Measurement of electrons from semileptonic heavy-flavour hadron decays in pp collisions at $\sqrt{s}$= 7 TeV

The differential production cross section of electrons from semileptonic heavy-flavour hadron decays has been measured at mid-rapidity ($|y|<0.5$) in proton-proton collisions at $\sqrt{s} = 7$ TeV with ALICE at the LHC. Electrons were measured in the transverse momentum range 0.5 $<p_{\rm T}<$ 8 GeV/$c$. Predictions from a fixed order perturbative QCD calculation with next-to-leading-log resummation agree with the data within the theoretical and experimental uncertainties.


Introduction
The measurement of heavy-flavour (charm and beauty) production serves as an important testing ground of quantum chromodynamics (QCD), the theory of the strong interaction. Because of the large quark masses, heavy-flavour production in proton-proton (pp) collisions proceeds mainly through initial hard parton-parton collisions. Therefore, the production cross sections of charm and beauty quarks should provide a precision test of perturbative QCD (pQCD) for all values of transverse momenta p t . In previous experiments with pp collisions at the Tevatron ( √ s = 1.96 TeV), charm production cross sections were measured at high p t only and were found to exceed, by about 50% [1], the cross sections expected from pQCD calculations [2][3][4]. This, however, is still compatible with the substantial theoretical uncertainties. Beauty production at the Tevatron is well described by such calculations [5].
While the measurement of heavy-flavour production in pp collisions is important in its own interest, it also provides a crucial baseline for corresponding measurements in ultrarelativistic heavy-ion collisions. In such collisions a strongly interacting partonic medium is formed [6][7][8][9]. Heavy quarks interact with this medium after they have been produced in the initial stage of the collision. Consequently, heavy quarks suffer energy loss while they propagate through the medium, and they participate in the collective dynamics. The resulting modifications of the heavy-flavour momentum distributions in heavy-ion collisions with respect to those in pp collisions present a sensitive probe for the medium properties [10].
Heavy-flavour production can be investigated, among other channels, via the measurement of the contribution of semileptonic heavy-flavour decays to the inclusive lepton spectra. Both charm and beauty hadrons have substantial branching ratios (∼ 10%) to single electrons or single muons [11], giving rise to a large ratio of signal leptons from heavy-flavour hadron decays to background from other lepton sources, in particular at high p t .
Single electrons from heavy-flavour decays were first observed in the range 1.6 < p t < 4.7 GeV/c in pp collisions at the CERN ISR at √ s = 52.7 GeV [12], before the actual discovery of charm. At the CERN SppS, the UA1 experiment measured beauty production via single muons (10 < p t < 40 GeV/c) at √ s = 630 GeV [13] while the UA2 experiment used single electrons (0.5 < p t < 2 GeV/c) to measure the charm production cross section [14]. At the Tevatron, both the CDF and D0 experiments measured beauty production via single electrons (7 < p t < 60 GeV/c) [15] and single muons (3.5 < p t < 60 GeV/c) [16], respectively.
At RHIC, semileptonic heavy-flavour decays were extensively studied in pp and, for the first time, in heavy-ion collisions, mainly in the electron channel. With the PHENIX experiment the range 0.3 < p t < 9 GeV/c was covered [17], and with the STAR experiment electrons from heavy-flavour hadron decays were measured in the range 3 < p t < 10 GeV/c [18]. Within experimental and theoretical uncertainties pQCD calculations are in agreement with the measured production cross sections of electrons from charm [18,19] and beauty decays [20,21] at mid-rapidity in pp collisions at √ s = 0.2 TeV. In Au-Au collisions, the total yield of electrons from heavy-flavour decays was observed to scale with the number of binary nucleon-nucleon collisions [22]. However, a strong suppression of the electron yield was discovered for p t > 2 GeV/c [23, 24] with a simultaneous observation of a nonzero electron elliptic flow strength v 2 for p t < 2 GeV/c [10], indicating the substantial interaction of heavy quarks with the medium produced in Au-Au collisions at RHIC.
At the LHC, heavy-flavour production is studied in pp collisions at higher energies. Perturbative QCD calculations agree well with lepton production cross sections from heavy-flavour hadron decays measured for p t > 4 GeV/c with the ATLAS experiment at √ s = 7 TeV [25]. Furthermore, pQCD calculations of beauty hadron decays are in good agreement with production cross sections of non-prompt J/ψ at mid-rapidity as measured with the CMS experiment at high p t (p t > 6.5 GeV/c) [26] and with ALICE (A Large Ion Collider Experiment) at lower p t (p t > 1.3 GeV/c) [27]. D-meson production cross sections measured with ALICE are reproduced by corresponding calculations within substantial uncertainties at 7 TeV [28] and at 2. 76 TeV [29]. In addition, pQCD calculations are in agreement with the spectra of muons from heavy-flavour hadron decays at moderate p t as measured with ALICE at 7 TeV [30] and at 2. 76 TeV [31]. It is of particular importance to investigate charm production at low p t [28] in order to measure the total charm production cross section with good precision. Furthermore, low-p t charm measurements at the LHC probe the parton distribution function of the proton in the region of parton fractional momenta x ∼ 10 −4 and squared momentum transfers Q 2 ∼ (4 GeV) 2 , where gluon saturation effects might play a role [32]. This paper presents a measurement of single electrons, (e + +e − )/2, from semileptonic decays of charm and beauty hadrons in the transverse momentum range 0.5 < p t < 8 GeV/c at mid-rapidity (|y| < 0. 5) in pp collisions at √ s = 7 TeV with ALICE. For such a measurement an excellent electron identification (eID) and precise knowledge of the remaining hadron background in the electron candidate sample are mandatory. Two complementary eID approaches are employed. Both are based on the particle specific energy loss dE/dx in the ALICE Time Projection Chamber, required to be compatible with the energy loss of electrons. To increase the purity of the electron candidate sample, in the first approach a combination of time-of-flight measurements and the response of the transition radiation detector is employed (TPC-TOF/TPC-TRD-TOF analysis). In the second approach, electromagnetic calorimetry is used (TPC-EMCal analysis).
This article is organised as follows: Section 2 gives an overview over the ALICE detector systems that are relevant for the analysis presented here. The details of the data analysis are described in Section 3. The differential production cross section of electrons from semileptonic heavy-flavour decays is presented in Section 4. In the same Section, pQCD calculations at fixed order with next-to-leading-log resummation (FONLL [2,3,33]) are compared with the data, which extend the ATLAS measurement of electrons from heavy-flavour hadron decays to lower p t . This article concludes with a summary in Section 5. of the ITS are built with Silicon Drift Detectors (SDD) and the two outermost layers consist of doublesided Silicon Strip Detectors (SSD). Their radii extend from 15 to 43 cm. The ITS modules were aligned using survey information, cosmic-ray tracks, and pp data with the methods described in [35]. The material budget of the entire ITS corresponds on average to about 7.18% of X 0 at η = 0 [34]. The exact knowledge of the material budget in the innermost ITS layers is crucial here as the conversion of photons into electron-positron pairs in material is the source of an important background component in the present analysis. In the ALICE experiment, the reconstruction of such conversion pairs has resulted in a measurement of the relevant material budget with a precision of 4.5% [36].
The most important detector for the track reconstruction and the momentum measurement is the Time Projection Chamber (TPC), which is also used for particle identification [37]. The ALICE TPC is a large cylindrical drift detector whose active volume extends radially from 85 to 247 cm, and from -250 to +250 cm along the beam direction. The active volume of nearly 90 m 3 is filled with a Ne (85.5%), CO 2 (9.5%), and N 2 (4.8%) gas mixture. A central high-voltage electrode maintained at -100 kV divides the TPC into two sections. The end-caps are equipped with multiwire proportional chambers with cathode pad readout. For a particle traversing the TPC, up to 159 space points (clusters) are recorded. The cluster data are used to reconstruct the charged particle trajectory in the magnetic field as well as to calculate the particle's specific energy loss dE/dx in the TPC gas. Simultaneous measurements of the dE/dx and momentum allow the identification of the particle species which has produced the track. The dE/dx resolution of the TPC, σ TPC−dE/dx , was approximately 5.5% for minimum ionising particles crossing the full detector [38]. The dE/dx resolution was determined using minimum ionising pions and cosmic ray muons at the Fermi plateau. Charged particle tracks are reconstructed in the ITS and TPC with a transverse momentum resolution ranging from about 1% at 1 GeV/c, to about 3% at 10 GeV/c [37].
The TPC is surrounded by the Transition Radiation Detector (TRD) at a radial distance of 2.9 m from the beam axis. The TRD is segmented in the azimuth direction in 18 individual super-modules, seven of which were installed in the 2010 running period of ALICE as indicated in Fig. 1. Each super-module is segmented further in five units (stacks) along the beam direction. Each stack comprises six layers in the radial direction. Each detector element consists of a fibre sandwich radiator of 48 mm thickness [39], a drift section of 30 mm thickness, and a multiwire proportional chamber section (7 mm thickness) with pad readout. The gas is a mixture of Xe (85%) and CO 2 (15%) [40][41][42][43]. The scope of the TRD is to provide a good separation of electrons from pions, particularly for momenta above 1 GeV/c. This is accomplished by measuring transition radiation photons, which are produced only by electrons [44]. The TRD is also designed to provide a fast trigger with particle identification information to discriminate electrons from hadrons [45]. This trigger was not used in the 2010 data taking.
At larger radii, at a distance of 3.7 m from the beam axis, the Time-Of-Flight (TOF) detector provides further essential information for the particle identification. The TOF detector is segmented in 18 sectors and covers the full azimuth. Each sector contains 91 Multigap Resistive Plate Chambers (MRPCs). In total, 152,928 sensitive pads of dimension 2.5×3.5 cm 2 are read out. The TOF resolution of the particle arrival time is, at present, better than 100 ps [46]. The start time of the collision is measured by the ALICE T0 detector, an array of Cherenkov counters located at +350 cm and -70 cm along the beam-line, or it is estimated using the particle arrival times at the TOF detector in events without a T0 signal. In the case that neither of the two methods provides an output an average start time is used. Depending on the start time method used, the corresponding resolution is taken into account in the overall TOF PID resolution. The particle identification is based on the difference between the measured time-of-flight and its expected value, computed for each mass hypothesis from the track momentum and length of the trajectory. The overall resolution of this difference σ TOF−PID is about 160 ps [28].
The Electromagnetic Calorimeter (EMCal) is a Pb-scintillator sampling calorimeter, located at a radial distance of about 4.5 m from the beam line. The full detector covers the pseudorapidity range −0.7 < η < 0.7 with an azimuthal acceptance of ∆φ = 107 o . In the 2010 running period of ALICE the azimuthal coverage of the EMCal was limited to ∆φ = 40 o , since only part of the detector was installed. The calorimeter is of the 'Shashlik' type built from alternating lead and scintillator segments of 1.44 mm and 1.76 mm thickness, respectively, together with longitudinal wavelength-shifting fibres for light collection. The cell size of the EMCal is approximately 0.014 × 0.014 rad in ∆φ × ∆η, and the depth corresponds to 20.1 X 0 . From electron test beam data, the energy resolution of the EMCal was determined to be 1.7 11.1/ E(GeV) 5.1/E(GeV)% [47].
A minimum p t of about 0.3 GeV/c is needed for the particles to reach the TRD, TOF, and EMCal detectors in the magnetic field of 0.5 T.
The VZERO detector is used for event selection and background rejection. It consists of two arrays of 32 Electrons from heavy-flavour decays in pp collisions at √ s = 7 TeV 5 scintillators each, which are arranged in four rings around the beam pipe on either side of the interaction region, covering the pseudorapidity ranges 2.8 < η < 5.1 and −3.7 < η < −1.7, respectively. The time resolution of this detector is better than 1 ns. Information from the VZERO response is recorded in a time window of ± 25 ns around the nominal beam crossing time. The VZERO is used to select beam-beam interactions in the central region of ALICE and to discriminate against interactions of the beam with gas molecules in the beam pipe.
The ALICE minimum bias trigger required at least one hit in either of the two SPD layers or in the VZERO detector. In addition, collision events had to be in coincidence with signals from the beam position monitors, indicating the passage of proton bunches from both beams.

