Dilepton mass spectra in p+p collisions at sqrt(s)= 200 GeV and the contribution from open charm

The PHENIX experiement has measured the electron-positron pair mass spectrum from 0 to 8 GeV/c^2 in p+p collisions at sqrt(s)=200 GeV. The contributions from light meson decays to e^+e^- pairs have been determined based on measurements of hadron production cross sections by PHENIX. They account for nearly all e^+e^- pairs in the mass region below 1 GeV/c^2. The e^+e^- pair yield remaining after subtracting these contributions is dominated by semileptonic decays of charmed hadrons correlated through flavor conservation. Using the spectral shape predicted by PYTHIA, we estimate the charm production cross section to be 544 +/- 39(stat) +/- 142(syst) +/- 200(model) \mu b, which is consistent with QCD calculations and measurements of single leptons by PHENIX.

Abstract PHENIX has measured the electron-positron pair mass spectrum from 0 to 8 GeV/c 2 in p+p collisions at √ s = 200 GeV. The contributions from light meson decays to e + e − pairs have been determined based on measurements of hadron production cross sections by PHENIX. They account for nearly all e + e − pairs in the mass region below ∼1 GeV/c 2 . The e + e − pair yield remaining after subtracting these contributions is dominated by semileptonic decays of charmed hadrons correlated through flavor conservation. Using the spectral shape predicted by PYTHIA, we estimate the charm production cross section to be 544 ± 39(stat) ± 142(syst) ± 200(model) µb, which is consistent with QCD calculations and measurements of single leptons by PHENIX.
Because of the large mass of the charm quark, approximately 1.3 GeV/c 2 , it is commonly expected that the charm production cross section can be calculated in quantum chromo dynamics (QCD) using perturbative methods (pQCD). Comparing such calculations with experimental data serves as a test of pQCD and helps to quantify the importance of higher order terms. Perturbative calculations suggest that charm production at RHIC energies results primarily from gluon fusion, so charm can probe gluonic interactions in the matter formed in heavy ion collisions at RHIC [1]. Medium modifications of heavy quark production and the suppression of bound charmonium states like the J/ψ have received considerable attention and are thought to be keys to better understanding properties of strongly interacting matter. Experiments at RHIC with polarized proton beams will allow the measurement of spin asymmetries in charm production, which gives access to the spin contribution of the gluons to the proton in a new channel [2].
To date, charm production has been calculated in next-to-leading-order (NLO) and fixed-order plus next-to-leading-log approximations (FONLL) [3]. These calculations are consistent with the measured D meson cross sections in 1.96 TeV pp collisions published by CDF [4] as well as with single lepton measurements, electrons [5] and muons [6], in 200 GeV p+p collisions from PHENIX. However, the theoretical uncertainties are considerable, at least a factor of two [3] or even larger [7], and the data prefer larger cross sections within these uncertainties 3 . In this Letter we present a different method to determine the charm cross section using electron-positron pairs measured with PHENIX during the RHIC p+p run in 2005.
Electrons are measured in the two PHENIX central arm spectrometers [10], which each cover |η| ≤ 0.35 in pseudo-rapidity and ∆φ = π/2 in azimuth in a nearly back-to-back configuration. For charged particles drift chambers (DC) measure the deflection angles in a magnetic field to determine their momenta. Ring imaging Cerenkov counters (RICH) as well as electromagnetic calorimeters (EMCal) distinguish electrons from other particles. The electron 1 Deceased 2 PHENIX Spokesperson: jacak@skipper.physics.sunysb.edu 3 The STAR collaboration reports an even larger cross section [8,9], which is about a factor of 2-3 above of what can be accommodated in pQCD calculations.
analysis is described in detail in [5].
