2018 102 9 May

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

ALICE Collaboration††thanks: See Appendix A for the list of collaboration
members ALICE Collaboration

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 (DCAee), 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
DCAee. 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 DCAee 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 DCAee 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.

##  1 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 ($m_{{\rm ee}}$ $<$ 1.1 GeV/$c^{2}$),
${\rm{e}}^{+}{\rm{e}}^{-}$ spectra are sensitive to the properties of vector
mesons $\rho$, $\omega$, and $\phi$ in the medium. The $\rho$ meson has a
shorter lifetime ($\approx$ 1.3 fm/$c$ in its rest frame) than that of the
medium ($\approx$ 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 $<$ $m_{{\rm ee}}$ $<$ 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
${\rm{e}}^{+}{\rm{e}}^{-}$ pairs from semileptonic decays of charm and beauty
hadrons, correlated through flavour conservation111These contributions are
referred to as charm/beauty or
$\rm{c}\overline{\rm{c}}$/$\rm{b}\overline{\rm{b}}$ contributions throughout
this paper. 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 $\overline{{\rm{c}}}$ 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
${\sqrt{s}}$ $=$ 200 GeV is well described by a cocktail of expected hadronic
sources [24, 25, 26]. In addition, PHENIX measured the total
${\rm{c}}{\overline{{\rm{c}}}}$ and ${\rm{b}}{\overline{{\rm{b}}}}$ cross
sections in pp and d-Au collisions at ${\sqrt{s_{\mathrm{NN}}}}$ $=$ 200 GeV
by fitting the spectra of ${\rm{e}}^{+}{\rm{e}}^{-}$ pairs from heavy-flavour
hadron decays simultaneously in $m_{{\rm ee}}$ and pair transverse momentum
$p_{\rm T,ee}$ [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 $p_{\rm T,ee}$ $>$ 2.5 GeV/$c$, whereas the
${\rm{c}}{\overline{{\rm{c}}}}$ contribution is preeminent for $m_{{\rm ee}}$
$<$ 3 GeV/$c^{2}$ and $p_{\rm T,ee}$ $<$ 2 GeV/$c$. The extraction of the
heavy-flavour cross sections, in particular the total
${\rm{c}}{\overline{{\rm{c}}}}$ cross section, depends nevertheless on the
event generator used to extrapolate the measurements to full phase space.
Finally, at lower masses ($m_{{\rm ee}}$ $<$ 0.3 GeV/$c^{2}$) and high $p_{\rm
T,ee}$ ($p_{\rm T,ee}$ $>$ 1 GeV/$c$), i.e. the quasi-real virtual-photon
region where the $p_{\rm T,ee}$ of the dilepton pair is much larger than its
mass ($p_{{\rm T,ee}}^{2}$ $\gg$ $m_{\rm ee}^{{\rm 2}}$), the measured
${\rm{e}}^{+}{\rm{e}}^{-}$ 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 $p_{{\rm T}}<$ 16 GeV/$c$ could be extracted from
the inclusive photon measurements in pp collisions at $\sqrt{s}=$ 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 $\sqrt{s}$.

In heavy-ion collisions, a strong enhancement at low invariant mass of
dilepton pairs ($m_{\rm ll}<$ 1 GeV/$c^{2}$) is observed at different
energies, at the Super Proton Synchroton (SPS) by the CERES and NA60
Collaborations [31, 32, 33, 34, 35, 36] and at RHIC energies by the PHENIX and
STAR Collaborations [25, 37, 38, 39]. The data can be explained by thermal
radiation of the hadronic phase, dominated by the $\rho$ meson, which appears
strongly broadened [40, 41, 42, 43, 44, 45, 46, 47, 48] with essentially no
change of the pole mass. This broadening is consistent with chiral symmetry
restoration [15]. At RHIC, the data show a further excess of the direct-photon
yield over the pp expectation, which is exponential in $p_{\rm T}$ with an
inverse slope $T$ of about 221 MeV [25]. This excess can be attributed to
thermal radiation from the partonic and/or hadronic phase [49, 47, 50]. At the
LHC, a similar enhancement of the direct-photon production, with $T\approx$
297 MeV, is observed in central Pb–Pb collisions at $\sqrt{s_{\rm NN}}=$ 2.76
TeV [51]. In the IMR, a significant excess over the yield from semileptonic
decays of heavy-flavour hadrons is found at the SPS [35, 36, 52, 53], whereas
at RHIC the data can be fairly well described by calculations including heavy-
flavour contributions estimated in pp collisions and scaled with the number of
binary collisions [25, 37, 38, 39]. At the SPS, the NA60 Collaboration showed,
by using precise vertex information, that the excess is associated with a
prompt source, as opposed to $\mu^{+}\mu^{-}$ pairs from D mesons that decay
further away from the interaction point [52]. The analysis of the $p_{{\rm
T,\mu\mu}}$-spectra, with the extraction of the slope parameter $T_{{\rm
eff}}$ as a function of $m_{{\rm\mu\mu}}$, revealed that the IMR is dominated
by an early source of dileptons, i.e. partonic radiation, where radial flow is
negligible [53]. Models including thermal radiation from the QGP [40, 42, 54,
43] can reproduce the data in the IMR.

In this paper, the first measurement of the ${\rm{e}}^{+}{\rm{e}}^{-}$ pair
production in pp collisions at $\sqrt{s}$ = 7 TeV with ALICE at the LHC is
presented. The invariant yield is studied within the central barrel acceptance
of ALICE ($|\eta_{{\rm{e}}}|$ $<$ 0.8) as a function of $m_{{\rm ee}}$
($m_{{\rm ee}}$ $<$ 3.3 GeV/$c^{2}$), $p_{{\rm T,ee}}$ ($p_{{\rm T,ee}}$ $<$ 8
GeV/$c$), and DCAee (DCAee $<$ 10 $\sigma$), i.e. the average distance of
closest approach of the reconstructed electron and positron tracks to the
collision vertex, normalised to its resolution. The latter allows the prompt
and non-prompt dielectron sources to be separated and provides an additional
variable to disentangle the contributions from ${\rm{c}}{\overline{{\rm{c}}}}$
(with $c\tau\approx$ 150 µm for D mesons) and ${\rm{b}}{\overline{{\rm{b}}}}$
(with $c\tau\approx$ 470 µm for B mesons). The data are compared with a
cocktail of expected ${\rm{e}}^{+}{\rm{e}}^{-}$ sources from known hadrons
based on measured cross sections. Correlated pairs from heavy-flavour hadron
decays are calculated with two different MC event generators, PYTHIA [55] and
POWHEG [56, 57, 58, 59]. Finally, the relative contribution of virtual direct
photons is shown and compared with NLO pQCD calculations.

This article is organised as follows: the experimental apparatus and data
sample used in the analysis are presented in Section 2. The analysis strategy,
including the electron identification, the background subtraction, and the
efficiency corrections are described in Section 3, together with the
associated systematic uncertainties. In Section 4, the procedures used to
calculate the expected dielectron cross section from the known hadronic
sources are explained. The results, i.e. the invariant mass spectrum, the
$p_{\rm T,ee}$ and ${\rm{DCA_{\rm ee}}}$ distributions, are finally presented
and discussed in Section 5. In the same section, the charm and beauty total
cross sections, as well as the fraction of direct photons to inclusive
photons, are extracted from the data.

##  2 Experimental apparatus and data sample

The ALICE apparatus and its performance are described in detail in [1, 2, 3,
60]. In the following, only the subsystems relevant for the dielectron
analysis are briefly discussed. Electrons222The term ‘electron’ is used for
both electrons and positrons throughout this paper. are reconstructed and
identified at mid-rapidity ($|\eta_{{\rm e}}|$ $<$ 0.8) in the central barrel
of ALICE with the Inner Tracking System (ITS), the Time Projection Chamber
(TPC), and the Time-Of-Flight system (TOF). These detectors are located inside
a large solenoidal magnet that provides a uniform magnetic field of $B=0.5$ T
along the beam direction.

The ITS [61] is the detector closest to the beam axis. It is composed of six
cylindrical layers of silicon detectors, with radial distances ranging from
3.9 cm to 43 cm. The two innermost layers are equipped with Silicon Pixel
Detectors (SPD). The two intermediate layers consist of Silicon Drift
Detectors (SDD), and the two outermost layers are made of Silicon Strip
Detectors (SSD). The high spatial resolution of the silicon sensors allows the
Distance-of-Closest-Approach (DCA) of the track to the reconstructed collision
vertex (primary vertex) to be measured. The DCA resolution in the plane
transverse to the beam direction is better than 75 µm for charged particles
with transverse momenta $p_{\rm T}$ $>$ 1 GeV/$c$. Moreover, the four SDD and
SSD layers provide charged-particle identification via the measurement of
their specific energy loss d$E$/d$x$.

At larger radii (85 $<$ $r$ $<$ 247 cm), a 500 cm long cylindrical TPC [62]
provides identification of charged particles and reconstruction of their
trajectories. Up to 159 three-dimensional space points per track, which
corresponds to the number of pad rows in one TPC sector out of 18 in azimuth,
are recorded and used to estimate the d$E$/d$x$ of charged particles in the
gas. The d$E$/d$x$ resolution in pp collisions is about 5.2% for minimum-
ionising particles passing through the full detector [60].

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 $p_{\rm T}$ of about 300 MeV/$c$ to reach the TOF detector.
Since the TOF matching efficiency is of the order of 30% at a $p_{\rm T}$ 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 V0 detector [64], used for triggering, consists of two arrays of 32
scintillators each, placed around the beam vacuum tube on either side of the
interaction region at $z=-90$ cm and $z=+340$ cm. The two arrays cover the
pseudorapidity ranges $2.8<\eta<5.1$ (V0A) and $-3.7<\eta<-1.7$ (V0C),
respectively.

The data used in this paper were recorded with ALICE at the LHC during the pp
run at ${\sqrt{s}}$ = 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 $\pm 10$ cm of the nominal interaction point along the beam direction
in order to provide a uniform pseudo-rapidity acceptance of the detectors. A
total of 370 million pp events at ${\sqrt{s}}$ = 7 TeV pass the offline event
selection criteria, corresponding to an integrated luminosity of $L_{\rm int}$
= (6.0$\pm$0.2) nb-1 [65].

##  3 Data analysis

###  3.1 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 $|\eta|$ $<$ 0.8 and $p_{\rm T}$ $>$ 0.2 GeV/$c$. For the
${\rm{DCA_{\rm ee}}}$ analysis, the tracks must have a $p_{\rm T}$ $>$ 0.4
GeV/$c$ to assure a sufficient separation between prompt and non-prompt e+e-
sources. The DCA resolution worsens at low $p_{\rm T}$ and is larger than 150
µm for tracks reconstructed in the ITS and TPC with $p_{\rm T}$ $<$ 0.35
GeV/$c$ [60], which is of the same order of magnitude as the decay length of
the D0 and D${}^{\pm}_{\rm s}$ mesons ($c\tau$ $\approx$ 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 the ITS track segments must have a hit in at least 5 of the 6
detector layers. The maximum $\chi^{2}$ 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. This
rejects about 63% of the conversion electron tracks, keeping 83% of the signal
electrons from light and heavy-flavour hadron decays. 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,
rejecting 38% of the remaining conversion contamination after the requirement
of a hit in the first SPD layer and keeping 97% of the signal electrons. For
e+e- pairs from photon conversions, where both electrons pass the default
track selection, the rejection factor is even higher, about 92%.

The PID information is based on the measurement of the specific ionisation
energy loss (d$E$/d$x$) 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 $n^{\rm
DET}_{\sigma_{\rm{i}}}$ are normalised to units of standard deviations of the
respective detector (DET) resolution.

