Observation of Enhanced Double Parton Scattering in Proton-Lead Collisions at sNN =8.16 TeV

A study of prompt charm-hadron pair production in proton-lead collisions at is performed using data corresponding to an integrated luminosity of about 30 nb − 1 , collected with the LHCb experiment. Production cross sections for different pairs of charm hadrons are measured and kinematic correlations between the two charm hadrons are investigated. This is the first measurement of associated production of two charm hadrons in proton-lead collisions. The results confirm the predicted enhancement of double parton scattering production in proton-lead collisions compared to the single parton scattering production.


Observation of Enhanced Double Parton Scattering in Proton-Lead
Collisions at ffiffiffiffiffiffiffi ffi s NN p = 8.16 TeV R. Aaij et al. * (LHCb Collaboration) (Received 13 July 2020;revised 4 September 2020;accepted 14 October 2020;published 20 November 2020) A study of prompt charm-hadron pair production in proton-lead collisions at ffiffiffiffiffiffiffi ffi s NN p ¼ 8.16 TeV is performed using data corresponding to an integrated luminosity of about 30 nb −1 , collected with the LHCb experiment. Production cross sections for different pairs of charm hadrons are measured and kinematic correlations between the two charm hadrons are investigated. This is the first measurement of associated production of two charm hadrons in proton-lead collisions. The results confirm the predicted enhancement of double parton scattering production in proton-lead collisions compared to the single parton scattering production. DOI: 10.1103/PhysRevLett.125.212001 At high-energy hadron colliders, particles are produced in fundamental collisions of internal partons in the beam projectiles. The underlying parton densities are described by parton distribution functions (PDFs). A collision event can produce multiple heavy-flavor hadrons via a single parton scattering (SPS) or multiple parton scatterings. The latter, generating on average a larger number of charged tracks, could explain the heavy-flavor production rate in high-multiplicity events [1][2][3][4]. In a simple model, assuming that the PDFs of two partons in the same projectile are independent, the associated production cross section of final-state particles A and B from two separate partonic interactions, i.e., a double parton scattering (DPS) process, is related to the inclusive production cross section of A and B, σ A and σ B , as [5][6][7][8][9][10][11][12][13][14], Here, δ AB ¼ 1 if A and B are identical and is zero otherwise, and σ eff is the so-called effective cross section. The parameter σ eff is related to the collision geometry and is expected to be independent of the final state [15][16][17]. In proton-ion collisions, following the Glauber model [18], SPS production cross section is expected to scale with the ion mass number in the absence of nuclear matter effects. However, DPS production is enhanced compared to a mass number scaling due to collisions of partons from two different nucleons in the ion, and the enhancement factor is about three in proton-lead (p-Pb) collisions [10,[19][20][21][22][23][24][25].
The production of two open charm hadrons, D 1 D 2 , and J=ψD meson pairs is of particular interest in the study of SPS and DPS processes, as the cross section is relatively large and the high charm-quark mass permits perturbative calculations even at low transverse momentum (p T ). In this Letter, D and D 1;2 refer to either a D 0 , D þ , or D þ s meson and the inclusion of charge conjugate states is implied. Both like-sign (LS) and opposite-sign (OS) open charm hadron pairs are considered. In an LS pair the two hadrons have the same charm-quark flavor, while in an OS pair they have opposite charm flavors. Pairs of OS charm hadrons can be produced from a cc pair via SPS, thus the kinematics of the two hadrons are correlated, while DPS produces correlated and uncorrelated OS pairs. The correlation in SPS production may be modified in heavy-ion data compared to proton-proton (pp) collisions, due to nuclear matter effects [26][27][28][29][30][31][32][33]. The OS correlation is predicted to be sensitive to the properties of the hot medium formed in ultrarelativistic heavy nucleus-nucleus collisions [34][35][36][37][38][39][40][41][42][43][44].
The two hadrons in an LS pair produced in a DPS process are expected to be uncorrelated. Studies of LS pair production and correlation in different environments help to test the universality of the parameter σ eff and gain insight into the underlying parton correlations [45]. Since DPS production involves two parton pairs, it is very sensitive to the nuclear PDF (NPDF) in proton-ion collisions, including its possible dependence on the position inside the nucleus [46].
Production of OS charm and beauty pairs has been studied in fully reconstructed decays [47-51] and using partially reconstructed decays [52][53][54][55][56][57][58][59], and the hadron and antihadron are found to be correlated; in particular, the azimuthal angle Δϕ between the two hadron directions projected to the plane transverse to the beam line favors values close to Δϕ ¼ 0 or π. Production of LS charm pairs, double quarkonium and multiple jets at the Tevatron and the LHC revealed evidence of DPS signals [51,[60][61][62][63][64][65][66][67][68]. The effective cross section is measured to be in the range of 10 to 20 mb for most final states, however, a value as low as 5 mb is extracted using double quarkonium production [69][70][71]. More measurements are required to resolve this puzzle.