Two data sets are used in the analysis. A reference sample of events was selected with a minimum bias interaction trigger (MB) that was based on beam-beam counters (BBC). The BBC trigger cross section is 23.0±2.2 mb or 55% of the inelastic p+p cross section. Simulations, and data collected without requiring the BBC trigger, indicate that the triggered events include 79% of events with particles in the central arm acceptance. This number coincides with the fraction of non-diffractive events triggered by the BBC. The bulk of the data sample was recorded requiring a coincidence of the BBC trigger with a single electron trigger (ERT) that matches hits in the RICH to 2x2 trigger tiles in the EMCal with a minimum energy of 400 MeV/c. In the active area the ERT trigger has a very high efficiency for electrons; around 500 MeV/c it reaches approximately 50% and then saturates around 1 GeV/c close to 100%. After applying an interaction-vertex cut of ±30 cm the total integrated luminosities were 43 nb −1 and 2.25 pb −1 for the MB and ERT trigger, respectively.
All electrons and positrons with p T > 200 MeV/c are combined into like-and unlike-sign pairs. For each pair we check that at least one of the tracks was registered by the ERT trigger. The event is rejected if the two tracks of the pair overlap in any of the detectors; this cut removes 2% of the e + e − pairs. This cut is necessary to assure that the combinatorial pair background is reproduced from mixed events. Pairs originating from photon conversions in the detector material are removed by a cut on the orientation of the pairs in the magnetic field [11]. Fig. 1 shows the raw yields as a function of pair mass for both like-and unlike-sign pairs. The unlike-sign spectrum measures the signal from hadron decays and open charm plus background, while the like-sign spectrum measures only the background. Due to the different acceptance for like-and unlike-sign pairs the shape of the background is different for the two charge combinations.
We have developed two independent methods to subtract the background. In the first method we decompose the background into two components: a combinatorial background made of uncorrelated pairs and a background of correlated pairs. The combinatorial background is determined from mixed events using the procedure described in more detail in [11,12]. Since our data sample required a single electron trigger the mixed events are generated from the MB sample, with the trigger condition applied to each pair, i.e. one of the tracks must have fired the ERT trigger. The like-sign mixed event background and the measured like-sign pairs do not have the same distribution, which is an indication of a correlated background in the data. However, in the region roughly corresponding to a mass of 300 MeV/c 2 , p T above 400 MeV/c and a transverse mass m T = m 2 + (p T /c) 2 below 1.2 GeV/c 2 the distributions are very similar. We therefore normalize the pairs from mixed events to the data in this region 4 . This normalization has a statistical accuracy of 2.4%. After normalization the data show relatively more yield both at low mass and large p T as well as at low p T and large mass. By integrating the normalized like-sign mixed events we determine the number of like-sign background pairs N ++ and N −− , which then give the normalization of the unlike-sign mixed events as The mixed event backgrounds as well as the distributions after subtraction are also shown in Fig. 1. The remaining pairs, like and unlike, are considered correlated pairs, where the like-sign distribution only contains correlated background pairs while the unlike contains also the signal. The correlated background pairs stem from two sources. "Cross pairs" result from decays of single π 0 or η mesons with two electron pairs in the final state, such as double Dalitz decays, Dalitz decays plus conversion of the accompanying photon, and γγ decays where both photons convert. These pairs have a mass lower than the η mass of 548 MeV/c 2 . Cross pairs were simulated using our hadron decay generator EXODUS including the PHENIX acceptance [13]. "Jet pairs" are produced by two independent hadron decays yielding electron pairs, either within the same jet or in the back-to-back jets. Jet pairs were simulated using minimum bias events generated with PYTHIA [14] with the branching ratio of the π 0 Dalitz decay set to 100% to enhance the sample of jet pairs per event. The resulting e + e − pairs are filtered through the PHENIX acceptance. Pairs from mixed events are subtracted from the like-and unlike-sign pair distributions to find the correlated pair distributions. This procedure excludes "signal" such as unlike-sign pairs from a single hadron decay. The mixed event background is normalized by the same method used in the data analysis, described previously. It was found that correlated pairs from the same jet typically have small mass and large p T while those from back-to-back jets have large mass and smaller p T . Since the correlated background pairs populate like-and unlike-sign combinations equally, their yield was determined by simultaneously fitting simulated cross and jet pair mass distributions to the measured correlated like-sign pair mass spectrum. The resulting two normalization factors, one for cross-the other for jet-pairs, are then applied to the unlike-sign correlated background. Contributions of both correlated background sources are also shown in Fig. 1. The signal is extracted by subtracting the unlike-sign correlated backgrounds from the distribution of all correlated pairs.