General strategy
For the measurement of the differential invariant cross section of electrons from semileptonic decays of heavy-flavour hadrons the following strategy was adopted. First, charged particle tracks which fulfil a set of electron identification cuts were selected. From the electron candidate tracks the remaining contamination from misidentified hadrons was subtracted. After corrections for geometrical acceptance and efficiency the inclusive electron yield per minimum bias triggered collision was determined for two different electron identification strategies. Since for all relevant sources the spectra of decay positrons and electrons are identical (e + /e − = 1), the average spectrum of positrons and electrons, (e + + e − )/2, was used for the further analysis. The electron background from sources other than semileptonic heavyflavour hadron decays was calculated using a cocktail approach and subtracted from the inclusive electron spectra. The resulting spectra of electrons from heavy-flavour hadron decays were normalised using the cross section of minimum bias triggered pp collisions. A weighted average of the two measurements obtained with different electron identification strategies led to the final result.

Data set and event selection
The data used in the present analysis were recorded during the 2010 running period. The luminosity was limited to 0.6 − 1.2 × 10 29 cm −2 s −1 in order to keep the probability of collision pile-up per triggered event below 2.5%. This was cross-checked by looking at events with more than one vertex reconstructed with the SPD.
The primary collision vertex can be determined using the reconstructed tracks in the event or the correlated hits in the two pixel layers. Only events with a reconstructed primary vertex using one of the two methods were selected for further analysis. In order to minimise edge effects at the limit of the central barrel acceptance, the vertex was required to be within ±10 cm from the centre of the ALICE experiment along the beam direction. Integrated luminosities of 2.6 nb −1 and 2.1 nb −1 were used for the TPC-TOF/TPC-TRD-TOF and TPC-EMCal analysis, respectively.
In the offline analysis, pile-up events were identified using the SPD. Events with a second interaction vertex reconstructed with at least three tracklets (short tracks from SPD clusters) and well separated from the first vertex by more than 8 mm, are rejected from further analysis. Taking into account the efficiency of the pile-up event identification, less than 2.5% of the triggered events have been found to be related to more than one interaction. The effect of the remaining undetected pile-up was negligible for the analysis. Moreover, background from beam-gas interactions was eliminated using the VZERO timing information as well as the correlation in the SPD between the number of reconstructed charged particle track segments and the number of hits. ≥ 3 SPD layer in which a hit is requested in TPC-TOF/TPC-TRD-TOF first SPD layer in which a hit is requested in TPC-EMCal any χ 2 /ndf of the momentum fit in the TPC < 2 Distance of Closest Approach in xy (cm) < 1 Distance of Closest Approach in z (cm) < 2