In the TPC, electrons are selected in the interval $-1.5<n^{\rm
TPC}_{\sigma_{{\rm{e}}}}~{}<4.0$. Additionally, pions are rejected by
requiring that the measured TPC d$E$/d$x$ of the track is far from the
expectation value for pions: $n^{\rm TPC}_{\sigma_{\pi}}~{}>3.5$. Since
electrons have a larger energy loss in the TPC than pions for momenta above
0.25 GeV/$c$, the $n^{\rm TPC}_{\sigma_{\pi}}~{}$ requirement is asymmetric.
The remaining contamination by kaons and protons occurs mainly in the crossing
regions of the expected d$E$/d$x$ 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
$n^{\rm TPC}_{\sigma_{{\rm{e}}}}$ is shown as a function of $n^{\rm
ITS}_{\sigma_{{\rm{e}}}}$ 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 $-3<n^{\rm ITS}_{\sigma_{{\rm{e}}}}~{}<1$.
Further reduction of the hadron contamination can be achieved using the TOF
information with $|n^{\rm TOF}_{\sigma_{{\rm{e}}}}~{}|<3$ (in case the
selected tracks have an associated hit in the TOF detector). The electron
purity $P_{\rm e}$ is estimated at low momenta ($p$ $<$ 3 GeV/$c$) by fitting
the $n^{\rm TPC}_{\sigma_{{\rm{e}}}}$ distribution in momentum slices after
the ITS and TOF selection, as well as the $n^{\rm TPC}_{\sigma_{\pi}}$
rejection, following a procedure explained in [66]. At higher momenta, the
$n^{\rm TPC}_{\sigma_{\pi}}~{}$ distribution is fitted after the requirements
on $n^{\rm ITS}_{\sigma_{\rm e}}$, $n^{\rm TOF}_{\sigma_{\rm e}}$, and $n^{\rm
TPC}_{\sigma_{\rm e}}$, 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 ($p$ $\approx$ 0.5
GeV/$c$) or protons ($p$ $\approx$ 1.2 GeV/$c$) have similar d$E$/d$x$ as
electrons in the TPC.

Figure 1: (Colour online) TPC PID signal expressed as $n^{\rm
TPC}_{\sigma_{{\rm{e}}}}$ (see text) as a function of the ITS PID signal
($n^{\rm ITS}_{\sigma_{{\rm{e}}}}$) for selected tracks with 0.5 $<$ $p$ $<$
0.52 GeV/$c$ after applying the pion rejection in the TPC (left). Electron
purity $P_{\rm e}$ as a function of momentum (right). Only statistical
uncertainties are shown.

###  3.2 Dielectron spectrum

All electron candidates from the same event are combined into pairs,
characterised by their $m_{\rm ee}$, $p_{\rm T,ee}$, and DCAee. The latter is
calculated from the single-electron DCAs as:

${\rm{DCA_{\rm ee}}}~{}=\sqrt{\frac{({\rm DCA}_{xy,1}/\sigma_{xy,1})^{2}+({\rm
DCA}_{xy,2}/\sigma_{xy,2})^{2}}{2}},$ (1)

where DCAxy,i is the DCA of the electron $i$ in the transverse plane and
$\sigma_{xy,i}$ is its resolution estimated from the covariance matrix of the
track reconstruction parameters obtained with the Kalman filter technique [67,
60]. The absolute DCA resolution worsens at low $p_{\rm T}$ 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 $m_{{\rm ee}}$ and $p_{\rm{T,ee}}$ (see below).
Therefore, the minimisation of $B$ and a careful subtraction of the remaining
background are key aspects of this analysis.

Figure 2: (Colour online) Opening angle vs invariant mass of e+e- pairs from
$\pi^{0}$ Dalitz decays (left) and from photon conversions (right) in MC
simulations after the single track selection criteria. The lines indicate the
prefilter requirement.

The main sources of electrons contributing to $B$ are $\pi^{0}$ 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 $\pi^{0}$
Dalitz decays and photon conversions have small invariant masses and opening
angles ($\omega_{{\rm ee}}$), 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 the
prefilter algorithm are $m_{{\rm eh}}$ $<$ 0.06 GeV/$c^{2}$ and $\omega_{{\rm
eh}}$ $<50$ 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$$/$$\sqrt{S+{\rm{2}}B}$ by a factor of about 1.2 for $m_{\rm ee}$ $<$ 1
GeV/$c^{2}$, as can be seen in the left and right panels of Fig. 3,
respectively. For $m_{\rm ee}$ $<$ 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 $m_{{\rm ee}}$
$<0.14~{}$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.

Figure 3: Signal to background ratio (left) and significance (right) obtained
with and without applying the prefilter. Only statistical uncertainties are
shown. The background is estimated as explained in the text later.

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 $\varphi_{\rm v}$ which measures the
orientation of the opening angle relative to the magnetic field is calculated
according to:

$\cos(\varphi_{\rm
v})=\frac{\bf{w}\cdot\bf{u_{a}}}{|{\bf{w}}||{\bf{u_{a}}}|}.$ (2)

The two vectors $\bf{w}$ and $\bf{u_{a}}$ are given by:

$\bf{w}={\bf{u}}\times{\bf{v}},$ (3)
$\bf{u_{a}}=\frac{{\bf{u}}\times{\bf{z}}}{|{\bf{u}}\times{\bf{z}}|},$ (4)
$\bf{u}=\frac{{\bf{p_{\rm e^{+}}}}+{\bf{p_{\rm e^{-}}}}}{|{\bf{p_{\rm
e^{+}}}}+{\bf{p_{\rm e^{-}}}}|},$ (5) $\bf{v}=\frac{{\bf{p_{\rm
e^{+}}}}\times{\bf{p_{\rm e^{-}}}}}{|{\bf{p_{\rm e^{+}}}}\times{\bf{p_{\rm
e^{-}}}}|},$ (6)

where $\bf{p_{\rm e^{+}}}$, $\bf{p_{\rm e^{-}}}$, and $\bf{z}$ 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 $\varphi_{\rm{v}}$ distribution without ITS shared-
cluster cut for $m_{{\rm ee}}$ $<$ 0.1 GeV/$c^{2}$ and $p_{\rm T,ee}$ $<$ 8
GeV/$c$ is compared with the sum of two MC templates, one for pairs from
$\pi^{0}$ and $\eta$ Dalitz decays and one for pairs from photon conversions,
fitted to the data. Prompt pairs with finite invariant mass have an almost
uniform $\varphi_{\rm{v}}$ distribution in this kinematic domain, while
conversion pairs show a peak around $\varphi_{\rm{v}}$ $=$ $\pi$. 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
$\varphi_{\rm{v}}$ distribution after this requirement is shown in the right
panel of Fig. 4. The conversion peak around $\varphi_{\rm{v}}$ $=$ $\pi$ is
clearly suppressed. The MC simulations describe the data very well. Moreover,
dielectron pairs with $\varphi_{\rm{v}}$ $>$ 2 rad and $m_{{\rm ee}}~{}$ $<$
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 $m_{{\rm ee}}$ $=$ 0.

Figure 4: Measured $\varphi_{\rm{v}}$ distribution of correlated e+e- pairs
with $m_{{\rm ee}}$ $<$ 0.1 GeV/$c^{2}$ and $p_{\rm T,ee}$ $<$ 8 GeV/$c$
compared with a sum of MC templates for different dielectron sources. The
distributions are shown for all tracks including those that share some ITS
clusters with other tracks (left) and with such tracks removed (right), as in
the analysis. Only statistical uncertainties are shown for the data points.
Figure 5: Relative acceptance correction factor $R_{\rm acc}$ as a function of
$m_{\rm ee}$ (left) and $p_{\rm T,ee}$ (right). Statistical uncertainties are
represented by vertical bars.

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 $m_{\rm ee}$, $p_{\rm
T,ee}$, and ${\rm{DCA_{\rm ee}}}$ as the $OS$ distributions by forming in each
bin the geometric mean $SS$ $=$ 2$\cdot\sqrt{N_{++}N_{--}}$ 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 $p_{\rm T}$. 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.

Figure 6: Opposite-sign $m_{{\rm ee}}$-differential yield integrated in
$p_{\rm T,ee}$ and ${\rm{DCA_{\rm ee}}}$ overlaid with the same-sign spectrum
corrected by the acceptance correction factor $R_{\rm acc}$. Statistical
uncertainties are represented by vertical bars.

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 mixing. The relative acceptance
correction factor $R_{\rm acc}=M_{+-}$/(2$\cdot\sqrt{M_{++}M_{--}}$) is
calculated, where $M_{+-}$ and $M_{\pm\pm}$ are the mixed-event opposite-sign
and same-sign pair distributions. The relative acceptance correction factor
$R_{\rm acc}$ as a function of $m_{{\rm ee}}$ and $p_{\rm T,ee}$ is shown in
Fig. 5. For $\sqrt{(m_{{\rm{ee}}}c)^{2}+p_{{\rm T,ee}}^{2}}$ $>$ 1 GeV/$c$,
$R_{\rm acc}$ is consistent with unity and no correction is applied, while at
smaller $m_{{\rm ee}}$ and $p_{\rm T,ee}$ deviations of up to 5% are observed.
The relative acceptance correction factor is applied differentially in $m_{\rm
ee}$, $p_{\rm T,ee}$, and DCAee.

In Fig. 6, the opposite-sign and relative-acceptance corrected same-sign
$m_{{\rm ee}}$ spectra, i.e. $OS$ and $R_{\rm acc}\cdot SS$, are shown
integrated over $p_{\rm T,ee}$ and DCAee. The raw pair signal ${S}~{}$ is
obtained with the formula:

${S}~{}={OS}~{}-R_{\rm acc}\cdot SS.$ (7)

###  3.3 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 ($\epsilon_{\rm e}$) for single-electron tracks does not show any
dependence on the electron DCA, for which loose selection criteria were
applied (DCAxy $<$ 1 cm and DCAz $<$ 3 cm). Also no strong $\eta$ dependence
of $\epsilon_{\rm e}$ is observed within $|\eta|<$ 0.8 as well, whereas the
dead zones of the first ITS layer can be seen in the $\varphi$ 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 $p_{{\rm T}}$. The resulting pair efficiency $\epsilon^{\rm
ee}_{\rm rec}(m_{{\rm ee}},p_{{\rm T,ee}})$, shown in a few selected intervals
of $m_{\rm ee}$ in Fig. 7, is calculated and applied to the data as a function
of $m_{{\rm ee}}$ and $p_{\rm T,ee}$. The efficiency of the $\varphi_{\rm v}$
requirement for dielectron pairs with $m_{{\rm ee}}$ $<$ 0.1 GeV/$c^{2}$ is
estimated assuming that the $\varphi_{\rm v}$ distribution of the signal
dielectron pairs is flat (see Fig. 4). For $m_{{\rm ee}}$ $>$ 0.8 GeV/$c^{\rm
2}$, $\epsilon^{\rm ee}_{\rm rec}(m_{{\rm ee}},p_{{\rm T,ee}})$ reaches about
15%. At lower $m_{{\rm ee}}$, the pair efficiency drops at low $p_{\rm T,ee}$.

Figure 7: Pair efficiency as a function of $p_{\rm T,ee}$ for different
$m_{{\rm ee}}$ intervals for the default electron selection criteria.

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 $m_{{\rm ee}}$
distributions, which develop tails towards lower $m_{{\rm ee}}$. Moreover, the
reconstructed momentum of the electrons is also affected by the finite
detector resolution. Such effects, i.e. $p_{{\rm T}}$, $\theta$, and $\varphi$
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:

$\frac{{\rm{d}}^{3}N_{{\rm e}^{+}{\rm e}^{-}}}{{\rm{d}}m_{{\rm
ee}}~{}{\rm{d}}p_{\rm T,ee}~{}{\rm{d}}{\rm{DCA_{\rm ee}}}~{}}=\frac{1}{\Delta
p_{\rm T,ee}~{}}\frac{1}{\Delta m_{{\rm ee}}~{}}\frac{1}{\Delta{\rm{DCA_{\rm
ee}}}~{}}\frac{S(m_{{\rm ee}},p_{{\rm T,ee}},\rm{DCA}_{{\rm
ee}})}{\epsilon^{\rm ee}_{\rm rec}(m_{{\rm ee}},p_{{\rm T,ee}})~{}},$ (8)

where $\Delta p_{\rm T,ee}$, $\Delta m_{\rm ee}$, and $\Delta{\rm{DCA_{\rm
ee}}}~{}$ are the width of the $p_{{\rm T,ee}}$, $m_{{\rm ee}}$, and DCAee
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
${\sqrt{s}}$ = 7 TeV, of $\sigma_{\rm MB}=62.4\pm 2.2$ mb, which is estimated
from the cross section $\sigma_{\rm V0AND}$ of the coincidence V0AND between
signals in the two VZERO detectors, measured in a van der Meer scan [65]. The
relative factor $\sigma_{\rm V0AND}$/$\sigma_{\rm MB}$ is given by the
fraction of MB events where the L0 trigger input corresponding to the V0AND
condition has fired. Its value is 0.87, and is stable within 0.5% over the
analyzed data sample. The corresponding normalisation uncertainty is $\pm
3.5\%$.