In our second method we make no assumptions about the shape of the correlated background nor about the decomposition of correlated and uncorrelated background. The measured like-sign distribution is corrected for the acceptance difference between like-and unlike-sign pairs, i.e. the ratio of the acceptance, binned in p T and mass, of unlike-to like-sign pairs. Since the acceptance is a function of mass and p T , we have checked that for different e + e − pair sources, which span reasonable variations in mass and p T shapes of the e + e − pairs, the relative acceptance is unchanged. The corrected like-sign distribution is then subtracted from the unlike-sign pairs. Up to 3.5 GeV/c 2 the difference between the signal extracted using the two background subtrac- Compilation of meson production cross sections in p+p collisions at √ s =200 GeV. Shown are data for neutral [17] and charged pions [18], η [19], Kaons [18], ω [20], and J/ψ [22]. The data are compared to the parameterization based on m T scaling used in our hadron decay generator. tion techniques agrees to better than ±10%. Above 3.5 GeV/c the difference becomes much larger, which may indicate additional correlated background. In this region we subtract the measured like-sign yield, the larger of our two background estimates, and include the difference of the two methods as asymmetric systematic uncertainty on the signal yield.
In the next step the signal is corrected for electron reconstruction efficiency and trigger efficiency. The electron reconstruction efficiency was determined with a Monte Carlo simulation of the PHENIX detector (similar to [12]). The trigger efficiency for single electrons was measured using the MB sample. For each of the 8 calorimeter sectors we determine the ratio of electrons that fired the ERT trigger to all electrons reconstructed as function of p T . Pairs from hadron decays simulated with EXODUS are filtered by the acceptance and then folded with the ERT trigger efficiency to extract the pair trigger efficiency as function of mass. At high masses the trigger efficiency saturates at 72%, limited by the active area of the trigger, from 1.5 to 0.5 GeV/c 2 the pair efficiency gradually drops to 32% and remains approximately constant at lower masses. In addition, the yield is corrected by 0.79/0.55 = 1.44 to account for the fraction of the inelastic p+p cross section missed by our interaction trigger. The systematic uncertainties on the fully corrected spectrum shown in Fig. 3 are summarized in Table 1. Table 1 Systematic uncertainties of the dilepton yield due to different sources and for different mass ranges. The uncertainties vary with mass and the largest uncertainties are quoted for each mass range. The contribution quoted for the jet pair subtraction also accounts for the difference in the signal observed between our two background subtraction techniques.  We model the e + e − pair contributions from hadron decays using the EXODUS decay generator. We follow closely the approach given in [5,15], however, we have updated all input to match the most recent PHENIX data. We assume that all hadrons have a constant rapidity density in the range |∆η| ≤ 0.35 and a homogeneous distribution in azimuthal angle. Transverse momentum distributions are based on measurements in the same experiment where possible.
The key input is the rapidity density dN/dy = 1.06 ± 0.11 of neutral pions, which we determine from a fit to PHENIX data on charged and neutral pions, as shown in Fig. 2. The functional form of the pion transverse momentum distribution is given by:  The contribution from open charm production is fitted to match the data. The inset shows the same data but focuses on the low mass region.
with A = 377±60 mb GeV −2 c 3 , a = 0356±0.014 (GeV/c) −1 , b = 0.068±0.019 (GeV/c) −2 , p 0 = 0.7±0.02 GeV/c and the power n = 8.25±0.04. For all other mesons we assume m T scaling, replacing p T by m 2 − m 2 π + (p T /c) 2 , where m is the mass of the meson. For the η, ω, φ, and J/ψ we fit a normalization factor to PHENIX data. In Fig. 2 the results are compared to published PHENIX data; excellent agreement with the data is achieved. The η meson is measured only at higher p T , however, the fit is in good agreement with the p T distribution of Kaons, which have similar mass.