Track reconstruction and selection
Charged particle tracks reconstructed in the TPC and ITS were propagated towards the outer detectors using a Kalman filter approach [48]. Geometrical matching was applied to associate tracks with hits in the outer detectors.
In the currently limited active area in azimuth of the TRD, the tracks were associated with track segments, called tracklets, reconstructed in individual chambers. This tracklet reconstruction assumed straight trajectories of charged particles passing a chamber. As the ALICE TRD comprises six layers, a track can include up to six tracklets. In the TPC-TRD-TOF analysis a minimum of four associated TRD tracklets was required for each electron candidate track. For each tracklet the charge deposited in the corresponding chamber was measured. This information was used for electron identification.
The EMCal coverage was limited in the 2010 run. In azimuth, the installed EMCal sectors neither overlap with the installed TRD supermodules nor with the area of the innermost SPD layer which was operational in 2010 as indicated in Fig. 1. Electromagnetic showers reconstructed in the EMCal were associated with charged particle tracks if the distance between the track projection on the EMCal surface and the reconstructed shower was small in η and φ . The quadratic sum of the difference between track projection and reconstructed position had to be less than 0.05 in (η,φ ) space for a track-shower pair to be accepted, where φ is measured in radians.
The pseudorapidity ranges used in the TPC-TOF/TPC-TRD-TOF and TPC-EMCal analyses were restricted to |η| < 0.5 and |η| < 0.6, respectively, because towards larger absolute values of η the systematic uncertainties related to particle identification increase considerably.
Electron candidate tracks were required to fulfil several track selection cuts. Table 1 summarises these selection criteria. A cut on the χ 2 per degree of freedom (ndf) of the momentum fit in the TPC was applied to reject fake tracks which comprise a significant number of clusters originating from more than one charged particle trajectory. A track reconstructed within the TPC is characterised by the number of clusters used for the track reconstruction and fit (up to a maximum of 159 clusters). Not all of these clusters are used for the energy loss calculation: those close to the borders of the TPC sectors are not considered. Separate cuts are applied on these two quantities. To guarantee good particle identification based on the specific dE/dx in the TPC, tracks were required to include a minimum number of 80 clusters used for the energy loss calculation. A cut on the number of clusters for tracking is used to enhance the electron/pion separation. As the energy deposit of electrons on the Fermi plateau is approximately 1.6 times larger than for minimum ionizing particles, the associated clusters are insensitive to detector threshold effects and electron tracks have, on average, a higher number of clusters. The stringent request for at least 120 clusters from the maximum of 159 enhances electrons relative to hadrons. Kink candidates, i.e. tracks which are not consistent with the track model of continuous particle trajectories but show deviations due to decays in flight or the emission of Bremsstrahlung, were discarded from further analysis since the dE/dx resolution of the TPC is worse for such kink tracks than for regular tracks. In order to minimise the contribution from photon conversions in the ITS, a hit in the innermost SPD layer was required for all selected tracks in the TPC-TOF/TPC-TRD-TOF analysis. In total, at least four ITS hits were required to be associated with a track. Since the active area in azimuth of the EMCal overlapped with an inactive area of the first SPD layer, this approach had to be modified for the TPC-EMCal analysis. For the latter case, a matching hit was required in any of the two SPD layers and the required total number of ITS hits was reduced to three. Charged pion tracks from the weak decay K 0 S → π + π − occurring beyond the first SPD layer were used to demonstrate that the probability of random matches between tracks and uncorrelated hits in the ITS is negligible. A cut on the distance of closest approach (DCA) to the primary vertex in the transverse plane (xy) as well as in the beam direction (z) was applied to reject background tracks and non-primary tracks.

Electron identification
Electrons were identified using the information provided by various detector subsystems of the ALICE central barrel. The detector which played the most important role in particle identification for both analyses discussed here is the TPC. Particle identification in the TPC is based on the measurement of the specific energy loss dE/dx in the detector gas. The dE/dx distribution, expressed in arbitrary units, as a function of the particle momentum for tracks measured in 7 TeV pp collisions, is shown in the left panel of Fig. 2. The solid lines depict the energy loss for electrons, pions, kaons, protons, and deuterons expected from the Bethe-Bloch formula [49]. For the electron selection, the energy loss was expressed as a deviation from the parameterised electron Bethe-Bloch line, divided by the energy loss resolution σ TPC−dE/dx , as shown in the right panel of Fig. 2. Figure 2 demonstrates that the electron identification provided by the TPC is not sufficient at low momentum (below 1.5 GeV/c) because the kaon and proton dE/dx lines cross the electron line. In addition, the merging of the dE/dx lines of electrons, muons, pions, and other hadrons limits the particle identification at high momentum. Therefore, a high purity electron candidate sample can only be selected with the help of other detectors. Two different strategies were used in this analysis, one employing in addition the information from the TOF and TRD detectors, and the other one based on the EMCal response.

TPC-TOF/TPC-TRD-TOF analysis
The information provided by the TOF detector is complementary to that from the TPC in the low momentum region and it is used to resolve the ambiguities in the crossing regions of the TPC electron, kaon, and proton lines. The time-of-flight information allows the rejection of kaons up to a momentum of approximately 1.5 GeV/c and protons up to about 3 GeV/c. The selection was done by comparing the measured time-of-flight with the value expected assuming the particle being an electron. Only tracks compatible with the electron hypothesis within 3 σ TOF−PID were considered as electron candidates for further analysis. The difference between the measured time-of-flight and the expected time-of-flight, as a function of the momentum, is shown in the upper left panel of Fig. 3. Lines indicate the selection band. This criterion combined with the selection of tracks between 0 and 3 σ TPC−dE/dx resulted in a pure sample of electron candidates up to a momentum of approximately 4 GeV/c. In this momentum range, the hadron contamination remained below 1%, while above 4 GeV/c the pion contamination became significant again. At such high momenta the TOF information could not be used to reduce further the hadron contamination in the electron candidate sample. Therefore, the TPC-TOF analysis was restricted to the p t range below 4 GeV/c. To extend the accessible range to higher momenta, information from the TRD was used. As for the TPC, particle identification in the TRD makes use of the specific energy loss in the detector gas. In addition, the measurement of transition radiation photons produced by electrons traversing the dedicated radiators in front of the TRD drift chambers enhances distinctively the capability of the TRD to separate electrons from hadrons. The charge deposit per tracklet was compared with reference charge distributions obtained from dedicated test beam data [50], where electron and pion beams were provided at a number of different, discrete momenta. The probability of identifying a particle of given momentum as an electron was derived from a linear interpolation between the nearest measured data points in momentum. The electron probabilities were calculated for each TRD tracklet (up to six per track). They were combined for a given track and a likelihood value was calculated on which the eID is based.
The TRD electron likelihood distribution as a function of momentum for tracks passing the TOF selection and having six TRD tracklets is shown in the upper right panel of Fig. 3. The electron candidate selection was performed applying a momentum dependent cut defined such that it provided a constant electron efficiency of 80%. The p t dependence of this cut was determined using a clean sample of electrons from photon conversions. Furthermore, this cut depends on the exact number of charge measurements (tracklets) available per track (four to six in the present analysis). The lower right panel of Fig. 3 depicts the cut described for six tracklets. Cuts for tracks with four or five tracklets were applied in the same way. The TRD selection was applied only for tracks with a momentum above 4 GeV/c because at lower momenta the TPC-TOF selection was sufficient. For tracks passing the TRD selection, the lower left panel of Fig. 3 shows the particle dE/dx in the TPC, expressed as the distance to the expected energy deposit of electrons, normalised by the energy loss resolution. Having used the TRD information, an excellent separation of electrons from pions is already visible in the whole momentum range up to 8 GeV/c. The selection of tracks between 0 and 3 σ TPC−dE/dx results in an almost pure sample of electrons with a remaining hadron contamination of less than 2% over the full p t range (see below).

