Inclusive J/ψ production at midrapidity in pp collisions at √s = 13 TeV

This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details. Author(s): Title: Year: Version: Copyright: Rights: Rights url: Please cite the original version: CC BY 4.0 https://creativecommons.org/licenses/by/4.0/ Inclusive J/ψ production at midrapidity in pp collisions at √s = 13 TeV © CERN for the benefit of the ALICE collaboration 2021 Published version ALICE Collaboration ALICE Collaboration. (2021). Inclusive J/ψ production at midrapidity in pp collisions at √s = 13 TeV. European Physical Journal C, 81(12), Article 1121. https://doi.org/10.1140/epjc/s10052- 021-09873-4 2021 Eur. Phys. J. C (2021) 81:1121 https://doi.org/10.1140/epjc/s10052-021-09873-4 Regular Article - Experimental Physics Inclusive J/ψ production at midrapidity in pp collisions at √s=13 TeV ALICE Collaboration CERN, 1211 Geneva 23, Switzerland Received: 2 September 2021 / Accepted: 22 November 2021 © CERN for the benefit of the ALICE collaboration 2021 Abstract We report on the inclusive J/ψ production cross section measured at the CERN Large Hadron Collider in proton–proton collisions at a center-of-mass energy √s=13 TeV. The J/ψ mesons are reconstructed in the e+e−decay channel and the measurements are performed at midrapidity (|y|<0.9) in the transverse-momentum interval 0 <pT<40 GeV/c, using a minimum-bias data sample corresponding to an integrated luminosity Lint =32.2nb −1 and an Electromagnetic Calorimeter triggered data sample with Lint =8.3pb −1.ThepT-integrated J/ψ production cross section at midrapidity, computed using the minimumbias data sample, is dσ/dy|y=0=8.97 ±0.24 (stat)± 0.48 (syst)±0.15 (lumi)μb. An approximate logarithmic dependence with the collision energy is suggested by these results and available world data, in agreement with model predictions. The integrated and pT-differential measurements are compared with measurements in pp collisions at lower energies and with several recent phenomenological calculations based on the non-relativistic QCD and Color Evaporation models. 1 Introduction Quarkonium production in hadronic interactions is an excellent case of study for understanding hadronization in quantum chromodynamics (QCD), the theory of strong interactions [1]. In particular, the production of the J/ψ meson, a bound state of a charm and an anti-charm quark and the lightest vector charmonium state, is the subject of many theoretical calculations. The cornerstone of all the theoretical approaches is the factorization theorem, according to which theJ/ψ productioncrosssectioncanbefactorizedintoashort distance part describing the cc production and a long distance part describing the subsequent formation of the bound state. In this way, the cc pair production cross section can be computed perturbatively. The widely used Non-Relativistic QCD (NRQCD) approach [2] describes the transition prob- e-mail: [email protected] abilities of the pre-resonant cc pairs to bound states with a set of long-distance matrix elements (LDME) fitted to experimental data, assumed to be universal. Next-to-leading order (NLO) calculations involving collinear parton densities are able to describe production yields for transverse momentum (pT) larger than the mass of the bound state [3,4], but have difficulties describing the measured polarization [5,6]. Calculations employing the kT-factorization approach [7] can reach lower pTbut have similar difficulties when compared to data [8]. The low-pTrange of quarkonium production is modelled also within the Color Glass Condensate effective theory coupled to leading order NRQCD calculations [9], which involves a saturation of the small Bjorken-x gluon densities that dampens the heavy-quark pair production yields. An alternative to the universal LDME approach to hadronization used in the NRQCD framework is provided by the Color Evaporation Model (CEM) [10,11] and its more recent implementation using the kT-factorization approach, the Improved CEM (ICEM) [12]. In the ICEM, the transition probability to a given bound state is proportional to the cc pair production cross section integrated over an invariantmass range spanning between the mass of the bound state and twice the mass of the lightest charmed meson. Finally, in the Color Singlet Model (CSM) [13–15], the pre-resonant cc pair is produced directly in the color-singlet state with the same quantumnumbers as the bound state. Calculationswithin this model at NLO precision are known to strongly underpredict the measured production cross sections [16]. In this context, apT-differential measurement of J/ψ production cross section covering a wide pTrange, starting from pT=0 and up to high-pT, can discriminate between the different models of quarkonium production. In this paper, we present the integrated, and the pTand rapidity(y)differential productioncross sections ofinclusive J/ψ production at midrapidity (|y|<0.9) in proton–proton (pp) collisions at the center-of-mass energy √s=13 TeV. The inclusive J/ψ yields include contributions from directly produced J/ψ, feed-down from prompt decays of highermass charmonium states, and non-prompt J/ψ from the 0123456789().: V,-vol 123 1121 Page 2 of 18 Eur. Phys. J. C (2021) 81:1121 decays of beauty hadrons. The pT-differential production cross section of inclusive J/ψ is measured in the 0 <pT< 15 GeV/cinterval using a minimum-bias triggered data sample and in the 15 <pT<40 GeV/cinterval using an Electromagnetic Calorimeter triggered data sample. These results complement existing measurements at midrapidity at √s=13 TeV performed by the CMS Collaboration [17], which report the prompt J/ψ production cross section for pT >20 GeV/c. Previous measurements of the J/ψ production cross section in pp collisions performed by the ALICE Collaboration at midrapidity at lower energies were published in Refs. [18–20]. The inclusive J/ψ production cross section in pp collisions at √s=13 TeV was published by the ALICE Collaboration at forward rapidity in Ref. [21] and the prompt and non-prompt production cross sections were reported by the LHCb Collaboration in Ref. [22]. In the next sections, the ALICE detector and the data sample are described in Sect. 2, and the data analysis and the determination of the systematic uncertainties are described in Sects. 