as isolated clusters in the ECAL.The cluster must not belong to a charged particle or a π 0 decay with 80% confidence level as determined by neural network algorithms.The photon must be in the ECAL acceptance 2 < η < 4.5 and have transverse momentum p T,γ > 400 MeV/c.The detector performance for the J/ψ and χ c signals are studied using simulated samples generated by Pythia [20] and embedded with events generated by EPOS [21], which accounts for the underlying event activity of pPb collisions.Decays of short-lived particles are performed with the EvtGen decay package [22].Radiative QED corrections to the decays containing charged particles in the final state are applied with the Photos package [23].The generated χ c1 and χ c2 decays are required to have both muons from the J/ψ decay in the LHCb acceptance.The response of the LHCb detector is modelled using Geant4 [24].Weights are assigned to the simulated events such that the VELO cluster multiplicity matches that of the data.The LHCb detection efficiency correction ε χc/J/ψ is obtained from the simulated χ c sample using Eq. ( 1), where F χc→J/ψ = 1 by definition.
The selected sample is overwhelmingly composed of combinatorial background (CBG).The remaining components are correlated background, also called physics background, and the signal χ c decays.This analysis uses the invariant mass difference ∆M = M µ + µ − γ − M µ + µ − for fitting, minimizing the impact of the muon pair mass resolution.The shape of the combinatorial background distribution, Y CBG (∆M ), is determined by mixing J/ψ decays and photons from different events.The two events must have similar track multiplicities and collision vertex positions.The overall combinatorial background yield N CBG is determined by normalizing the CBG shape Y CBG to have the same integral as the default sample in the mass region 700 < ∆M < 900 MeV/c 2 , where the signal and the correlated background are expected to be negligible.Figure 1(a) shows the ∆M distribution after the combinatorial background subtraction.
The correlated background is composed of radiative J/ψ decays (J/ψ → µ + µ − γ) and partially reconstructed ψ(2S) → J/ψπ 0 π 0 → µ + µ − γ decays which are studied using simulated samples.The partially reconstructed ψ(2S) contribution is 8 (30) times smaller than the J/ψ radiative decay at high (low) p T,J/ψ when considering its measured yield relative to J/ψ decays [12] and the branching ratio B(ψ(2S) → J/ψπ 0 π 0 ) [13].The ∆M distribution accounting for the total correlated background is described by with p T,γ -dependent parameters B, ∆M 0 and σ ∆M b initially determined from the simulation and A corr is its normalization.The two χ c states are described by the sum of two Gaussian functions, G, with a common resolution term as where 0.4 < f χ c1 < 0.6 is the contribution of the χ c1 decay to the total χ c yield as obtained in Ref. [16], ∆M χ c1 = M χ c1 − M J/ψ is the free parameter accounting for the mass difference of the χ c1 state as measured by the detector, ∆M 1,2 = 45.5 MeV/c 2 is the known mass difference between the χ c1 and χ c2 states [13].The total shape of the ∆M distribution accounting for the χ c signal and background is given by where N corr is the yield of the correlated background.The signal yields are obtained with a maximum-likelihood fit of Eq. ( 4 Candidates/(15 Candidates/(4 MeV c 2 ) data fit BG parameters determined from simulation.The total χ c yields, integrated over p T,J/ψ , are (11.8 ± 0.6) × 10 3 and (15.2 ± 0.8) × 10 3 in the forward and backward rapidity samples, respectively.The χ c yields are independently obtained in eight p T,J/ψ ranges and are stable with Gaussian variation of the initial parameters determined from simulation. Figure 1(a) shows the ∆M distribution, integrated over p T,J/ψ , with the fit results overlaid.The J/ψ yield is determined in eight p T,J/ψ ranges using a maximum-likelihood fit to the µµ invariant mass distribution.The fitting function is defined by the sum of a Crystal Ball function, CB pdf , [25] for signal and an exponential function for background to the µ + µ − invariant mass distribution using the log-likelihood method.The parameters A and b define the scale and slope of the exponential components.The parameters α and n are determined from a p T,J/ψ -integrated fit and fixed for the fits in different p T,J/ψ ranges.The parameter M J/ψ is fixed to the known value of the J/ψ mass [13].The p T,J/ψ -integrated M µ + µ − distribution and the results of the fit are shown in Fig. 1(b).Variation of the initial parameters when fitting the ∆M distribution and the fixed mass resolution parameter ∆σ M cause the largest systematic uncertainties on the χ c yields, mostly for the lowest p T,J/ψ interval.These variations account for potential multiple local minima in the log-likelihood function used in the fits.Any deviation from the Gaussian shape assumption for the χ c peaks is tested by comparing the yields obtained by fitting Eq. ( 4) and from the integral over 300 < ∆M < 600 MeV/c 2 after subtracting the fitted background contributions Y CBG + Y corr .The difference between the yield obtained from the fit and the integral is assigned as a systematic uncertainty on the yield.The statistical uncertainties associated to the mixed J/ψ and γ event samples are negligible.However, variations on the mass range used to normalize the mixed event distribution Y CBG contribute to the uncertainty in the χ c yields.The only significant uncertainty in the J/ψ yield determination comes from the difference between the result obtained from the mass peak fitting and the integral over the J/ψ peak region after subtracting the background component.