TPC-EMCal analysis
An alternative approach to separate electrons from hadrons, over a wide momentum range, is based on electromagnetic calorimetry. Tracks were geometrically matched with clusters reconstructed in the EMCal. For each track, the momentum information was provided by the track reconstruction algorithms in the TPC and ITS. The corresponding energy deposit E was measured in the EMCal. The energy information was provided by a cluster of cells: the energy deposition was summed over adjacent cells, with an energy measurement above a threshold of ≈48 MeV around a seed cell.  tracks, the ratio E/p of the energy deposited in the EMCal and the measured momentum was calculated to identify electrons. The distribution of E/p is shown in Fig. 4 for tracks with transverse momenta in the range 4 < p t < 5 GeV/c. Electrons deposit their total energy in the EMCal and, due to their small mass, the ratio E/p should be equal to unity. Therefore, the peak around one in Fig. 4 confirms the good pre-selection of electron candidate tracks using the TPC. The exact shape of the E/p distribution depends on the EMCal response, Bremsstrahlung in the material crossed by electrons along their trajectory, and the remaining background from charged hadrons. The E/p distribution was fitted with the sum of a Gaussian and an exponential function. Electron candidates were required to have E/p between −3 and +3 σ E/p of the E/p distribution, where σ E/p is the width of the fitted Gaussian function. Due to the loose ITS cuts, the TPC-EMCal analysis suffers from a large background from photon conversions and, consequently, a small signal to background ratio for electrons from heavy-flavour hadron decays at low p t . Therefore, the p t range was limited to p t > 3 GeV/c, where a significant heavy-flavour signal could be measured.  Fig. 4: (Colour online) Ratio E/p of the energy deposit in the EMCal and the measured momentum for charged particle tracks in the range 4 < p t < 5 GeV/c. The distribution was fitted with the sum of a Gaussian for the electron signal and an exponential for the remaining hadron background. Arrows indicate the selection window for electron candidates. Table 2: Overview over the hadron contamination subtracted in the inclusive electron spectrum for the three analysis strategies.

Hadron contamination
The residual hadron contamination, after the electron identification cuts, was estimated by fitting the measured detector signal distributions with functions modelling the background and signal contributions. The hadron contamination is summarised in Table 2 for the three analysis strategies.

TPC-TOF/TPC-TRD-TOF analysis
For the TPC-TOF/TPC-TRD-TOF analysis, the TPC dE/dx distribution after TOF-and TRD-PID cuts was fitted in momentum slices. The residual contamination to the electron sample is given by the contribution of misidentified charged particles after the cut on the TPC dE/dx. The cut on the TPC dE/dx applied for electrons was chosen to have 50% efficiency for all momenta. The electron line was parameterised using a Gaussian function, which describes well the shape of the TPC dE/dx distribution, expressed as deviation from the parameterised electron Bethe-Bloch line normalised by the energy loss resolution, for a given particle species close to the maximum of this distribution. The dominant contribution to the contamination of the electron candidate sample at momenta above 1 GeV/c comes from the tail of the pion dE/dx distribution. This tail is not adequately described by a Gaussian for the purpose of an estimation of the contamination. A better description of the tail of the pion dE/dx distribution is obtained by multiplying a Landau distribution with an exponential term. The validity of this approach was confirmed using a clean pion sample from K 0 S decays which was selected using the V0-finder and  tagged using topological cuts [51]. At low momenta, protons and kaons are suppressed by the eID cut applied using the TOF detector, while at higher momenta the kaon and proton dE/dx lines approach each other. Therefore, a single slightly skewed Gaussian distribution was used to fit the combined contribution of both particle types. The contribution of muons was fitted jointly with that of the pions.
The combined fit of the TPC dE/dx distribution in the momentum range 3 < p < 4 GeV/c is shown in Fig. 5. To demonstrate that the fit does not introduce any additional systematic uncertainty, the difference between data and fit was compared with the expected statistical fluctuations. The fit is in good agreement with the data within statistical uncertainties.
The relative contamination was calculated as the ratio of the fitted background contribution to the overall distribution after the TPC dE/dx cut. The contamination remained insignificant (below 2%) up to a momentum of 8 GeV/c, and it was subtracted from the electron candidate sample in the TPC-TOF/TPC-TRD-TOF analysis.

TPC-EMCal analysis
For the TPC-EMCal analysis, the hadron contamination in the electron candidate sample was estimated based on fits to the E/p distribution in momentum slices with a function describing the signal (Gaussian for E/p ∼ 1) and background (exponent) as shown in Fig. 4. Furthermore, the contamination has been constrained with the ratio of the integrals of the E/p distribution in two intervals: µ E/p to µ E/p + n · σ E/p and µ E/p − n · σ E/p to µ E/p for n = 3, where µ, σ are the parameters of the Gaussian and µ E/p is the mean of the distribution. This ratio is sensitive to the amount of background in the measured E/p and its evolution has been studied by varying n between 1 and 3. Based on these estimates the hadron contamination in the electron candidate sample was determined to be (7±4)% in the range 3 < p t < 7 GeV/c, and it was subtracted from the electron sample.