In order to extract the meson yield per inelastic p+p collision we integrate the fits over all p T . Results, systematic uncertainties, and references to data are given in Table. 2. For the ρ meson we assume σ ρ /σ ω = 1.15 ± 0.15, consistent with values found in jet fragmentation [16]. The η ′ yield is scaled to be consistent with jet fragmentation σ η ′ /σ η = 0.15 ± 0.15 [16]. The ψ ′ is adjusted to the value of σ ψ ′ /σ J/ψ = 0.14 ± 0.03 [23]. For the η, ω, φ, and J/ψ the quoted uncertainties include those on the data as well as those using different shapes of the p T distributions to extrapolate to zero p T . Specifically we have fitted the functional form given in equation 1 with all parameters free and also an exponential distribution in m T . For the ρ, η ′ , and ψ ′ the uncertainty is given by the uncertainty we assumed for the cross section ratios. We note that the dilepton spectra from meson decays are rather insensitive to the exact shape of the p T distribution. Table 2 Hadron rapidity densities used in our hadron decay generator. For the ω and φ meson data from this analysis were used together with data from the quoted references. dN dy | y=0 relative err. data used π 0 1.065 ± 0.11 10% PHENIX [17], [18] η 0.11 ± 0.03 30% PHENIX [19] ρ 0.089 ± 0.025 28% jet fragmentation [16] ω 0.078 ± 0.018 23% PHENIX [20] φ 0.009 ± 0.002 24% PHENIX [21] η ′ 0.016 ± 0.016 100% jet fragmentation [16] J/ψ (1.77 ± 0.27) × 10 −5 15% PHENIX [22] ψ ′ (2.5 ± 0.7) × 10 −6 27% [23] Once the meson yields and p T spectra are known the dilepton spectrum is given by decay kinematics and branching ratios, which are implemented in our decay generator EXODUS following earlier work published in [5,15]. The branching ratios are taken from the compilation of particle properties in [16]. For the Dalitz decays π 0 , η, η ′ → e + e − γ and the decay ω → e + e − π 0 we use the Kroll-Wada expression [24] with electromagnetic transition form factors measured by the Lepton-G collaboration [25,26]. For the decays of the vector mesons ρ, ω, φ → e + e − we use the expression derived by Gounaris and Sakurai [27], extending it to 2 GeV/c 2 , slightly beyond its validity range. For the J/ψ and ψ ′ → e + e − we use the same expression modified to include radiative corrections as discussed in [22]. The resulting dilepton spectra are compared to our data in Fig. 3 with the systematic uncertainties shown as a band. They are calculated as a function of mass and are dominated by the uncertainties on the meson yield tabulated in Tab. 2. The uncertainty from the measured electromagnetic transition form factors, in particular for the ω → e + e − π 0 decay, is also included but contributes visibly only in the range around 500 to 600 MeV/c 2 . Also shown on Fig. 3 are the contributions from open charm and bottom production, discussed in more detail below, as well as from the Drell-Yan process, which is negligible. The data agree very well with the sum of all known sources.
Except for the vector meson peaks, the dilepton yield in the mass range above 1.1 GeV/c 2 is dominated by semileptonic decays of D and B mesons correlated through flavor conservation. To determine this contribution we subtract the meson decay cocktail from the dilepton data, the resulting mass spectrum is shown in Fig. 4. In the PHENIX acceptance the integrated e + e − pair yield per event from heavy flavor decays in the range from 1.1 to 2.5 GeV/c 2 is 4.21 ± 0.28(stat) ± 1.02(syst) ×10 −8 . The systematic uncertainties are those tabulated in Tab. 1 plus the uncertainty on the cocktail subtraction. Since the cocktail subtraction is dominated by the high mass end of the broad ρ resonance, which is not very well known, we assume 100% systematic uncertainty. To estimate the rapidity density of cc pairs the measured e + e − pair yield is corrected for the geometrical acceptance, i.e. corrected from requiring both electron and positron within the PHENIX central arm acceptance to having the electron pair within one unit of rapidity at mid-rapidity. It then is extrapolated to zero e + e − pair mass and converted to cc using known branching ratios of semileptonic decays [16]. This correction is model dependent; we used our tuned PYTHIA simulation [28] to directly relate e + e − pairs from charm in the PHENIX acceptance and in the mass range from 1.1 to 2.5 GeV/c 2 to the cc rapidity density.