The photon detection efficiency is the main contribution to the factor ε χc/J/ψ .A validation of the photon detection efficiency ε γ is performed by studying partially reconstructed η decays in data and simulation.Clear peaks are observed in the π + π − γ invariant mass distribution (well separated from the fully reconstructed η → π + π − γ peak) and the π + π − mass distribution coming from η → π + π − (π 0 → γ S γ) and η → π + π − (π 0 → S γ S γ) decays, where S γ is a missing photon.The detection efficiency in η decays is measured in data and simulation by where M γ(ππ) is a matrix, obtained from simulation, that unfolds the p T,γ distribution from η → π + π − (π 0 → S γ S γ) decays as a function of p T,π + π − .The efficiencies measured in data and simulation are consistent within 3% in the photon p T range 400 < p T,γ < 5000 MeV/c.Initial-state effects in the nucleus on the input kinematics are accounted for in simulation by weighting events according to the nuclear parton density function EPPS21 [26].
All the measurements assume χ c production with zero polarization.The effects of a potential χ c polarization on the detector efficiency are studied by weighting the simulated events according to different polarization scenarios as reported in Ref. [27].The measured J/ψ polarization by LHCb [28] and the observation that either χ c1 or χ c2 states is strongly polarized by the CMS collaboration [29] poses constraints to the scenarios adopted when weighting simulated events.The standard deviation of the F χc→J/ψ values after polarization weighting is taken as the systematic uncertainty.
Any potential B-meson decay contamination of the prompt J/ψ yield is checked by tightening the collision point and χ c vertex association requirement, and the results are consistent with the default selection within the statistical uncertainties.Table 1 summarizes the maximum systematic uncertainty contributions.The largest uncertainties are found at the lowest p T,J/ψ range.The total systematic uncertainty corresponds to the standard deviation of the F χc→J/ψ results obtained from the different systematic uncertainty sources.The p T,J/ψ -dependent values of F χc→J/ψ are shown in Fig. 2. The points are located at the mean p T,J/ψ of each bin determined by a fit to the prompt J/ψ differential cross-section reported by the LHCb collaboration in Ref. [30].The new results are compared with those obtained in pp collisions at √ s = 7 TeV [27].The F χc→J/ψ results obtained in pPb and in pp collisions have an overall consistency.The fraction is slightly larger in the backward rapidity region for p T,J/ψ < 3 GeV/c.The result is also consistent with results obtained by the HERA-B experiment in pC and pW collisions at √ s NN = 41.6 GeV [14].
The HERA-B result covers a rapidity range −5.2 < y * < −2.2 and p T,J/ψ < 2 GeV/c.A measurement of F χc→J/ψ was performed by the PHENIX collaboration in dAu collisions at √ s NN = 200 GeV [15], covering the mid-rapidity range1 |y * | < 0.5 and integrated over p T,J/ψ , and is consistent with the p T,J/ψ < 2 GeV/c result presented here, though the PHENIX measurement has large statistical uncertainties.
Table 2: F χc→J/ψ results for wide p T,J/ψ bins.The two uncertainties are statistical and systematic respectively.
The F χc→J/ψ result in pPb collisions suggests that neither J/ψ mesons, produced directly in the collisions, nor χ c states are dissociated in the medium formed in pPb collisions, consistent with the similar nuclear modification factor measurement of J/ψ and D 0 yields in pPb collisions [8].The non-dissociation of the χ c states leads to a constraint on the free energy (or temperature) of the system to be no larger than 180 MeV in pPb collisions, based on the smallest binding energy among the χ c states.This maximum temperature is close to the estimated freeze-out temperature in pPb collisions, which ranges between 155-160 MeV [4][5][6].The result presented here is integrated over collision centrality.Future studies selecting central events could be more sensitive to a short-lived hot medium in pPb collisions.
The most common method to quantify quarkonium dissociation in medium is the use of the quarkonium state yield ratios r relative to their corresponding ground state J/ψ for cc and Υ (1S) for bb or to an open heavy flavor meson (D 0 and B + for cc and bb, respectively).The double ratio R = r pPb /r pp compares the r values between pp and pPb collisions.It is obtained for χ c states from the 2 < p T,J/ψ < 20 GeV/c integrated result presented in Table 2 and  Figure 3: Double ratio between quarkonium states vs. binding energy along with the estimated freeze-out temperature in pPb collisions [4][5][6].The quarkonium state ratio r is indicated for each point and described in Table 3.