3and 4, respectively. The results are presented and discussed together with recent model calculations in Sect. 5 and conclusions are drawn in Sect. 6. 2 The ALICE detector, data set and event selection A detailed description of the ALICE detector and its performance is provided in Refs. [23,24]. Here we mention only the detector systems used for the reconstruction of the J/ψ mesons decaying in the e+e−channel at midrapidity. Unless otherwise specified, the term electrons will be used throughout the text to refer to both electrons and positrons. Thereconstruction ofcharged-particletracks isperformed using the Inner Tracking System (ITS) [25] and the Time Projection Chamber (TPC) [26], which are placed inside a solenoidal magnet providing a uniform magnetic field of B=0.5 T oriented along the beam direction. The ITS is a silicon detector consisting of six cylindrical layers surrounding the beam pipe at radii between 3.9 and 43.0cm. The two innermost layers consist of silicon pixel detectors (SPD), followed by two layers of silicon drift (SDD) and two layers of silicon strip (SSD) detectors. The TPC is a cylindrical gas drift chamber which extends radially between 85 and 250 cm and longitudinally over 250 cm on each side of the nominal interaction point. Both TPC and ITS have full coverage in azimuth and provide tracking in the pseudorapidity range |η|<0.9. Additionally, the measurement of the specific energy loss (dE/dx) in the TPC active gas volume is used for electron identification. The ElectromagneticCalorimeter(EMCal)and theDi-jetCalorimeter(DCal) [27–29] are employed for triggering and electron identification. The EMCal/DCal is a Shashlik-type lead-scintillator sampling calorimeter located at a radius of 4.5 m from the beam vacuum tube. The EMCal detector covers a pseudorapidity range of |η|<0.7 over an azimuthal angle of 80◦<ϕ<187◦, and the DCal covers 0.22 <|η|<0.7 for 260◦<ϕ<320◦and |η|<0.7 for 320◦<ϕ<327◦. The EMCal and DCal have identical granularity and intrinsic energy resolution, and they form a two-arm electromagnetic calorimeter, which in this paper will be referred to jointly as EMCal. In addition to these central barrel detectors, the V0 detectors, composed of two scintillator arrays [30] placed along the beam line on either side of the interaction point and covering the pseudorapidity intervals −3.7<η<−1.7 and 2.8<η<5.1, respectively, are used for event triggering. Together with the SPD detector, the V0 is also used to reject background from beam-gas collisions and pileup events. The measurement of the pT-integrated and pT-differential production cross sections up to pT=15 GeV/c, the upper limit being determined by the available integrated luminosity, utilizes the minimum-bias (MB) trigger, defined as the coincidence of signals in both V0 scintillator arrays. For the pTinterval from 15 up to 40 GeV/c, the EMCal trigger is employed to select events with high-pTelectrons. The lower pTlimit is chosen such that the trigger efficiency does not vary with pTabove this value, thus avoiding systematic uncertainties related to trigger threshold effects. The EMCal trigger is an online trigger which includes a Level 0 (L0) and a Level 1 (L1) component [27]. The calorimeter is segmented into towers and Trigger Region Units (TRUs), the latter being composed of 384 towers each [27]. The L0 trigger is based on the analog charge sum of 4 ×4 groups of adjacent towers evaluated within each TRU, in coincidence with the MB trigger. The L1 trigger decision requires the L0 trigger and, in addition, scans for 4 ×4 groups of adjacent towers across the entire EMCal surface. The EMCal-triggered analysis presented in this paper uses the L1 trigger, and requires that at least one of the charge sums of the 4 ×4 adjacent towers is above 9 GeV. This analysis includes all the data recorded by the ALICE Collaboration during the LHC Run 2 data-taking campaigns of 2016, 2017 and 2018 for pp collisions at √s=13 TeV. The maximum interaction rate for the dataset was 260 kHz, with a maximum pileup probability in the same bunch crossing of 0.5 ×10−3. The events selected for analysis were required to have a reconstructed vertex within the interval |zvtx|<10 cm to ensure a uniform detector acceptance. Beam-gas events and pileup collisions occurring within the readout time of the SPD were rejected offline using timing selections based on the V0 detector information. Pileup collisions occurring within the same LHC bunch crossing were rejected using offline algorithms which identify multiple vertices [24]. The remaining fraction of pileup events surviving the selections is negligible for both the MB and EMCal data samples. 123 Eur. Phys. J. C (2021) 81:1121 Page 3 of 18 1121 The analyzed MB sample, satisfying all the quality selections, consists of about 2×109events, corresponding to an integrated luminosity Lint =32.2nb −1±1.6% (syst), and the EMCal-triggered sample consists of approximately 9×107events which corresponds to an integrated luminosity Lint =8.3pb −1±2.0% (syst). The integrated luminosities are obtained based on the MB trigger cross section (σMB), measured in a van der Meer scan [31], separately for each year, as described in Ref. [32]. For each of the used triggers, MB and EMCal, the integrated luminosity is obtained as Lint =NMB σMB ×dstrig dsMB ×LT trig LT MB (1) where NMB is the number of MB-triggered events in the triggered sample, dstrig is the downscaling factor applied to the considered trigger by the ALICE trigger processor and LT trig is the trigger live time, i.e. the fraction of time where the detector cluster1assigned to the trigger was available for readout. 3J/ψ reconstruction Inthis workwestudythe integrated,andthe rapidity-and pT- differential inclusive J/ψ production at midrapidity (|y|< 0.9) reconstructing the J/ψ from the e+e−decay channel. The MB sample analysis follows closely the one performed in pp collisions at √s=5.02 TeV [20]. 