ALICE Collaboration / Physics Letters B 753 (2016) 511–525 513
In order to account for a non-uniform detector response which can
generate a bias in the
EP, n
azimuthal distribution, the compo-
nents
of the Q
n
-vectors are adjusted using a re-centering proce-
dure
[41,42]. The V0A and V0C detectors cover different η regions
in which multiplicity N and background flow v
n
may differ. The
total V0 Q -vector is therefore constructed using weights χ
n
[40]
that
are approximately proportional to the event plane resolution
in each detector,
Q
n,V0
=χ
2
n
,V0A
Q
n,V0A
+χ
2
n
,V0C
Q
n,V0C
, (3)
to achieve the optimal combined event plane resolution. The event
planes are reconstructed from the real and imaginary parts of Q
n
as
EP, n
= arctan
[
Q
n
]
[
Q
n
]
/
n. (4)
The v
ch jet
2
itself is measured with respect to the second har-
monic
event plane angle. It is corrected for the finite precision
with which the true symmetry plane is measured in the V0 system
by applying an event plane resolution correction, see Sec. 2.4.
2.2. Jet reconstruction in the presence of background flow
Jet finding is performed using the FastJet [43,44] implementa-
tion
of the infrared and collinear safe k
T
and anti-k
T
sequential
recombination algorithms using the p
T
recombination scheme and
taking massless jet constituents. The resolution parameter R = 0.2
determines
the characteristic maximum distance of constituent
tracks to the jet axis in the η–ϕ plane.
In
heavy-ion collisions, a large combinatorial background is
present from particles that are not related to the hard scattering
that produced a given jet. This background is subtracted from each
jet on an event-by-event basis. The anti-k
T
algorithm is used to
find signal jets. A fiducial cut of |η
jet
| < 0.7is applied on the sig-
nal
jets to ensure that all jets are fully contained within the ITS
and TPC acceptances and edge effects are avoided. The contribu-
tion
of combinatorial (or ‘fake’) jets (clustered underlying event
energy) to the measured jet spectrum is reduced by requiring
that reconstructed jets contain at least one charged particle with
p
T
> 3GeV/c and have an area of at least 0.56 π R
2
. These selec-
tion
criteria leave the hard part of the jet spectrum unaltered while
significantly reducing the number of combinatorial jets which sta-
bilizes
the unfolding procedure [4,5,45].
The
k
T
-algorithm is used to estimate the average transverse
momentum density of the underlying event, ρ
ch
, on an event-by-
event
basis. The quantity ρ
ch
is the median of the distribution of
p
raw
T
,chjet
/A (the ratio of transverse momentum to jet area) of recon-
structed
R = 0.2 k
T
-jets, excluding the leading two jets from the
sample as proposed in [46] and implemented in earlier ALICE jet
studies [4,5,45]. The k
T
jets are required to lie within |η
jet
| < 0.7
and
have an area A > 0.01. The jet area A is determined by em-
bedding
a fixed number of near zero-momentum ghost particles
per
event prior to jet finding; the number of ghost particles in
each reconstructed jet then gives a direct measure of the jet area.
Aghost density of 200 particles per unit area is used, so that ap-
proximately
25 ghost particles are clustered into a jet with a radius
of 0.2.
In
each event, the anisotropy of the underlying event is mod-
eled
using the dominant [47] flow harmonics v
2
and v
3
,
ρ
ch
(ϕ) = ρ
0
1 +2{v
2
cos
2
ϕ −
EP, 2
+
v
3
cos
3
ϕ −
EP, 3
}
.
(5)
Fig. 1. Transverse momentum density of charged tracks as a function of azimuthal
angle for a single event from the most central 0–5% event class. Data points (blue)
are given with statistical uncertainties only. The red curve is the fit of Eq. (5) to
the distribution, the green and gray curves, obtained from the fit of Eq. (5) as well,
show the independent contributions of v
2
and v
3
to ρ
ch
(ϕ). The dashed magenta
line is the normalization constant ρ
0
. (For interpretation of the references to color
in this figure legend, the reader is referred to the web version of this article.)
Here, ρ
ch
(ϕ) is the azimuthal distribution of summed track p
T
for
tracks with 0.15 < p
T
< 5GeV/c and |η
track
| < 0.9. The parame-
ters
ρ
0
and v
n
are determined event-by-event from a fit of the
right side of Eq. (5) to the data. The event plane angles
EP, n
are not fitted, but fixed to the V0 event plane angles. Asingle
event example of this procedure is illustrated in Fig. 1, where the
data points represent the transverse momentum density distribu-
tion
in a single event, the red curve represents the full functional
description of ρ
ch
(ϕ) (Eq. (5)), the green and gray curves give the
contributions of the separate harmonics v
2
and v
3
, and the dashed
magenta line is the normalization constant ρ
0
. To reduce the bias
of hard jets in the estimates of v
n
in Eq. (5) while retaining az-
imuthal
uniformity, the leading jet in each event is removed by
rejecting all tracks for which |η
jet
− η
track
| < R. The η separation
between the tracks and the V0 detectors also removes short range
correlations between the event planes and tracks.
The
number of bins to which Eq. (5) is fitted is set on an event-
by-event
basis to the square root of the number of tracks. The fit
maximizes the estimated likelihood [48], which is based on a Pois-
son
distribution for the bin content. Since the bin contents are
not pure counts, but weighted by p
T
, the statistical uncertainties
on each bin σ
i
are estimated as the sum of the squares of the
p
T
of the individual particles: σ
i
= σ (
p
T
) =
√
p
2
T
. Ascaled
Poisson distribution P(x
i
/w
i
|mu
i
/w
i
) is used as the probability
distribution for the data points in the likelihood calculation, with
a scale factor w
i
= σ
2
i
/y
i
where y
i
is the bin content and μ
i
is the expected signal from the fit function. The compatibility of
each fit with the data is tested by calculating the χ
2
and eval-
uating
the probability of finding a test statistic at least as large
as the observed one in the χ
2
distribution. When this probabil-
ity
is less than 0.01, the average event background density ρ
ch
is used instead of ρ
ch
(ϕ); this occurs in 3% (most central) to 7%
(semi-central) of events. The acceptance criterion is varied in the
systematic studies; the sensitivity to it is small.
The
corrected transverse momentum p
chjet
T
of a jet of area A is
calculated from the measured raw jet momentum, p
raw
T
,chjet
, as
p
chjet
T
= p
raw
T
,chjet
−ρ
ch local
A (6)
where ρ
ch local
is obtained from integration of ρ
ch
(ϕ) around
ϕ
jet
± R
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