Corrections and normalization
Corrections were applied to the electron candidate spectra for the geometrical acceptance of the detectors (ε geo ), the reconstruction efficiency (ε reco ), and the electron identification efficiency (ε eID ).  Due to the finite azimuthal angle covered by the TRD and the EMCal detectors in the 2010 run, the maximum geometrical acceptance was 38% for the TPC-TRD-TOF analysis and 11% for the TPC-EMCal analysis. The geometrical acceptance and reconstruction efficiency were computed from a full numerical Monte Carlo simulation of the experiment. Monte Carlo events were produced by the PYTHIA 6.4.21 event generator [52] using the Perugia-0 parameter tuning [53] with the same primary vertex distribution as in the data. The generated particles were propagated through the apparatus using GEANT3 [54]. The same reconstruction algorithms and cuts were used as for the analysis of data. For the calculation of ε geo and ε reco in the TPC-TOF/TPC-TRD-TOF analysis, which requires a hit in the first SPD layer, only those electrons were considered in the simulation which were produced within 3 cm distance from the interaction vertex in the transverse direction and which were reconstructed in the pseudorapidity range |η| < 0.5. For the TPC-EMCal analysis, which requires a hit in any of the two SPD layers, electrons produced within 7 cm transverse distance from the vertex and with |η| < 0.6 were considered for the calculation of ε geo and ε reco .
The evaluation of the electron transverse momentum is affected by the finite momentum resolution and by the electron energy loss due to Bremsstrahlung in the material in front of and in the tracking detectors, where the dominant contribution is from the ITS (X/X 0 = 7.18% at η = 0 [34]). These effects distort the shape of the p t distribution, which falls steeply with increasing momentum, and have to be taken into account. The necessary correction grows with increasing steepness of the p t distribution and with increasing widths of the p t bins. To determine this correction, an unfolding procedure based on Bayes' theorem was applied. The Monte Carlo generated and reconstructed transverse momentum distributions of electrons were used to obtain a smearing matrix. A detailed description of the procedure can be  found elsewhere [55]. The maximum unfolding correction of the measured electron yield was ≈ 20% at p t = 2 GeV/c, becoming smaller towards higher p t .
The product of the overall acceptance and efficiency (ε geo × ε reco × ε eID ) as function of p t for the TPC-TOF/TPC-TRD-TOF analysis as well as the overall efficiency for the TPC-EMCal analysis are shown in Figure 6.
To cross check the value of the acceptance times efficiency calculated via the simulation and to determine TRD PID efficiencies, a data-driven method was employed. A pure sample of electrons from photon conversions in the detector material was selected. Reconstructed conversion electron vertices were selected using the V0-finder [51]. The same cuts as in the analysis were applied to the pure electron sample except for the requirements in the ITS which were relaxed such that the electron candidates needed to have only two hits in the ITS, from which at least one is required to be in any of the two pixel layers. The cross-check was done in the momentum range where the sample of electrons from photon conversions is statistically significant (up to 6 GeV/c). The good agreement of the TRD acceptance and tracking efficiency (ε geo TRD × ε reco TRD ) for electrons from conversions in data and in the simulation, which have at least five TRD tracklets, is demonstrated in Fig. 7. The TOF tracking and PID efficiency after the TRD requirement (ε geo TOF × ε reco TOF × ε eID TOF ) is also well reproduced in the simulations (see Fig. 7). For the TPC-EMCal analysis, the electron identification efficiency from the TPC dE/dx cut was estimated using the data driven method. Particles were selected with a dE/dx in the range between −1.5 and 3 σ TPC−dE/dx . The corresponding efficiency was about 93% with respect to the full distribution. The efficiency of the electron identification with EMCal, i.e. track matching and eID employing the E/p cut, was estimated using the simulation.
The p t -differential invariant yield N e ± of inclusive electrons, (e + + e − )/2, was calculated from the cor- Table 3: Variation of the electron selection criteria to estimate the systematic uncertainties due to track reconstruction and particle identification.

TPC-TRD-TOF analysis:
Fixed electron efficiency 85% 80% 75% for TRD likelihood cut TPC-EMCal analysis: rected electron p t spectrum and the number N MB of minimum bias pp collisions as: where p centre t are the centres of the p t bins with widths ∆p t chosen here, and ∆y is the width of the rapidity interval covered. In the following, invariant yields or cross sections within a given p t bin are always quoted at the bin centre without a bin-shift correction for the fact that the electron yield decreases with increasing p t . When ratios of yields or cross sections are calculated the same p t bins are used for both the numerator and the denominator and average yields or cross sections are used for every individual p t bin to avoid bin-shift effects.

TPC-TOF-TRD analysis
The following sources of systematic uncertainties were considered: the corrections of the ITS, TPC, TOF, and TRD tracking efficiencies, the TOF, TPC, and TRD particle identification efficiencies, the p t unfolding procedure, and the absolute normalisation.
To estimate the contributions from tracking and particle identification, the analysis was repeated with Electrons from heavy-flavour decays in pp collisions at √ s = 7 TeV 15 modified selection criteria as summarised in Table 3.
For each variation of the selection criteria, the inclusive electron spectra were fully corrected. The resulting spectra were compared by inspecting their ratio. As function of p t , these ratios define the relative systematic uncertainties as listed in Table 4. A general systematic uncertainty of 2%, due to the ITS-TPC track matching efficiency, was taken from dedicated tracking investigations. It is important to note that for each cut related to the particle identification the hadron contamination may change and has to be re-evaluated.
In addition, the corrected spectra of positrons and electrons, as well as the corrected spectra obtained in the positive (η + ) and negative η (η − ) range, were compared. Deviations from the expected ratios e + /e − = 1 and η + /η − = 1 were taken into account in the systematics.
The systematic uncertainty related to the MC p t -distribution used for the corrections, named "unfolding" in Table 4, was extracted from the comparison of the data corrected with two different Monte Carlo samples. In addition to the PYTHIA 6.4.21 based sample, used already for the evaluation of the geometrical acceptance and the reconstruction efficiency (see Sec. 3.6), a second PYTHIA based sample with artificially enhanced heavy-flavour hadron yields was employed.
Up to electron transverse momenta of 4 GeV/c the electron identification was based on the TPC-TOF selection only. For higher momenta the TRD selection was included. Therefore, the TRD contribution to the systematic uncertainties was only considered for the part of the spectrum above 4 GeV/c.
The systematic uncertainties are summarised in Table 4. The systematic uncertainty of the DCA cuts increases at low p t , where the DCA resolution decreases and electrons from photon conversion in the material do not point to the primary vertex. The total systematic uncertainty is calculated as the quadratic sum of all contributions and it is of the order of 8.5% for the TPC-TOF and between 20% and 26% for the TPC-TRD-TOF parts of the spectrum, respectively.

TPC-EMCal analysis
Systematic uncertainties from the electron identification on the inclusive electron spectrum obtained with the TPC-EMCal approach arise from the dE/dx measured in the TPC and the E/p matching. The uncertainties were estimated by measuring the spectra with changing cuts on dE/dx and E/p. The variation of the cuts are summarised in Table 3. The resulting uncertainty of the electron identification is 5% from the E/p matching, which includes the subtraction of contamination, and 6% from the dE/dx selection. The systematic uncertainties due to the track selection were estimated by applying the same variation of cuts as for the TPC-TOF/TPC-TRD-TOF analysis, except for the ITS cut. The individual contributions are summarised in Table 4. The total systematic uncertainty is approximately 20% on the inclusive electron spectrum.

Inclusive invariant p t -differential electron yield
The electron yield per minimum bias pp collision was measured as function of p t . The hadron contamination was subtracted statistically from the spectrum and corrections for acceptance, reconstruction, and electron identification efficiency were applied. The corrected inclusive electron spectra measured with the TPC-TOF and TPC-TRD-TOF analyses are shown in the upper panel of Fig. 8. The spectra were parameterised simultaneously using a Tsallis function as depicted in Fig. 8. The results from both analyses agree well in the p t region between 1 and 4 GeV/c as demonstrated in the lower panel of Fig. 8, which shows the ratios of the data to the common fit on a linear scale. However, the systematic uncertainties in the TPC-TOF analysis are substantially smaller than in the TPC-TRD-TOF analysis. Therefore, for the combined TPC-TOF/TPC-TRD-TOF inclusive yield the TPC-TOF result is used for p t < 4 GeV/c. The extension towards higher p t is given by the TPC-TRD-TOF measurement. The corresponding result employing the TPC-EMCal eID is also depicted in Fig. 8. Since the relevant material budget was not the same for the two approaches the contribution from photon conversions is different and, hence, the inclusive electron yield is larger for the TPC-EMCal analysis than for the TPC-TOF/TPC-TRD-TOF analysis.