3.1 Track selection Electron-track candidates are reconstructed employing the ITS and TPC. They are required to be within the acceptance of the central barrel (|η|<0.9), and to have a minimum transverse momentum of 1 GeV/c, which suppresses the background with only a moderate J/ψ efficiency loss. The tracks are selected to have at least 2 hits in the ITS, one of which having to be in one of the SPD layers, and share at most one hit with other tracks. A minimum of 70 out of a maximum of 159 clusters are required in the TPC. In order to reject tracks originating from weak decays and interactions with the detector material, a selection based on the distance-of-closest approach (DCA) to the primary vertex is applied to the tracks. For the MB analysis the tracks are required to have a minimum DCA lower than 0.2 cm in the transverse direction and 0.4 cm along the beam axis. Such tight selection criterion is used in order to improve the signal-to-background ratio and the signal significance. It was checked with Monte Carlo (MC) simulations that these 1A detector cluster is a set of ALICE detectors readout with the same set of triggers. All triggers assigned to a given cluster share the same live-time, determined by the slowest detector in the cluster. requirementsdonot leadtoefficiencyloss forthenon-prompt J/ψ relative to the prompt J/ψ. For the EMCal-triggered event analysis, a looser selection on the DCA to the primary vertex at 1 and 3 cm is applied to avoid rejecting non-prompt J/ψ from highly boosted beauty hadron decays. The electrons are identified using the specific energy loss dE/dxin the TPC gas. Their dE/dxis required to be within a band of [−2,3]σrelative to the expectation for electrons at the given track momentum, with σbeing the dE/dxresolution. The contamination from protons which occurs in the momentum range p<1.5GeV/cand from pions for momentaabove2 GeV/cis mitigatedbyrejectingtracks compatible with the proton or pion hypothesis within 3σ. For the analysis of EMCal-triggered events, both the TPC and the EMCal are used for electron identification. At least one of the J/ψ decay-electron tracks, initially identified by the TPC, is required to be matched to an EMCal cluster (a group of adjacent towers belonging to the same electromagnetic shower). In order to ensure a constant trigger efficiency on the selected events, the matched clusters are selected to have a minimal energy of 14 GeV, a value that is significantly higher than the applied online threshold of 9 GeV. Electrons are identified by applying a selection on the energy-to-momentum ratio of the EMCal matched track of 0.8<E/p<1.3 and on the dE/dxin the TPC of [−2.25,3]σ. Due to the additional use of the EMCal for electron identification with respect to the MB based analysis, no explicit hadron rejection was used for the EMCal sample. Secondary electrons from photon conversions, the main background source for both analyses, are rejected using the requirement of a hit in the SPD detector. This requirement rejects most of the electrons from photon conversions occurring beyond the SPD layers. An additional selection based on track pairing, as described in detail in Ref. [20], is applied to further reject conversion electrons, especially those from photons converting in the beam pipe or in the SPD. 3.2 Signal extraction The number of reconstructed J/ψ mesons is extracted from the invariant mass (mee) distribution of all possible oppositesign (OS) pairs constructed combining the selected electron tracks within the same event (SE). Besides the J/ψ signal, i.e.pairs of electrons originatingfrom the decay ofa common J/ψ mother, the invariant mass distribution contains a background with contributions from combinatorial and correlated sources. In the MB analysis, the combinatorial background, i.e. pairs of electrons originating from uncorrelated processes, is estimated using the event-mixing technique (ME), in which pairs are built from opposite-sign electrons belonging to differentevents. Themixing is doneconsidering eventsfrom the 123 1121 Page 4 of 18 Eur. Phys. J. C (2021) 81:1121 same run (a collection of events taken during a period of time of up to a few hours) with a similar vertex position. The normalized combinatorial background distribution Bcomb(mee) is obtained as Bcomb(mee)=NME OS (mee)×miNSE LS (mi) miNME LS (mi)(2) where NSE LS ,NME OS and NME LS are the number of same-event like-sign (LS), mixed-event OS and mixed-event LS pairs, respectively. Here, the mixed-event OS distribution is normalizedusingtheratio ofSEto MElike-signpairssincethese are not expected to contain any significant correlated source. The summation extends over all the mass bins mibetween 0 and 5 GeV/c2to minimize the statistical uncertainty on the background matching. The correlated background in the mass region relevant for this analysis originates mainly from semi-leptonic decays of heavy-flavor hadrons [33]. In order to extract the number of reconstructed J/ψ,NJ/ψ , the combinatorial background-subtracted invariant mass distribution is fitted with a two-component function: one empirical function to describe the correlated background shape, which is a second order polynomial at low pair pT(pee T<1GeV/c) and an exponential at high-pT(pee T>1GeV/c), plus a template shape obtained from MC simulations, described in Sect. 3.3, for the J/ψ signal. For the analysis of theEMCal-triggered event sample, due to the relatively large contribution from correlated sources at high pT, the event mixing technique is not used. Instead, a fit of the invariant mass distribution is performed using the MC template for the signal and a third-order polynomial function todescribeboththecombinatorialandcorrelatedbackground contributions. In both analyses, the contribution from ψ(2S)decaying in thedielectron channelis notincluded in thefit asthe expected number of such pairs is ∼1% of the J/ψ raw yield and it is statistically not significant in the analyzed data samples. The number of J/ψ is obtained by counting the number of e+e− pairs in the mass range 2.92 ≤mee ≤3.16 GeV/c2remain- ing after subtracting the background. The SE-OS dielectron invariant mass distribution for a few of the pTintervals is shown in Fig. 1, together with the estimated signal and background components. 