###  3.4 Systematic uncertainties

Requirements | Variations
---|---
Hits required in the SPD |  in the first layer, in both layers
Minimum number of ITS clusters | 4, 5, 6
Maximum $\chi^{2}$ per ITS cluster |  4.5, 3.5, 2.5
Maximum number of ITS shared clusters |  0, 1, 2, 3, 4, 6
Minimum number of TPC clusters | 80, 100, 120
Minimum number of crossed rows in TPC | 80, 100, 130
Minimum ratio of crossed pad-rows to findable TPC clusters | 0.5, 0.7, 0.9
Maximum $\chi^{2}$ per TPC cluster |  4, 3, 2.5
TOF electron identification |  $|$$n^{\rm TOF}_{\sigma_{{\rm{e}}}}$ $|$ $<$ 2, 3, 4
TPC electron identification |  $-$1.5, $-$1, $-$0.5 $<$ $n^{\rm TPC}_{\sigma_{{\rm{e}}}}$ $<$ 2, 3, 4
TPC pion rejection |  $n^{\rm TPC}_{\sigma_{\pi}}$ $<$ 3, 3.5, 4
ITS electron identification |  $-$4, $-$3.5, $-$3 $<$ $n^{\rm ITS}_{\sigma_{{\rm{e}}}}$ $<$ 0, 0.5, 1
Table 1: Summary of the single-track selection criterion variations to
determine the systematic uncertainties. The default values are shown in bold.

The systematic uncertainties arise from limitations in the determination of
the background, the relative acceptance correction factor $R_{\rm acc}$, the
electron selection efficiency, the prefilter efficiency, and the pair-cut
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 single-track selection criteria
variations. The signal is extracted and corrected for 22 random combinations
of selection criteria, which probe different but still reasonable single-
electron efficiencies and $S/B$ ratios, ranging from 0.22 to 0.42 at $p_{\rm
T}$ $=$ 1 GeV/$c$ and from about 0.05 to 0.15 at $m_{{\rm ee}}$ $=$ 0.5
GeV/$c^{2}$, respectively. More than one selection criteria are varied at the
same time to take into account possible correlations between them. 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 $\varphi_{\rm v}$ requirement for pairs
with $m_{{\rm ee}}$ $<$ 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 $\varphi_{\rm v}$
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 $\varphi_{\rm v}$ requirement. The resulting systematic uncertainties
from the selection criterion variation is listed in Table 2 in the case of the
DCA analysis with $p_{{\rm T,e}}$ $>$ 0.4 GeV/$c$.

An additional source of systematic uncertainty is considered for the DCAee-
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 between $p_{\rm T,ee}$ and DCAee. In the $\pi^{0}$
mass region (0.08 $<$ $m_{{\rm ee}}$ $<$ 0.14 GeV/$c^{2}$), the mean $p_{\rm
T,ee}$ is approximately constant as a function of DCAee, which is expected
since the electron tracks should always point to the primary vertex for a
prompt source, and the finite DCAee values are only due to the detector
resolution. This is not the case for the $J/\psi$ region (2.7 $<$ $m_{{\rm
ee}}$ $<$ 3.3 GeV/$c^{2}$), where the mean $p_{\rm T,ee}$ exhibits an increase
as a function of DCAee. The reasons are twofold: first, non-prompt $J/\psi$
from feed-down from B-mesons have a harder $p_{\rm T}$ spectrum than prompt
$J/\psi$, and second, high-$p_{\rm T}$ non-prompt $J/\psi$ decay farther away
than low-$p_{\rm T}$ non-prompt $J/\psi$ so that the decay electrons have
larger DCAs and larger $p_{\rm T}$ compared to electrons from low-$p_{\rm T}$
non-prompt $J/\psi$. The possible remaining uncertainty from this correlation
is estimated by half the difference of the pair efficiency at the maximum and
minimum mean-$p_{\rm T,ee}$, seen as a function of ${\rm{DCA_{\rm ee}}}$ in a
given mass region. This systematic uncertainty is found to be less than 5%,
increasing from low to high $m_{{\rm ee}}$. Table 2 summarises the systematic
uncertainties arising from the DCA analysis.

Mass region | Uncertainty from | Uncertainty from
---|---|---
| DCAee-$p_{\rm T,ee}$ correlation | selection criterion variation
$m_{{\rm ee}}$ $<$ 0.14 GeV/$c^{2}$ | $-$ | 8.7%
0.14 $<$ $m_{{\rm ee}}$ $<$ 1.1 GeV/$c^{2}$ | 1.5% | 11%
1.1 $<$ $m_{{\rm ee}}$ $<$ 2.7 GeV/$c^{2}$ | 3.0% | 17%
2.7 $<$ $m_{{\rm ee}}$ $<$ 3.3 GeV/$c^{2}$ | 4.9% | 17%
Table 2: Summary of the systematic uncertainties for the DCAee analysis
($p_{\rm T,e}>0.4{\rm\,GeV}$/$c$ and $|\eta_{\rm e}|<0.8$).

##  4 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 vector-meson decays as well as
from semileptonic decays of heavy-flavour hadrons.

###  4.1 e+e- pairs from light-flavour hadrons and $J/\psi$ mesons

The Dalitz decays of light neutral mesons,
$\pi^{0}\to{\rm{e}}^{+}{\rm{e}}^{-}~{}\gamma$,
$\eta\to{\rm{e}}^{+}{\rm{e}}^{-}~{}\gamma$,
$\eta^{\prime}\to{\rm{e}}^{+}{\rm{e}}^{-}~{}\gamma$,
$\eta^{\prime}\to{\rm{e}}^{+}{\rm{e}}^{-}~{}\omega$,
$\omega\to{\rm{e}}^{+}{\rm{e}}^{-}~{}\pi^{0}$,
$\phi\to{\rm{e}}^{+}{\rm{e}}^{-}~{}\eta$, and
$\phi\to{\rm{e}}^{+}{\rm{e}}^{-}~{}\pi^{0}$, and the dielectron decays of the
vector mesons, $\rho$, $\omega$, $\phi$, and $J/\psi$ are simulated with the
phenomenological event generator EXODUS [24]. The radiative decay of $J/\psi$
($J/\psi\to{\rm{e}}^{+}{\rm{e}}^{-}~{}\gamma$) 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 $\rho$ 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 $\pi^{0}$, $\eta$, $\phi$, and $J/\psi$ are
obtained by fitting the spectra measured by the ALICE Collaboration [78, 79,
80, 81] with a modified Hagedorn function [82]. The measured $\pi^{\pm}$ and
$\pi^{0}$ spectra agree within their systematic uncertainties. Since the
$\pi^{\pm}$ measurement extends to lower $p_{{\rm T}}$, and exhibits smaller
uncertainties than the $\pi^{0}$, charged pions are used to approximate
neutral pions. For the other mesons, $\rho$, $\omega$, and $\eta^{\prime}$,
the shape of their $p_{\rm T}$ spectra is derived from the $\pi^{\pm}$
spectrum. The $\eta^{\prime}$ mesons are generated assuming $m_{\rm T}$
scaling [83, 84, 85], implying that the spectra of all light mesons as a
function of $m_{\rm T}=\sqrt{m^{2}+p_{\rm T}^{2}}$ are the same and only
differ by a normalisation factor. The normalisation factors are based on the
ratio of the $p_{{\rm T}}$ spectra of the given hadron to the $p_{{\rm T}}$
spectrum of the $\pi^{\pm}$ at high $p_{{\rm T}}$: $0.4\pm 0.08$ for
$\eta^{\prime}$ from PYTHIA 6 calculations of pp collisions at $\sqrt{s}=$ 7
TeV, $0.85\pm 0.17$ for $\omega$ obtained from measurements in pp collisions
at $\sqrt{s}=$ 7 TeV [86], and $1.0\pm 0.2$ for $\rho$ obtained from
measurements in pp collisions at $\sqrt{s}=$ 2.76 TeV [87]. The momentum
distributions of $\omega$ and $\rho$ are obtained from the $\omega/\pi^{\pm}$
and $\rho/\pi^{\pm}$ ratios in simulated pp collisions at $\sqrt{s}=$ 7 TeV
with the Monash 2013 tune of PYTHIA 8 [88, 89]. This tune describes the
measured $\omega/\pi^{0}$ and $\rho/\pi^{0}$ ratios in pp collisions at
$\sqrt{s}=$ 7 TeV and 2.76 TeV, respectively. Since the $\omega$ measurement
does not extend to low $p_{{\rm T}}$ (the $\omega$ meson is measured for
$p_{{\rm T}}>2$ GeV/$c$), fits of the data are used only to estimate the
systematic uncertainties.

The expected dielectron yield as a function of $m_{{\rm ee}}$ and $p_{\rm
T,ee}$ is computed in a fast simulation by filtering 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 $\pi^{\pm}$, $\eta$, $\omega$, $\phi$, and
$J/\psi$ $p_{\rm T}$ spectra and those of the $m_{{\rm T}}$ 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 ${\rm{e}}^{+}{\rm{e}}^{-}$ pairs is then
generated again based on these new parametrisations. For the $\rho$ mesons,
$m_{\rm T}$ scaling is used to estimate the systematic uncertainties
originating from the $\rho$ $p_{\rm T}$ spectrum. The uncertainties from the
different decay branching ratios [90] are also taken into account.

###  4.2 Open-charm and open-beauty contributions to the dielectron yield

Electron pairs that originate from the semileptonic decays of
${\rm{c}}{\overline{{\rm{c}}}}$ and ${\rm{b}}{\overline{{\rm{b}}}}$ 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 ${\rm{c}}{\overline{{\rm{c}}}}$ and
${\rm{b}}{\overline{{\rm{b}}}}$ pairs are produced at leading order through
pair creation, predominantly $gg\to Q\overline{Q}$ with a small contribution
of $q\overline{q}\to Q\overline{Q}$, 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 $2\to 2$ processes
together with a leading-logarithmic $p_{{\rm T}}$-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. $\sigma_{{\rm{c}}{\overline{{\rm{c}}}}~{}}^{{\rm REF}}=7.44\pm
0.14{\rm(stat.)}\pm 0.58{\rm(syst.)}$ mb [94] and
$\sigma_{{\rm{b}}{\overline{{\rm{b}}}}~{}}^{{\rm REF}}=288\pm 4{\rm(stat.)}\pm
48{\rm(syst.)}$ 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
$\sigma_{{\rm{c}}{\overline{{\rm{c}}}}~{}}^{{\rm REF}}$ and
$\sigma_{{\rm{b}}{\overline{{\rm{b}}}}~{}}^{{\rm REF}}$ measurements are
propagated to the final hadronic cocktail. Whereas the effective beauty-to-
electron branching ratio is taken from PYTHIA (${\rm BR}_{\rm b(\to c)\to
e}={\rm BR}_{\rm b\to c\to e}+{\rm BR}_{\rm b\to e}=11.7+10.2=21.9\%$
consistent with [90]), the one for charm-to-electron (BRc→e) is assumed to be
$(9.6\pm 0.4)$% as reported in [90], which is slightly smaller than what has
been estimated with PYTHIA (BR${}_{{\rm c\to e}}=10.6$%). An additional
uncertainty of 9.3% is added in quadrature for the BRc→e to take into account
differences in the $\Lambda_{\rm c}^{+}$/D0 ratio measured by the ALICE
Collaboration, $0.543\pm 0.061{\rm(stat.)}\pm 0.160{\rm(syst.)}$ (for $p_{\rm
T}>$ 1 GeV/$c$) in pp collisions at $\sqrt{s}=$ 7 TeV [96], and the LEP
average of $0.113\pm 0.013{\rm(stat.)}\pm 0.006{\rm(syst.)}$ [97]. This
translates into a 22% uncertainty at the pair level. The uncertainties of the
effective beauty- and charm-to-electron branching ratios are propagated to the
final hadronic cocktail. For both generators, the $p_{\rm{T}}$-differential
cross-section of single electrons from charm- and beauty-hadron decays at mid-
rapidity is found to be consistent with FONLL calculations [98] and to
reproduce the measurements reasonably well within the theoretical and
experimental uncertainties [99]. To obtain the dielectron yield of correlated
${\rm{e}}^{+}{\rm{e}}^{-}$ pairs from heavy-flavour hadron decays, the
distribution of same-sign pairs is subtracted from the
${\rm{e}}^{+}{\rm{e}}^{-}$ spectrum, as in data.

