Measurement of the prompt-production cross-section ratio $\sigma(\chi_{c2})/\sigma(\chi_{c1})$ in $p$Pb collisions at $\sqrt{s_{NN}}$ = 8.16 TeV

This Letter reports the first measurement of prompt $\chi_{c1}$ and $\chi_{c2}$ charmonium production in nuclear collisions at Large Hadron Collider energies. The cross-section ratio $\sigma(\chi_{c2}) / \sigma(\chi_{c1})$ is measured in $p$Pb collisions at $\sqrt{s_{NN}}$ = 8.16 TeV, collected with the LHCb experiment. The $\chi_{c1,2}$ states are reconstructed via their decay to a $\rm{J}/\psi$ meson, subsequently decaying into a pair of oppositely charged muons, and a photon, which is reconstructed in the calorimeter or via its conversion in the detector material. The cross-section ratio is consistent with unity in the two considered rapidity regions. Comparison with a corresponding cross-section ratio previously measured by the LHCb collaboration in $pp$ collisions suggests that $\chi_{c1}$ and $\chi_{c2}$ states are similarly affected by nuclear effects occurring in $p$Pb collisions.


Introduction
the interaction region, a set of four planar tracking stations coupled to a dipole magnet with a 4 Tm bending power, a pair of ring-imaging Cherenkov detectors to discriminate between different types of charged hadrons, followed by calorimetric and muon systems that are of particular importance in this measurement. The calorimetric system allows for identification of electrons and photons and consists of a scintillating pad detector (SPD), a pre-shower 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 ECAL and HCAL provide the energy measurement and identify electromagnetic radiation and neutral hadrons. Muons are identified by a system composed of alternating layers of iron and multiwire proportional chambers.
The pPb data were collected with the LHCb experiment in two distinct beam configurations. In the forward configuration, the particles produced in the direction of the proton beam are measured in a center-of-mass rapidity region 1.5 < y * < 4.0, while in the backward configuration, particles produced in the lead-beam direction are measured at center-of-mass rapidity −5.0 < y * < −2.5. The forward (backward) data sample corresponds to an integrated luminosity of about 14 µb −1 (21 µb −1 ).

Data selection
The analyzed events are selected by a set of triggers designed to record collisions containing the decay J/ψ → µ + µ − . The J/ψ candidates are reconstructed from a pair of oppositely charged muons with momentum component transverse to the beam, p T , larger than 700 MeV/c, originating from a common vertex and an invariant mass within ±42 MeV/c 2 of the known J/ψ mass [24] (corresponding to three times the dimuon mass resolution). The J/ψ candidates are combined with a photon candidate to form a χ c1,2 candidate. Photons used in this analysis are classified in two mutually exclusive types: those that converted in the detector material upstream of the dipole magnet and of which the electron and positron tracks were reconstructed in the tracking system (converted photons), or those reconstructed through their energy deposits in the calorimetric system (calorimetric photons). The calorimetric photon sample is about an order of magnitude larger than the converted photon sample but has worse mass resolution. Converted photons are reconstructed from a pair of oppositely charged electron candidates and are required to have a transverse momentum p T > 600 MeV/c and a good-quality conversion vertex γ → e + e − . Calorimetric photons are identified using the ratio of their energy deposited in the hadronic and electromagnetic calorimeters and a pair of likelihood-based classifiers that discriminate photons from electrons and hadrons [25,26]. Calorimetric photons accepted for analysis are required to have p T > 1 GeV/c. The two measurements discussed here are independent given the different reconstruction between the converted and the calorimetric photons. The selected µ + µ − γ combinations, which comprise the χ c1,2 candidates, are required to be reconstructed within the pseudorapidity window 2 < η < 4.5 and in the transverse momentum range of 3 < p T < 15 GeV/c for the converted and 5 < p T < 15 GeV/c for the calorimetric candidates. In order to select the χ c1,2 candidates produced promptly at the primary-collision vertex and to suppress nonprompt production from b-hadron decays occurring away from the primary vertex, an upper limit is imposed on the pseudo-decay time of the candidates, defined as where z decay − z PV is the difference between the positions of the reconstructed vertex of the χ c1,2 candidate and the primary proton-nucleus collision vertex along the beam axis, p z is the longitudinal component of the χ c1,2 candidate momentum and M χ c1 is the known mass of the χ c1 meson [24]. The pseudo-decay time is limited to t z < 0.1 ps. The χ c1 and χ c2 candidates originating from decays of short-lived resonances, such as ψ(2S) produced at the interaction point, are also considered in the analysis. The effects of the detector acceptance as well as of the reconstruction and selection efficiencies are investigated with simulated events. The χ c1,2 signal is generated in Pythia [27] with an LHCb specific configuration [28]. The χ c1 and χ c2 states are generated assuming unpolarized production. The underlying minimum bias forward and backward pPb collisions are generated using the Epos event generator configured for the LHC [29]. Unstable particles are decayed via EvtGen [30]. The J/ψ → µ + µ − decays are corrected for final-state electromagnetic radiation using Photos [31]. The response of the detector to the interactions of the generated particles is implemented using the Geant4 toolkit [32]; for a detailed description see Ref. [33].