3.3 Corrections The double differential J/ψ production cross section is calculated as d2σJ/ψ dydpT =NJ/ψ BR(J/ψ →e+e−)×A××y×pT×Lint. , (3) where NJ/ψ is the number of reconstructed J/ψ inagiven interval of rapidity yand transverse momentum pT, BR(J/ψ →e+e−)is the decay branching ratio into the dielectron channel [34], A×is the average acceptance and efficiency factor and Lint is the integrated luminosity of the data sample. The correction for acceptance and efficiency is the product of the kinematical acceptance factor, the reconstruction efficiency, which includes both tracking and particleidentification (PID) efficiency, and the fraction of signal in the signal counting mass window. For the EMCal-triggered events analysis, the efficiency for the EMCal cluster reconstruction is also considered. The efficiency related to the EMCal trigger is estimated using a parameterized simulation of the L1 trigger which includes decalibration and noise based on measured data, and takes into account the timedependent detector conditions. With the exception of the PID efficiency,allthecorrectionsareobtainedbasedonaMCsimulation of unpolarized J/ψ mesons embedded in inelastic pp collisions simulated using PYTHIA 6.4 [35] with the Perugia 2011 tune [36]. The prompt J/ψ are generated with a flat rapidity distribution and a pTspectrum obtained from a phenomenological interpolation of J/ψ measurements at RHIC, CDF and the LHC at lower energies [37]. For the non-prompt J/ψ,b b pairs are generated using the PYTHIA Perugia 2011 tune. The J/ψ decays are simulated using PHOTOS [38], which includes the radiative component of the J/ψ decay. The generated particles are transported through the ALICE detector setup using the GEANT3 package [39]. The PID efficiency is determined with a data-driven method by using a clean sample of electrons from tagged photon conversion processes, passing the same quality criteria as the electrons selected for the J/ψ reconstruction. The PID selection efficiency for single electrons is propagated to the J/ψ level using a simulation of the J/ψ decay. The acceptance times efficiency correction factor for the MB sample analysis varies with pTbetween 7.6% and 16% while in the caseofthe EMCal-triggeredsampleanalysis itincreaseswith pTfrom2to8%. Due to the finite size of the pTintervals, there is a mild dependenceofthecorrectionfactorsontheshapeoftheinclusive J/ψ pTdistribution used in the simulation. This is mitigated iteratively by using the corrected J/ψ pT-differential production cross section to reweight the acceptance times efficiency correction factor and obtain an updated corrected cross section. The procedure is stopped when the difference between the input and output corrected pT-differential production cross section drops below 1%, which typically occurs within 1 to 2 iterations, depending on the pTinterval. Additionally, to check if the default MC used in the analysis could introduce a bias on the EMCal trigger efficiency, due to the enhancement of J/ψ, another MC simulation, based on a di-jet production generated by PYTHIA8 [40], 123 Eur. Phys. J. C (2021) 81:1121 Page 5 of 18 1121 2.5 3 3.5 100 200 300 400 =13 TeVsALICE pp -1 = 8.3 pb EMCal int L, -1 = 32.2 nb MB int L |<0.9y, | − e + e→ ψ J/ (MB)c < 2 GeV/ ee T p1 < (EMCal)c < 20 GeV/ ee T p15 < 2× 2.5 3 3.5 0 50 100 150 (MB)c < 7 GeV/ ee T p5 < MB: Signal Correlated bkg. Combinatorial bkg. 2.5 3 3.5 (EMCal)c < 30 GeV/ ee T p25 < EMCal: Signal Total bkg. ) 2 c (GeV/ ee m 2 ccounts per 40 MeV/ Fig. 1 Invariant-mass distributions for SE e+e−pairs in two pee Tintervals from the MB event analysis (left panels) and two pee Tintervals from the EMCal-triggered event analysis (right panels). The signal and background components obtained from the fit procedure are shown separately. For the top-right panel, the distributions are scaled for convenience by a factor of 2 at √s=13 TeV, is used as a cross-check. As a result, the default MC and the di-jet MC lead to a compatible EMCal trigger efficiency. 4 Systematic uncertainties There are several sources of systematic uncertainties affecting this analysis, namely the ITS-TPC tracking, the electron identification, the signal extraction procedure, the J/ψ input kinematic distributions used in MC simulations, the determination of the integrated luminosity and the branching ratio of the dielectron decay channel. A summary of these is given in Table 1. The uncertainty of the ITS-TPC tracking efficiency is one of the dominant sources of systematic uncertainty and has two contributions: one due to the TPC-ITS matching and one related to the track-quality requirements. The former is obtained from the residual difference observed for the ITS- TPCsingle-trackmatchingbetweendataandMCsimulations [41], which is further propagated to J/ψ dielectron pairs. It varies between 2.8% and 5.4%, depending on pT. The uncertainty related to the track-quality requirements is estimated byrepeatingtheanalysiswithvariationsoftheselectioncriteria and taking the root mean square (RMS) of the distribution of the results as systematic uncertainty. This uncertainty also depends on pTand is equal to 3.7% for pT<5GeV/cand approximately 2% for pT>5GeV/c. In Table 1, both contributions are added in quadrature and provided as ranges for the pT- and y-differential results. As described in Sect. 3.3, the particle identification efficiencyisdeterminedvia adata-drivenprocedureusing asample of identified electrons from tagged photon conversions. For the MB data sample, the uncertainty of this procedure is estimated by repeating the analysis with a looser and a tighter hadron (pion and proton combined) rejection criteria and taking the largest deviation from the results obtained with the standard PID selection divided by √12. In addition, the statistical uncertainty of the pure electron sample used