###  4.3 ${\rm{DCA_{\rm ee}}}$ template distributions

Whereas the differential $p_{\rm T,ee}$ and $m_{{\rm ee}}$ distributions of
the hadronic cocktail are estimated from a fast simulation, the ${\rm{DCA_{\rm
ee}}}$ 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
$\Lambda_{\rm c}^{\pm}$ to 311.8 µm for D± mesons [90], their relative yields
are relevant to build the ${\rm{DCA_{\rm ee}}}$ template of correlated
${\rm{e}}^{+}{\rm{e}}^{-}$ pairs from charm-hadron decays. The measured
production ratios of charm hadrons [100, 96] and their semileptonic decay
branching ratios [90] are used to obtain the ${\rm{c}}{\overline{{\rm{c}}}}$
${\rm{DCA_{\rm ee}}}$ distribution. Finally, ${\rm{DCA_{\rm ee}}}$ templates
are extracted for ${\rm{e}}^{+}{\rm{e}}^{-}$ pairs from $\pi^{0}$ Dalitz
decays, from charm- and beauty-hadron decays, and from the decays of prompt
and non-prompt $J/\psi$. In Fig. 8, the $\pi^{0}$, $\rm{c}\overline{\rm{c}}$,
and ${\rm{b}}{\overline{{\rm{b}}}}$ templates are shown integrated over
$p_{\rm T,ee}$ and $m_{{\rm ee}}$. Whereas the distributions for prompt
sources, like $\pi^{0}$, 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
($c\tau_{{\rm D}}$ $\approx$ 150 µm and $c\tau_{{\rm B}}$ $\approx$ 470 µm
[90]). The ${\rm{DCA_{\rm ee}}}$ spectrum of ${\rm{e}}^{+}{\rm{e}}^{-}$ pairs
from $\pi^{0}$ Dalitz decays is taken as an approximation for all prompt
light-flavour decays into dielectrons.

Figure 8: ${\rm{DCA_{\rm ee}}}$ distributions of ${\rm{e}}^{+}{\rm{e}}^{-}$
pairs from $\pi^{0}$ Dalitz decays, from semileptonic decays of charm and
beauty hadrons in MC simulations (see text), integrated over $m_{{\rm ee}}$
and $p_{{\rm T,ee}}$.

Each contribution is normalised to its expected yield from the hadronic
cocktail in the same $m_{{\rm ee}}$ and $p_{\rm T,ee}$ range and after the
same fiducial selection criteria ($|\eta_{{\rm e}}|$ $<$ 0.8 and $p_{{\rm
T,e}}>0.4$ GeV/$c$). Since ${\rm{e}}^{+}{\rm{e}}^{-}$ pairs from prompt and
non-prompt $J/\psi$ have different ${\rm{DCA_{\rm ee}}}$ distributions, the
measured fraction of non-prompt $J/\psi$ in pp collisions at 7 TeV [101],
$f_{\rm B}$, is used to scale the templates accordingly. To evaluate the
uncertainty originating from $f_{\rm B}$, the ${\rm{DCA_{\rm ee}}}$
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 ${\rm{DCA_{\rm ee}}}$ distributions, in
particular those of ${\rm{e}}^{+}{\rm{e}}^{-}$ pairs from prompt sources like
$\pi^{0}$ and prompt $J/\psi$, at around 1-3 $\sigma$. Second, the
uncertainties on the charm-hadron production ratios [100, 96] and on their
semileptonic decay branching ratios [90] are propagated to the final
${\rm{DCA_{\rm ee}}}$ distribution of correlated ${\rm{e}}^{+}{\rm{e}}^{-}$
pairs from charm-hadron decays. Third, the PYTHIA simulations used to create
the ${\rm{DCA_{\rm ee}}}$ templates for the heavy-flavour contributions have
been performed with the PYTHIA Perugia-0 tune [68], which does not reproduce
well the measured $p_{{\rm T}}$ distribution of electrons from charm-hadron
decays at high $p_{\rm T}$ ($p_{\rm T}$ $>$ 3 GeV/$c$) [99]. This was found to
have a negligible effect on the final ${\rm{DCA_{\rm ee}}}$ template, by
varying the maximum $p_{\rm T}$ requirement on the single electron track
($p_{\rm T}$ $<$ 3 GeV/$c$). Moreover, the charm and beauty ${\rm{DCA_{\rm
ee}}}$ templates do not exhibit any strong dependence on $p_{\rm T,ee}$ and
$m_{{\rm ee}}$, as well as on the minimum electron $p_{\rm T}$ 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 $p_{\rm T,ee}$ and $m_{{\rm ee}}$ range, is
not. The same ${\rm{DCA_{\rm ee}}}$ 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.

##  5 Results and discussion

###  5.1 Comparison of the data to the cocktail

The differential ${\rm{e}}^{+}{\rm{e}}^{-}$ cross section
d$\sigma/{\rm{d}}m_{{\rm ee}}$ in minimum bias pp collisions at ${\sqrt{s}}$ =
7 TeV is presented in Fig. 9 in the ALICE acceptance ($|\eta_{{\rm e}}|$ $<$
0.8 and $p_{{\rm T,e}}$ $>$ 0.2 GeV/$c$) as a function of $m_{{\rm ee}}$.
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 ${\rm{e}}^{+}{\rm{e}}^{-}$ 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 ($m_{{\rm ee}}$ $<$ 3.3 GeV/$c^{2}$).

Figure 9: (Colour online) Inclusive ${\rm{e}}^{+}{\rm{e}}^{-}$ cross section
in pp collisions at ${\sqrt{s}}$ = 7 TeV in the ALICE acceptance as a function
of mass. The data are compared with a cocktail of expected sources. In the
lower panel, the ratio of data to cocktail is shown. Statistical and
systematic uncertainties of the data are plotted as vertical bars and boxes,
respectively. The total uncertainty of the cocktail is represented as a grey
band.

For a more detailed discussion, the results are presented differentially below
in $p_{\rm T,ee}$ and ${\rm{DCA_{\rm ee}}}$ in four different mass regions,
i.e. the $\pi^{0}$ region ($m_{{\rm ee}}$ $<$ 0.14 GeV/$c^{2}$), the low-mass
region (0.14 $<$ $m_{{\rm ee}}$ $<$ 1.1 GeV/$c^{2}$), the IMR (1.1 $<$
$m_{{\rm ee}}$ $<$ 2.7 GeV/$c^{2}$), and the $J/\psi$ region (2.7 $<$ $m_{{\rm
ee}}$ $<$ 3.3 GeV/$c^{2}$).

####  5.1.1 $\pi^{0}$ mass region

The mass region $m_{{\rm ee}}$ $<$ 0.14 GeV/$c^{2}$ is dominated by $\pi^{0}$
Dalitz decays ($\pi^{0}\to\rm{e}^{+}\rm{e}^{-}\gamma$), with a small
contribution from $\eta$ Dalitz decays ($\eta\to\rm{e}^{+}\rm{e}^{-}\gamma$)
of about 10%. In the left panel of Fig. 10, the measured $p_{{\rm
T,ee}}$-differential cross section of ${\rm{e}}^{+}{\rm{e}}^{-}$ 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 ${\rm{e}}^{+}{\rm{e}}^{-}$ cross section.

Figure 10: (Colour online) Inclusive ${\rm{e}}^{+}{\rm{e}}^{-}$ cross section
in pp collisions at ${\sqrt{s}}$ = 7 TeV in the ALICE acceptance as a function
of $p_{\rm T,ee}$ (left) and ${\rm{DCA_{\rm ee}}}$ (right) for $m_{{\rm ee}}$
$<$ 0.14 GeV/$c^{2}$ and 0.08 $<$ $m_{{\rm ee}}$ $<$ 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 $p_{\rm
T,ee}$ (left) and the pull distribution as a function of ${\rm{DCA_{\rm ee}}}$
(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 ${\rm{e}}^{+}{\rm{e}}^{-}$ cross
section is shown as a function of ${\rm{DCA_{\rm ee}}}$ in the mass range 0.08
$<$ $m_{{\rm ee}}$ $<$ 0.14 GeV/$c^{2}$ for $p_{\rm T,ee}$ $<$ 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
${\rm{e}}^{+}{\rm{e}}^{-}$ pairs from photon conversions with large
${\rm{DCA_{\rm ee}}}$ values are suppressed. The blue line represents the
expected cross section of all prompt light-flavour sources, for which the
$\pi^{0}$ ${\rm{DCA_{\rm ee}}}$ template is used as an approximation. Some
small statistical fluctuations can be seen in the tail of the distribution,
which would require a very large amount of fully simulated pp collisions to be
removed. In this mass range, the contributions from non-prompt sources
(${\rm{c}}{\overline{{\rm{c}}}}$ and ${\rm{b}}{\overline{{\rm{b}}}}$) are
negligible, which allows the ${\rm{DCA_{\rm ee}}}$ resolution in data and in
MC to be directly compared. To quantify the agreement between data and the
expected ${\rm{DCA_{\rm ee}}}$ 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 ${\rm{DCA_{\rm ee}}}$ distribution obtained from
the full simulations of the ALICE detector describes the data well. A slight
excess of the data is observed in 1 $<$ ${\rm{DCA_{\rm ee}}}$ $<$ 3 $\sigma$
which is the range mostly affected by discrepancies in the DCA resolution
between data and MC.

####  5.1.2 Low-mass region

The low-mass region, $0.14<m_{\rm ee}<1.1$ GeV/$c^{2}$, is expected to be
dominated by the light mesons $\eta$, $\eta^{{}^{\prime}}$, $\rho$, $\omega$,
$\phi$, and the contribution of correlated ${\rm{e}}^{+}{\rm{e}}^{-}$ 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 $<$ $m_{{\rm ee}}$ $<$ 0.7 GeV/$c^{2}$ and 4 $<$ $p_{\rm T,ee}$ $<$ 8
GeV/$c$). The latter is not included in the hadronic cocktail and will be
discussed in section 5.2. At low $m_{{\rm ee}}$ ($m_{{\rm ee}}$ $\leq$
$m_{\eta}$), the $\eta$ Dalitz decay is the main source of
${\rm{e}}^{+}{\rm{e}}^{-}$ pairs for all $p_{{\rm T,ee}}$, as shown in the
left panel of Fig. 11, whereas at larger $m_{\rm ee}$, the heavy-flavour
contributions start to dominate, followed by the $\omega$, $\rho$, and $\phi$
contributions (see right panel of Fig. 11). The requirement on the single
electron track of $p_{\rm T}$ $>$ 0.2 GeV/$c$ produces an acceptance hole at
low $m_{{\rm ee}}$ and $p_{\rm{T,ee}}$, which can be seen in the data in the
$m_{{\rm ee}}$ interval 0.14 $<$ $m_{{\rm ee}}$ $<$ 0.7 GeV/$c^{2}$ for the
$p_{\rm T,ee}$ range 0 $<$ $p_{\rm T,ee}$ $<$ 0.4 GeV/$c$ (see left panel of
Fig. 11). Due to their characteristic $m_{{\rm ee}}$ and $p_{\rm T,ee}$
distributions, the ${\rm{e}}^{+}{\rm{e}}^{-}$ 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.

Figure 11: (Colour online) Inclusive ${\rm{e}}^{+}{\rm{e}}^{-}$ cross section
in pp collisions at ${\sqrt{s}}$ = 7 TeV in the ALICE acceptance as a function
of $p_{\rm T,ee}$ in the mass range 0.14 $<$ $m_{{\rm ee}}$ $<$ 0.7
GeV/$c^{2}$ (left) and 0.7 $<$ $m_{{\rm ee}}$ $<$ 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 $p_{\rm T,ee}$ 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 ${\rm{DCA_{\rm ee}}}$ variable. In Fig. 12, the DCAee-
differential cross section of ${\rm{e}}^{+}{\rm{e}}^{-}$ pairs is shown
integrated over $p_{\rm T,ee}$ in the mass range 0.14 $<$ $m_{{\rm ee}}$ $<$
1.1 GeV/$c^{2}$. The template for ${\rm{e}}^{+}{\rm{e}}^{-}$ pairs from prompt
light-flavour hadron decays cannot describe the tail of the ${\rm{DCA_{\rm
ee}}}$ 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.

