Dielectron production in proton-proton collisions at $\sqrt{s}$ = 7 TeV

The first measurement of e$^+$e$^-$ pair production at mid-rapidity ($|\eta_{{\rm e}}|$ $<$ 0.8) in pp collisions at $\sqrt{s} = 7$ TeV with ALICE at the LHC is presented. The dielectron production is studied as a function of the invariant mass ($m_{\rm ee}$ $<$ 3.3 GeV/$c^{2}$), the pair transverse momentum ($p_{\rm T,ee}$ $<$ 8 GeV/$c$), and the pair transverse impact parameter (DCA$_{{\rm ee}}$), i.e., the average distance of closest approach of the reconstructed electron and positron tracks to the collision vertex, normalised to its resolution. The results are compared with the expectations from a cocktail of known hadronic sources and are well described when PYTHIA is used to generate the heavy-flavour contributions. In the low-mass region (0.14 $<$ $m_{\rm ee}$ $<$ 1.1 GeV/$c^{2}$), prompt and non-prompt e$^+$e$^-$ sources can be separated via the DCA$_{\rm ee}$. In the intermediate-mass region (1.1 $<$ $m_{\rm ee}$ $<$ 2.7 GeV/$c^{2}$), a double-differential fit to the data in $m_{\rm ee}$ and $p_{\rm T,ee}$ and a fit of the DCA$_{\rm ee}$ distribution allow the total ${\rm c\overline c}$ and ${\rm b\overline b}$ cross sections to be extracted. Two different event generators, PYTHIA and POWHEG, can reproduce the shape of the two-dimensional $m_{\rm ee}$ and $p_{\rm T,ee}$ spectra, as well as the shape of the DCA$_{\rm ee}$ distribution, reasonably well. However, differences in the ${\rm c\overline c}$ and ${\rm b\overline b}$ cross sections are observed when using the generators to extrapolate to full phase space. Finally, the ratio of inclusive to decay photons is studied via the measurement of virtual direct photons in the transverse-momentum range 1 $<$ $p_{\rm T}$ $<$ 8 GeV/$c$. This is found to be unity within the statistical and systematic uncertainties and consistent with expectations from next-to-leading order perturbative quantum chromodynamic calculations.


Introduction
The main goal of the ALICE [1][2][3] Collaboration is to study strongly-interacting matter at the high energy density and temperature reached in ultra-relativistic heavy-ion collisions at the CERN Large Hadron Collider (LHC). In such collisions, the formation of a deconfined state of quarks and gluons, the Quark−Gluon Plasma (QGP), is predicted by Quantum ChromoDynamic (QCD) calculations on the lattice [4][5][6][7][8]. Moreover, chiral symmetry is expected to be restored in the QGP phase [9,10].
Electron-positron pairs are produced at all stages of the collision. Since they are not affected by the strong interaction, they can escape from the dense medium without final-state interaction, and are suited to probe the entire time evolution and dynamics of the system. At low invariant masses of the dielectron pairs (m ee < 1.1 GeV/c 2 ), e + e − spectra are sensitive to the properties of vector mesons ρ, ω, and φ in the medium. The ρ meson has a shorter lifetime (≈ 1.3 fm/c in its rest frame) than that of the medium (≈ 10 fm/c [11]). Therefore, its spectral function, which can be measured through its dielectron decay channel, is affected by the dense medium and the predicted restoration of chiral symmetry [12][13][14][15]. Thermal radiation emitted by the system, both during the partonic and hadronic phase [9,10], contributes to the dielectron yield over a broad mass range. In the intermediate-mass region (IMR, 1.1 < m ee < 2.7 GeV/c 2 ), the measurement of thermal dielectrons from the QGP is very challenging at the LHC due to the dominant contribution of e + e − pairs from semileptonic decays of charm and beauty hadrons, correlated through flavour conservation 1 . The continuum produced by these decays is sensitive to the energy loss [16][17][18][19][20] and the degree of thermalisation of charm and beauty quarks in the medium, as well as the heavy-quark hadronisation mechanism, e.g. recombination of heavy quarks with light quarks from the thermalised medium [21][22][23]. To single out the interesting signal characteristics of the QGP, it is crucial to understand the dielectron yield from primordial heavy-flavour production. The latter can be studied in proton-proton (pp) collisions, which serve as a reference for the analysis of heavy-ion collisions and provide a test for perturbative QCD (pQCD) calculations and Monte Carlo (MC) event generators. Complementary to single-electron or D meson measurements, the yield of correlated e + e − pairs from charm-hadron decays contains information about kinematical correlations between the c and c quarks, i.e. the production mechanisms, and is sensitive to soft heavy-flavour production.
At the Relativistic Heavy Ion Collider (RHIC), the PHENIX and STAR Collaborations found that the dielectron production in pp collisions at √ s = 200 GeV is well described by a cocktail of expected hadronic sources [24][25][26]. In addition, PHENIX measured the total cc and bb cross sections in pp and d-Au collisions at √ s NN = 200 GeV by fitting the spectra of e + e − pairs from heavy-flavour hadron decays simultaneously in m ee and pair transverse momentum p T,ee [27,28]. At this energy and in the PHENIX acceptance, the yield from correlated pairs from beauty-hadron decays dominates across all mass regions for p T,ee > 2.5 GeV/c, whereas the cc contribution is preeminent for m ee < 3 GeV/c 2 and p T,ee < 2 GeV/c. The extraction of the heavy-flavour cross sections, in particular the total cc cross section, depends nevertheless on the event generator used to extrapolate the measurements to full phase space. Finally, at lower masses (m ee < 0.3 GeV/c 2 ) and high p T,ee (p T,ee > 1 GeV/c), i.e. the quasi-real virtual-photon region where the p T,ee of the dilepton pair is much larger than its mass (p 2 T,ee m 2 ee ), the measured e + e − yield was used to study the production of virtual direct photons. The corresponding yield of real direct photons in pp and d-Au collisions is reproduced by next-to-leading order perturbative quantum chromodynamic (NLO pQCD) calculations [25,29]. At the LHC, no significant signal of direct photons for p T < 16 GeV/c could be extracted from the inclusive photon measurements in pp collisions at √ s = 2.76 TeV and 8 TeV by the ALICE Collaboration [30]. However, the results are consistent with expectations from NLO pQCD calculations, which predict a smaller contribution of direct photons to the inclusive photon spectrum with increasing √ s.
In heavy-ion collisions, a strong enhancement at low invariant mass of dilepton pairs (m ll < 1 GeV/c 2 ) is 1 These contributions are referred to as charm/beauty or cc/bb contributions throughout this paper The charged-particle identification capability of the TPC and ITS is supplemented by the TOF [63], which is located at a radial distance of 3.7 m from the beam axis. It provides a measurement of the time of flight for particles from the interaction point up to the detector itself. The event collision time is either measured with the T0 detector, which consists of two arrays of Cherenkov counters located at z = +375 cm and z = −72.7 cm from the nominal interaction point, or estimated using the particle arrival times at the TOF for events with sufficiently large multiplicity [60]. Due to their curved paths in the magnetic field of the solenoidal magnet, charged particles need a minimum p T of about 300 MeV/c to reach the TOF detector. Since the TOF matching efficiency is of the order of 30% at a p T of 500 MeV/c, the TOF information is used in this analysis only if the particle has an associated hit in the TOF detector, otherwise the particle is identified with the ITS and TPC only.
The data used in this paper were recorded with ALICE at the LHC during the pp run at √ s = 7 TeV in 2010. Minimum bias (MB) collisions were triggered by requiring at least one hit in the SPD or in one of the two forward scintillator systems V0A and V0C. In addition, the timing information from the V0 and the correlation between the number of hits and track segments in the SPD detector were used offline to remove background from beam-gas interactions. The primary vertex is reconstructed by extrapolating charged-particle tracks in the TPC and ITS to the beam line. It is required to be within ±10 cm of the nominal interaction point along the beam direction in order to provide a uniform pseudorapidity acceptance of the detectors. A total of 370 million pp events at √ s = 7 TeV pass the offline event selection criteria, corresponding to an integrated luminosity of L int = (6.0±0.2) nb −1 [65].