Data analysis
This paper aims at measuring the ratio of the cross sections for prompt χ c1 and χ c2 production. The cross-section ratio is defined as Here, N χ c2 and N χ c1 represent the signal yields of the χ c2 and χ c1 states, respectively, and ε χ c2 and ε χ c1 denote the efficiencies to reconstruct and select the corresponding state. The branching fractions for the χ c1,2 decays are B(χ c1 → J/ψγ) = (34.3 ± 1.0) % and B(χ c2 → J/ψγ) = (19.0 ± 0.5) % [24]. The χ c1 and χ c2 signal yields are determined by performing a binned maximumlikelihood fit to the spectra of the difference between the invariant mass of the µ + µ − γ candidate and that of the µ + µ − pair, ∆M ≡ M (µ + µ − γ) − M (µ + µ − ). The fit function comprises a Gaussian shape for the χ c1 and χ c2 resonances and a background component described with a second-order Chebyshev polynomial. In the fit, the difference between the values of the χ c1 and χ c2 masses is set to the known mass difference [24]. The widths of the χ c1 and χ c2 peaks are set to be equal, following expectations from simulation, and left as a free parameter. The χ c0 peak is also included in the fit, however no significant χ c0 yield is observed. The fit to the spectra of converted candidates is performed in the range 200 < ∆M < 800 (850) MeV/c 2 at forward (backward) rapidity. For the calorimetric candidates, the invariant-mass difference spectrum is fitted between 250 < ∆M < 650 MeV/c 2 in the two rapidity intervals. The mass-difference spectra of the converted and calorimetric samples are shown, together with the fit components, in Figs. 1 and 2, respectively. In the converted samples, the yield ratio N χ c2 /N χ c1 is determined to be 0.51 ± 0.23 at forward and 0.56 ± 0.26 at backward rapidity, where the uncertainties are statistical. In the calorimetric samples, these ratios are found to be 0.63 ± 0.08 at forward and 0.67 ± 0.10 at backward rapidity. Individual yields as well as their corresponding significance are listed in Table 1.
Since the kinematics of χ c1 and χ c2 decays are nearly identical, various detector effects such as tracking and particle-identification efficiencies cancel out in the ratio, so that the efficiency ratio in Eq. (2) can be expressed as . The factor ε acc expresses Table 1: Yields of χ c1 and χ c2 signals with statistical uncertainties and corresponding significance (given in standard deviations).

Data sample
13.3 676 ± 82 8.5 the geometrical acceptance of the decay products to fall within the LHCb acceptance, while the factor ε reco represents the efficiency of selection and reconstruction of the signal candidates. These correction factors are computed from dedicated simulated events.