Figure 12: (Colour online) Inclusive ${\rm{e}}^{+}{\rm{e}}^{-}$ cross section
in pp collisions at ${\sqrt{s}}$ = 7 TeV in the ALICE acceptance as a function
of ${\rm{DCA_{\rm ee}}}$ in the mass range 0.14 $<$ $m_{{\rm ee}}$ $<$ 1.1
GeV/$c^{2}$. The data are compared with a cocktail of expected sources. In the
bottom panel, the pull distribution is 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.

####  5.1.3 Intermediate-mass region

The IMR, 1.1 $<$ $m_{{\rm ee}}$ $<$ 2.7 GeV/$c^{2}$, is dominated by
correlated ${\rm{e}}^{+}{\rm{e}}^{-}$ pairs from semileptonic decays of charm
and beauty hadrons. The $p_{{\rm{T,ee}}}$-differential cross section of
${\rm{e}}^{+}{\rm{e}}^{-}$ pairs measured in this $m_{{\rm ee}}$ region is
shown in comparison with the hadronic cocktail in the left panel of Fig. 13.
The cross section of ${\rm{e}}^{+}{\rm{e}}^{-}$ pairs from
${\rm{c}}{\overline{{\rm{c}}}}$ is the dominant dielectron source for $p_{\rm
T,ee}$ $<$ 3 GeV/$c$, whereas most of the ${\rm{e}}^{+}{\rm{e}}^{-}$ pairs
originate from ${\rm{b}}{\overline{{\rm{b}}}}$ for $p_{\rm T,ee}$ $>$ 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 ${\rm{c}}{\overline{{\rm{c}}}}$ and
${\rm{b}}{\overline{{\rm{b}}}}$ contributions. The NLO event generator
predicts harder $p_{\rm T,ee}$ spectra for the ${\rm{c}}{\overline{{\rm{c}}}}$
and ${\rm{b}}{\overline{{\rm{b}}}}$ contributions. For the same global
normalisation to $\sigma_{{\rm{c}}{\overline{{\rm{c}}}}~{}}^{{\rm REF}}$ and
$\sigma_{{\rm{b}}{\overline{{\rm{b}}}}~{}}^{{\rm REF}}$ as for the PYTHIA
cocktail, the POWHEG calculations tend to underestimate the data, in
particular in the region where the ${\rm{c}}{\overline{{\rm{c}}}}$
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
$Q\overline{Q}$ pair and therefore different probabilities for the
${\rm{e}}^{+}{\rm{e}}^{-}$ pair to enter the detector acceptance.

Figure 13: (Colour online) Inclusive ${\rm{e}}^{+}{\rm{e}}^{-}$ cross section in pp collisions at ${\sqrt{s}}$ = 7 TeV in the ALICE acceptance as a function of $p_{\rm T,ee}$ in the mass range 1.1 $<$ $m_{{\rm ee}}$ $<$ 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 ${\rm{c}}{\overline{{\rm{c}}}}$ and ${\rm{b}}{\overline{{\rm{b}}}}$ contributions. In the bottom panels, the corresponding ratios of data to cocktail as a function of $p_{\rm T,ee}$ 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. ${\rm{c}}{\overline{{\rm{c}}}}$ | PYTHIA | POWHEG | PYTHIA/POWHEG
---|---|---|---
4$\pi$ | 1. | 1. |
$|\eta_{\rm e}|$ $<$ 0.8 | 0.0754 | 0.0518 | 1.46
(uncorrelated e+e-) | (0.0428) | (0.0299) | (1.43)
$|\eta_{\rm e}|$ $<$ 0.8 | 0.0148 | 0.0100 | 1.48
1.1 $<$ $m_{{\rm ee}}$ $<$ 2.7 GeV/$c^{2}$ |  |  |
$|\eta_{\rm e}|$ $<$ 0.8 $\&$ $p_{{\rm T,e}}>$ 0.2 GeV/$c$ | 0.0146 | 0.0098 | 1.49
1.1 $<$ $m_{{\rm ee}}$ $<$ 2.7 GeV/$c^{2}$ |  |  |
$|\eta_{\rm e}|$ $<$ 0.8 $\&$ $p_{{\rm T,e}}>$ 0.4 GeV/$c$ | 0.0115 | 0.0077 | 1.49
1.1 $<$ $m_{{\rm ee}}$ $<$ 2.7 GeV/$c^{2}$ |  |  |
${\rm{b}}{\overline{{\rm{b}}}}$ | PYTHIA | POWHEG | PYTHIA/POWHEG
4$\pi$ | 1 | 1 |
$|\eta_{\rm e}|$ $<$ 0.8 | 0.1250 | 0.1167 | 1.07
(uncorrelated e+e-) | (0.0581) | (0.0506) | (1.15)
$|\eta_{\rm e}|$ $<$ 0.8 | 0.0495 | 0.0472 | 1.05
1.1 $<$ $m_{{\rm ee}}$ $<$ 2.7 GeV/$c^{2}$ |  |  |
$|\eta_{\rm e}|$ $<$ 0.8 $\&$ $p_{{\rm T,e}}>$ 0.2 GeV/$c$ | 0.0484 | 0.0460 | 1.05
1.1 $<$ $m_{{\rm ee}}$ $<$ 2.7 GeV/$c^{2}$ |  |  |
$|\eta_{\rm e}|$ $<$ 0.8 $\&$ $p_{{\rm T,e}}>$ 0.4 GeV/$c$ | 0.0413 | 0.0390 | 1.06
1.1 $<$ $m_{{\rm ee}}$ $<$ 2.7 GeV/$c^{2}$ |  |  |
Table 3: Fraction of correlated ${\rm{e}}^{+}{\rm{e}}^{-}$ pairs in 4$\pi$ 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 ${\rm{e}}^{+}{\rm{e}}^{-}$ pairs
in the full phase space (4$\pi$) and after consecutive acceptance selection
criteria for the ${\rm{c}}{\overline{{\rm{c}}}}$ and
${\rm{b}}{\overline{{\rm{b}}}}$ contributions. The fraction of dielectron
pairs from charm-hadron decays where both electrons are found at mid-rapidity
($|\eta_{{\rm e^{\pm}}}|$ $<$ 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
${\rm{c}}{\overline{{\rm{c}}}}$ 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 (17.3%) as
compared to PYTHIA (20.7%). Second, the pseudorapidity correlation between the
electron and positron from charm-hadron decays gives rise to a larger
acceptance for ${\rm{e}}^{+}{\rm{e}}^{-}$ 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 7%. The rapidity distributions of beauty quarks
predicted by POWHEG and PYTHIA are quite similar. Moreover, about 50% of the
correlated ${\rm{e}}^{+}{\rm{e}}^{-}$ pairs from beauty hadron decays
originate from a single B hadron (${\rm B}\to\overline{\rm D}{\rm e}^{+}{\rm
X}\to{\rm e}^{+}{\rm e}^{-}{\rm X}$) and are insensitive to the correlations
between the B and $\overline{\rm{B}}$ 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 ${\rm{e}}^{+}{\rm{e}}^{-}$
pairs originating from different B hadrons is less related to the correlation
between the b and $\overline{\rm b}$ but more driven by decay kinematics.

The measured ${\rm{DCA_{\rm ee}}}$ distribution of ${\rm{e}}^{+}{\rm{e}}^{-}$
pairs is shown in Fig. 14 integrated over $p_{\rm T,ee}$ in the mass range 1.1
$<$ $m_{{\rm ee}}$ $<$ 2.7 GeV/$c^{2}$. The results are compared with the MC
templates normalised to the PYTHIA cocktail. The shape of the MC
${\rm{DCA_{\rm ee}}}$ distribution for correlated ${\rm{e}}^{+}{\rm{e}}^{-}$
pairs from charm-hadron decays deviates from the data at large DCAee. The
additional contribution from ${\rm{e}}^{+}{\rm{e}}^{-}$ pairs from beauty-
hadron decays allows the data to be well described, as can be seen with the
pull distribution presented in the bottom panel of Fig. 14. The ${\rm{DCA_{\rm
ee}}}$ variable gives additional constraints to separate
${\rm{e}}^{+}{\rm{e}}^{-}$ pairs from charm- and beauty-hadron decays. No
indication for a prompt source is observed in the IMR.

Figure 14: (Colour online) Inclusive ${\rm{e}}^{+}{\rm{e}}^{-}$ cross section
in pp collisions at ${\sqrt{s}}$ = 7 TeV in the ALICE acceptance as a function
of ${\rm{DCA_{\rm ee}}}$ in the mass range 1.1 $<$ $m_{{\rm ee}}$ $<$ 2.7
GeV/$c^{2}$. The data are compared with a cocktail of expected sources. In the
bottom panel, the pull distribution is 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 total ${\rm{c}}{\overline{{\rm{c}}}}$ and ${\rm{b}}{\overline{{\rm{b}}}}$
cross sections, $\sigma_{{\rm{c}}{\overline{{\rm{c}}}}~{}}$ and
$\sigma_{{\rm{b}}{\overline{{\rm{b}}}}~{}}$, can be extracted from the data by
fitting the measured ${\rm{e}}^{+}{\rm{e}}^{-}$ cross section of heavy-flavour
hadron decays in the IMR with the sum of two contributions:

$f^{{\rm{GEN}}}=S_{{\rm{c}}{\overline{{\rm{c}}}}~{}}f^{{\rm{GEN}}}_{{\rm{c}}{\overline{{\rm{c}}}}~{}}+S_{{\rm{b}}{\overline{{\rm{b}}}}~{}}f^{{\rm{GEN}}}_{{\rm{b}}{\overline{{\rm{b}}}}~{}},$
(9)

where $f^{{\rm{GEN}}}_{{\rm{c}}{\overline{{\rm{c}}}}~{}}$ and
$f^{{\rm{GEN}}}_{{\rm{b}}{\overline{{\rm{b}}}}~{}}$ are the cross sections for
dielectron pairs from charm and beauty-hadron decays, calculated with the
event generator GEN and normalised to
$\sigma_{{\rm{c}}{\overline{{\rm{c}}}}~{}}^{{\rm REF}}$ and
$\sigma_{{\rm{b}}{\overline{{\rm{b}}}}~{}}^{{\rm REF}}$ [94, 95]. The two fit
parameters are the scaling factors $S_{{\rm{c}}{\overline{{\rm{c}}}}~{}}$ and
$S_{{\rm{b}}{\overline{{\rm{b}}}}~{}}$, defined also as:

$\sigma_{{\rm{c}}{\overline{{\rm{c}}}}~{}}=S_{{\rm{c}}{\overline{{\rm{c}}}}~{}}\cdot\sigma_{{\rm{c}}{\overline{{\rm{c}}}}~{}}^{{\rm
REF}},$ (10)
$\sigma_{{\rm{b}}{\overline{{\rm{b}}}}~{}}=S_{{\rm{b}}{\overline{{\rm{b}}}}~{}}\cdot\sigma_{{\rm{b}}{\overline{{\rm{b}}}}~{}}^{{\rm
REF}},$ (11)

The ${\rm{e}}^{+}{\rm{e}}^{-}$ spectra from heavy-flavour hadron decays are
obtained by subtracting the expected cross section of
${\rm{e}}^{+}{\rm{e}}^{-}$ pairs originating from vector meson and $J/\psi$
decays, from the measured ${\rm{e}}^{+}{\rm{e}}^{-}$ 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 ${\rm{DCA_{\rm ee}}}$ and in ($m_{{\rm
ee}}$, $p_{{\rm T,ee}}$). For each combination of scaling factors,
$S_{{\rm{c}}{\overline{{\rm{c}}}}~{}}$ and
$S_{{\rm{b}}{\overline{{\rm{b}}}}~{}}$, the $\chi^{2}$ value is calculated:

$\chi^{2}={\sum_{i=1}^{n}}\left(\frac{x_{{\rm i}}-\mu_{\rm
i}}{\sqrt{(\sigma_{x_{\rm i}}^{{\rm{stat}}})^{2}+(\sigma_{\mu_{\rm
i}}^{{\rm{stat}}})^{2}}}\right)^{2}.$ (12)

The values of the data points and MC calculations in bin $i$ are given by
$x_{\rm i}$ and $\mu_{\rm i}$, respectively, while $\sigma_{x_{\rm
i}}^{{\rm{stat}}}$ and $\sigma_{\mu_{\rm i}}^{{\rm{stat}}}$ represent their
statistical uncertainties. The result of the fit is determined by the minimum
of $\chi^{2}$.