This Letter presents the first measurement of charm pair production in proton-lead collisions at a nucleon-nucleon center-of-mass energy of ffiffiffiffiffiffiffi ffi s NN p ¼ 8.16 TeV. The data were collected with the LHCb experiment at a low interaction rate in two distinct beam configurations. In the pPb configuration, particles produced in the direction of the proton beam are analyzed, while in the Pbp configuration particles are analyzed in the Pb beam direction. The pPb (Pbp) data correspond to an integrated luminosity of 12.2 AE 0.3 nb −1 (18.6 AE 0.5 nb −1 ). The detector coordinate system is defined to have the z axis aligned with the proton beam direction. In the following, particle rapidities (y) are defined in the nucleon-nucleon rest frame.
The LHCb detector is a single-arm forward spectrometer described in detail in Refs. [72,73]. The online event selection is performed by a trigger, which consists of a hardware stage, based on information from the calorimeter and muon systems, followed by a software stage, which applies a full event reconstruction. Charm hadrons and J=ψ → μ þ μ − . The data samples are selected by the hardware trigger based on the calorimeter activity for D candidates and based on the muon system for J=ψ candidates. Candidate pairs are formed by D 0 D 0 , D 0D0 , and D þ D AE combinations (same species), and D 0 D AE , D 0 D AE s , D þ D AE s , and J=ψD 0;þ combinations (different species). Other charm pairs are not considered due to their limited yield in the data. The tracks used to reconstruct the D mesons are required to be positively identified as kaons or pions and must be separated from every primary p-Pb collision vertex (PV). These tracks are also required to have p T > 250 MeV=c and at least one track must have p T > 500 MeV=c (p T > 1000 MeV=c) for D 0 (D þ , D þ s ) final states. The tracks are required to form a vertex of good quality that is separated from every PV. The reconstructed D mesons are required to be consistent with originating from a PV, which favors prompt production over mesons from beauty-hadron decays (denoted as charm-from-b). The two muons used to reconstruct J=ψ candidates are required to have p T > 500 MeV=c and form a goodquality vertex.
In the off-line selection, kaons and pions are required to have momentum p > 3 GeV=c, and muons to have p > 6 GeV=c, p T > 750 MeV=c and be positively identified by using information from all subdetectors [74,75].
The K − K þ invariant mass from the D þ s → K − K þ π þ decay is required to be within AE20 MeV=c 2 of the known ϕð1020Þ mass [76]. A kinematic fit is performed on each charm hadron and on the pair, constraining them to originate from a PV. Requirements on the fit qualities strongly reduce charm-from-b contributions but retain more than 99% of prompt pairs.
The cross section for a charm pair is calculated as where L is the integrated luminosity, and N corr is the signal yield after efficiency correction and the subtraction of charm-from-b background. The branching fractions of the two charm-hadron decays B 1;2 are taken from Ref. [76] for the D 0 , D þ , J=ψ decays, and B½D þ s → ðK þ K − Þ ϕ π þ ¼ ð2.24 AE 0.13Þ% from Refs. [79,80]. The raw signal yield is determined from an unbinned maximum likelihood fit to the distribution of the invariant masses m 1 and m 2 of the two charm hadrons. The two-dimensional probability densities comprise four components: signal-signal, background-background, signal-background, and background-signal for the first-second charm hadron in a pair. The background is mainly from random combinations of tracks. The signal component for each charm hadron is described by the sum of a Gaussian and a Crystal Ball function [81] and the background component by an exponential function. The distribution for pairs of same-species hadrons is constructed to be independent of the ordering of m 1 and m 2 . As an example, the ðm 1 ; m 2 Þ distribution for D 0 D 0 candidates and its projection on m 1 and m 2 are shown in Fig. 1 for pPb data, with the fit projections overlaid. More distributions are shown in the Supplemental Material [82]. The raw signal yield is between 100 and 4000 for all hadron pairs considered.