for the determination of the efficiency, which becomes nonnegligibleathigh pT,ispropagatedtothetotaluncertaintyfor the PID. The total PID systematic uncertainty is larger than 1% only for pT>7GeV/c, reaching 4% in the pTinterval 10 <pT<15 GeV/c. For the EMCal-triggered analysis, the particle identification systematic uncertainty has contributions from the electron identification in both the TPC and the EMCal. The values are estimated by varying the dE/dx range for the electron selection in the TPC, the E/pselection range in the EMCal, and the minimum energy of the matched clusters. The total PID uncertainty, obtained in an analogous way as for the MB sample, increases with pTfrom 2.8% to 5.4%. For pTup to 15 GeV/c, the systematic uncertainties associated to the J/ψ signal extraction procedure is dominated by the J/ψ invariant mass signal shape template used to calculate the fraction of reconstructed J/ψ mesons within the 123 1121 Page 6 of 18 Eur. Phys. J. C (2021) 81:1121 Table 1 Summary of contributions to systematic uncertainties of the measured J/ψ production cross section (in percentage) Source (pT,y)-integrated y-differential pT-differential (MB) pT-differential (EMCal) 0<pT<15 (GeV/c)15<pT<40 (GeV/c) Tracking 4.9 4.9 4.7–6.5 5.7 PID 0.6 0.6 0.0–4.1 2.8–5.4 Signal shape 1.9 1.9 1.4–2.2 1.0–4.0 Background fit 0.3 0.3–0.4 0.2–1.2 1.0–6.0 MC input 1.0 1.0 0.0–0.9 0.9 EMCal trigger Not used Not used Not used 0.5 Luminosity 1.6 1.6 1.6 2.0 Branching ratio 0.5 0.5 0.5 0.5 Total uncorrelated 0.3 0.3–0.4 0.2–1.2 1.0–6.0 Total correlated 5.4 5.4 5.2–7.4 6.5–8.8 Global 1.7 1.7 1.7 2.0 Total (w/o global) 5.4 5.4 5.3–7.5 7.0–11.0 signal counting mass window. This uncertainty amounts to 1.9% and is evaluated by repeating the extraction of the corrected yield with different invariant mass intervals used for the signal counting and taking the RMS of the variations as a systematic uncertainty. An additional source of uncertainty, due to the fit of the correlated background, is determined by varying the fit mass range and is typically below 1%. For pT>15 GeV/c, the systematic uncertainty associated to the J/ψ signal extraction are evaluated similarly to the MB analysis, however, the components associated to the signal shape and the background fit have similarly large contributions. This is one of the main sources of uncertainty in this pTrange. The total uncertainty of the signal extraction varies with pTbetween about 2 and 7%. The uncertainty on the EMCal trigger efficiency is studied varying the contribution from random noise (evaluated using energy resolution measurements in data) applied to the 4×4 groups of adjacent towers. It was also studied using the dijet production generated by PYTHIA8 at √s=13 TeV mentioned in Sect. 3.3. The latter study showed a difference in the EMCal trigger efficiency of 0.5%, which is assigned as a systematic uncertainty. Since the J/ψ efficiency has a dependence on pT, the particularJ/ψ kinematic distributionusedin the MCsimulation, from which efficiencies are derived, can have an impact on the average efficiency computed for finite pTintervals. As described in Sect. 3.3, this is mitigated via an iterative procedure and the remaining uncertainty is related to the precision of the measured J/ψ spectrum. This uncertainty is estimated by fitting the measured pTspectrum with a power law function and allowing the fitted parameters to vary according to the covariance matrix. For each of such a variation, the average efficiency in a given kinematic interval is recomputed and the RMS of the distribution obtained from the variation of efficiency with respect to the central value is taken as a systematic uncertainty. This amounts to 1% for the pT- integrated case and is smaller for all of the considered pT intervals. The uncertainty of the integrated luminosity arising from the vdM-scan based measurements amounts to 1.6% for both the MB and EMCal-triggered data samples, and is determined as described in Ref. [32]. For the EMCal-triggered data sample only, an additional uncertainty of 1.1% arising fromtheprecision ofthetriggerdownscalingis assigned.The uncertainty on the J/ψ decay branching ratio to the dielectron channel amounts to 0.53% as reported by the Particle Data Group [34]. The uncertainties of the integrated luminosity and branchingratio aretreated asglobal systematicuncertainties.All the otheruncertaintiesareconsideredas pointtopointcorrelated, with the exception of the one due to the background fit which is considered to be fully uncorrelated. The systematic uncertainties are thus dominated by correlated sources. The total correlated, uncorrelated and global uncertainties obtained as the sum in quadrature of the corresponding sources are given in Table 1. 5 Results The inclusive pT-differential J/ψ production cross section in pp collisions at √s=13 TeV at midrapidity, obtained from the combined analysis of the MB-triggered (pT<15 GeV/c) and EMCal-triggered (15 <pT<40 GeV/c) samples is shown in the upper panels of Fig. 2. Statistical uncertainties are shown as error bars, while the boxes around the data points represent the correlated and uncorrelated systematic uncertainties added in quadrature, excluding the global 123 Eur. Phys. J. C (2021) 81:1121 Page 7 of 18 1121 0 5 10 15 20 25 30 35 )c (GeV/ T p 4− 10 3− 10 2− 10 1− 10 1 ))cb/(GeV/ μ ( T pdyd σ 2 d |<0.9y| 1.6% ± -1 = 32.2 nb MB int L 2.0% ± -1 = 8.3 pb EMCal int L <4y 2.5< 3.4%± -1 = 3.2 pb int L = 13 TeVs , pp ψ ALICE, inclusive J/ 5 10152025303540 )c (GeV/ T p 0.5 1 data / mid-y fit 02468101214 )c (GeV/ T p 4− 10 3− 10 2− 10 1− 10 1 ))cb/(GeV/ μ ( T pdyd σ 2 d 1.6%± -1 = 32.2 nb int L = 13 TeV, s x 0 0.2 4%± -1 = 5.6 nb int L = 7 TeV, s x 1 0.2 2.1% ± -1 = 19.5 nb int L = 5.02 TeV, s x 2 0.2 ALICE pp |<0.9y, | ψ Inclusive J/ 2468101214 )c (GeV/ T p 0 0.5 1 data / 13 TeV fit Fig. 2 Inclusive J/ψ production cross section at midrapidity (|y|< 0.9) in pp collisions at √s=13 TeV compared with the ALICE forward-rapidity measurement at √s=13 TeV [21] (left panel) and the scaled ALICE midrapidity measurements at √s=5.02 TeV [20] and √s=7TeV[18] (right panel). The error bars represent statistical uncertainties while the boxes around the data points represent the total systematic uncertainty, excluding the global uncertainty from the luminosity and branching ratio. The lower panels show the ratio between the measurements at different rapidity and energies, and the power law fit, discussed in the text, to the J/ψ production cross section (red dashed line) at midrapidity at √s=13 TeV. The boxes in the lower panels include the systematic uncertainty of the data points and the uncertainty of the integral of the fit function in the given pTinterval added in quadrature uncertainty from luminosity determination and branching ratio. The x-axis extent of the boxes illustrates the size of the pTinterval with the data points placed in the center. A simple power law function of the type f(pT)=A×pT/(1+(pT/p0)2)n,(4) with A,p0and nbeing free parameters, is used to fit the measured distribution. Since the systematic uncertainties are largely correlated, only the statistical ones are used in the fit. DuetothelargepTintervals, the fit is performed by considering the mean value of the function in the pTinterval rather than its value at the center of the interval. The values obtained for the fitted parameters are A=2.15±0.18 μb/(GeV/c)2, p0=4.09 ±0.22 GeV/cand n=3.04 ±0.09. The fit function, shown in Fig. 2as a dashed red line, provides a good description of the data points measured with both MB and EMCal data samples, and illustrates the consistency between the two analyses. In the left panel of Fig. 2, the production cross section measured at midrapidity is compared with the forward rapidity measurement at the same energy [21]. The bottom panel shows the ratio between the forward rapidity data points and the mean cross section at midrapidity obtained by integrating the fit function described above in the pTintervals of the forward-rapidity measurement. The displayed uncertainty boxes include the systematic uncertainty of the forward rapidity measurement and the uncertainty of the function mean, added in quadrature. A monotonic drop of this ratio can be observed towards high pT, indicating a harder J/ψ pTdistribution at midrapidity. The right panel of Fig. 2shows a comparison with midrapidity measurements performed by the ALICE Collaboration inppcollisionsatthelowercollisionenergiesof√s=7TeV [18]and5.02TeV [20].Inthebottompanel,theratiobetween the lower energy measurements and the fitted 13 TeV results is shown. The displayed uncertainty boxes include the systematic uncertainty of the lower energy data points and the uncertainty of the fit function mean, added in quadrature. Although the uncertainties of the measurement at 7 TeV are large, the data indicates an increase of the production cross section with increasing collision energy. In addition, the monotonic drop of the ratio between the 5.02 TeV and 13 TeV measurements indicates a hardening of the pTspectrum with increasing collision energy, as also observed from the energy dependence of the inclusive J/ψ average pTdiscussed in Ref. [20]. The measured inclusive J/ψ production cross section is compared with several phenomenological calculations of the prompt J/ψ production in the left panel of Fig. 3.In addition, to illustrate the impact of the unaccounted feeddown from beauty decays in the theory predictions, a calculation of the non-prompt J/ψ production by Cacciari et al., using the Fixed-Order Next-to-Leading-Logarithms approach(FONLL) [45], isshowninthesamepanel. Accord- 123 1121 Page 8 of 18 Eur. Phys. J. C (2021) 81:1121 0 5 10 15 20 25 30 35 40 )c (GeV/ T p 4− 10 3− 10 2− 10 1− 10 1 ))cb/(GeV/ μ ( T pdyd σ 2 d ψ prompt J/ ICEM NRQCD + CGC NRQCD NRQCD CS + CO factorization T kNRQCD from b ψ J/ FONLL = 13 TeV sALICE pp |<0.9y, | ψ Inclusive J/ 1.6%± -1 = 32.2 nb MB int L 2.0%± -1 = 8.3 pb EMCal int L 0 5 10 15 20 25 30 35 4− 10 3− 10 2− 10 1− 10 1 ))cb/(GeV/ μ ( T pdyd σ 2 d ψ inclusive J/ ICEM NRQCD + CGC NRQCD NRQCD CS + CO factorization T kNRQCD from b, FONLL, added) ψ (J/ = 13 TeV sALICE pp |<0.9y, | ψ Inclusive J/ 1.6%± -1 = 32.2 nb MB int L 2.0%± -1 = 8.3 pb EMCal int L 0 5 10 15 20 25 30 35 40 )c (GeV/ T p 1 2 3 4 model / 13 TeV fit Fig. 3 Inclusive J/ψ production cross section compared with calculations for the prompt J/ψ production cross section using ICEM [42], NLO NRQCD [3,4,43], LO NRQCD + CGC [44] and for the nonprompt J/ψ from beauty-hadron feed-down using FONLL [45](left panel). Inclusive J/ψ production cross section compared with the corresponding calculations obtained as the sum of the prompt J/ψ component shown in the left panel and the non-prompt contribution from FONLL (right panel). The bottom panel shows the ratios between the model calculations and a fit to the data points. The bands illustrate the theoretical uncertainties centered around the ratio between the model calculation and the power-law fit to the data (see text for details) ing to the FONLL calculations, the non-prompt contribution to the inclusive J/ψ yield is approximately 10% at lowpTand grows to approximately 50% at pT=40GeV/c.In the right panel of Fig. 3, the measured inclusive production cross section is compared to predictions for inclusive J/ψ production obtained as the sum of the prompt J/ψ calculations listed above and the beauty feed-down contribution calculated using FONLL. The bottom panel shows the ratio between each theoretical calculation and the fit to the data. The colored bands represent the theoretical uncertainties for each model, centered around the model to data ratio. These uncertainties are typically due to the variation of the renormalization and factorization scales, and of the charm quark mass. Several phenomenological approaches are used for the calculation of the J/ψ yields shown in Fig. 3. The green and blue dashed lines represent NLO NRQCD calculations from Ma et al. [4] and Butenschoen et al. [3], respectively, using collinear gluon parton distribution functions (PDFs). Although the calculation of the short distance terms is very similar, the predictions of these