310 ALICE Collaboration / Direct photon elliptic flow in Pb–Pb
which is also known as cocktail simulation. The PCM and PHOS
measurements of inclusive photon flow are performed indepen-
dently.
They are then combined and used with the combined ratio
R
γ
as well as the calculated decay photon flow.
The
photon elliptic flow v
2
is calculated with the Scalar Prod-
uct
(SP) method, which is a two-particle correlation method [56],
using a pseudorapidity gap of |η| > 0.9 between the photon and
the reference flow particles. The applied gap reduces correlations
not related to the event plane
n
, such as the ones due to reso-
nance
decays and jets, known as non-flow effects. The SP method
uses the Q -vector, computed from a set of reference flow particles
(RFP) defined as:
Q
n
=
i∈RFP
w
i
e
inϕ
i
, (3)
where ϕ
i
is the azimuthal angle of the i-th RFP, n is the order of
the harmonic and w
i
is a weight applied for every RFP. The RFPs
are taken from the V0–A and V0–C detectors. Since these detectors
do not provide tracking information, we sum over the V0–A/V0–C
cells, while the amplitudes of the signal from each cell, which are
proportional to the number of particles that cause a hit, are used
as a weight w
i
. The non-uniformity of the detector azimuthal effi-
ciency
is taken into account by applying the inverse of the event-
averaged
signal as a weight for each of the V0 segments, together
with a recentering procedure [50,57]. More specifically, the ellip-
tic
flow v
2
is calculated using the unit flow vector
u
2
= e
i2ϕ
built
from reconstructed photons
v
2
=
u
2
·
Q
A∗
2
M
A
u
2
·
Q
C∗
2
M
C
Q
A
2
M
A
·
Q
C∗
2
M
C
,
(4)
where the two pairs of brackets in the numerator indicate an av-
erage
over all photons and over all events; M
A
and M
C
are the
estimates of multiplicity from the V0–A and V0–C detectors, re-
spectively;
and
Q
A∗
2
,
Q
C∗
2
are the complex conjugates of the flow
vector calculated in sub-event A and C, respectively.
In the PCM analysis, photons converting into e
+
e
−
pairs are
reconstructed with an algorithm which searches for displaced ver-
tices
with two oppositely charged daughter tracks. Only good
quality TPC tracks with a transverse momentum above 50 MeV/c
and
a pseudorapidity of |η| < 0.9are considered. The vertex
finding algorithm uses the Kalman filter technique for the de-
cay/conversion
point and four-momentum determination of the
neutral parent particle (V
0
) [58]. Further selection is performed
on the level of the reconstructed V
0
. Only V
0
s with a con-
version
points at radii between 5 < R < 180 cm are accepted
such that the π
0
and η-meson Dalitz decays are rejected and
to ensure a good coverage by the tracking detectors of the con-
version
daughters. To identify an e
+
e
−
pair, the specific energy
loss (dE/dx) in the TPC [50]of both daughters is used. The trans-
verse
momentum component q
T
of the electron momentum, p
e
,
with respect to the V
0
momentum-vector is restricted to be q
T
<
0.05
1 −
(
α/0.95
)
2
GeV/c, where α is the energy asymmetry of
the conversion daughters. Random associations of electrons and
positrons are further reduced by selecting V
0
s with cos(θ) > 0.85,
where θ is the pointing angle, which is the angle between the
momentum-vector of the e
+
e
−
pair and the vector that connects
the primary vertex and the conversion point. Based on the invari-
ant
mass of the e
+
e
−
pair and the pointing angle of the V
0
to
the primary vertex, the vertex finder calculates a χ
2
value which
reflects the level of consistency with the hypothesis that the V
0
Table 1
Summary
of the relative systematic uncertainties (in %) of the inclusive photon el-
liptic
flow in the PCM and PHOS analysis, and of the decay photon simulation. All
contributions are expected to be correlated in p
T
with the magnitude of the relative
uncertainty varying point-by-point.
Centrality 0–20% 20–40%
p
T
(GeV/c) 2.0 5.0 2.0 5.0
PCM
Photon selection 2.4 4.2 2.1 4.0
Energy resolution 1.0 1.0 1.0 1.0
Efficiency 3 3 1.9 1.9
Total 4.0 5.3 3.0 4.5
PHOS
Efficiency & contamination 3.0 3.0 0.7 0.7
Event plane flatness 2.0 2.0 1.4 1.4
Total 3.5 3.5 1.6 1.6
Decay photon calculation
Parameterization of v
π
2
1.3 3.6 0.8 2.2
η/π
0
normalization 1.7 3.2 1.7 2.4
Total 2.2 4.8 1.9 3.3
comes from a photon originating from the primary vertex. A selec-
tion
based on this χ
2
value is used to further reduce contamina-
tion
in the photon sample. The main sources of background that
remain after these selection criteria are V0s reconstructed from
π
±
e
∓
, π
±
π
∓
, π
±
K
∓
and e
±
K
∓
pairs, which is important to take
into account as shown in [59]. The elliptic flow of this background
is subtracted using a side-band method approach. In this method,
the dE/dx information of both conversion daughters is combined
into a 1-dimensional quantity. The signal is a peaked distribution
and the side-bands are dominated by background sources. The v
2
of the side-bands is measured and subtracted from the main signal
region using the purity of the photon sample, which is obtained
by fitting Monte Carlo templates to the data. The correction to the
measured inclusive photon flow is of the order of 5% for central
and 2.5% for semi-central collisions, respectively.
The
systematic uncertainties of the inclusive photon flow mea-
sured
with PCM are summarized in Table 1. The uncertainties
related to the photon selection (|η|, R, min p
T
, q
T
, χ
2
/ndf and
cos(θ)) are obtained by varying the selection criteria, and the sys-
tematic
uncertainties related to the contamination of the photon
sample are quantified by the uncertainty on the background flow
subtraction. The energy resolution uncertainties, which are due to
detector resolution effects and bremsstrahlung of electrons, are
estimated by comparing v
γ ,inc
2
distributions as a function of the
reconstructed and true p
T
using MC simulations. The uncertainties
related to the variation of reconstruction efficiency in- and out-
of-plane
are calculated from studying the photon reconstruction
efficiency as a function of the track multiplicity. For most of these
sources only a small dependence on p
T
and collision centrality is
observed.
In
the PHOS analysis, the same photon selection criteria are ap-
plied
as in the direct-photon spectra analysis [23]. Cells with a
common edge with another cell that are both above the energy
threshold of 25 MeV are combined into clusters which are used as
photon candidates. To estimate the photon energy, the energies of
all cells or only those with centers within a radius R
core
= 3.5cm
from
the cluster center of gravity are summed. Compared to the
full cluster energy, the core energy is less sensitive to overlaps with
low-energy clusters in a high multiplicity environment, and is well
reproduced by GEANT3 Monte Carlo simulations [23]. The full en-
ergy
is used for the systematic uncertainty estimate. The contribu-
tion
of hadronic clusters is reduced by requiring E
cluster
> 0.3GeV,
N
cells
> 2 and by accepting only clusters above a minimum lat-