The total detection efficiency for each individual charm hadron is evaluated from simulated signal decays, properly corrected using control samples of p-Pb collisions. These control samples are used to calibrate track finding and particle identification (PID) efficiencies [83]. In the simulation, minimum-bias p-Pb collisions are produced using the EPOS generator [84] according to beam configurations of the data. Charm hadrons are generated in pp collisions at ffiffi ffi s p ¼ 8.16 TeV using PYTHIA8 [85,86] and are embedded finding efficiency in data and simulation is studied with a tag-and-probe method using J=ψ → μ þ μ − decays [90]. Similarly, the PID efficiency is measured using large control samples of D 0 → K − π þ and J=ψ → μ þ μ − decays for K − , π þ , and μ − tracks, in bins of track momentum and pseudorapidity ðp; ηÞ. The average charged-track multiplicity in OS data is similar to the one in the control samples, while for LS data it is about 13% higher, which is consistent with a larger contribution of multiple parton scattering in LS data [1][2][3][4]. The corresponding difference in detector occupancy results in different detection efficiencies in LS and OS data, which is evaluated in control samples. Efficiencies from control samples are combined with simulation to obtain the efficiency for each charm hadron as a function of p T and y, ϵðp T ; yÞ, which is used to determine the efficiency corrected signal yield P i ½w i =ϵ 1 ðp i T ; y i Þϵ 2 ðp i T ; y i Þ. Here, w i is the signal sPlot weight [91] used to remove the contribution of background and is obtained from the fit to the invariant-mass distribution, and ϵ 1;2 ðp T i ; y i Þ is the efficiency for the first and second hadron in the ith candidate pair in data. The signal yield is then corrected for the charm-from-b contamination, which is estimated to be less than 1% for open charm pairs and ð4 AE 2Þ% (ð3.0 AE 1.5Þ%) for J=ψD pairs in pPb (Pbp) data.
Several sources of systematic uncertainties are investigated. The variation of the signal yield is studied with fits to the invariant-mass distribution using a different signal or background model. A maximum relative variation of 2% is obtained on the signal yield. The dominant systematic uncertainty arises from the limited control sample size to determine the track finding efficiency, which is on average about 5% (10%) per track in pPb (Pbp) data. An uncertainty of 2% per hadron track is introduced to account for the loss of particles due to interactions with the detector material. Because of the small sample size and the choice of ðp; ηÞ binning for each track, the PID efficiencies obtained from control samples introduce an uncertainty of less than 1% on the total efficiency of each charm hadron. Other contributions include the uncertainty on the total efficiency due to the size of the simulation sample, the uncertainty on the charm decay branching fractions, the uncertainty on the luminosity measurements and on the charm-from-b fraction. These uncertainties are propagated to the cross-section measurements.
Total cross sections are determined for all charm pairs. Results are detailed in the Supplemental Material [82]. For LS open charm pairs, the measurements are in good agreement with theoretical calculations including both SPS and DPS production [24]. The J=ψD 0 cross section is found to be generally higher than SPS production, calculated using the weighted EPPS16 NPDF [92][93][94][95].
Prompt single charm cross sections in pPb data were measured to be smaller than those of Pbp data [78,96], which is explained by modifications of the NPDF. The same effect would result in even stronger suppression of DPS production in pPb compared to Pbp data due to the participation of two pairs of partons. For charm pairs, the cross-section ratio between pPb and Pbp data, the forward-backward ratio (R FB ), is determined for 2.7 < jyðH c Þj < 3.7; p T ðH c Þ > 2 GeV=c, to be 0.40 AE 0.05 AE 0.10 (0.61 AE 0.04 AE 0.12) averaged over LS (OS) open charm pairs, and is 0.26 AE 0.06 AE 0.04 for J=ψD pairs. Here and in the following, the first uncertainty is statistical and the second is systematic. The results indicate reduced production in pPb compared to Pbp data for both LS and OS pairs. The R FB of OS production is compatible with that of prompt D 0 mesons [78,96], while that of LS production is smaller. The ratio between the R FB of LS and OS production, 0.66 AE 0.09 AE 0.03, is in good agreement with the R FB of OS data and the R FB of prompt D 0 production. The measurements favor the interpretation of LS production via DPS.
The LS over OS cross-section ratio, R D 1 D 2 ≡ σ D 1 D 2 =σ D 1D2 , is determined for all studied D 1 D 2 pairs under the p T ðDÞ > 2 GeV=c requirement, giving an average value of 0.308 AE 0.015 AE 0.010 and 0.391 AE 0.019 AE 0.025 for pPb and Pbp data, respectively. The measurements agree with the calculations in Ref. [24] of 0.57 þ0.16 pairs in p-Pb collisions. The differential results as a function of yðH c Þ is shown in the Supplemental Material [82].
The correlations of kinematics between the two charm hadrons in a pair are investigated from the distributions of the two-charm invariant mass (m DD ) and their relative azimuthal angle Δϕ. The differential cross section for each variable is normalized by the total cross section, such that the largest systematic uncertainty, the one from the track finding efficiency, almost completely cancels. As examples, in Fig. 2, the m DD distribution is shown for D 0 D 0 and D 0D0 pairs without any requirement on p T ðDÞ. The difference between D 0 D 0 and D 0D0 pairs is determined to be more than three (two) standard deviations in pPb (Pbp) data, studied using a χ 2 test. For both D 0 D 0 and D 0D0 pairs, the m DD distribution is compatible between pPb and Pbp data. The D 0D0 pair shows a similar m DD distribution to that of the PYTHIA8 simulation, in which the fraction of inclusive charm production that contains more than one charm pair within the LHCb acceptance is about 7%.