Systematic uncertainties
The systematic uncertainties on the cross-section ratios are determined as follows. A systematic uncertainty on the signal extraction is determined by varying the models used in the mass-difference fits. Several different signal and background models are tested. The signal shapes are varied between Gaussian functions and Voigtian functions (a convolution of a Breit-Wigner and a Gaussian function), and the background shape is varied between second-and third-order Chebyshev polynomials. The natural widths of the χ c1 and χ c2 states are narrow compared to the resolution, the Breit-Wigner widths are therefore fixed to the known values [24]. The fit range is varied between 100 (150) < ∆M < 900 MeV/c 2 and 200 < ∆M < 800 (850) MeV/c 2 for the converted candidates at forward (backward) rapidity. For the calorimetric candidates, the fit range is varied between 250 < ∆M < 650 MeV/c 2 and 300 < ∆M < 600 MeV/c 2 in the two rapidity intervals. The various choices of signal shape, background parametrization, and range give a total of eight fits to each of the mass-difference spectra in each rapidity interval. In all cases, the χ c0 peak is also included in the fit; however, no significant χ c0 yield is observed. The systematic uncertainty on the yield ratios due to the fitting procedure is assigned as the standard deviation between the values returned by the eight individual fits. For the converted sample, this systematic uncertainty amounts to 4.9% (3.2%) at forward (backward) rapidity. For the calorimetric sample it is 2.6% (6.8%) at forward (backward) rapidity. The residual background from the nonprompt χ c1,2 production is verified as negligible and shown to cancel out in the ratio, hence no related uncertainty is assigned. The systematic uncertainty on the acceptance and efficiency corrections includes contributions from the limited size of the simulated samples used to compute the ε acc and ε reco factors, and the uncertainty due to the discrepancy of the χ c1,2 and photon properties between data and simulation. The latter is estimated using simulated samples, weighted to reproduce the kinematic distributions of χ c1,2 and photons in background-subtracted data, and obtained using the sPlot technique, with ∆M as the discriminating variable [34]. The weights are extracted by comparing the transverse momentum and rapidity dependent ratios of the simulated counts N χ c1 /N χ c2 with those in data. The simulated χ c1 samples are then weighted event-by-event and the uncertainty is assessed as the difference between the efficiency ratios computed from simulated samples prior to and after weighting. In the case of calorimetric photons, an additional weighting process is required in order to recover kinematic distributions of final-state photons observed in the data as well, in a similar event-by-event process as the weights obtained from χ c1,2 kinematic distributions. The effect of the photon-identification selection and the reproducibility of relevant variables in simulation are also taken into account. For the converted χ c1,2 sample, the total systematic uncertainty on the acceptance and efficiency equals 9.6% at forward and 14.9% at backward rapidity, while for the calorimetric sample the uncertainty is 8.1% at forward rapidity and 12.4% at backward rapidity. The ratio of the branching fractions of the χ c1,2 → J/ψγ decays contributes with an uncertainty of 3.9%. A summary of contributions to the statistical and systematic uncertainties of each analyzed sample is given in Table 2.
The cross-section ratios for both converted and calorimetric samples are consistent with unity in both rapidity regions. The significantly larger yield of the calorimetric sample allows more precise conclusions on the observed trend to be drawn. The cross-section ratio obtained in pPb data is compared with the corresponding ratio measured in pp collisions at √ s = 7 TeV by the LHCb collaboration [16]. The two measurements are consistent within two standard deviations. While the ratio in the pp data was measured at a lower center-of-mass energy than that of pPb collisions, results show that the relative cross-section of different charmonium states is independent of energy at the LHC energy scale [35]. Thus, the only aspect to consider in a direct comparison between the shown pPb and pp data is the rapidity range, where the pPb results are shifted by −0.5 in rapidity. Bearing that in mind, we can express the relative suppression of χ c2 and χ c1 states via the ratio of their nuclear modification factors Using the more precise calorimetric pPb results, the ratio of nuclear-modification factors amounts to R = 1.41±0.21 (stat.) ±0.18 (syst.) at forward and R = 1.44±0.24 (stat.) ± 0.25 (syst.) at backward rapidity, showing no significant change relative to the pp ratio in either rapidity region. The measured cross-section ratio and ratio of nuclear-modification factors suggest that the nuclear effects have the same impact on both χ c1 and χ c2 states within uncertainties, independent of rapidity.

Summary
In summary, we present the first measurement of χ c1,2 charmonium production in nuclear collisions at the LHC. The cross-section ratio σ(χ c2 )/σ(χ c1 ) is consistent with unity for both forward and backward rapidity regions. Moreover, comparison with the ratio measured in pp collisions hints at a suppression pattern between the two states, which is comparable within uncertainties. This suggests that the final-state nuclear effects impact the χ c1 and χ c2 states similarly within the achieved precision.    [24] Particle Data Group, P. A. Zyla et al., Review of particle physics, Prog. Theor. Exp. Phys. 2020 (2020) 083C01.
[26] C. Abellán Beteta et al., Calibration and performance of the LHCb calorimeters in Run 1 and 2 at the LHC, arXiv:2008.11556.