Figure 15: (Colour online) Total ${\rm{c}}{\overline{{\rm{c}}}}$ and
${\rm{b}}{\overline{{\rm{b}}}}$ cross sections extracted from a fit of the
measured dielectron yield from heavy-flavour hadron decays in ( $m_{{\rm
ee}}$, $p_{{\rm T,ee}}$) and in ${\rm{DCA_{\rm ee}}}$ with PYTHIA (left) and
POWHEG (right). The results and their uncertainties (see text) are compared to
published cross sections, for which the total uncertainty is represented by
dashed lines.

The extracted $\sigma_{{\rm{c}}{\overline{{\rm{c}}}}~{}}$ and
$\sigma_{{\rm{b}}{\overline{{\rm{b}}}}~{}}$ cross sections are shown in Fig.
15 for the ($m_{{\rm ee}}$, $p_{{\rm T,ee}}$) and the ${\rm{DCA_{\rm ee}}}$
analysis when PYTHIA (left) or POWHEG (right) are used to calculate
$f^{{\rm{GEN}}}_{{\rm{c}}{\overline{{\rm{c}}}}~{}}$ and
$f^{{\rm{GEN}}}_{{\rm{b}}{\overline{{\rm{b}}}}~{}}$. The statistical
uncertainties are plotted as ellipses and correspond to a confidence level of
68.3% (1$\sigma$) for each parameter (at $\chi^{2}=\chi^{2}_{{\rm{min}}}+1$
[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 $\sigma_{{\rm{c}}{\overline{{\rm{c}}}}~{}}^{{\rm
REF}}$ [94] and $\sigma_{{\rm{b}}{\overline{{\rm{b}}}}~{}}^{{\rm REF}}$ [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 ($m_{{\rm ee}}$, $p_{{\rm T,ee}}$)
and ${\rm{DCA_{\rm ee}}}$ fits. Both calculations, PYTHIA and POWHEG, are able
to reproduce the ($m_{{\rm ee}}$, $p_{{\rm T,ee}}$) and ${\rm{DCA_{\rm ee}}}$
spectra reasonably well and give similar minimum $\chi^{2}$ per number of
degree of freedom (0.999 for POWHEG and 0.989 for PYTHIA for the ($m_{{\rm
ee}}$, $p_{{\rm T,ee}}$) fit). The fit results of the ($m_{{\rm ee}}$,
$p_{{\rm T,ee}}$) and ${\rm{DCA_{\rm ee}}}$ spectra are in agreement within
the statistical and systematic uncertainties. The ${\rm{DCA_{\rm ee}}}$
distribution is slightly less sensitive to the total
${\rm{b}}{\overline{{\rm{b}}}}$ cross section. The ${\rm{e}}^{+}{\rm{e}}^{-}$
pairs from beauty-hadron decays only dominate the last ${\rm{DCA_{\rm ee}}}$
bin (see Fig. 14). The shapes of the MC ${\rm{DCA_{\rm ee}}}$ templates are
driven by the decay kinematics and assumed to be model independent. Therefore
the extracted $\sigma_{{\rm{c}}{\overline{{\rm{c}}}}~{}}$ and
$\sigma_{{\rm{b}}{\overline{{\rm{b}}}}~{}}$ directly reflect the different
probabilities for the ${\rm e}^{+}{\rm e}^{-}$ pair to enter the detector
acceptance calculated with PYTHIA or POWHEG (see Table 3). The ($m_{{\rm
ee}}$, $p_{{\rm T,ee}}$) fit depends in addition on the $p_{\rm{T,ee}}$
distributions of correlated ${\rm{e}}^{+}{\rm{e}}^{-}$ pairs from charm and
beauty-hadron decays, which are harder in POWHEG compared to PYTHIA. The total
${\rm{c}}{\overline{{\rm{c}}}}$ and ${\rm{b}}{\overline{{\rm{b}}}}$ 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
${\rm{c}}{\overline{{\rm{c}}}}$ cross section obtained by extrapolating in
rapidity the D0 $p_{\rm T}$ 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.

${\rm{c}}{\overline{{\rm{c}}}}$ | ($m_{{\rm ee}}$ , $p_{{\rm T,ee}}$) fit |  ${\rm{DCA_{\rm ee}}}$ fit
---|---|---
POWHEG | 11.6 $\pm$1.4 (stat.) $\pm$1.9 (syst.) mb | 11.7 $\pm$1.8 (stat.) $\pm$2.0 (syst.) mb
PYTHIA | 6.4 $\pm$0.9 (stat.) $\pm$1.1 (syst.) mb | 7.7 $\pm$1.2 (stat.) $\pm$1.3 (syst.) mb
Table 4: Summary of the total ${\rm{c}}{\overline{{\rm{c}}}}$ cross sections extracted from a fit of the measured dielectron spectra from heavy-flavour hadron decays in ($m_{{\rm ee}}$, $p_{{\rm T,ee}}$) and in ${\rm{DCA_{\rm ee}}}$ with PYTHIA and POWHEG. The uncertainty of 22% on the branching fractions and fragmentation functions (BRc→e) is not listed. ${\rm{b}}{\overline{{\rm{b}}}}$ | ($m_{{\rm ee}}$ , $p_{{\rm T,ee}}$) fit |  ${\rm{DCA_{\rm ee}}}$ fit
---|---|---
POWHEG | 0.162 $\pm$0.078 (stat.) $\pm$0.026 (syst.) mb | 0.175 $\pm$0.092 (stat.) $\pm$0.030 (syst.) mb
PYTHIA | 0.303 $\pm$0.077 (stat.) $\pm$0.050 (syst.) mb | 0.165 $\pm$0.086 (stat.) $\pm$0.028 (syst.) mb
Table 5: Summary of the total ${\rm{b}}{\overline{{\rm{b}}}}$ cross sections
extracted from a fit of the measured dielectron spectra from heavy-flavour
hadron decays in ($m_{{\rm ee}}$, $p_{{\rm T,ee}}$) and in ${\rm{DCA_{\rm
ee}}}$ with PYTHIA and POWHEG. The uncertainty of 6% [90] on the branching
fractions and fragmentation functions (BRb(→c)→e) is not listed.

####  5.1.4 $J/\psi$ mass region

The mass region 2.7 $<$ $m_{{\rm ee}}$ $<$ 3.3 GeV/$c^{2}$ is dominated by
$J/\psi$ decays with a small contribution from charm-hadron decays. In the
left panel of Fig. 16, the corresponding measured ${\rm{e}}^{+}{\rm{e}}^{-}$
cross section as a function of $p_{\rm T,ee}$ 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 ${\rm{DCA_{\rm ee}}}$ distribution of ${\rm{e}}^{+}{\rm{e}}^{-}$
pairs is sensitive to the large decay length of B mesons ($c\tau_{{\rm B}}$
$\approx$ 470 µm) and the contribution from $J/\psi$ originating from their
decays. The measured ${\rm{DCA_{\rm ee}}}$ spectrum shown in the right panel
of Fig. 16 cannot be reproduced with the MC template of the prompt $J/\psi$
alone. The contribution from non-prompt $J/\psi$, together with those from
correlated ${\rm{e}}^{+}{\rm{e}}^{-}$ pairs from heavy-flavour hadron decays,
leads to a reasonable description of the data by the MC calculations. The data
are consistent with the fraction $f_{\rm B}$ of non-prompt $J/\psi$
originating from B meson decays previously measured by the ALICE Collaboration
[101].

Figure 16: (Colour online) Inclusive ${\rm{e}}^{+}{\rm{e}}^{-}$ cross section
in pp collisions at ${\sqrt{s}}$ = 7 TeV in the ALICE acceptance as a function
of $p_{\rm T,ee}$ (left panel) and ${\rm{DCA_{\rm ee}}}$ (right panel) in the
mass range 2.7 $<$ $m_{{\rm ee}}$ $<$ 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 $p_{\rm T,ee}$ (left) and the pull distribution
as a function of ${\rm{DCA_{\rm ee}}}$ (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.

###  5.2 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 $p_{\rm T}$ $<$ 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 ${\rm{e}}^{+}{\rm{e}}^{-}$
pair. The advantage of this approach is that the main background originating
from $\pi^{0}$ decays can be suppressed by selecting
${\rm{e}}^{+}{\rm{e}}^{-}$ pairs with sufficiently large $m_{{\rm ee}}$
($m_{{\rm ee}}$ $>$ $m_{\pi^{0}}$). The drawback is the small internal
conversion probability of $O(10^{-2})$ and the rapidly decreasing cross
section as a function of $m_{{\rm ee}}$ ($\propto$1/$m_{{\rm 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 $p_{{\rm T,ee}}^{{\rm 2}}$ $\gg$ $m_{{\rm ee}}^{{\rm 2}}$, i.e. in the
limit of quasi-real virtual photons, to:

$\frac{{\rm d^{2}}N_{{\rm ee}}}{{\rm d}m_{{\rm ee}}{\rm d}p_{{\rm
T,ee}}}=\frac{2\alpha}{3\pi}\sqrt{1-\frac{4m_{{\rm e}}^{2}}{m_{{\rm
ee}}^{2}}}\left(1+\frac{2m_{{\rm e}}^{2}}{m_{{\rm
ee}}^{2}}\right)\cdot\frac{1}{m_{{\rm ee}}}\frac{{\rm d}N_{\gamma}}{{\rm
d}p_{{\rm T}}},$ (13)

with $\alpha$, ${\rm d}N_{\gamma}/{\rm d}p_{{\rm T}}$, and $m_{{\rm e}}$ being
the fine-structure constant, the number of real photons at a given $p_{\rm T}$
($=$ $p_{{\rm T,ee}}$), and the electron mass, respectively. To obtain the
final expected shape $f_{\rm dir}(m_{{\rm ee}})$ 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 ($|\eta_{{\rm e}}|$ $<$
0.8, $p_{{\rm T,e}}>$ 0.2 GeV/$c$).

Figure 17: Fit of the ${\rm{e}}^{+}{\rm{e}}^{-}$ cross section in pp
collisions at ${\sqrt{s}}$ = 7 TeV in the ALICE acceptance as a function of
$m_{{\rm ee}}$ in the range 3 $<$ $p_{\rm T,ee}$ $<$ 4 GeV/$c$ with the three-
component function defined by Eq. (14). Statistical and systematic
uncertainties on the data are shown separately as vertical bars and boxes,
respectively.

The measured $m_{{\rm ee}}$ distributions of e+e- pairs are fitted in
different $p_{\rm T,ee}$ bins with a three-component function:

$f(m_{{\rm ee}},r)=(1-r)f_{\rm LF}(m_{{\rm ee}})+r\,f_{\rm dir}(m_{{\rm
ee}})+f_{\rm HF}(m_{{\rm ee}}),$ (14)

where $f_{\rm LF}$ is the shape of the mass distribution of the light-flavour
component of the hadronic cocktail and $f_{\rm HF}$ is the
${\rm{e}}^{+}{\rm{e}}^{-}$ cross section of the expected heavy-flavour
contribution in the corresponding $p_{\rm T,ee}$ bin. The ratio $r$ of direct
to inclusive photons is the only fit parameter. The fit is limited to the mass
range 0.09 $<$ $m_{{\rm ee}}$ $<$ 0.39 GeV/$c^{2}$ to ensure the condition
$p_{{\rm T,ee}}^{\rm 2}$ $\gg$ $m_{{\rm ee}}^{\rm 2}$. Both $f_{\rm LF}$ and
$f_{\rm dir}$ are normalised such that they separately fit the data for
$m_{{\rm ee}}$ $<$ 0.04 GeV/$c^{2}$, because in this mass region the
functional shapes of $f_{{\rm LF}}$ and $f_{{\rm dir}}$ are essentially
identical. In Fig. 17, the measured $m_{{\rm ee}}$-differential
${\rm{e}}^{+}{\rm{e}}^{-}$ cross section is shown in the $p_{\rm T,ee}$ range
3 $<$ $p_{\rm T,ee}$ $<$ 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
${\rm{c}}{\overline{{\rm{c}}}}$ is evaluated by repeating the fit with $f_{\rm
HF}$ computed with the POWHEG generator and found to be below 0.75% in the
full $p_{{\rm T}}$ 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
$p_{{\rm T}}$ 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 $\eta$$/$$\pi^{0}$ ratio. In most of the
$p_{{\rm T,ee}}$ bins, this is the dominant source of systematic
uncertainties. Finally, $f_{\rm LF}$ and $f_{\rm dir}$ are normalised to the
data in the range 0 $<$ $m_{{\rm ee}}$ $<$ 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.
$R_{\gamma}=\sigma^{\gamma}_{{\rm inclusive}}/\sigma^{\gamma}_{{\rm
decay}}=1/(1-r)$, is shown as a function of $p_{{\rm T}}$. 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 $p_{{\rm T}}$ 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 $0.5p_{\rm T}<\mu_{\rm F}<2p_{\rm T}$ for the
factorization scale) used in the calculation. The upper limits at 90%
confidence level (C.L.) on $R_{\gamma}$, 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 $R_{\gamma}$
measured in pp collisions at $\sqrt{s}=$ 8 TeV with the real photon analysis
performed by the ALICE Collaboration [30].