The Δϕ distribution is shown in Fig. 3 for D 0 D 0 and D 0D0 pairs with and without the requirement p T ðD 0 Þ > 2 GeV=c. Without this condition, the Δϕ distribution is almost uniform for both LS and OS pairs, similar to that in PYTHIA8 simulation. However, with the  p T ðD 0 Þ > 2 GeV=c requirement, the D 0D0 pair favors values Δϕ ∼ 0, while that of D 0 D 0 pairs is still compatible with being flat, and both show inconsistency with the PYTHIA8 simulation. In general, the behavior that m DD distribution in D 0 D 0 pairs peaks at higher values compared to that of D 0D0 pairs and the flat D 0 D 0 Δϕ distribution are qualitatively consistent with a large DPS contribution in LS pair production. Distributions of the pair transverse momentum and the two-charm relative rapidity are found to be compatible in OS data, LS data, and the PYTHIA8 simulation.
The effective cross section σ eff;pPb is calculated according to Eq. (1) using the D 0 D 0 and J=ψD 0 cross sections [6], assuming solely DPS production, where the prompt J=ψ and D 0 production are evaluated from LHCb measurements [77,78]. The results are displayed in Table I with a typical value of order 1b. Table I ("pp extrapolation") also provides the σ eff;pp result [80] scaled by the Pb nucleus mass number 208, which is valid under the assumption of SPS production and absence of nuclear modification. The result confirms the expectation that DPS production in p-Pb collisions is enhanced by a factor of 3 compared to SPS production, consistent with the expectation from the Glauber model. The σ eff;pPb value measured using J=ψD 0 production is smaller than that observed in D 0 D 0 production, as measured in pp data [80], which may be due to SPS contamination [97] or more than expected J=ψD 0 DPS production. The pPb data show a higher σ eff;pPb value compared to Pbp data, which may suggest a complicated structure of the NPDF, as studied in Ref. [46].
The nuclear modification factor, R ≡ σ pPb =208σ pp , is measured for J=ψD 0 and D 0 D 0 pairs with R H c H 0 c ¼ R H c × R H 0 c × 208σ eff;pp =σ eff;pPb , where σ pPb and σ pp are the cross sections of charm pairs in p-Pb and pp collisions, respectively. Assuming variations of R and σ eff;pp as a function of collision energy are small for p T -integrated production, using measurements of σ eff;pp [51], R J=ψ [77], and R D 0 [96], R D 0 D 0 ¼ 1.3 AE 0.2 (4.2 AE 0.8) and R J=ψD 0 ¼ 1.5 AE 0.5 (4.6 AE 1.3) for pPb (Pbp) data are obtained, where the uncertainties are the total. The results are about a factor of 3 larger compared to that of single J=ψ or D 0 hadron production [77,96].
To summarize, the production of LS and OS open charm hadron pairs as well as J=ψD pairs are studied in p-Pb collisions at ffiffiffiffiffiffiffi ffi s NN p ¼ 8.16 TeV using fully reconstructed decays. The cross-section ratio between LS and OS pairs is found to be a factor of 3 higher than that in pp data.
The forward-backward ratio of OS pairs is compatible with single charm production, while a smaller value is found for LS pairs. Distributions of the two-charm invariant mass and relative azimuthal angle show a difference between LS and OS pairs, and the LS pairs exhibit a flat relative azimuthal angle distribution independent of charm hadron p T . The effective cross-section and nuclear modification factor for J=ψD 0 and D 0 D 0 are in general compatible with the expected enhancement factor of 3 for DPS over SPS production ratio from pp to p-Pb collisions. This is the first direct observation of such an enhancement using LS charm production in p-Pb data. The σ eff;pPb result is different between pPb and Pbp data and between J=ψD 0 and D 0 D 0 pairs may suggest additional effects not considered yet, which deserve further investigation using future LHCb data samples.
We would like to thank Hannu Paukkunen and Huasheng Shao for providing theoretical predictions and helpful discussions. We express our gratitude to our colleagues in the CERN accelerator departments for the excellent performance of the LHC. We thank the technical and administrative staff at the LHCb institutes. We acknowledge support from CERN and from the national agencies:  I. The effective cross section σ eff;pPb (in b) measured using J=ψD 0 and D 0 D 0 pair production in p-Pb data and the extrapolated values from pp data [80].