For single tracks the acceptance is known to better than 5%. Neglecting correlations between the electron and positron this implies an uncertainty of less than 10% for pairs. However, the fraction of e + e − pairs from correlated heavy flavor decays at mid-rapidity depends on the dynamical correlations between the quarks. These are not very accurately known [29], in particular in the azimuthal direction. Therefore additional systematic uncertainties need to be considered. In PYTHIA the intrinsic k T parameter modifies the azimuthal correlation between c andc. We have varied k T between 1 and 3 GeV/c 2 and reevaluate the fraction of e + e − pairs at mid-rapidity. A ±20% variation was found. Different choices of parton distribution functions (PDF's) lead to modifications of the longitudinal correlation of the pair, often expressed as the rapidity gap between the c andc quarks. We used different parton distribution functions available in PYTHIA, specifically we have used CTEQ5L, CTEQ4L, GRV94LO, GRV98LO, and MRST(c-g). We find ±11% deviations for the e + e − pair yield in the PHENIX acceptance. When converting the e + e − pair yield to cc pairs there is also a ±21% uncertainty resulting from uncertainies of relative abundance of charmed hadrons and of the branching ratios to semileptonic decays. We use an effective branching ratio for c → e of 9.5%± 1%, which was calculated from D + /D 0 = 0.45 ± 0.1, D s /D 0 = 0.25 ± 0.1, and Λ c /D 0 = 0.1±0.05 and the branching ratios from [16]. The overall uncertainty on the extrapolation is approximately 33%.
We also subtract a 7% contribution from bottom decays and the Drell Yan mechanism for which we assign a 100% systematic uncertainty. For the bottom cross section we assume 3.7 µb [31], in agreement with our data above 4 GeV/c 2 . Though negligible, we have also included the contribution from the Drell-Yan mechanism based on a cross section of 0.04 µb [30]. For the rapidity density of cc pairs at mid-rapidity we find: dσ cc dy | y=0 = 118.1 ± 8.4(stat) ± 30.7(syst) ± 39.5(model)µb The systematic uncertainties on the data analysis and on the model dependent extrapolation are quoted separately. Using the rapidity distribution from HVQMNR [32] with CTEQ5M [33] PDF as in [5], the total charm cross section is σ cc = 544 ± 39(stat) ± 142(syst) ± 200(model) µb. The extrapolation to 4π adds another 15% systematic uncertainty, which is included in the last term. This result is compatible with our previous measurement of single electrons, which gave σ cc =567 ± 57(stat) ± 224(syst) µb [5], and with the FONLL prediction of 256 +400 −146 µb [3].
Instead of fixing the bottom cross section, we have tried an alternative ap-proach. We take the shape of the bottom and charm e + e − pair distributions from PYTHIA filtered into the PHENIX acceptance and then fit the charm and bottom contribution to the data. For the charm cross section we obtain σ cc =518 ± 47(stat) ± 135(syst) ± 190(model) µb, consistent with our earlier analysis. The bottom cross section is σ bb = 3.9 ± 2.5(stat) +3 −2 (syst) µb. In addition to the model dependent systematic uncertainties, which are similar to those on the charm extraction, the subtraction of e + e − pairs from the Drell-Yan mechanism contributes an extra 10-20% [34]. We estimate that the combined systematic uncertainty is about 50% and thus similar to the statistical error. The value for the bottom cross section is consistent with our earlier assumption of 3.7 µb as well as with the FONLL prediction of 1.87 +0.99 −0.67 µb [3].
In conclusion, we have measured e + e − pairs in the mass range from 0 to 8 GeV/c 2 in p+p collisions at √ s = 200 GeV. Within the systematic uncertainties the data can be described by known contributions from light meson decays, mostly measured in the same experiment, as well as from semileptonic decays of mesons carrying heavy flavor. The required charm and bottom production cross sections are consistent with the upper FONLL predictions and with the PHENIX measurement of single electrons.