two approaches differ due to the LDME sets which are obtained in separate fits of the Tevatron and HERA data with different low-pTcut- offs. In addition, the calculation from Ref. [3] does not include the feed-down from higher mass charmonium states. The brown solid line represents a calculation obtained with the MC generator PEGASUS [43] developed by Lipatov et al. which employs a kT-factorization approach using pT- dependent gluon distribution functions and NRQCD matrix elements combined with LDMEs extracted from an NLO high-transverse momentum analysis [8]. Using the KMR [46] technique to construct the unintegrated gluon PDFs, this calculation can extend down to J/ψ pT=0. A different model to calculate the low pTJ/ψ production cross section, by Ma and Venugopalan [44] (green solid line) is based on a Color-Glass Condensate (CGC) approach coupled to a Leading Order (LO) NRQCD calculation which includes a soft-gluon resummation. The calculations obtained using the ICEM model by Cheung and Vogt [42] within the kT- factorization approach are shown by the violet solid line. In this calculation, LDMEs are not used, however one normalization parameter per charmonium state is used to account for long distance effects [47]. The feed down from the higher mass charmonium states is taken into account in this model. As shown in the right panel of Fig. 3, all the models provide a reasonable description of the inclusive J/ψ production cross section within the theoretical uncertainties over the entire pTrange covered by this measurement. In particular, both the ICEM and NRQCD + CGC calculations show very good agreement with the data in the low-pTrange. 123 Eur. Phys. J. C (2021) 81:1121 Page 15 of 18 1121 X. Zhang7, Y. Zhang131, V. Zherebchevskii115,Y.Zhi 11, N. Zhigareva95, D. Zhou7, Y. Zhou92,J.Zhu 7,110,Y.Zhu 7, A. Zichichi26, G. Zinovjev3,N.Zurlo 59,142 1A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation, Yerevan, Armenia 2AGH University of Science and Technology, Cracow, Poland 3Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Kiev, Ukraine 4Department of Physics and Centre for Astroparticle Physics and Space Science (CAPSS), Bose Institute, Kolkata, India 5Budker Institute for Nuclear Physics, Novosibirsk, Russia 6California Polytechnic State University, San Luis Obispo, CA, USA 7Central China Normal University, Wuhan, China 8Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana, Cuba 9Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City and Mérida, Mexico 10 Chicago State University, Chicago, IL, USA 11 China Institute of Atomic Energy, Beijing, China 12 Chungbuk National University, Cheongju, Republic of Korea 13 Faculty of Mathematics Physics and Informatics, Comenius University Bratislava, Bratislava, Slovakia 14 COMSATS University Islamabad, Islamabad, Pakistan 15 Creighton University, Omaha, NE, USA 16 Department of Physics, Aligarh Muslim University, Aligarh, India 17 Department of Physics, Pusan National University, Pusan, Republic of Korea 18 Department of Physics, Sejong University, Seoul, Republic of Korea 19 Department of Physics, University of California, Berkeley, CA, USA 20 Department of Physics, University of Oslo, Oslo, Norway 21 Department of Physics and Technology, University of Bergen, Bergen, Norway 22 Dipartimento di Fisica dell’Università ’La Sapienza’ and Sezione INFN, Rome, Italy 23 Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy 24 Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy 25 Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy 26 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Bologna, Italy 27 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Catania, Italy 28 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Padua, Italy 29 Dipartimento di Fisica e Nucleare e Teorica, Università di Pavia, Pavia, Italy 30 Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo Collegato INFN, Salerno, Italy 31 Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy 32 Dipartimento di Scienze e Innovazione Tecnologica dell’Università del Piemonte Orientale and INFN Sezione di Torino, Alessandria, Italy 33 Dipartimento di Scienze MIFT, Università di Messina, Messina, Italy 34 Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari, Italy 35 European Organization for Nuclear Research (CERN), Geneva, Switzerland 36 Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, Split, Croatia 37 Faculty of Engineering and Science, Western Norway University of Applied Sciences, Bergen, Norway 38 Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Prague, Czech Republic 39 Faculty of Science, P.J. Šafárik University, Košice, Slovakia 40 Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany 41 Fudan University, Shanghai, China 42 Gangneung-Wonju National University, Gangneung, Republic of Korea 43 Department of Physics, Gauhati University, Guwahati, India 44 Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, Germany 45 Helsinki Institute of Physics (HIP), Helsinki, Finland 46 High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico 47 Hiroshima University, Hiroshima, Japan 48 Hochschule Worms, Zentrum für Technologietransfer und Telekommunikation (ZTT), Worms, Germany 49 Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania 123 1121 Page 16 of 18 Eur. Phys. J. C (2021) 81:1121 50 Indian Institute of Technology Bombay (IIT), Mumbai, India 51 Indian Institute of Technology Indore, Indore, India 52 Indonesian Institute of Sciences, Jakarta, Indonesia 53 INFN, Laboratori Nazionali di Frascati, Frascati, Italy 54 INFN, Sezione di Bari, Bari, Italy 55 INFN, Sezione di Bologna, Bologna, Italy 56 INFN, Sezione di Cagliari, Cagliari, Italy 57 INFN, Sezione di Catania, Catania, Italy 58 INFN, Sezione di Padova, Padua, Italy 59 INFN, Sezione di Pavia, Pavia, Italy 60 INFN, Sezione di Roma, Rome, Italy 61 INFN, Sezione di Torino, Turin, Italy 62 INFN, Sezione di Trieste, Trieste, Italy 63 Inha University, Incheon, Republic of Korea 64 Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University/Nikhef, Utrecht, The Netherlands 65 Institute for Nuclear