Figure 18: Ratio of inclusive to decay photon cross sections extracted from the dielectron spectra measured in pp collisions at ${\sqrt{s}}$ = 7 TeV. The results are compared with NLO pQCD calculations [103, 104, 105, 106]. Statistical and systematic uncertainties are shown as vertical bars and boxes for the data, respectively, and as a band for the NLO pQCD calculations. $p_{{\rm T}}$ interval | Upper limits at 90% C.L.
---|---
| on $R_{\gamma}=\sigma^{\gamma}_{{\rm inclusive}}/\sigma^{\gamma}_{{\rm
decay}}$
1 $<$ $p_{{\rm T}}$ $<$ 1.5 GeV/$c$ | 1.035
1.5 $<$ $p_{{\rm T}}$ $<$ 2 GeV/$c$ | 1.027
2 $<$ $p_{{\rm T}}$ $<$ 3 GeV/$c$ | 1.030
3 $<$ $p_{{\rm T}}$ $<$ 4 GeV/$c$ | 1.096
4 $<$ $p_{{\rm T}}$ $<$ 8 GeV/$c$ | 1.197
Table 6: Upper limits at 90% C.L. on the ratio of inclusive to decay photon
cross sections.

##  6 Conclusion

A measurement of ${\rm{e}}^{+}{\rm{e}}^{-}$ pair production at mid-rapidity
($|\eta_{{\rm e}}|$ $<$ 0.8) in minimum bias pp collisions at $\sqrt{s}$ = 7
TeV with ALICE at the LHC is shown. The results are presented as a function of
the invariant mass $m_{{\rm ee}}$ (0 $<$ $m_{{\rm ee}}$ $<$ 3.3 GeV/$c^{2}$)
of the ${\rm{e}}^{+}{\rm{e}}^{-}$ pair, its transverse momentum $p_{\rm T,ee}$
(0 $<$ $p_{\rm T,ee}$ $<$ 8 GeV/$c$), and the pair transverse impact parameter
DCAee.

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
${\rm{c}}{\overline{{\rm{c}}}}$ and ${\rm{b}}{\overline{{\rm{b}}}}$ cross
sections [94, 95]. The shape of the ${\rm{DCA_{\rm ee}}}$ distribution of each
source is obtained using a full simulation of the ALICE detector. The obtained
${\rm{DCA_{\rm ee}}}$ templates are normalised to the cocktail calculations
integrated over the same $m_{{\rm ee}}$ and $p_{\rm T,ee}$ range.

Overall good agreement between data and cocktail is observed for all $m_{{\rm
ee}}$, $p_{\rm T,ee}$, and ${\rm{DCA_{\rm ee}}}$ intervals considered. In the
$\pi^{0}$ mass region ($m_{{\rm ee}}$ $<$ 0.14 GeV/$c^{2}$), the comparison of
the measured ${\rm{DCA_{\rm ee}}}$ distribution with the MC templates shows
that the detector resolution is well reproduced in the simulations. In the
low-mass region (0.14 $<$ $m_{{\rm ee}}$ $<$ 1.1 GeV/$c^{2}$), prompt and non-
prompt contributions can be separated with the ${\rm{DCA_{\rm ee}}}$
observable. In the intermediate-mass region, 1.1 $<$ $m_{{\rm ee}}$ $<$ 2.7
GeV/$c^{2}$, the measured ${\rm{e}}^{+}{\rm{e}}^{-}$ cross section is
dominated by correlated ${\rm{e}}^{+}{\rm{e}}^{-}$ pairs from charm- and
beauty-hadron decays. The ${\rm{c}}{\overline{{\rm{c}}}}$ and
${\rm{b}}{\overline{{\rm{b}}}}$ total cross sections can be extracted from the
data by a double-differential fit of the measured spectra in ($m_{{\rm ee}}$,
$p_{{\rm T,ee}}$) and by fitting the ${\rm{DCA_{\rm ee}}}$ 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 $J/\psi$ mass
region (2.7 $<$ $m_{{\rm ee}}$ $<$ 3.3 GeV/$c^{2}$), the measured ${\rm
DCA}_{{\rm ee}}$\- and $p_{{\rm T,ee}}$-differential cross sections are well
described by the hadronic cocktail. The ${\rm{DCA_{\rm ee}}}$ distribution is
sensitive to the fraction $f_{\rm B}$ of non-prompt $J/\psi$ originating from
B-meson decays. The data are consistent with the previously measured $f_{\rm
B}$ by the ALICE Collaboration [101].

In the quasi-real virtual-photon region, at low mass ($m_{{\rm ee}}$ $<$ 0.4
GeV/$c^{2}$) and high $p_{\rm T,ee}$ ($p_{\rm T,ee}$ $>$ 1 GeV/$c$), the
contribution of virtual direct photons is extracted from the data by fitting
the $m_{{\rm ee}}$ distributions in $p_{\rm T,ee}$ 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 ${\rm{e}}^{+}{\rm{e}}^{-}$ 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
starting in 2021 [108, 109, 110, 111]. In particular, the measurement of the
${\rm{DCA_{\rm ee}}}$ 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].

## Acknowledgements

The ALICE collaboration would like to thank Werner Vogelsang for providing the
NLO calculations for direct photon production.

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 gratefully acknowledges the resources and support
provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG)
collaboration. The ALICE Collaboration acknowledges the following funding
agencies for their support in building and running the ALICE detector: A. I.
Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation
(ANSL), State Committee of Science and World Federation of Scientists (WFS),
Armenia; Austrian Academy of Sciences and Nationalstiftung für Forschung,
Technologie und Entwicklung, Austria; Ministry of Communications and High
Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional
de Desenvolvimento Científico e Tecnológico (CNPq), Universidade Federal do
Rio Grande do Sul (UFRGS), Financiadora de Estudos e Projetos (Finep) and
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Brazil;
Ministry of Science & Technology of China (MSTC), National Natural Science
Foundation of China (NSFC) and Ministry of Education of China (MOEC) , China;
Ministry of Science and Education, Croatia; Ministry of Education, Youth and
Sports of the Czech Republic, Czech Republic; The Danish Council for
Independent Research — Natural Sciences, the Carlsberg Foundation and Danish
National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics
(HIP), Finland; Commissariat à l’Energie Atomique (CEA) and Institut National
de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre
National de la Recherche Scientifique (CNRS), France; Bundesministerium für
Bildung, Wissenschaft, Forschung und Technologie (BMBF) and GSI
Helmholtzzentrum für Schwerionenforschung GmbH, Germany; General Secretariat
for Research and Technology, Ministry of Education, Research and Religions,
Greece; National Research, Development and Innovation Office, Hungary;
Department of Atomic Energy Government of India (DAE), Department of Science
and Technology, Government of India (DST), University Grants Commission,
Government of India (UGC) and Council of Scientific and Industrial Research
(CSIR), India; Indonesian Institute of Science, Indonesia; Centro Fermi -
Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi and Istituto
Nazionale di Fisica Nucleare (INFN), Italy; Institute for Innovative Science
and Technology , Nagasaki Institute of Applied Science (IIST), Japan Society
for the Promotion of Science (JSPS) KAKENHI and Japanese Ministry of
Education, Culture, Sports, Science and Technology (MEXT), Japan; Consejo
Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación
Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de
Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse Organisatie voor
Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Council of Norway,
Norway; Commission on Science and Technology for Sustainable Development in
the South (COMSATS), Pakistan; Pontificia Universidad Católica del Perú, Peru;
Ministry of Science and Higher Education and National Science Centre, Poland;
Korea Institute of Science and Technology Information and National Research
Foundation of Korea (NRF), Republic of Korea; Ministry of Education and
Scientific Research, Institute of Atomic Physics and Romanian National Agency
for Science, Technology and Innovation, Romania; Joint Institute for Nuclear
Research (JINR), Ministry of Education and Science of the Russian Federation
and National Research Centre Kurchatov Institute, Russia; Ministry of
Education, Science, Research and Sport of the Slovak Republic, Slovakia;
National Research Foundation of South Africa, South Africa; Centro de
Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba and
Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas
(CIEMAT), Spain; Swedish Research Council (VR) and Knut & Alice Wallenberg
Foundation (KAW), Sweden; European Organization for Nuclear Research,
Switzerland; National Science and Technology Development Agency (NSDTA),
Suranaree University of Technology (SUT) and Office of the Higher Education
Commission under NRU project of Thailand, Thailand; Turkish Atomic Energy
Agency (TAEK), Turkey; National Academy of Sciences of Ukraine, Ukraine;
Science and Technology Facilities Council (STFC), United Kingdom; National
Science Foundation of the United States of America (NSF) and United States
Department of Energy, Office of Nuclear Physics (DOE NP), United States of
America.

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##  Appendix A The ALICE Collaboration