Electron background cocktail
The inclusive electron spectrum can be subdivided into five components:   The signal of electrons from heavy-flavour decays is small compared to the background at low p t but rises with increasing p t as will be shown in Section 4 ( Fig. 10). One technique to extract the heavy-flavour signal from the inclusive electron spectrum is the so-called "cocktail subtraction" method described in detail here. In this approach, a cocktail of electrons from different background sources was calculated using a Monte Carlo hadron-decay generator which, by construction, produces identical spectra for decay positrons and electrons. The resulting background spectra were then subtracted from the inclusive electron spectrum. This approach relies on the availability of the momentum distributions of the relevant background sources.
The most important background source is the neutral pion. The contribution from π 0 decays to the background is twofold. First, the Dalitz decay of neutral pions (π 0 → e + e − γ, with a branching ratio BR of 1.174 ± 0.035% [11]) is a primary source of electrons from the collision vertex. Second, photons from the decay π 0 → γγ (BR = 98.823 ± 0.034% [11]) can convert in material into e + e − pairs in the ALICE acceptance. This process gives rise to a secondary source of electrons not originating from the collision vertex. It is important to point out that, although the total material budget in the ALICE central barrel acceptance is relatively large (11.4 ± 0.5% of a radiation length X 0 integrated over a radial distance up to 180 cm from the beam line in the range |η| < 0.9) [36], the material budget relevant for the present analysis is much less (see below). In fact, electron candidate tracks considered here are required to be associated with either a hit in the first pixel layer of the ALICE ITS in case of the TPC-TOF/TPC-TRD-TOF analysis or a hit in any of the two pixel layers in the TPC-EMCal analysis. Therefore, only conversions in the beam pipe and in a fraction of the ITS material are relevant here. Consequently, the background contribution from photon conversions is similar to the contribution from Dalitz decays (see below for a detailed calculation).
The rapidity distribution of mesons is assumed to be flat around mid-rapidity. The momentum distributions of π 0 and η mesons are obtained via fitting the spectra as measured by the ALICE collaboration [56]. In this measurement, π 0 and η decays in the γγ channel are reconstructed using two complementary techniques. As it is done conventionally, in the first approach the two decay photons are measured via electromagnetic calorimetry. This technique becomes notoriously difficult at low photon energy and, consequently, low meson p t . In this region, it becomes advantageous to reconstruct photons in a second approach via the conversion into e + e − pairs in the detector acceptance. The large acceptance, high resolution ALICE TPC is ideally suited to perform such a measurement, which extends the π 0 spectrum down to 300 MeV/c. Combining the measurements via calorimetry and the reconstruction of photon conversions, the π 0 and η transverse momentum spectra from pp collisions at √ s = 7 TeV Electrons from heavy-flavour decays in pp collisions at √ s = 7 TeV Table 5: Fit parameters of the Tsallis parameterisation (see Eq. 2) of the differential cross section of π 0 and η meson production.
The invariant differential cross section of π 0 and η meson production in pp collisions at √ s = 7 GeV was parameterised with a Tsallis function [57] given by: where the parameters dN/dy, T , and n were obtained by fitting the experimental data as shown in Fig. 9, σ pp is the inelastic pp cross section, m is the relevant meson's mass and m t is the corresponding transverse mass m t = m 2 + p 2 t . The values of the fit parameters are listed in Table 5. Given that pion decays and the corresponding conversion of decay photons are the most important cocktail ingredient up to intermediate p t , the systematic uncertainty of the background cocktail is dominated by the uncertainty of the pion input. To evaluate this uncertainty the measured differential pion cross section was moved up (down) in all p t bins by the individual uncertainties in the bins, the parameterization according to Eq. 2 was repeated, and full cocktails were generated with these upper (lower) pion spectra as input. Thus, the uncertainty of the pion input was propagated to the electron cocktail. The same approach was followed for the η meson.
Other light mesons (ρ, ω, η , and φ ) contribute to the background electron cocktail through their Dalitz and/or dielectron decay channels as well as through the conversion of photons from their decays. However, none of the contributions from these mesons is of any practical importance compared to the pion and the η meson. For the cocktail calculation, the shape of the invariant p t distributions and the relative normalisations to the π 0 are required as input parameters for the heavier mesons. The shape of the p t spectra was derived from the pion spectrum assuming m t scaling, i.e. the spectral shapes of heavier mesons and pions were consistent as a function of m t . Since the m t scaling approach ensures that, at high p t , the spectral shapes of all meson distributions are the same, the normalisation of the heavier meson spectra relative to the pion spectrum was determined by the ratios of heavier meson yields to neutral pion yields at high p t (5 GeV/c in the present analysis). The values used are summarised in Table 6. The quoted systematic uncertainties correspond to conservative estimates of 30% on all meson-to-pion ratios, which were propagated to the corresponding contributions to the background electron spectrum.
A precise knowledge of the material budget is important for the calculation of the electron spectrum from photon conversions. An analysis of the reconstruction of photon conversions in ALICE demonstrated that the material budget implemented in the Monte Carlo simulation is in agreement within an uncertainty of 4.5% with the actual material budget of the experiment [36]. Since, for the present analysis, electron candidate tracks were required to be associated with a hit in the SPD, only the beam pipe, air, and a fraction of the ITS material contributed to the effective converter thickness. The beam pipe is made out of beryllium with a polyimide wrapping and its thickness in terms of radiation lengths is X/X 0 = 0.26%. The corresponding thickness of a pixel layer is X/X 0 = 1.14% for the full layer, including the sensor, the readout chip, and the infrastructure [34]. The construction of the first pixel layer is such that the active sensor layer is closer to the beam line than the readout and most of the infrastructure, i.e. conversions in the latter do not give rise to a recorded hit in this detector. In the second pixel layer, the order is reversed, i.e. the readout and most of the infrastructure are closer to the beam line than the sensor itself. Therefore, for the TPC-EMCal analysis, the thickness of most of both pixel layers had to be considered in the calculation of the electron background from photon conversions. Including an overall systematic uncertainty of 4.5% on the material budget [36], the resulting converter thickness was X/X 0 = (2.15 ± 0.11)%, including the beam pipe and air, for photons impinging perpendicularly on the beam pipe and the ITS, i.e. for photons at η = 0. For the TPC-TOF/TPC-TRD-TOF analysis only a fraction of the first pixel layer was relevant in addition to the beam pipe and air. For the latter case, from the known material budget and from full Monte Carlo simulations of photon conversions in the pixel detector the effective thickness of the first pixel layer was determined to be (45 ± 5)% of its total thickness. Including the beam pipe and air, the effective converter thickness was X/X 0 = (0.77 ± 0.07)% at η = 0. The geometric η dependence of the material budget was taken into account in the calculation of the photon conversion contribution in the electron background cocktail.
The ratio of conversion electrons to Dalitz electrons for π 0 decays was calculated as where BR γγ and BR Dalitz are the branching ratios into the two-photon and Dalitz channels, respectively. For the TPC-TOF/TPC-TRD-TOF analysis, with X/X 0 = (0.77 ± 0.07)%, this ratio Conversion/Dalitz is equal to 1.01 ± 0.09. Due to the larger material budget relevant for the TPC-EMCal analysis, which is X/X 0 = (2.15 ± 0.11)%, the relative contribution from photon conversions to Dalitz decays was larger: Conversion/Dalitz = 2.79 ± 0.14. For the decays of other light mesons the ratio is slightly smaller than for neutral pions due to the fact that BR Dalitz /BR γγ increases with increasing parent meson mass.
In addition, it was taken into account that the photon conversion probability is not constant but depends slightly on the photon energy, introducing a p t dependence of the ratio Conversion/Dalitz, which was determined in a full Monte Carlo simulation. The corresponding correction was applied in the calculation of the conversion contribution to the background electron cocktail. However, this correction is significant only for low momentum electrons (0.5 < p t < 1 GeV/c), where the ratio Conversion/Dalitz is reduced by 10% or less relative to its asymptotic value given in Eq. 3.
The contribution from weak K e3 decays of charged and neutral kaons can only be determined via simulations, which take into account the geometry of the experimental apparatus, the reconstruction algorithms, and the electron identification cuts. It turned out that the contribution from K e3 decays to the inclusive electron spectrum was essentially negligible. This was due to the fact that electron candidates considered in the present analysis were required to be associated with a hit in the first pixel layer of the ALICE ITS. Since this detector layer is close to the primary collision vertex (3.9 cm radial distance from the beam line) and because of the rather long life time of the relevant kaons (cτ(K ± ) = 3.712 m, cτ(K 0 L ) = 15.34 m [11]), only a tiny fraction of K e3 decays contributed to the background electron sample. For electrons with p t = 0.5 GeV/c the relative contribution from K e3 decays to the inclusive electron background was not more than 0.5%. For p t = 1 GeV/c this contribution decreased to ≈0.2% and towards higher p t it became even less. Given the limited statistics available in this simulation a conservative Electrons from heavy-flavour decays in pp collisions at √ s = 7 TeV 21 Table 7: Overview over the contributions to the systematic uncertainties of the background cocktail. The contributions from mesons heavier than the η meson and the contribution from K e3 decays to the systematic uncertainty are less than 1% and, therefore, are not listed explicitly. For details on the error determination, see text.
p t (GeV/c) 0.5 2 8 Error source systematic uncertainty (%) systematic uncertainty of 100% is assigned to the K e3 contribution.
Electrons from the electromagnetic decays of heavy quarkonia have been added to the background electron cocktail based on measurements at the LHC. J/ψ production has been measured at mid-rapidity in pp collisions at 7 TeV by the ALICE [60,61] and CMS experiments [26]. A parameterisation of these data, obtained by a simultaneous fit according to Eq. 2 was used as input for the cocktail generator. ϒ production at mid-rapidity has been measured by the CMS experiment [62]. As for the J/ψ, the production cross section was parametrised and the decay contribution was included in the electron cocktail. While the contribution from J/ψ decays becomes relevant at high p t , the ϒ contribution is negligible for the electron cocktail in the current p t range. While the systematic uncertainties of the measured production cross sections of heavy quarkonia were directly propagated to the corresponding decay electron spectra, their contribution to the systematic uncertainty of the latter is less than 1%.
Contributions to the background electron cocktail from prompt photons are twofold. Real photons produced in initial hard scattering processes, e.g. via quark-gluon Compton scattering, can convert in the detector material just as photons from meson decays. In addition, every source of real photons also emit virtual photons, i.e. electron-positron pairs. The spectrum of real prompt photons from an NLO pQCD calculation [63][64][65] using CTEQ6M5 parton distribution functions [66] with GRV parton to photon fragmentation functions [67,68] was parameterised, and the corresponding conversion electron spectrum was added to the background electron cocktail. The ratio of virtual prompt photons to real prompt photons increases with increasing p t because the phase space for dielectron emission increases [69]. This has been taken into account in the calculation of the corresponding contribution to the background electron cocktail. Prompt photon production has not been measured in ALICE yet. Measurements at lower collision energy are in agreement with NLO pQCD calculations within uncertainties of significantly less than 50% at high p t [70]. Conservatively, a systematic uncertainty of 50% was assigned to the contribution from prompt photons to the total background electron cocktail.
Contributions from the Drell-Yan process are expected to be small in the p t range covered by the present analysis and, therefore, they were not included in the background electron cocktail.
To calculate the systematic uncertainty of the cocktails, the systematic uncertainties of all uncorrelated cocktail ingredients were estimated as discussed above, propagated to the corresponding electron spectra, and added in quadrature. The cocktail systematic uncertainties are smallest in the p t range between 1 and 2 GeV/c. The individual contributions and their dependence on p t are summarised in Table 7, where error sources with less than 1% systematic uncertainty are not listed.
The total background cocktail electron cross sections were divided by the minimum bias pp cross section 62.2 ± 2.2(sys.) mb [71] (see below) such that they can be directly compared to the measured inclusive electron yields per minimum bias triggered collision. These comparisons are shown in Fig. 10