R(χ c
) is 1.10 ± 0.12 at forward rapidity and 1.29 ± 0.17 at backward rapidity.Figure 3 shows the binding-energy dependence of R for all quarkonium states measured by the LHCb experiment in pPb collisions at backward rapidity, where pPb collisions achieve the highest particle multiplicities.The only dissociated (R < 1) quarkonium state with binding energy above the freeze-out temperature is the Υ (3S).With a similar binding energy and size as the χ c states, according to non-relativistic potential theory [3], the Υ (3S) resonance is 2.9 times heavier and may travel the medium slower than the χ c states favoring its dissociation by its interaction with comoving particles [7].In summary, this Letter presents the first LHC measurement of the fraction of χ c decays in the prompt J/ψ yield in heavy ion collisions.The ratio measured in pPb collisions is consistent with no dissociation of χ c states, indicating that the average free energy available in these collisions is not able to inhibit the formation of quarkonium states with binding energy equal or larger than 180 MeV.Such an energy is only 20-25 MeV larger than the expected freeze-out temperature estimated in these systems.

Figure 1 :
Figure 1: (a) Difference in the invariant mass of µ + µ − γ and µ + µ − combinations in the χ c region after combinatorial background subtraction.The red and gray bands represent the fit result and the physical background components, respectively.The widths of the bands represent 68% CL.(b) Invariant mass distribution of µ + µ − pairs in the J/ψ mass region along with the fitted function.

= 7 Figure 2 :
Figure 2: Fraction of χ c decays in the prompt J/ψ yield in pPb and pp collisions [27] as a function of p T,J/ψ .The error bars show the statistical uncertainties.Boxes represent systematic uncertainties and the gray band represents the maximum uncertainties from χ c and J/ψ polarization effects.
a weighted average of the pp results presented in Ref.[27].The double ratio 0

Table 1 :
Systematic uncertainty sources and maximum individual contributions.

Table 3 :
Description of the double ratio measurements shown in Figure3.