Research, Academy of Sciences, Moscow, Russia 66 Institute of Experimental Physics, Slovak Academy of Sciences, Košice, Slovakia 67 Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India 68 Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic 69 Institute of Space Science (ISS), Bucharest, Romania 70 Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany 71 Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Mexico City, Mexico 72 Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Brazil 73 Instituto de Física, Universidad Nacional Autónoma de México, Mexico City, Mexico 74 iThemba LABS, National Research Foundation, Somerset West, South Africa 75 Jeonbuk National University, Jeonju, Republic of Korea 76 Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik, Fachbereich Informatik und Mathematik, Frankfurt, Germany 77 Joint Institute for Nuclear Research (JINR), Dubna, Russia 78 Korea Institute of Science and Technology Information, Daejeon, Republic of Korea 79 KTO Karatay University, Konya, Turkey 80 Laboratoire de Physique des 2 Infinis, Irène Joliot-Curie, Orsay, France 81 Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-Alpes, CNRS-IN2P3, Grenoble, France 82 Lawrence Berkeley National Laboratory, Berkeley, CA, USA 83 Division of Particle Physics, Department of Physics, Lund University, Lund, Sweden 84 Moscow Institute for Physics and Technology, Moscow, Russia 85 Nagasaki Institute of Applied Science, Nagasaki, Japan 86 Nara Women’s University (NWU), Nara, Japan 87 Department of Physics, School of Science, National and Kapodistrian University of Athens, Athens, Greece 88 National Centre for Nuclear Research, Warsaw, Poland 89 National Institute of Science Education and Research, Homi Bhabha National Institute, Jatni, India 90 National Nuclear Research Center, Baku, Azerbaijan 91 National Research Centre Kurchatov Institute, Moscow, Russia 92 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark 93 Nikhef, National Institute for Subatomic Physics, Amsterdam, The Netherlands 94 NRC Kurchatov Institute IHEP, Protvino, Russia 95 NRC «Kurchatov»Institute-ITEP, Moscow, Russia 96 NRNU Moscow Engineering Physics Institute, Moscow, Russia 97 Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, UK 98 Nuclear Physics Institute of the Czech Academy of Sciences, ˇ Rež u Prahy, Czech Republic 99 Oak Ridge National Laboratory, Oak Ridge, TN, USA 100 Ohio State University, Columbus, OH, USA 101 Petersburg Nuclear Physics Institute, Gatchina, Russia 123 Eur. Phys. J. C (2021) 81:1121 Page 17 of 18 1121 102 Physics Department, Faculty of Science, University of Zagreb, Zagreb, Croatia 103 Physics Department, Panjab University, Chandigarh, India 104 Physics Department, University of Jammu, Jammu, India 105 Physics Department, University of Rajasthan, Jaipur, India 106 Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen, Germany 107 Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany 108 Physik Department, Technische Universität München, Munich, Germany 109 Politecnico di Bari and Sezione INFN, Bari, Italy 110 Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany 111 Russian Federal Nuclear Center (VNIIEF), Sarov, Russia 112 Saha Institute of Nuclear Physics, Homi Bhabha National Institute, Kolkata, India 113 School of Physics and Astronomy, University of Birmingham, Birmingham, UK 114 Sección Física, Departamento de Ciencias, Pontificia Universidad Católica del Perú, Lima, Peru 115 St. Petersburg State University, St. Petersburg, Russia 116 Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria 117 SUBATECH, IMT Atlantique, Université de Nantes, CNRS-IN2P3, Nantes, France 118 Suranaree University of Technology, Nakhon Ratchasima, Thailand 119 Technical University of Košice, Košice, Slovakia 120 The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland 121 The University of Texas at Austin, Austin, TX, USA 122 Universidad Autónoma de Sinaloa, Culiacán, Mexico 123 Universidade de São Paulo (USP), São Paulo, Brazil 124 Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil 125 Universidade Federal do ABC, Santo Andre, Brazil 126 University of Cape Town, Cape Town, South Africa 127 University of Houston, Houston, TX, USA 128 University of Jyväskylä, Jyväskylä, Finland 129 University of Kansas, Lawrence, KS, USA 130 University of Liverpool, Liverpool, UK 131 University of Science and Technology of China, Hefei, China 132 University of South-Eastern Norway, Tonsberg, Norway 133 University of Tennessee, Knoxville, TN, USA 134 University of the Witwatersrand, Johannesburg, South Africa 135 University of Tokyo, Tokyo, Japan 136 University of Tsukuba, Tsukuba, Japan 137 Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France 138 Institut de Physique des 2 Infinis de Lyon, Université de Lyon, CNRS/IN2P3, Lyon, France 139 Université de Strasbourg, CNRS, IPHC UMR 7178, 67000 Strasbourg, France 140 Départment de Physique Nucléaire (DPhN), Université Paris-Saclay Centre d’Etudes de Saclay (CEA), IRFU, Saclay, France 141 Università degli Studi di Foggia, Foggia, Italy 142 Università di Brescia, Brescia, Italy 143 Variable Energy Cyclotron Centre, Homi Bhabha National Institute, Kolkata, India 144 Warsaw University of Technology, Warsaw, Poland 145 Wayne State University, Detroit, MI, USA 146 Institut für Kernphysik, Westfälische Wilhelms-Universität Münster, Münster, Germany 147 Wigner Research Centre for Physics, Budapest, Hungary 148 Yale University, New Haven, CT, USA 149 Yonsei University, Seoul, Republic of Korea aAlso at: Italian National Agency for New Technologies, Energy and Sustainable Economic Development (ENEA), Bologna, Italy 123 1121 Page 18 of 18 Eur. Phys. J. C (2021) 81:1121 bAlso at: Dipartimento DET del Politecnico di Torino, Turin, Italy cAlso at: M.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute of Nuclear Physics, Moscow, Russia dAlso at: Department of Applied Physics, Aligarh Muslim University, Aligarh, India eAlso at: Institute of Theoretical Physics, University of Wroclaw, Wroclaw, Poland fAlso at: University of Kansas, Lawrence, KS, USA gDeceased 123