S. Acharyaorg139&F.T.-. Acostaorg22&D. Adamováorg94&J. Adolfssonorg81&M.M.
Aggarwalorg98&G. Aglieri Rinellaorg36&M. Agnelloorg33&N. Agrawalorg49&Z.
Ahammedorg139&S.U. Ahnorg77&S. Aiolaorg144&A. Akindinovorg65&M. Al-
Turanyorg104&S.N. Alamorg139&D.S.D. Albuquerqueorg120&D. Aleksandrovorg88&B.
Alessandroorg59&R. Alfaro Molinaorg73&Y. Aliorg16&A. Aliciorg11,org54,org29&A.
Alkinorg3&J. Almeorg24&T. Altorg70&L. Altenkamperorg24&I. Altsybeevorg138&M.N.
Anaamorg7&C. Andreiorg48&D. Andreouorg36&H.A. Andrewsorg108&A.
Andronicorg142,org104&M. Angelettiorg36&V. Anguelovorg102&C. Ansonorg17&T.
Antičićorg105&F. Antinoriorg57&P. Antonioliorg54&R. Anwarorg124&N.
Apadulaorg80&L. Aphecetcheorg112&H. Appelshäuserorg70&S. Arcelliorg29&R.
Arnaldiorg59&O.W. Arnoldorg103,org115&I.C. Arseneorg23&M. Arslandokorg102&B.
Audurierorg112&A. Augustinusorg36&R. Averbeckorg104&M.D. Azmiorg18&A.
Badalàorg56&Y.W. Baekorg61,org42&S. Bagnascoorg59&R. Bailhacheorg70&R.
Balaorg99&A. Baldisseriorg134&M. Ballorg44&R.C. Baralorg86&A.M.
Barbanoorg28&R. Barberaorg30&F. Barileorg53&L. Barioglioorg28&G.G.
Barnaföldiorg143&L.S. Barnbyorg93&V. Barretorg131&P. Bartaliniorg7&K.
Barthorg36&E. Bartschorg70&N. Bastidorg131&S. Basuorg141&G. Batigneorg112&B.
Batyunyaorg76&P.C. Batzingorg23&J.L. Bazo Albaorg109&I.G. Beardenorg89&H.
Beckorg102&C. Beddaorg64&N.K. Beheraorg61&I. Belikovorg133&F. Belliniorg36&H.
Bello Martinezorg2&R. Bellwiedorg124&L.G.E. Beltranorg118&V. Belyaevorg92&G.
Bencediorg143&S. Beoleorg28&A. Bercuciorg48&Y. Berdnikovorg96&D.
Berenyiorg143&R.A. Bertensorg127&D. Berzanoorg36,org59&L. Betevorg36&P.P.
Bhaduriorg139&A. Bhasinorg99&I.R. Bhatorg99&H. Bhattorg49&B.
Bhattacharjeeorg43&J. Bhomorg116&A. Bianchiorg28&L. Bianchiorg124&N.
Bianchiorg52&J. Bielčíkorg39&J. Bielčíkováorg94&A. Bilandzicorg115,org103&G.
Biroorg143&R. Biswasorg4&S. Biswasorg4&J.T. Blairorg117&D. Blauorg88&C.
Blumeorg70&G. Bocaorg136&F. Bockorg36&A. Bogdanovorg92&L. Boldizsárorg143&M.
Bombaraorg40&G. Bonomiorg137&M. Bonoraorg36&H. Borelorg134&A.
Borissovorg20,org142&M. Borriorg126&E. Bottaorg28&C. Bourjauorg89&L.
Bratrudorg70&P. Braun-Munzingerorg104&M. Bregantorg119&T.A. Brokerorg70&M.
Brozorg39&E.J. Bruckenorg45&E. Brunaorg59&G.E. Brunoorg36,org35&D.
Budnikovorg106&H. Bueschingorg70&S. Bufalinoorg33&P. Buhlerorg111&P.
Buncicorg36&O. Buschorg130org*&Z. Butheleziorg74&J.B. Buttorg16&J.T.
Buxtonorg19&J. Cabalaorg114&D. Caffarriorg90&H. Cainesorg144&A.
Calivaorg104&E. Calvo Villarorg109&R.S. Camachoorg2&P. Cameriniorg27&A.A.
Caponorg111&F. Carenaorg36&W. Carenaorg36&F. Carnesecchiorg29,org11&J.
Castillo Castellanosorg134&A.J. Castroorg127&E.A.R. Casulaorg55&C. Ceballos
Sanchezorg9&S. Chandraorg139&B. Changorg125&W. Changorg7&S. Chapelandorg36&M.
Chartierorg126&S. Chattopadhyayorg139&S. Chattopadhyayorg107&A.
Chauvinorg103,org115&C. Cheshkovorg132&B. Cheynisorg132&V. Chibante
Barrosoorg36&D.D. Chinellatoorg120&S. Choorg61&P. Chochulaorg36&T.
Chowdhuryorg131&P. Christakoglouorg90&C.H. Christensenorg89&P.
Christiansenorg81&T. Chujoorg130&S.U. Chungorg20&C. Cicaloorg55&L.
Cifarelliorg11,org29&F. Cindoloorg54&J. Cleymansorg123&F. Colamariaorg53&D.
Colellaorg66,org36,org53&A. Colluorg80&M. Colocciorg29&M. Concasorg59orgI&G.
Conesa Balbastreorg79&Z. Conesa del Valleorg62&J.G. Contrerasorg39&T.M.
Cormierorg95&Y. Corrales Moralesorg59&P. Corteseorg34&M.R. Cosentinoorg121&F.
Costaorg36&S. Costanzaorg136&J. Crkovskáorg62&P. Crochetorg131&E.
Cuautleorg71&L. Cunqueiroorg142,org95&T. Dahmsorg103,org115&A. Daineseorg57&S.
Daniorg67&M.C. Danischorg102&A. Danuorg69&D. Dasorg107&I. Dasorg107&S.
Dasorg4&A. Dashorg86&S. Dashorg49&S. Deorg50&A. De Caroorg32&G. de
Cataldoorg53&C. de Contiorg119&J. de Cuvelandorg41&A. De Falcoorg26&D. De
Gruttolaorg11,org32&N. De Marcoorg59&S. De Pasqualeorg32&R.D. De
Souzaorg120&H.F. Degenhardtorg119&A. Deistingorg104,org102&A. Delofforg85&S.
Delsantoorg28&C. Deplanoorg90&P. Dhankherorg49&D. Di Bariorg35&A. Di
Mauroorg36&B. Di Ruzzaorg57&R.A. Diazorg9&T. Dietelorg123&P.
Dillensegerorg70&Y. Dingorg7&R. Diviàorg36&Ø. Djuvslandorg24&A. Dobrinorg36&D.
Domenicis Gimenezorg119&B. Dönigusorg70&O. Dordicorg23&L.V.R.
Doremalenorg64&A.K. Dubeyorg139&A. Dublaorg104&L. Ducrouxorg132&S.
Dudiorg98&A.K. Duggalorg98&M. Dukhishyamorg86&P. Dupieuxorg131&R.J.
Ehlersorg144&D. Eliaorg53&E. Endressorg109&H. Engelorg75&E. Eppleorg144&B.
Erazmusorg112&F. Erhardtorg97&M.R. Ersdalorg24&B. Espagnonorg62&G.
Eulisseorg36&J. Eumorg20&D. Evansorg108&S. Evdokimovorg91&L.
Fabbiettiorg103,org115&M. Fagginorg31&J. Faivreorg79&A. Fantoniorg52&M.
Faselorg95&L. Feldkamporg142&A. Felicielloorg59&G. Feofilovorg138&A. Fernández
Téllezorg2&A. Ferrettiorg28&A. Festantiorg31,org36&V.J.G. Feuillardorg102&J.
Figielorg116&M.A.S. Figueredoorg119&S. Filchaginorg106&D. Finogeevorg63&F.M.
Fiondaorg24&G. Fiorenzaorg53&F. Flororg124&M. Florisorg36&S. Foertschorg74&P.
Fokaorg104&S. Fokinorg88&E. Fragiacomoorg60&A. Francesconorg36&A.
Franciscoorg112&U. Frankenfeldorg104&G.G. Fronzeorg28&U. Fuchsorg36&C.
Furgetorg79&A. Fursorg63&M. Fusco Girardorg32&J.J. Gaardhøjeorg89&M.
Gagliardiorg28&A.M. Gagoorg109&K. Gajdosovaorg89&M. Gallioorg28&C.D.
Galvanorg118&P. Ganotiorg84&C. Garabatosorg104&E. Garcia-Solisorg12&K.
Gargorg30&C. Gargiuloorg36&P. Gasikorg115,org103&E.F. Gaugerorg117&M.B. Gay
Ducatiorg72&M. Germainorg112&J. Ghoshorg107&P. Ghoshorg139&S.K. Ghoshorg4&P.
Gianottiorg52&P. Giubellinoorg104,org59&P. Giubilatoorg31&P.
Glässelorg102&D.M. Goméz Coralorg73&A. Gomez Ramirezorg75&V. Gonzalezorg104&P.
González-Zamoraorg2&S. Gorbunovorg41&L. Görlichorg116&S. Gotovacorg37&V.
Grabskiorg73&L.K. Graczykowskiorg140&K.L. Grahamorg108&L. Greinerorg80&A.
Grelliorg64&C. Grigorasorg36&V. Grigorievorg92&A. Grigoryanorg1&S.
Grigoryanorg76&J.M. Gronefeldorg104&F. Grosaorg33&J.F. Grosse-
Oetringhausorg36&R. Grossoorg104&R. Guernaneorg79&B. Guerzoniorg29&M.
Guittiereorg112&K. Gulbrandsenorg89&T. Gunjiorg129&A. Guptaorg99&R.
Guptaorg99&I.B. Guzmanorg2&R. Haakeorg36&M.K. Habiborg104&C.
Hadjidakisorg62&H. Hamagakiorg82&G. Hamarorg143&M. Hamidorg7&J.C.
Hamonorg133&R. Hanniganorg117&M.R. Haqueorg64&J.W. Harrisorg144&A.
Hartonorg12&H. Hassanorg79&D. Hatzifotiadouorg54,org11&S. Hayashiorg129&S.T.
Heckelorg70&E. Hellbärorg70&H. Helstruporg38&A. Herghelegiuorg48&E.G.
Hernandezorg2&G. Herrera Corralorg10&F. Herrmannorg142&K.F. Hetlandorg38&T.E.
Hildenorg45&H. Hillemannsorg36&C. Hillsorg126&B. Hippolyteorg133&B.
Hohlwegerorg103&D. Horakorg39&S. Hornungorg104&R. Hosokawaorg130,org79&J.
Hotaorg67&P. Hristovorg36&C. Huangorg62&C. Hughesorg127&P. Huhnorg70&T.J.
Humanicorg19&H. Hushnudorg107&N. Hussainorg43&T. Hussainorg18&D.
Hutterorg41&D.S. Hwangorg21&J.P. Iddonorg126&S.A. Iga Buitronorg71&R.
Ilkaevorg106&M. Inabaorg130&M. Ippolitovorg88&M.S. Islamorg107&M.
Ivanovorg104&V. Ivanovorg96&V. Izucheevorg91&B. Jacakorg80&N.
Jacazioorg29&P.M. Jacobsorg80&M.B. Jadhavorg49&S. Jadlovskaorg114&J.
Jadlovskyorg114&S. Jaelaniorg64&C. Jahnkeorg119,org115&M.J.
Jakubowskaorg140&M.A. Janikorg140&C. Jenaorg86&M. Jercicorg97&O.
Jevonsorg108&R.T. Jimenez Bustamanteorg104&M. Jinorg124&P.G. Jonesorg108&A.
Juskoorg108&P. Kalinakorg66&A. Kalweitorg36&J.H. Kangorg145&V. Kaplinorg92&S.
Karorg7&A. Karasu Uysalorg78&O. Karavichevorg63&T. Karavichevaorg63&P.
Karczmarczykorg36&E. Karpechevorg63&U. Kebschullorg75&R. Keidelorg47&D.L.D.
Keijdenerorg64&M. Keilorg36&B. Ketzerorg44&Z. Khabanovaorg90&A.M. Khanorg7&S.
Khanorg18&S.A. Khanorg139&A. Khanzadeevorg96&Y. Kharlovorg91&A. Khatunorg18&A.
Khuntiaorg50&M.M. Kielbowiczorg116&B. Kilengorg38&B. Kimorg130&D.
Kimorg145&D.J. Kimorg125&E.J. Kimorg14&H. Kimorg145&J.S. Kimorg42&J.
Kimorg102&M. Kimorg61,org102&S. Kimorg21&T. Kimorg145&T. Kimorg145&S.
Kirschorg41&I. Kiselorg41&S. Kiselevorg65&A. Kisielorg140&J.L. Klayorg6&C.
Kleinorg70&J. Kleinorg36,org59&C. Klein-Bösingorg142&S. Klewinorg102&A.
Klugeorg36&M.L. Knichelorg36&A.G. Knospeorg124&C. Kobdajorg113&M.
Kofaragoorg143&M.K. Köhlerorg102&T. Kolleggerorg104&N. Kondratyevaorg92&E.
Kondratyukorg91&A. Konevskikhorg63&M. Konyushikhinorg141&O. Kovalenkoorg85&V.
Kovalenkoorg138&M. Kowalskiorg116&I. Králikorg66&A. Kravčákováorg40&L.
Kreisorg104&M. Krivdaorg66,org108&F. Krizekorg94&M. Krügerorg70&E.
Kryshenorg96&M. Krzewickiorg41&A.M. Kuberaorg19&V. Kučeraorg94,org61&C.
Kuhnorg133&P.G. Kuijerorg90&J. Kumarorg49&L. Kumarorg98&S. Kumarorg49&S.
Kunduorg86&P. Kurashviliorg85&A. Kurepinorg63&A.B. Kurepinorg63&A.
Kuryakinorg106&S. Kushpilorg94&J. Kvapilorg108&M.J. Kweonorg61&Y.
Kwonorg145&S.L. La Pointeorg41&P. La Roccaorg30&Y.S. Laiorg80&I.
Lakomovorg36&R. Langoyorg122&K. Lapidusorg144&C. Laraorg75&A. Lardeuxorg23&P.
Larionovorg52&E. Laudiorg36&R. Lavickaorg39&R. Leaorg27&L. Leardiniorg102&S.
Leeorg145&F. Lehasorg90&S. Lehnerorg111&J. Lehrbachorg41&R.C. Lemmonorg93&I.
León Monzónorg118&P. Lévaiorg143&X. Liorg13&X.L. Liorg7&J. Lienorg122&R.
Lietavaorg108&B. Limorg20&S. Lindalorg23&V. Lindenstruthorg41&S.W.
Lindsayorg126&C. Lippmannorg104&M.A. Lisaorg19&V. Litichevskyiorg45&A.
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Luparelloorg60&M. Lupiorg36&A. Maevskayaorg63&M. Magerorg36&S.M.
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