.1 Electron identification
The strategy to identify electrons relies on a combination of tracking and particle identification (PID) information from different detectors in the central barrel. Reconstructed charged-particle tracks in the ITS and TPC are selected in |η| < 0.8 and p T > 0.2 GeV/c. For the DCA ee analysis, the tracks must have a p T > 0.4 GeV/c to assure a sufficient separation between prompt and non-prompt e + e − sources. The DCA resolution worsens at low p T and is larger than 150 µm for tracks reconstructed in the ITS and TPC with p T < 0.35 GeV/c [60], which is of the same order of magnitude as the decay length of the D 0 and D ± s mesons (cτ ≈ 122.9 and 149.9 µm, respectively). The tracks are required to have at least 100 out of a maximum of 159 reconstructed space points in the TPC with at least 100 crossed pad-rows, while Dielectron production in proton-proton collisions at √ s = 7 TeV ALICE Collaboration the ITS track segments must have a hit in at least 5 of the 6 detector layers. The maximum χ 2 per space point in the TPC (ITS) from the track fit must be less than 4 (4.5). Only tracks with a DCA to the primary vertex smaller than 1 cm in the xy-plane and 3 cm along the z-axis are accepted. To suppress electron tracks from photon conversions in the detector material at large radii, a hit in the first layer of the SPD is required. A small fraction of electrons from photon conversions in the second ITS layer may still have a hit in the first layer associated wrongly to their reconstructed track. Such cases are further removed from the sample by requiring that the reconstructed track does not share any ITS cluster with other tracks (see below). This requirement also reduces the amount of conversion electrons from the first ITS layer.
The PID information is based on the measurement of the specific ionisation energy loss (dE/dx) in the TPC and ITS, and the time-of-flight information from TOF. The cut values for electron selection and hadron rejection are expressed in terms of the deviation of the respective PID signal from its expectation value for a particle species i. The PID variables n DET σ i are normalised to units of standard deviations of the respective detector (DET) resolution.
In the TPC, electrons are selected in the interval −1.5 < n TPC σ e < 4.0. Additionally, pions are rejected by requiring that the measured TPC dE/dx of the track is far from the expectation value for pions: n TPC σ π > 3.5. Since electrons have a larger energy loss in the TPC than pions for momenta above 0.25 GeV/c, the n TPC σ π requirement is asymmetric. The remaining contamination by kaons and protons occurs mainly in the crossing regions of the expected dE/dx values in the TPC for these particle species and for electrons, i.e. around a momentum of 0.5 and 1.1 GeV/c, respectively. This contamination can be reduced by using the ITS information, where the crossings occur at higher momenta around 0.7 and 1.5 GeV/c for kaons and protons, respectively. In the left panel of Fig. 1, the variable n TPC σ e is shown as a function of n ITS σ e for selected tracks with 0.5 < p < 0.52 GeV/c after the pion rejection in the TPC was applied. In this momentum interval, kaons and electrons have a very similar energy loss in the TPC, whereas they are still separated in the energy loss measurements of the ITS. The electron selection criterion in the ITS is −3 < n ITS σ e < 1. Further reduction of the hadron contamination can be achieved using the TOF information with |n TOF σ e | < 3 (in case the selected tracks have an associated hit in the TOF detector). The electron purity P e is estimated at low momenta (p < 3 GeV/c) by fitting the n TPC σ e distribution in momentum slices after the ITS and TOF selection, as well as the n TPC σ π rejection, following a procedure explained in [66]. At higher momenta, the n TPC σ π distribution is fitted after the requirements on n ITS σ e , n TOF σ e , and n TPC σ e , are fulfilled. The result is shown in the right panel of Fig. 1. The purity ranges from 60% to 99%, depending on the particle momentum p. The lowest purity is observed where kaons (p ≈ 0.5 GeV/c) or protons (p ≈ 1.2 GeV/c) have similar dE/dx as electrons in the TPC.

Dielectron spectrum
All electron candidates from the same event are combined into pairs, characterised by their m ee , p T,ee , and DCA ee . The latter is calculated from the single-electron DCAs as: where DCA xy,i is the DCA of the electron i in the transverse plane and σ xy,i is its resolution estimated from the covariance matrix of the track reconstruction parameters obtained with the Kalman filter technique [60,67]. The absolute DCA resolution worsens at low p T due to multiple scattering in the detector material. Therefore, the analysis is performed using the DCA normalised to its resolution, which decreases the sensitivity to the particle momentum.
The distribution of same-event pairs of opposite sign (OS) is composed of true signal pairs (S) as well as background pairs (B). The background pairs are mainly combinatorial but contain also residual correlations such as from jets and from conversions of correlated decay photons originating from the same mother particle. Typical values of S/B range between O(1) and O(10 −1 ), depending on m ee and p T,ee Dielectron production in proton-proton collisions at √ s = 7 TeV ALICE Collaboration  σ e (see text) as a function of the ITS PID signal (n ITS σ e ) for selected tracks with 0.5 < p < 0.52 GeV/c after applying the pion rejection in the TPC (left). Electron purity P e as a function of momentum (right). Only statistical uncertainties are shown.
(see below). Therefore, the minimisation of B and a careful subtraction of the remaining background are key aspects of this analysis.  The main sources of electrons contributing to B are π 0 Dalitz decays and photon conversions. To reject these most efficiently, a prefilter algorithm is applied where tracks from the selected electron candidate sample are combined with charged-particle tracks from a sample with relaxed tracking selection criteria and no PID. Dielectron pairs originating from π 0 Dalitz decays and photon conversions have small invariant masses and opening angles (ω ee ), as shown in Fig. 2. Therefore, if an opposite-sign pair with small invariant mass and opening angle is formed with a track h of the sample with relaxed selection criteria, the electron candidate is rejected and not used for further pairing. The cut values applied in Dielectron production in proton-proton collisions at √ s = 7 TeV ALICE Collaboration the prefilter algorithm are m eh < 0.06 GeV/c 2 and ω eh < 50 mrad. These selection criteria lead to an improvement of the S/B by a factor of about 1.5 and an increase of the significance S/ √ S + 2B by a factor of about 1.2 for m ee < 1 GeV/c 2 , as can be seen in the left and right panels of Fig. 3, respectively. For m ee < 0.06 GeV/c 2 , the prefilter algorithm cuts systematically into the signal acceptance. Since the S/B is large in the low-mass region, no prefilter is applied for m ee < 0.14 GeV/c 2 . The random rejection probability, caused by accidental combinations of electron candidates with an uncorrelated track, is small (about 3%) and taken into acount in the efficiency corrections.   To further suppress the contamination by dielectron pairs from photon conversions in the dielectron yield, two additional selection criteria are applied. Conversions occur in the beam pipe or in the detector material, mainly of the ITS, and are characterised by a common secondary vertex of the dielectron pair. Any electron candidate found to form such a secondary vertex with another track is rejected from the analysis. In addition, dielectron pairs from photon conversions are characterised by a finite apparent invariant mass. The extrapolation of displaced conversion electron tracks to the collision point results in a non-vanishing artificial opening angle that is caused by the deflection of the tracks in the magnetic field. The opening angle is preferentially in the plane perpendicular to the magnetic field direction, which can be used to further reject such conversion dielectron pairs [25]. To this end, the angle ϕ v which measures the orientation of the opening angle relative to the magnetic field is calculated according to: The two vectors w and u a are given by: where p e + , p e − , and z are the 3-momentum vectors of the positron, electron, and the orientation of the magnetic field parallel to the beam axis, respectively. In the left panel of Fig. 4, the measured Dielectron production in proton-proton collisions at √ s = 7 TeV ALICE Collaboration ϕ v distribution without ITS shared-cluster cut for m ee < 0.1 GeV/c 2 and p T,ee < 8 GeV/c is compared with the sum of two MC templates, one for pairs from π 0 and η Dalitz decays and one for pairs from photon conversions, fitted to the data. Prompt pairs with finite invariant mass have an almost uniform ϕ v distribution in this kinematic domain, while conversion pairs show a peak around ϕ v = π. To reject these conversions, reconstructed electron tracks that share at least one ITS cluster with another track are not used in the analysis. The measured ϕ v distribution after this requirement is shown in the right panel of Fig. 4. The conversion peak around ϕ v = π is clearly suppressed. The MC simulations describe the data very well. Moreover, dielectron pairs with ϕ v > 2 rad and m ee < 0.1 GeV/c 2 are removed from the selected pairs to further reduce the amount of conversion electrons. From MC studies, their final contribution is expected to be below 1% down to m ee = 0.  The remaining background B is estimated from the distribution of same-sign pairs, SS, from the same event. In comparison to a mixed-event approach, the same-sign approximation of the combinatorial background has the advantage of containing all residual correlations arising from charge-symmetric processes such as jet fragmentation or conversions of decay photons from the same mother particle that are present in B, but the disadvantage of suffering from the limited statistics available in the analysed data sample. The same-sign distribution SS is computed in the same bins of m ee , p T,ee , and DCA ee as the OS distributions by forming in each bin the geometric mean SS = 2· √ N ++ N −− of the number of (++) and (−−) pairs, N ++ and N −− , respectively. The geometric mean is robust against charge asymmetries in the electron sample, as they may arise from acceptance differences of positive and negative tracks, and from charge asymmetries of the hadronic background. In the present data set, charge asymmetries of up to 5% are observed, depending on p T . MC simulations confirm that such asymmetries do not lead to a bias in the estimate of B if the geometric mean is used for the same-sign background calculation. In a few bins with low pair statistics, however, N ++ or N −− is zero. In such bins, the arithmetic sum SS = N ++ +N −− is used instead, to avoid underestimation of the combinatorial background.
A bias in the estimate of B using the same-sign technique can occur as a consequence of differences of the detector acceptance for same-sign and opposite-sign pairs. Due to the full coverage of the ALICE central barrel in azimuth, i.e. in the bending plane of the spectrometer, such acceptance differences are small. Residual effects arise due to malfunctioning detector segments and can be estimated by event Dielectron production in proton-proton collisions at √ s = 7 TeV ALICE Collaboration   Fig. 6: Opposite-sign m ee -differential yield integrated in p T,ee and DCA ee overlaid with the same-sign spectrum corrected by the acceptance correction factor R acc . Statistical uncertainties are represented by vertical bars.

mixing. The relative acceptance correction factor
where M +− and M ±± are the mixed-event opposite-sign and same-sign pair distributions. The relative acceptance correction factor R acc as a function of m ee and p T,ee is shown in Fig. 5. For (m ee c) 2 + p 2 T,ee > 1 GeV/c, R acc is consistent with unity and no correction is applied, while at smaller m ee and p T,ee deviations of up to 5% are observed. The relative acceptance correction factor is applied differentially in m ee , p T,ee , and DCA ee .
In Fig. 6, the opposite-sign and relative-acceptance corrected same-sign m ee spectra, i.e. OS and R acc · SS, Dielectron production in proton-proton collisions at √ s = 7 TeV ALICE Collaboration are shown integrated over p T,ee and DCA ee . The raw pair signal S is obtained with the formula:

Efficiency corrections
The single-electron and pair efficiencies, including all tracking and PID selection criteria, are calculated using a detailed MC simulation. The event generator PYTHIA 6.4.25 [55] with the Perugia 2011 tune [68] is used to generate pp events. A realistic detector response is modelled using GEANT3 [69], with the same detector configurations as in data. The reconstruction efficiency (ε e ) for single-electron tracks does not show any dependence on the electron DCA, for which loose selection criteria were applied (DCA xy < 1 cm and DCA z < 3 cm). Also no strong η dependence of ε e is observed as well, whereas the dead zones of the first ITS layer can be seen in the ϕ distribution of the electron candidates due to the requirement of a hit in the first pixel. The random rejection probability of the prefilter algorithm is estimated by embedding test particles in real data events. It is found to be about 3% independent of p T . The resulting pair efficiency ε ee rec (m ee , p T,ee ), shown in a few selected intervals of m ee in Fig. 7, is calculated and applied to the data as a function of m ee and p T,ee . The efficiency of the ϕ v requirement for dielectron pairs with m ee < 0.1 GeV/c 2 is estimated assuming that the ϕ v distribution of the signal dielectron pairs is flat (see Fig. 4). For m ee > 0.8 GeV/c 2 , ε ee rec (m ee , p T,ee ) reaches about 15%. At lower m ee , the pair efficiency drops at low p T,ee .  Electrons suffer from Bremsstrahlung in the detector material, for which no correction is applied during the tracking procedure. This results in a smaller reconstructed momentum and distorts the shape of the m ee distributions, which develop tails towards lower m ee . Moreover, the reconstructed momentum of the electrons is also affected by the finite detector resolution. Such effects, i.e. p T , θ , and ϕ single-track resolution and Bremsstrahlung, are not accounted for by the efficiency corrections, which do not contain any unfolding procedure. However, the detector reponses are folded into the particle spectrum generated by the hadronic cocktail, as explained in detail in [70].
The corrected number of dielectron pairs is expressed as: Dielectron production in proton-proton collisions at √ s = 7 TeV ALICE Collaboration where ∆p T,ee , ∆m ee , and ∆DCA ee are the width of the p T,ee , m ee , and DCA ee intervals, respectively. The spectra are finally normalised by the number of minimum bias pp collisions corrected for the primary vertex reconstruction efficiency, which is about 88%. The invariant dielectron cross section is obtained by multiplying the yield by the minimum bias pp cross section at √ s = 7 TeV, of σ MB = 62.2 ± 2.2 mb [65]. The corresponding normalisation uncertainty is ±3.5%.

Requirements
Variations  The systematic uncertainties arise from limitations in the determination of the background, the relative acceptance correction factor R acc , the electron selection efficiency, the prefilter efficiency, and the paircut efficiency. These uncertainties are evaluated by varying all the electron and pair selection criteria simultaneously and by comparing the results with and without prefilter. Table 1 summarises the singletrack selection criteria variations. The signal is extracted and corrected for 22 random combinations of selection criteria, which probe different single-electron efficiencies and S/B ratios, ranging from 0.22 to 0.42 at p T = 1 GeV/c and from about 0.05 to 0.15 at m ee = 0.5 GeV/c 2 , respectively. The final systematic uncertainty is calculated as the root mean square of the variation of the final data points. These extracted systematic uncertainties contain not only systematic effects from the signal efficiency, but also from the background estimation. The maximum ϕ v requirement for pairs with m ee < 0.1 GeV/c 2 is also varied, around the default value of 2 rad, from 1.57 to 2.5 rad. Deviations from a flat ϕ v distribution for the signal dielectron pairs are estimated with a MC simulation and found to lead to a systematic uncertainty below 1% for the default ϕ v requirement. The resulting systematic uncertainties from the selection criterion variation is listed in Table 2 in the case of the DCA analysis with p T,e > 0.4 GeV/c.
An additional source of systematic uncertainty is considered for the DCA ee -differential dielectron cross section. The electron efficiency is found to be independent on the single-track DCA within the range under study by checking the fraction of reconstructed electrons as a function of the distance of their production vertex to the reconstructed primary vertex in MC. However, some correlations still remain Dielectron production in proton-proton collisions at √ s = 7 TeV ALICE Collaboration p T compared to electrons from low-p T non-prompt J/ψ. The possible remaining uncertainty from this correlation is estimated by half the difference of the pair efficiency at the maximum and minimum meanp T,ee , seen as a function of DCA ee in a given mass region. This systematic uncertainty is found to be less than 5%, increasing from low to high m ee . Table 2 summarises the systematic uncertainties arising from the DCA analysis.

Cocktail of hadronic sources
To allow for a detailed interpretation of the data, the contribution from all known hadronic sources must be estimated. The so-called hadronic cocktail contains contributions from pseudoscalar and vectormeson decays as well as from semileptonic decays of heavy-flavour hadrons.

e + e − pairs from light-flavour hadrons and J/ψ mesons
The Dalitz decays of light neutral mesons, and φ → e + e − π 0 , and the dielectron decays of the vector mesons, ρ, ω, φ , and J/ψ are simulated with the phenomenological event generator EXODUS [24]. The radiative decay of J/ψ (J/ψ → e + e − γ) is also included. The pair mass distribution from the Dalitz decays follows the Kroll-Wada expression [71] multiplied by the electromagnetic form factors measured by the Lepton-G Collaboration [72,73] and more recently by the NA60 Collaboration [74,75]. The ρ line shape has been studied in detail in p−A collisions at 400 GeV by the NA60 Collaboration [74], who confirmed the need for a Boltzmann term beyond the standard description [76] and provided a precise measurement of the effective temperature parameter. For the decay of the other vector mesons, which are assumed to be unpolarised, the Gounaris-Sakurai expression [77] is used.
The rapidity distribution of the mesons is assumed to be flat at mid-rapidity. The momentum distributions of π 0 , η, φ , and J/ψ are obtained by fitting the spectra measured by the ALICE Collaboration [78][79][80][81] with a modified Hagedorn function [82]. The measured π ± and π 0 spectra agree within their systematic uncertainties. Since the π ± measurement extends to lower p T , and exhibits smaller uncertainties than the π 0 , charged pions are used to approximate neutral pions. For the other mesons, ρ, ω, and η , the shape of their p T spectra is derived from the π ± spectrum. The η mesons are generated assuming m T scaling [83][84][85], implying that the spectra of all light mesons as a function of m T = m 2 + p 2 T are the same and only differ by a normalisation factor. The normalisation factors are based on the ratio of the p T spectra of the given hadron to the p T spectrum of the π ± at high p T : 0.4 ± 0.08 for η (from PYTHIA 6 calculations), 0.85 ± 0.17 for ω [86], and 1.0 ± 0.2 for ρ [87]. The momentum distributions of ω and ρ are obtained from the ω/π 0 and ρ/π 0 ratios in simulated pp collisions at √ s = 7 TeV with the Monash 2013 tune of PYTHIA 8 [88,89]. This tune describes the measured ω/π 0 and ρ/π 0 ratios in pp collisions at √ s = 7 TeV and 2.76 TeV, respectively. Since the ω measurement does not extend to low p T (the ω meson is measured for p T > 2 GeV/c), fits of the data are used only to estimate the systematic uncertainties.
The expected dielectron yield as a function of m ee and p T,ee is computed in a fast simulation by filtering Dielectron production in proton-proton collisions at √ s = 7 TeV ALICE Collaboration the generated hadronic cocktail through the ALICE acceptance, while applying the detector responses including the momentum and opening angle resolutions, and the Bremsstrahlung effect [70], since no unfolding procedure is applied to the data. The momentum transformation matrices are determined with full GEANT3 [69] simulations of the interactions of the primary electrons produced in pp collisions with the material of the ALICE apparatus.
The main systematic uncertainties on the hadronic cocktail arise from the uncertainties of the measured π ± , η, ω, φ , and J/ψ p T spectra and those of the m T normalisation factors. The first is evaluated by parameterising the data along the upper and lower ends of their statistical and systematic uncertainties added in quadrature. The complete cocktail of e + e − pairs is then generated again based on these new parametrisations. For the ρ mesons, m T scaling is used to estimate the systematic uncertainties originating from the ρ p T spectrum. The uncertainties from the different decay branching ratios [90] are also taken into account.

Open-charm and open-beauty contributions to the dielectron yield
Electron pairs that originate from the semileptonic decays of cc and bb are simulated with two different generators, the leading-order (LO) event generator PYTHIA 6.4.25 [55], and the next-to-leading order (NLO) event generator POWHEG [56,57]. The cc and bb pairs are produced at leading order through pair creation, predominantly gg → QQ with a small contribution of qq → QQ, where g, q, and Q are gluons, up or down quarks, and charm or beauty quarks, respectively. At higher order, flavour excitations and gluon splitting give rise to further contributions.
PYTHIA simulations utilise LO-pQCD matrix elements for 2 → 2 processes together with a leadinglogarithmic p T -ordered parton shower, and an underlying-event simulation including multiple parton interactions. The fragmentation and hadronisation of the charm and beauty quarks are based on the Lund string model. In this paper, the Perugia-2011 tune [68] is used, for which the first LHC data, mainly from multiplicity and underlying-event related measurements, have been considered. In this tune, the parton distribution functions are parametrised with the CTEQ5L [91] functions.
POWHEG is a NLO-pQCD generator that can be interfaced to a parton shower MC (e.g. from PYTHIA or HERWIG [92]) to provide final-state particles. The calculations presented in this paper (POWHEG) are obtained with the POWHEG BOX framework [58,59] and the tune Perugia-2011 of PYTHIA 6.4.25. The CTEQ6.6 [93] functions are used for the input parton distribution functions. To be consistent with the PYTHIA simulations, the mass of the charm and beauty quarks are set to 1.5 GeV/c 2 and 4.75 GeV/c 2 , respectively.
The simulations are normalised to the measured total charm and beauty cross section, i.e. σ REF cc = 7.44 ± 0.14(stat.) ± 0.58(syst.) mb [94] and σ REF bb = 288 ± 4(stat.) ± 48(syst.) µb [95] and passed through the ALICE acceptance after applying the detector responses including the momentum and opening angle resolutions, and the Bremsstrahlung effect [70]. The systematic uncertainties of the σ REF cc and σ REF bb measurements are propagated to the final hadronic cocktail. Whereas the effective beauty-toelectron branching ratio is taken from PYTHIA, the one for charm-to-electron (BR c→e ) is assumed to be (9.6 ± 0.4(stat.) ± 1.1(syst.))% as reported in [96], which is slightly smaller than what has been estimated with PYTHIA (BR c→e = 10.6%). The recent ALICE measurements of D mesons [97] and Λ ± c [98] in pp collisions at √ s = 7 TeV were found to lead to a similar value of BR c→e with comparable uncertainties. The uncertainties of the effective beauty-and charm-to-electron branching ratios are propagated to the final hadronic cocktail. For both generators, the p T -differential cross-section of single electrons from charm-and beauty-hadron decays at mid-rapidity is found to be consistent with FONLL calculations [99] and to reproduce the measurements reasonably well within the theoretical and experimental uncertainties [100]. To obtain the dielectron yield of correlated e + e − pairs from heavy-flavour hadron decays, the distribution of same-sign pairs is subtracted from the e + e − spectrum, as in data.
Dielectron production in proton-proton collisions at √ s = 7 TeV ALICE Collaboration

DCA ee template distributions
Whereas the differential p T,ee and m ee distributions of the hadronic cocktail are estimated from a fast simulation, the DCA ee distributions are determined with a full GEANT3 [69] simulation of the ALICE detector. For this purpose, PYTHIA 6.4.25 events are passed through the full detector simulation tuned to describe the performance of each detector subsystem. In particular, all relevant charactereristics of the SPD, such as a map of dead channels, are included in the simulation. The same analysis selection criteria as in data are applied. Since the various charm hadrons have quite different decay lengths, ranging from about 59.9 µm for Λ ± c to 311.8 µm for D ± mesons [90], their relative yields are relevant to build the DCA ee template of correlated e + e − pairs from charm-hadron decays. The measured production ratios of charm hadrons [97,98] and their semileptonic decay branching ratios [90] are used to obtain the cc DCA ee distribution. Finally, DCA ee templates are extracted for e + e − pairs from π 0 Dalitz decays, from charm-and beauty-hadron decays, and from the decays of prompt and non-prompt J/ψ. In Fig. 8, the π 0 , cc, and bb templates are shown integrated over p T,ee and m ee . Whereas the distributions for prompt sources, like π 0 , directly reflect the detector DCA resolution, those of non-prompt sources, like heavy-flavour hadrons, are characterised by the convolution of the DCA resolution and the decay length of the mother particle (cτ D ≈ 150 µm and cτ B ≈ 470 µm [90]). The DCA ee spectrum of e + e − pairs from π 0 Dalitz decays is taken as an approximation for all prompt light-flavour decays into dielectrons. Each contribution is normalised to its expected yield from the hadronic cocktail in the same m ee and p T,ee range and after the same fiducial selection criteria (|η e | < 0.8 and p T,e > 0.4 GeV/c). Since e + e − pairs from prompt and non-prompt J/ψ have different DCA ee distributions, the measured fraction of non-prompt J/ψ in pp collisions at 7 TeV [101], f B , is used to scale the templates accordingly. To evaluate the uncertainty originating from f B , the DCA ee distributions are shifted to the upper and lower bounds of the statistical and systematic uncertainties added in quadrature.
Additional sources of systematic uncertainties are considered. First, the resolution of the single-track DCA is found to be better in MC as compared to data by about 15%. This affects the DCA ee distributions, in particular those of e + e − pairs from prompt sources like π 0 and prompt J/ψ, at around 1-3 σ . Second, the uncertainties on the charm-hadron production ratios [97,98] and on their semileptonic decay branching ratios [90] are propagated to the final DCA ee distribution of correlated e + e − pairs from charm-hadron decays. Third, the PYTHIA simulations used to create the DCA ee templates for the heavy-flavour contri-Dielectron production in proton-proton collisions at √ s = 7 TeV ALICE Collaboration butions have been performed with the PYTHIA Perugia-0 tune [68], which does not reproduce well the measured p T distribution of electrons from charm-hadron decays at high p T (p T > 3 GeV/c) [100]. This was found to have a negligible effect on the final DCA ee template, by varying the maximum p T requirement on the single electron track (p T < 3 GeV/c). Moreover, the charm and beauty DCA ee templates do not exhibit any strong dependence on p T,ee and m ee , as well as on the minimum electron p T requirement. The latter is varied from 0.4 GeV/c to 0.7 GeV/c. Therefore, the shape of the heavy-flavour MC templates is assumed to be model independent, whereas their absolute normalisation, i.e. the dielectron yields from charm-and beauty-hadron decays in the given p T,ee and m ee range, is not. The same DCA ee distributions are used for the two event generators, PYTHIA and POWHEG, and normalised to the dielectron yield predicted in each mass interval by the corresponding event generator.

Comparison of the data to the cocktail
The differential e + e − cross section dσ /dm ee in minimum bias pp collisions at √ s = 7 TeV is presented in Fig. 9 in the ALICE acceptance (|η e | < 0.8 and p T,e > 0.2 GeV/c) as a function of m ee . Statistical and systematic uncertainties of the data are indicated by vertical bars and boxes, respectively. The measured spectrum is compared with the cocktail of expected e + e − sources, where PYTHIA is used to calculate the correlated pairs from heavy-flavour decays. The total systematic uncertainty of the cocktail is shown by the grey band. The bottom panel shows the ratio of data to cocktail. Good agreement is observed over the full mass range (m ee < 3.3 GeV/c 2 ).  For a more detailed discussion, the results are presented differentially below in p T,ee and DCA ee in four different mass regions, i.e. the π 0 region (m ee < 0.14 GeV/c 2 ), the low-mass region (0.14 < m ee < 1.1 GeV/c 2 ), the IMR (1.1 < m ee < 2.7 GeV/c 2 ), and the J/ψ region (2.7 < m ee < 3.3 GeV/c 2 ). Dielectron production in proton-proton collisions at √ s = 7 TeV ALICE Collaboration

π 0 mass region
The mass region m ee < 0.14 GeV/c 2 is dominated by π 0 Dalitz decays (π 0 → e + e − γ), with a small contribution from η Dalitz decays (η → e + e − γ) of about 10%. In the left panel of Fig. 10, the measured p T,ee -differential cross section of e + e − pairs is shown in comparison with the hadronic cocktail. Good agreement between data and cocktail is observed within the systematic uncertainties. This confirms that the dielectron analysis is consistent with the previous light-meson measurements [78][79][80]86] taken as input for the calculations of the expected e + e − cross section. TeV in the ALICE acceptance as a function of p T,ee (left) and DCA ee (right) for m ee < 0.14 GeV/c 2 and 0.08 < m ee < 0.14 GeV/c 2 , respectively. The data are compared with a cocktail of expected sources. In the bottom panels, the ratio of data to cocktail as a function of p T,ee (left) and the pull distribution as a function of DCA ee (right) are shown. Statistical and systematic uncertainties on the data are plotted as vertical bars and boxes, respectively. The total uncertainty of the cocktail is represented as a grey band.
In the right panel of Fig. 10, the measured e + e − cross section is shown as a function of DCA ee in the mass range 0.08 < m ee < 0.14 GeV/c 2 for p T,ee < 8 GeV/c. The results are compared with the expectations from MC. The low-mass cut-off at 0.08 GeV/c 2 is chosen such that residual contaminations of e + e − pairs from photon conversions with large DCA ee values are suppressed. The red line represents the expected cross section of all prompt light-flavour sources, for which the π 0 DCA ee template is used as an approximation. In this mass range, the contributions from non-prompt sources (cc and bb) are negligible, which allows the DCA ee resolution in data and in MC to be directly compared. To quantify the agreement between data and the expected DCA ee distribution from MC, the pull distribution is shown in the bottom right panel of Fig. 10. It is defined as the difference between data and MC normalised by the quadratic sum of their statistical and systematic uncertainties. The DCA ee distribution obtained from the full simulations of the ALICE detector describes the data well. A slight excess of the data is observed in 1 < DCA ee < 3 σ which is the range mostly affected by discrepancies in the DCA resolution between data and MC.

Low-mass region
The low-mass region, 0.14 < m ee < 1.1 GeV/c 2 , is expected to be dominated by the light mesons η, η , ρ, ω, φ , and the contribution of correlated e + e − pairs from semileptonic decays of charm hadrons. A very small contribution of virtual direct photons is also expected (3-5% of the total measured yield in 0.14 < Dielectron production in proton-proton collisions at √ s = 7 TeV ALICE Collaboration m ee < 0.7 GeV/c 2 and 4 < p T,ee < 8 GeV/c). The latter is not included in the hadronic cocktail and will be discussed in section 5.2. At low m ee (m ee ≤ m η ), the η Dalitz decay is the main source of e + e − pairs for all p T,ee , as shown in the left panel of Fig. 11, whereas at larger m ee , the heavy-flavour contributions start to dominate, followed by the ω, ρ, and φ contributions (see right panel of Fig. 11). The requirement on the single electron track of p T > 0.2 GeV/c produces an acceptance hole at low m ee and p T,ee , which can be seen in the data in the m ee interval 0.14 < m ee < 0.7 GeV/c 2 for the p T,ee range 0 < p T,ee < 0.4 GeV/c (see left panel of Fig. 11). Due to their characteristic m ee and p T,ee distributions, the e + e − pairs of the various expected sources are differently affected. The hadronic cocktail is well in agreement with the data within the statistical and systematic uncertainties.  TeV in the ALICE acceptance as a function of p T,ee in the mass range 0.14 < m ee < 0.7 GeV/c 2 (left) and 0.7 < m ee < 1.1 GeV/c 2 (right). The data are compared with the hadronic cocktail. In the bottom panels, the ratios of data to cocktail as a function of p T,ee are shown. Statistical and systematic uncertainties on the data are plotted as vertical bars and boxes, respectively. The total uncertainty of the cocktail is represented as a grey band.
The mixture of prompt and non-prompt sources in the low-mass region makes it well suited to test the feasibility to separate prompt and non-prompt contributions via the DCA ee variable. In Fig. 12, the DCA ee -differential cross section of e + e − pairs is shown integrated over p T,ee in the mass range 0.14 < m ee < 1.1 GeV/c 2 . The template for e + e − pairs from prompt light-flavour hadron decays cannot describe the tail of the DCA ee distribution. The latter is well reproduced by additional contributions from correlated pairs of heavy-flavour hadron decays. The good agreement between data and MC validates the possibility to separate prompt from non-prompt dielectron sources via this observable.

Intermediate-mass region
The IMR, 1.1 < m ee < 2.7 GeV/c 2 , is dominated by correlated e + e − pairs from semileptonic decays of charm and beauty hadrons. The p T,ee -differential cross section of e + e − pairs measured in this m ee region is shown in comparison with the hadronic cocktail in the left panel of Fig. 13. The cross section of e + e − pairs from cc is the dominant dielectron source for p T,ee < 3 GeV/c, whereas most of the e + e − pairs originate from bb for p T,ee > 4 GeV/c. This allows the correlated pairs from semileptonic decays of charm and beauty hadrons to be separated. Reasonable agreement between data and cocktail is seen in the bottom left panel of Fig. 13. The data are compared with a hadronic cocktail in the right panel of Fig. 13 where POWHEG is used to calculate the cc and bb contributions. The NLO event generator predicts harder p T,ee spectra for the cc and bb contributions. as for the PYTHIA cocktail, the POWHEG calculations tend to underestimate the data, in particular in the region where the cc contribution dominates. This indicates a sensitivity of the present data to the underlying heavy-quark production mechanism implemented in the two models. The latter can result in different kinematic correlations of the QQ pair and therefore different probabilities for the e + e − pair to enter the detector acceptance.  TeV in the ALICE acceptance as a function of p T,ee in the mass range 1.1 < m ee < 2.7 GeV/c 2 . The data are compared with the hadronic cocktail, where PYTHIA [55] (left) and POWHEG [56][57][58][59] (right) are used to calculate the cc and bb contributions. In the bottom panels, the corresponding ratios of data to cocktail as a function of p T,ee are shown. Statistical and systematic uncertainties on the data are plotted as vertical bars and boxes, respectively. The total uncertainty of the cocktails is represented as a grey band.  Table 3: Fraction of correlated e + e − pairs in 4π and after consecutive acceptance selection criteria (left column) for two different event generators (PYTHIA/POWHEG) and their relative difference (right column). Table 3 summarises the fraction of correlated e + e − pairs in the full phase space (4π) and after consecutive acceptance selection criteria for the cc and bb contributions. The fraction of dielectron pairs from charm-hadron decays where both electrons are found at mid-rapidity (|η e ± | < 0.8) is about 5.2% and 7.5% for the POWHEG and PYTHIA simulation, respectively. Since the hadronisation of the charm and beauty quarks, as well as the decay kinematics of the heavy-flavour hadrons, are the same in both calculations, this difference results from different treatments of the various production processes of the cc pair by the two event generators. First, the rapidity distribution of charm quarks predicted by POWHEG is slighly broader than the one from PYTHIA, leading to a smaller probability for single electrons to fall into the acceptance at mid-rapidity in POWHEG (20.7%) as compared to PYTHIA (17.3%). Second, the pseudorapidity correlation between the electron and positron from charm-hadron decays gives rise to a larger acceptance for e + e − pairs at mid-rapidity than from a purely random correlation. The pseudorapidity correlation is model-dependent which increases the difference in acceptance between the two generators to about 46%. For electrons from beauty-hadron decays, the model dependences are smaller, on the order of 6%. The rapidity distributions of beauty quarks predicted by POWHEG and PYTHIA are quite similar. Moreover, about 50% of the correlated e + e − pairs from beauty hadron decays originate from a single B hadron (B → De + X → e + e − X) and are insensitive to the correlations between the B and B hadrons. Due to the large mass of the B hadrons, the correlation between the decay electron and the parent meson is diluted and the pseudorapidity correlation of the e + e − pairs originating from different B hadrons is less related to the correlation between the b and b but more driven by decay kinematics.
The measured DCA ee distribution of e + e − pairs is shown in Fig. 14 integrated over p T,ee in the mass range 1.1 < m ee < 2.7 GeV/c 2 . The results are compared with the MC templates normalised to the PYTHIA cocktail. The shape of the MC DCA ee distribution for correlated e + e − pairs from charmhadron decays deviates from the data at large DCA ee . The additional contribution from e + e − pairs from beauty-hadron decays allows the data to be well described, as can be seen with the pull distribution Dielectron production in proton-proton collisions at √ s = 7 TeV ALICE Collaboration presented in the bottom panel of Fig. 14. The DCA ee variable gives additional constraints to separate e + e − pairs from charm-and beauty-hadron decays. No indication for a prompt source is observed in the IMR. The total cc and bb cross sections, σ cc and σ bb , can be extracted from the data by fitting the measured e + e − cross section of heavy-flavour hadron decays in the IMR with the sum of two contributions: where f GEN cc and f GEN bb are the cross sections for dielectron pairs from charm and beauty-hadron decays, calculated with the event generator GEN and normalised to σ REF cc and σ REF bb [94,95]. The two fit parameters are the scaling factors S cc and S bb , defined also as: The e + e − spectra from heavy-flavour hadron decays are obtained by subtracting the expected cross section of e + e − pairs originating from vector meson and J/ψ decays, from the measured e + e − distributions.
In the mass range 1.1-2.7 GeV/c 2 these contributions are small, of the order of 4%. The fit is performed separately in DCA ee and in (m ee , p T,ee ). For each combination of scaling factors, S cc and S bb , the χ 2 value is calculated: The values of the data points and MC calculations in bin i are given by x i and µ i , respectively, while σ stat x i and σ stat µ i represent their statistical uncertainties. The result of the fit is determined by the minimum of χ 2 . The extracted σ cc and σ bb cross sections are shown in Fig. 15  parameter (at χ 2 = χ 2 min + 1 [102]). The error bars represent the systematic uncertainties determined by the fit result after moving the data points coherently up-and downward by their systematic uncertainties. The uncertainties of the effective beauty-and charm-to-electron branching ratios are shown as coloured bands. Finally the full and dashed lines show σ REF cc [94] and σ REF bb [95] with their total uncertainties. The statistical and systematic uncertainties are fully correlated between the PYTHIA-and POWHEG-based results, whereas they are partially correlated between the (m ee , p T,ee ) and DCA ee fits. Both calculations, PYTHIA and POWHEG, are able to reproduce the (m ee , p T,ee ) and DCA ee spectra reasonably well and give similar minimum χ 2 per number of degree of freedom (0.999 for POWHEG and 0.989 for PYTHIA for the (m ee , p T,ee ) fit). The fit results of the (m ee , p T,ee ) and DCA ee spectra are in agreement within the statistical and systematic uncertainties. The DCA ee distribution is slightly less sensitive to the total bb cross section. The e + e − pairs from beauty-hadron decays only dominate the last DCA ee bin (see Fig. 14). The shapes of the MC DCA ee templates are driven by the decay kinematics and assumed to be model independent. Therefore the extracted σ cc and σ bb directly reflect the different probabilities for the e + e − pair to enter the detector acceptance calculated with PYTHIA or POWHEG (see Table 3). The (m ee , p T,ee ) fit depends in addition on the p T,ee distributions of correlated e + e − pairs from charm and beauty-hadron decays, which are harder in POWHEG compared to PYTHIA. The total cc and bb cross sections show model dependences of about a factor of two. The fitted cross sections are summarised in Tables 4 and 5. For comparison, the total cc cross section obtained by extrapolating in rapidity the D 0 p T spectrum measured by the ALICE Collaboration [94] is of the order of 8.6 mb with POWHEG, and 7 mb with PYTHIA. The dielectron measurements can give further constraints on the MC event generators aiming to reproduce the heavy-flavour production mechanisms, once the uncertainties, which are fully correlated between the PYTHIA-and POWHEG-based results, are reduced.

J/ψ mass region
The mass region 2.7 < m ee < 3.3 GeV/c 2 is dominated by J/ψ decays with a small contribution from charm-hadron decays. In the left panel of Fig. 16, the corresponding measured e + e − cross section as a function of p T,ee is shown in comparison with the hadronic cocktail. Good agreement between data and cocktail is observed, as can be seen on the bottom left panel of Fig. 16 in the ratio of data to cocktail.   The DCA ee distribution of e + e − pairs is sensitive to the large decay length of B mesons (cτ B ≈ 470 µm) and the contribution from J/ψ originating from their decays. The measured DCA ee spectrum shown in the right panel of Fig. 16 cannot be reproduced with the MC template of the prompt J/ψ alone. The contribution from non-prompt J/ψ, together with those from correlated e + e − pairs from heavyflavour hadron decays, leads to a reasonable description of the data by the MC calculations. The data are consistent with the fraction f B of non-prompt J/ψ originating from B meson decays previously measured by the ALICE Collaboration [101].  Fig. 16: (Colour online) Inclusive e + e − cross section in pp collisions at √ s = 7 TeV in the ALICE acceptance as a function of p T,ee (left panel) and DCA ee (right panel) in the mass range 2.7 < m ee < 3.3 GeV/c 2 . The data are compared with a cocktail of expected sources. In the bottom panels, the ratio of data to cocktail as a function of p T,ee (left) and the pull distribution as a function of DCA ee (right) are shown. Statistical and systematic uncertainties on the data are plotted as vertical bars and boxes, respectively. The total uncertainty of the cocktail is represented as a grey band. Dielectron production in proton-proton collisions at √ s = 7 TeV ALICE Collaboration

Direct photons
Direct photons are defined as photons that do not originate from hadronic decays. In pp collisions, they are produced predominantly in hard partonic interactions and their production rate can be calculated with perturbative QCD.
The direct-photon cross section can be extracted from the measurement of real photons detected in the electromagnetic calorimeters or via photon conversion in the detector material of ALICE [30,51]. For p T < 5 GeV/c, the extraction of the direct photon signal is difficult because of a large background from decay photons. An alternative way to measure direct-photon production is via its internal conversion into an e + e − pair. The advantage of this approach is that the main background originating from π 0 decays can be suppressed by selecting e + e − pairs with sufficiently large m ee (m ee > m π 0 ). The drawback is the small internal conversion probability of O(10 −2 ) and the rapidly decreasing cross section as a function of m ee (∝1/m ee ).
The mass dependence of the virtual-photon production for a given real-photon yield is given by the Kroll-Wada equation [71] which can be simplified in the case of p 2 T,ee m 2 ee , i.e. in the limit of quasireal virtual photons, to: with α, dN γ /dp T , and m e being the fine-structure constant, the number of real photons at a given p T (= p T,ee ), and the electron mass, respectively. To obtain the final expected shape f dir (m ee ) of the virtual direct photon mass distribution, the decay electrons are smeared by the detector resolution and passed through the acceptance of the ALICE barrel (|η e | < 0.8, p T,e > 0.2 GeV/c).
where f LF is the shape of the mass distribution of the light-flavour component of the hadronic cocktail and f HF is the e + e − cross section of the expected heavy-flavour contribution in the corresponding p T,ee bin.
Dielectron production in proton-proton collisions at √ s = 7 TeV ALICE Collaboration The ratio r of direct to inclusive photons is the only fit parameter. The fit is limited to the mass range 0.09 < m ee < 0.39 GeV/c 2 to ensure the condition p 2 T,ee m 2 ee . Both f LF and f dir are normalised such that they separately fit the data for m ee < 0.04 GeV/c 2 , because in this mass region the functional shapes of f LF and f dir are essentially identical. In Fig. 17, the measured m ee -differential e + e − cross section is shown in the p T,ee range 3 < p T,ee < 4 GeV/c, together with the fit result. The individual components are plotted separately. The systematic uncertainties due to the model dependence of the estimated e + e − yield from cc is evaluated by repeating the fit with f HF computed with the POWHEG generator and found to be below 0.75% in the full p T range.
The following sources of systematic uncertainty are considered: (1) the fit range, (2) the systematic uncertainties of the data, (3) the ones of the hadronic cocktail components, and (4) the normalisation range. The fit is thus repeated in different mass intervals between 0.09 GeV/c 2 and 0.39 GeV/c 2 . The corresponding uncertainty is found to be relevant only in the p T intervals 2-3 GeV/c and 3-4 GeV/c. The uncertainty arising from the systematic uncertainties of the data is evaluated by shifting all data points coherently to the upper and lower limits of their systematic uncertainties and by repeating the fit procedure. The systematic uncertainties from the light-flavour and heavy-flavour cocktail components are similarly estimated. The contribution of each light-flavour dielectron source is moved separately to its upper and lower systematic uncertainties. The largest source of uncertainty originates from the η/π 0 ratio. In most of the p T,ee bins, this is the dominant source of systematic uncertainties. Finally, f LF and f dir are normalised to the data in the range 0 < m ee < 0.09 GeV/c 2 to evaluate the normalisation uncertainty. All systematic uncertainties are added in quadrature to obtain the total systematic uncertainty. In Fig. 18, the ratio of inclusive to decay photon cross sections, i.e. R γ = σ γ inclusive /σ γ decay = 1/(1 − r), is shown as a function of p T . It is consistent with unity within the statistical and systematic uncertainties. Perturbative QCD calculations at NLO [103] performed with the CT10 PDFs [104][105][106] predict a small ratio of inclusive to decay photon cross sections over the measured p T range, compatible with the measurements within uncertainties. The uncertainty band of the calculation is given by the simultaneous variation of the factorisation, renormalisation, and fragmentation scales (with 0.5p T < µ F < 2p T for the factorization scale) used in the calculation. The upper limits at 90% confidence level (C.L.) on R γ , extracted with the Feldman-Cousins method [107], are summarised in Table. 6. Gaussian distributions are assumed for statistical and systematic uncertainties, which are treated independently and summed in quadrature. The results are consistent with the R γ measured in pp collisions at √ s = 8 TeV with the real photon analysis performed by the ALICE Collaboration [30].

Conclusion
A measurement of e + e − pair production at mid-rapidity (|η e | < 0.8) in minimum bias pp collisions at √ s = 7 TeV with ALICE at the LHC is shown. The results are presented as a function of the invariant mass m ee (0 < m ee < 3.3 GeV/c 2 ) of the e + e − pair, its transverse momentum p T,ee (0 < p T,ee < 8 GeV/c), and the pair transverse impact parameter DCA ee .
Dielectron production in proton-proton collisions at √ s = 7 TeV ALICE Collaboration The data are compared with a hadronic cocktail composed of the expected dielectron cross sections from the known hadronic sources. The contributions from semileptonic decays of heavy-flavour hadrons are calculated with PYTHIA and POWHEG, and normalised to the measured total cc and bb cross sections [94,95]. The shape of the DCA ee distribution of each source is obtained using a full simulation of the ALICE detector. The obtained DCA ee templates are normalised to the cocktail calculations integrated over the same m ee and p T,ee range.
Overall good agreement between data and cocktail is observed for all m ee , p T,ee , and DCA ee intervals considered. In the π 0 mass region (m ee < 0.14 GeV/c 2 ), the comparison of the measured DCA ee distribution with the MC templates shows that the detector resolution is well reproduced in the simulations. In the low-mass region (0.14 < m ee < 1.1 GeV/c 2 ), prompt and non-prompt contributions can be separated with the DCA ee observable. In the intermediate-mass region, 1.1 < m ee < 2.7 GeV/c 2 , the measured e + e − cross section is dominated by correlated e + e − pairs from charm-and beauty-hadron decays. The cc and bb total cross sections can be extracted from the data by a double-differential fit of the measured spectra in (m ee , p T,ee ) and by fitting the DCA ee distribution in the IMR. Both fits give consistent results within statistical and systematic uncertainties. The extracted cross sections show a large model-dependence between PYTHIA and POWHEG by up to a factor of two. In the J/ψ mass region (2.7 < m ee < 3.3 GeV/c 2 ), the measured DCA ee -and p T,ee -differential cross sections are well described by the hadronic cocktail. The DCA ee distribution is sensitive to the fraction f B of non-prompt J/ψ originating from B-meson decays. The data are consistent with the previously measured f B by the ALICE Collaboration [101].
In the quasi-real virtual-photon region, at low mass (m ee < 0.4 GeV/c 2 ) and high p T,ee (p T,ee > 1 GeV/c), the contribution of virtual direct photons is extracted from the data by fitting the m ee distributions in p T,ee bins. The extracted ratio of the inclusive-to-decay photon cross sections is found to be consistent with predictions from pQCD calculations at NLO [103][104][105][106] within statistical and systematic uncertainties.
The e + e − pair production will be further studied in pp, p−Pb and Pb-Pb collisions with the LHC Run 2 data, which are currently recorded, as well as with the expected high-statistics data from the LHC Run 3 Dielectron production in proton-proton collisions at √ s = 7 TeV ALICE Collaboration starting in 2021 [108][109][110][111]. In particular, the measurement of the DCA ee spectra in Run 3 will benefit from the new Inner Tracking System [111] with a smaller material budget and a resulting higher impact parameter resolution, while the upgrade of the Time Projection Chamber will provide a significant increase of the statistics [109,110].
Dielectron production in proton-proton collisions at √ s = 7 TeV ALICE Collaboration Dielectron production in proton-proton collisions at √ s = 7 TeV ALICE Collaboration