Heavy-flavour hadron decay electron cross section
The differential inclusive electron yield in pp collisions at √ s = 7 TeV, already shown in Fig. 8, is compared to the background electron yield as calculated within the cocktail approach in the left and right panels of Fig. 10 for the TPC-TOF/TPC-TRD-TOF and the TPC-EMCal analysis, respectively. Statistical uncertainties in the inclusive electron measurement are shown as error bars, while systematic uncertainties are indicated by boxes. The background contribution from photon conversions is smaller in the TPC-TOF/TPC-TRD-TOF analysis because in this case a hit in the first pixel layer is required for electron candidate tracks. Consequently, the ratio of the measured inclusive electron yield to the calculated electron background is larger for the TPC-TOF/TPC-TRD-TOF analysis than for the TPC-EMCal analysis as shown in the lower left and right panels of Fig. 10, respectively. The differential production cross section of electrons from heavy-flavour decays is calculated by first subtracting the background cocktail from the inclusive electron spectrum and then multiplying the difference with the minimum bias pp cross section σ MB . The corresponding systematic uncertainties propagated from the inclusive electron measurement and the electron background cocktail are summarised in Table 8. The value for σ MB is 62.2 ± 2.2(sys.) mb. This number was obtained by relating σ MB to the cross section σ VOAND sampled with the V0AND trigger [71]. The latter corresponds to the coincidence between signals in the two VZERO detectors as measured in a van der Meer scan [72]. The relative factor σ VOAND /σ MB is equal to 0.873 and stable within 1% over the analysed data sample. The corresponding Electrons from heavy-flavour decays in pp collisions at √ s = 7 TeV 23 Table 8: Systematic uncertainties of the electron cross section from heavy-flavour hadron decays propagated from the inclusive electron measurement and the electron background cocktail for the TPC-TOF/TPC-TRD-TOF analysis. For p t = 3, 5, and 7 GeV/c the corresponding uncertainties for the TPC-EMCal analysis are quoted in parentheses.
p t (GeV/c) 1 3 5 7 Error source Systematic uncertainty (%) systematic uncertainty of 3.5% is due to uncertainties of the measured beam intensities and in the analysis procedure of the van der Meer scan [73]. As demonstrated in Fig. 11, the resulting cross sections from the TPC-TOF/TPC-TRD-TOF and TPC-EMCal analyses agree with each other within the experimental uncertainties.
Since the azimuthal coverages of the TRD and the EMCal are mutually exclusive and because the electron identification is done following different approaches, the statistical uncertainties of the inclusive electron spectra measured, using these two methods, are uncorrelated. While the systematic uncertainties related to the electron identification are essentially uncorrelated, those originating from the track reconstruction are mostly correlated. In addition, the systematic uncertainties of the electron background cocktails are correlated completely for both analyses. The differential invariant cross section of electrons from semileptonic heavy-flavour decays is measured for transverse momenta above 0.5 GeV/c. It is interesting to note that according to calculations using the PYTHIA 6.4.21 event generator [52] with the Perugia-0 parameter tuning [53] ∼ 57% of the electrons from charm decays and ∼ 73% of the electrons from beauty decays are within the measured p t range in the rapidity interval |y| < 0.5. For FONLL [2,3,33] pQCD calculations similar values are obtained. In this case, ∼ 51% of the electrons from charm decays and ∼ 90% of the electrons from beauty decays are within the accessible p t range.
The ratio (e + +e − )/2π 0 of the production cross sections of electrons from heavy-flavour hadron decays and π 0 mesons, which are the main source of background in the relevant p t range, is depicted as a function of p t in Fig. 12. The comparison with corresponding measurements from lower energy pp collider experiments demonstrates the different √ s dependence of the heavy and light flavour production cross sections. At the CERN ISR, the CCRS experiment recorded a first low statistics data sample of electrons from heavy-flavour hadron decays in pp collisions at √ s = 52.7 GeV in the range 1.6 < p t < 4.7 GeV/c [12]. The charge-averaged inclusive charged pion production cross section was measured and parameterised by the British-Scandinavian Collaboration in the same collision system [77]. Assuming that the latter is equal to the neutral pion production cross section the ratio (e + +e − )/2π 0 was calculated with substantial statistical uncertainties as shown in Fig. 12. At ISR energies, the ratio (e + +e − )/2π 0 is of the order (1 − 2) × 10 −4 without a significant p t dependence in the range below 5 GeV/c, which is   [74][75][76] have been measured with the PHENIX experiment in pp collisions at RHIC. The ratio (e + +e − )/2π 0 was evaluated at given values of p t in the range 0.3 < p t < 9 GeV/c as shown in Fig. 12. In the charm-hadron decay dominated low p t region, the larger ratio (e + +e − )/2π 0 ≈ 5 × 10 −4 is consistent with a more rapid increase of the charm production cross section with √ s as compared to the light-flavour production cross section. At RHIC, a pronounced p t dependence of the ratio (e + +e − )/2π 0 is observed. From the low p t (∼1 GeV/c) to the beauty-hadron decay dominated high p t region (∼9 GeV/c) (e + +e − )/2π 0 rises by at least a factor two, consistent with the beauty production cross section rising faster with √ s than the charm production cross section. At the LHC, the increase of the ratio (e + +e − )/2π 0 with p t is even larger. In the present measurement at √ s = 7 TeV, (e + +e − )/2π 0 grows by almost an order of magnitude from the charm decay dominated low p t region to ≈ 10 −2 in the beauty dominated high p t region.

Comparison with FONLL pQCD
The measured differential invariant production cross section of electrons from heavy-flavour decays is compared with a FONLL pQCD calculation in Fig. 13, where error bars depict the statistical uncertainty while boxes show the total systematic uncertainty of the measurement. For the FONLL calculation CTEQ6.6 parton distribution functions [78] were used. To obtain the uncertainty of the calculation,   [74][75][76], and the CCRS experiment at the ISR [12,77]. Error bars are statistical errors. Systematic uncertainties are depicted by boxes (ALICE) and brackets (PHENIX). indicated by dashed-dotted lines in Fig. 13, the factorisation and renormalisation scales µ F and µ R , respectively, were varied independently in the ranges 0.5 < µ F /m t < 2 and 0.5 < µ R /m t < 2, with the additional constraint 0.5 < µ F /µ R < 2, where m t is the transverse mass of the heavy quarks. The charm quark mass was varied in FONLL within the range 1.3 < m c < 1.7 GeV/c 2 and the beauty quark mass was varied within 4.5 < m b < 5.0 GeV/c 2 [2]. For electrons from charm hadron decays, the contributions from D 0 and D + decays were weighted with the measured D 0 /D + ratio [28]. Variations due to different choices of the parton distributions functions were also included in the theoretical uncertainty. The differential cross section of electrons from heavy-flavour decays in the rapidity interval |y| < 0.5 is shown in comparison with the FONLL prediction on an absolute scale in the upper panel of Fig. 13. In addition to charm and beauty hadron decays to electrons also the cascade beauty to charm to electron is included. Statistical and systematic uncertainties of the measurement are depicted as error bars and boxes, respectively. The cross section and uncertainty from FONLL are shown as solid and dashed-dotted lines, respectively.
The ratio of the measured cross section and the FONLL calculation is drawn in the lower panel of Fig. 13. Error bars and boxes around the data points indicate the statistical and systematic uncertainties of the electron spectrum from heavy-flavour decays, respectively. These systematic error boxes do not include any contribution from the FONLL calculation. The relative systematic uncertainties of the plotted ratio originating from the FONLL calculation is indicated by the dashed-dotted lines around one. Within substantial theoretical uncertainties the FONLL pQCD calculation is in agreement with the data.  Electrons from heavy-flavour decays in pp collisions at √ s = 7 TeV 27

ALICE and ATLAS measurements of electrons from heavy-flavour hadron decays
The ATLAS experiment has measured electrons from heavy-flavour decays in pp collisions at √ s = 7 TeV in the p t range 7 < p t < 26 GeV/c and in the rapidity interval |y| < 2, where the regions 1.37 < |y| < 1.52 are excluded [25]. The p t -differential production cross section, dσ /d p t , published by ATLAS is divided bin-by-bin by 2π p t ∆y, where p t is the center of the individual transverse momentum bins chosen by AT-LAS and ∆y is the rapidity interval covered by the ATLAS measurement. The result is shown together with the electron cross section presented in this paper in Fig. 14. While the electron measurement by ALICE includes most of the total cross section, the data from ATLAS extend the measurement to higher p t . Corresponding FONLL pQCD calculations in the rapidity intervals covered by ALICE and ATLAS, respectively, are included for comparison in Fig. 14 as well. Within the experimental and theoretical uncertainties FONLL is in agreement with both data sets. It should be noted that the invariant cross section per unit rapidity decreases with increasing width of the rapidity interval because the heavy-flavour production cross section decreases towards larger absolute rapidity values. However, this effect is small in pp collisions at √ s = 7 TeV (< 5% for electrons from charm decays and < 10% for electrons from beauty decays according to FONLL calculations).

Summary
The inclusive differential production cross section of electrons from charm and beauty decays has been measured by ALICE in the transverse momentum range 0.5 <p t < 8 GeV/c at mid-rapidity in pp collisions at √ s = 7 TeV. Within experimental and theoretical uncertainties a perturbative QCD calculation in the framework of FONLL is consistent with the measured differential cross section. The data presented in this paper extend a corresponding measurement from ATLAS, which is restricted to the high p t region, towards substantially lower transverse momenta. This low p t region includes the dominant fraction of the total heavy-flavor production cross section, and future higher precision data might be sensitive to the parton distribution function of the proton at low x.

Acknowledgements
The ALICE collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE collaboration would like to thank M. Cacciari for providing the FONLL pQCD predictions for the cross sections of electrons from heavy-flavour hadron decays. Furthermore, the ALICE collaboration would like to thank W. Vogelsang for providing the NLO pQCD predictions for direct photon production cross sections which were used as one of the inputs for the electron background cocktail. The ALICE collaboration acknowledges the following funding agencies for their support in building and running the ALICE detector: