#### Elliptic flow of electrons from beauty-hadron decays extracted from Pb–Pb collision data at \(\sqrt{s_\mathrm{NN}} = 2.76\ \hbox {TeV}\)

Eur. Phys. J. C
Elliptic flow of electrons from beauty-hadron decays extracted from Pb-Pb collision data at √sNN = 2.76 TeV
D. Moreira de Godoy 2
F. Herrmann 2
M. Klasen 2
C. Klein-Bösing 1 2
A. A. P. Suaide 0
0 Universidade de São Paulo , R. do Matão 1371, São Paulo , Brazil
1 ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung , Planckstraße 1, 64291 Darmstadt , Germany
2 Westfälische Wilhelms-Universität Münster , Wilhelm-Klemm-Straße 9, Münster , Germany
We present a calculation of the elliptic flow of electrons from beauty-hadron decays in semi-central PbPb collisions at centre-of-mass energy per colliding nucleon pair, represented as √sNN, of 2.76 TeV. The result is obtained by the subtraction of the charm-quark contribution in the elliptic flow of electrons from heavy-flavour hadron decays in semi-central Pb-Pb collisions at √sNN = 2.76 TeV recently made publicly available by the ALICE collaboration.
1 Introduction
The nuclear matter exposed to conditions of high temperature
and energy density is expected to undergo a phase transition
to a colour deconfined state of matter [
1,2
], the Quark-Gluon
Plasma (QGP). The conditions for the phase transition can
be achieved in the laboratory with collisions of heavy ions
at high energies [1]. The properties of the medium formed
in the laboratory can be probed with a unique degree of
control by particles from decays of heavy flavours (charm and
beauty), since heavy quarks are mainly produced in hard
parton scattering processes [
3–5
] at the initial stage of
heavyion collisions [
6,7
] and participate in the entire evolution
of the created system. The partons traversing the medium
lose energy via collisional and radiative processes [
8–12
]
in the interaction with the medium constituents. The energy
loss of partons is predicted to be dependent on their colour
charge and mass, resulting in a hierarchy where beauty quarks
lose less energy than charm quarks, charm quarks lose less
energy than light quarks, and quarks lose less energy than
gluons [
10,13,14
]. The heavy-flavour energy loss can be
investigated experimentally with the nuclear modification factor
(RAA) of heavy-flavour particles, defined as
(1)
RAA =
1
TAA
d NAA/d pT
dσpp/d pT
where d NAA/d pT is the transverse momentum ( pT)
differential yield in nucleus-nucleus (AA) collisions; TAA is the
average nuclear overlap function in nucleus-nucleus
collisions, given by the ratio of the average number of binary
collisions and the inelastic cross section; and dσpp/d pT is
the pT-differential cross section in proton-proton (pp)
collisions. A suppression of the yield of D mesons and
leptons from heavy-flavour hadron decays (RAA < 1) for
pT > 3 GeV/c was observed in gold–gold (Au–Au)
collisions at √sNN = 200 GeV at the Relativistic Heavy Ion
Collider (RHIC) [
15–18
] and in lead-lead (Pb–Pb) collisions
at √sNN = 2.76 and 5.02 TeV at the Large Hadron Collider
(LHC) [
19–25
], indicating energy loss of heavy flavours in
the medium. An experimental hint to the quark mass
dependence of the heavy-flavour energy loss has been found in
the comparison of the RAA of D mesons and non-prompt
J/ψ from B-hadron decays in central Pb–Pb collisions at
√sNN = 2.76 TeV at the LHC [
20,26,27
]. The observed
difference of these measurements is described by model
calculations [
28,29
] as predominantly due to the quark mass
dependence of the parton energy loss.
The interaction of heavy quarks with the medium can be
further investigated with the azimuthal anisotropy of
heavyflavour particles, extracted from the coefficients vn of the
Fourier decomposition of the particle azimuthal distribution
in the transverse plane [
30
]
d N
d (ϕ − Ψn) ∝ 1 + 2
∞
n=1
where ϕ is the azimuthal angle of the heavy-flavour
particles and Ψn is the symmetry-plane angle of the nth-order
harmonic. The second Fourier coefficient v2, called elliptic
vn cos [n (ϕ − Ψn)] ,
(2)
flow, quantifies the elliptic azimuthal anisotropy of the
emitted particles. The origin of the elliptic azimuthal anisotropy
of heavy-flavour particles in non-central heavy-ion collisions
depends on the transverse-momentum interval. While the
v2 at low pT is sensitive to the collective motion of the
medium constituents caused by pressure gradients, the v2
at high pT can constrain the path-length dependence of the
in-medium energy loss of heavy quarks, resulting from the
direction of the particles that traverse the ellipsoidal nuclear
overlap region. The elliptic flow of prompt D mesons at
midrapidity is observed to be positive in 30–50% Pb–Pb
collisions at √sNN = 2.76 TeV at the LHC [
31,32
] with 5.7σ
significance in the interval 2 < pT < 6 GeV/c,
indicating that charm quarks participate in the collective motion
of the system. Measurements of the prompt D-meson v2 in
Pb–Pb collisions at √sNN = 5.02 TeV [
33,34
] have smaller
uncertainties compared to the ones in Pb–Pb collisions at
√sNN = 2.76 TeV. The results at the two collision
energies are compatible within uncertainties. The prompt Ds+v2
in semi-central Pb–Pb collisions at √sNN = 5.02 TeV is
compatible within uncertainties with the average of prompt
D0, D+, and D∗+v2 in the same collision system [
34
]. A
positive v2 is also observed for leptons from heavy-flavour
hadron decays at low and intermediate pT in semi-central
Au–Au collisions at √sNN = 200 GeV at RHIC [
17,35
] and
in semi-central Pb–Pb collisions at √sNN = 2.76 TeV at
the LHC [
25,36,37
]. In particular, the v2 of electrons from
heavy-flavour hadron decays is observed to be positive with
5.9σ significance in the range 2 < pT < 2.5 GeV/c in 20–
40% Pb–Pb collisions at √sNN = 2.76 TeV.
In view of the experimental results on the elliptic flow of
heavy-flavour particles, an important question that remains
open is whether beauty quarks take part in the collective
motion in the medium. The first measurement of the v2 of
non-prompt J/ψ mesons from B-hadron decays is
compatible with zero within uncertainties in two kinematic regions,
6.5 < pT < 30 GeV/c and |y| < 2.4, and 3 < pT <
6.5 GeV/c and 1.6 < |y| < 2.4, in 10–60% Pb–Pb
collisions at √sNN = 2.76 TeV at the LHC [
27
]. In this paper,
we present a method to subtract the contribution of charm
quarks in the published measurement of the elliptic flow of
electrons from heavy-flavour hadron decays in semi-central
Pb–Pb collisions at √sNN = 2.76 TeV performed by the
ALICE collaboration. The calculation uses as input the v2
coefficients of prompt D mesons and electrons from
heavyflavour hadron decays measured by the ALICE
collaboration [
32,36
] and three different results for the relative
contribution of electrons from beauty-hadron decays to the yield
of electrons from heavy-flavour hadron decays [
38–41
].
2 Methodology
The particle azimuthal distribution of electrons from
heavyflavour hadron decays (e ← c + b) can be separated into the
contributions of electrons from charm-hadron decays (e ←
c) and from beauty-hadron decays (e ← b). Consequently,
the elliptic flow of electrons from beauty-hadron decays can
be expressed as
(3)
v2e←b =
v2e←c+b − (1 − R)v2e←c
R
,
where R represents the relative contribution of electrons from
beauty-hadron decays to the yield of electrons from
heavyflavour hadron decays.
In the following, we present the currently published
measurements and, in case there is no available measurement,
our calculations of the three observables required to obtain
the elliptic flow of electrons from beauty-hadron decays.
Based on available results on open heavy flavours at RHIC
and LHC, the most suitable system for this analysis is the
Pb–Pb collision system at √sNN = 2.76 TeV in the 20–
40% centrality class, which corresponds to the centrality
range where the measured v2 of electrons from heavy-flavour
hadron decays is observed to be positive with a maximum
significance [
36
] and thus a possible elliptic flow of
electrons from beauty-hadron decays is expected to be more
significant. In this analysis, the v2 and RAA of
heavyflavour particles are assumed to be the same at slightly
different mid-rapidity ranges (|y| < 0.5, 0.7 and 0.8) in
which the measurements needed in the calculation are
available. Indeed, no dependence on rapidity was observed in
recent ALICE results on those observables for electrons from
heavy-flavour hadron decays at mid-rapidity (|y| < 0.7 for
v2 and |y| < 0.6 for RAA measurements) and muons from
heavy-flavour hadron decays at forward rapidity (2.5 < y <
4) [
24,36
].
2.1 Elliptic flow of electrons from heavy-flavour hadron
decays
The result on the elliptic flow of electrons from heavy-flavour
hadron decays (v2e←c+b) at mid-rapidity (|y| < 0.7) in 20–
40% Pb–Pb collisions at √sNN = 2.76 TeV published by
the ALICE collaboration [36] is used in this analysis. The
ve←c+b is measured in the interval 0.5 < pT < 13 GeV/c
2
with the event plane method [
30
]. A positive value is observed
in the interval 2 < pT < 2.5 GeV/c with significance of
5.9σ [
36
].
2.2 Relative contribution of electrons from beauty-hadron
decays to the yield of electrons from heavy-flavour
hadron decays
The measurement of the relative contribution of electrons
from beauty-hadron decays to the yield of electrons from
heavy-flavour hadron decays (R) has been published by
the ALICE collaboration only in pp collisions at √s =
2.76 TeV [
38,39
]. The factor R is measured using the track
impact parameter and electron-hadron azimuthal correlation
methods. Results obtained with both techniques are
compatible within uncertainties. The coefficient R measured in
pp collisions with the electron-hadron azimuthal correlation
method is used in the analysis with the caveat that initial- and
final-state effects modify the yield of electrons from
heavyflavour hadron decays in heavy-ion collisions. In particular,
the coefficient R at high pT is expected to be higher in Pb–
Pb collisions compared to pp collisions, since the in-medium
energy loss of charm quarks is predicted to be larger than the
one of beauty quarks [23]. Therefore, the factor R at high
pT in Pb–Pb collisions at √sNN = 2.76 TeV is expected to
have an exclusive value between the measured factor R in
pp collisions at √s = 2.76 TeV and unity. Consequently,
according to Eq. 3, the minimum value of the v2 of
electrons from beauty-hadron decays can be computed with the
R measured in pp collisions.
In addition to the available measurement, the coefficient
R is obtained with a Monte Carlo (MC) simulation based on
POWHEG [
42
], which provides the calculation of the
heavyflavour production in hadronic collisions at Next-to-Leading
Order (NLO) accuracy. The POWHEG results are interfaced
to PYTHIA [
43,44
] in order to generate the shower,
hadronisation and decay. In agreement with other heavy-flavour
production tools, e.g. pQCD calculation at Fixed Order plus
Next-to-Leading Logarithms (FONLL) [
4,45
] and earlier pp
calculations [
5
], the square root of the quadratic sum of the
quark mass (m Q ) and pT are used as renormalization and
factorization scales, i.e. μ = μ f = μr = m2Q + pT2. The
charm- and beauty-quark masses are set as 1.5 and 4.75 GeV,
respectively. Even though the calculated coefficient R is
sensitive to the choice of heavy-quark masses and scales [
5
],
only the central value is shown in this analysis. Admittedly,
the described framework is designed for pp collisions, but by
making use of the EPS09 [
46
] NLO nuclear Parton
Distribution Functions (nPDFs) the framework is able to account for
initial-state cold nuclear effects. The nPDF gluon shadowing
results in reduced pT-differential cross sections for electrons
from heavy-flavour hadron decays for pT < 6 GeV/c and
affects contributions from charm quarks stronger than those
from beauty quarks. Thus, it provides a lower baseline for
the factor R, which is suggested to be further enhanced by
medium interactions as it will be discussed in this paper. In
e 1
→0.9
b+0.8
/c0.7
e0.6
→)c0.5
addition, the R coefficient is also obtained with a leading
order (LO) calculation based on PYTHIA using EPS09 LO
nPDFs to study the impact of NLO corrections [
5
]. The
comparison of the calculations with LO and NLO approaches,
shown in Fig. 1, reveals that the factor R is reduced with the
NLO corrections, stressing the importance of NLO
calculations. In fact, the additional processes of heavy-flavour
production at NLO give rise to large logarithmic corrections to
the charm- and beauty-quark cross sections depending on the
heavy-flavour mass. The corresponding FONLL calculation
of the factor R using CTEQ6.6 PDFs, which is also shown
in Fig. 1, is similar to the POWHEG+PYTHIA(EPS09NLO)
result at high pT.
The result on the factor R from the BAMPS
heavyflavour transport model [
40,41
], which includes collisional
and radiative in-medium energy loss of heavy quarks, is also
employed in the analysis to obtain the v2 of electrons from
beauty-hadron decays. The choice of the BAMPS model is
justified by the good agreement of the predictions for the
RAA of electrons from beauty- and heavy-flavour hadron
decays for pT > 3 GeV/c in central Pb–Pb collisions at
√sNN = 2.76 TeV with what measured by the ALICE
collaboration [
23,24
].
In this analysis, the R coefficient measured in pp
collisions using the electron-hadron azimuthal correlation
technique and the ones obtained with POWHEG + PYTHIA
(EPS09NLO) and with the BAMPS model are used to
estimate the elliptic flow of electrons from beauty-hadron
decays.
2.3 Elliptic flow of electrons from charm-hadron decays
The elliptic flow of electrons from charm-hadron decays
(v2e←c) is estimated using a MC simulation of decays of D0
mesons into electrons with PYTHIA. The MC simulation is
based on two observables measured for D0 mesons in Pb–Pb
collisions at √sNN = 2.76 TeV:
– the pT-differential yield, which is used as a probability
distribution for finding a D0 meson with a certain pT;
– the pT-differential v2, which is used to obtain the ϕD0 −
Ψ2 probability distribution with Eq. 2.
In fact, the pT-differential yield of D0 mesons at
midrapidity (|y| < 0.8) in 20–40% Pb–Pb collisions at √sNN =
2.76 TeV is estimated from the ALICE results on the
pTdifferential yield and RAA of prompt D0 mesons at
midrapidity (|y| < 0.5) in 0–20% Pb–Pb collisions at the same
collision energy [
19
] as
d NAA
d pT
,
(4)
where the coefficient CΔy = 1.6 corresponds to the scaling
factor of the yield from |y| < 0.5 to |y| < 0.8 in pp
collisions, assuming a uniform distribution of the D0-meson yield
within the rapidity range. The terms C TAA = 0.362 ± 0.020
[
19
] and C RAA are the ratios of the average nuclear overlap
function and the D0-meson RAA, respectively, in Pb–Pb
collisions at √sNN = 2.76 TeV in the 20–40% centrality class
to the ones in the 0–20% centrality class. Note that the terms
CΔy and C TAA are constant, so they do not play a role in the
determination of the D0-meson pT probability distribution.
The non-measured RAA of D0 mesons in 20–40% Pb–Pb
collisions at √sNN = 2.76 TeV is estimated by the average of
the ALICE results on the D0-meson RAA in Pb–Pb collisions
at the same collision energy in the 0–20 and 40–80%
centrality classes [
19
] weighted by the corresponding yield of
D0 mesons in each centrality class. The resulting pT
distribution of D0 mesons in 20–40% Pb–Pb collisions obtained
from Eq. 4 is then fitted by a power-law function (top panel
of Fig. 2), considering the statistical uncertainty of the
experimental results. The fit function is used as the D0-meson pT
probability distribution.
The v2 of prompt D0 mesons in 20–40% Pb–Pb collisions
at √sNN = 2.76 TeV (bottom panel of Fig. 2) is obtained by
the arithmetic average of the measured prompt D0-meson v2
in Pb–Pb collisions at the same collision energy in the 10–
30 and 30–50% centrality classes [
32
]. Indeed, experimental
results show that the v2 of heavy-flavour particles increases
with the centrality class [
17, 32, 36, 37
], which is consistent
with the qualitative expectation of increasing of the elliptic
anisotropy from central to peripheral nucleus-nucleus
collisions. The statistical and systematic uncertainties are
propagated considering the prompt D0-meson v2 in the 10–30 and
) 10
V
e
/G 1
c
(
p1T0−1
d
/
dN10−2
10−3
10−4
10−5
0 D 0.4
t
p
rpom 02.3
v
0.2
0.1
0
−0.1
30–50% centrality classes as uncorrelated as a conservative
estimation. In the D0-meson v2 measurement by the ALICE
collaboration, the central value was obtained by assuming
that the v2 coefficients of prompt D mesons and D mesons
from B-meson decays are the same [
32
]. However, the
systematic uncertainty related to this assumption, referred to
as systematic uncertainty from the B feed-down subtraction,
was evaluated by the ALICE collaboration. It was assumed
that the v2 of prompt D mesons from B-meson decays should
be between zero and v2 of prompt D mesons, resulting in the
upper and lower limits of the systematic uncertainty,
respectively. Therefore, the B feed-down contribution decreases the
absolute value of the D0-meson v2 and thus the systematic
uncertainty is restricted to the upper (lower) limit when the v2
is positive (negative). Since the measured D0-meson v2
coefficients are negative in the 8 < pT < 12 and 12 < pT < 16
GeV/c intervals in the 10–30 and 30–50% centrality classes,
respectively, the resulting propagated systematic uncertainty
from the B feed-down subtraction contains lower and upper
limits.
Finally, the estimated pT and v2 distributions of D0
mesons in 20–40% Pb–Pb collisions at √sNN = 2.76 TeV
are used to obtain the v2e←c = cos [2 (ϕe − Ψ2)] in the
same collision system using the PYTHIA event generator.
The azimuthal angle of electrons (ϕe) takes into account
the angular separation between electrons and their parent D0
mesons.
2.3.1 Statistical uncertainty
The statistical uncertainty of the D0-meson v2 is used as input
for the MC simulation to obtain the statistical uncertainty of
the ve←c. The statistical uncertainties of the measurements
2
used to obtain the pT-differential yield of D0 mesons are
considered in the fit of the D0-meson probability distribution.
Further variations are considered as systematic uncertainties.
2.3.2 Systematic uncertainty
The systematic uncertainties from data and from the B
feeddown subtraction of the D0-meson v2 (bottom panel of Fig. 2)
are used as input for the MC simulation to obtain the
systematic uncertainty of the ve←c. The following is a discussion
2
on other sources of systematic uncertainty that can influence
the v2e←c estimation.
In order to validate the Eq. 4, the pT-differential yield and
RAA of prompt D0 mesons in 40–80% Pb–Pb collisions at
√sNN = 2.76 TeV [
19
] are also used as reference to obtain
the pT-differential yield of D0 mesons in the 20–40%
centrality class. The result is the same as the one obtained with
the 0–20% centrality class (top panel of Fig. 2).
The ALICE result on the D0-meson RAA in the 30–50%
centrality class [
32
] is used as an alternative for the D0-meson
RAA estimation in the 20–40% centrality class. No significant
difference is observed in the resulting ve←c with respect to
2
the one obtained with the RAA estimated by the average of
the D0-meson RAA measurements in the 0–20 and 40–80%
centrality classes weighted by the corresponding yield of D0
mesons in each centrality class.
The systematic uncertainties of the measurements of the
pT-differential yield and RAA of prompt D0 mesons are
considered in the fit of the D0-meson pT distribution in 20–40%
Pb–Pb collisions. No significant difference is observed in the
resulting ve←c with respect to the one considering only the
2
statistical uncertainty in the fit. For further investigation, The
BAMPS result on the pT distribution of D mesons at |y| <
0.8 in 20–40% Pb–Pb collisions at √sNN = 2.76 TeV [
40,41
]
is also used to compute the v2e←c. The relative difference of
the obtained v2e←c using the estimated pT distribution of D0
mesons and the BAMPS result, which increases from 1 to
20% in the interval 2 < pT < 8 GeV/c, is included in the
systematic uncertainty.
The effect of the D0-meson v2 estimation in 20–40%
Pb–Pb collisions using the arithmetic average of the
D0meson v2 measurements in the 10–30 and 30–50%
centrality classes is investigated in this analysis. For this purpose,
the trend of the unidentified charged particle v2 as a
function of the average number of binary collisions ( Ncoll ) [
47
]
is assumed to be the same as the one for D0 mesons. The
v2 as a function of Ncoll is obtained from a
parametrisation of the centrality-dependent v2 measurement of
unidentified charged particles integrated over the interval 0.2 <
pT < 5GeV/c [
48
]. The corresponding result exhibits a
linear dependence between v2 and Ncoll with a negative slope
for Ncoll > 220. For comparison, the parametrisation is
also obtained from the centrality-dependent v2 measurement
of unidentified charged particles integrated over the interval
10 < pT < 20 GeV/c [
49
]. The linear dependence between
v2 and Ncoll is the same as the one obtained for particles
in a lower pT interval. The D0-meson v2 is then obtained by
the average of the D0-meson v2 in the 10–30 and 30–50%
centrality classes weighted by the v2 coefficients of the
corresponding Ncoll values [
47
]. The relative difference of the
obtained D0-meson v2 with respect to the one obtained with
the arithmetic average is negligible for pT < 8 GeV/c and
its average is 19% for pT > 8 GeV/c, which is still
compatible within uncertainties. The v2e←c coefficients obtained
with the two approaches show a relative difference of 2% in
the range 2 < pT < 8 GeV/c. This deviation is considered
as a consequence of statistical fluctuations in the D0-meson
v2 measurement for pT > 8 GeV/c and thus no systematic
uncertainty is assigned for this effect.
In order to investigate the impact of the assumption of the
particle mass ordering of the elliptic flow [
50
] used to
determine the systematic uncertainty from the B feed-down
subtraction in the D0-meson v2 measurement, one can assume
that the v2 of prompt D mesons from B-meson decays should
be between zero and the unidentified charged particle v2. The
unidentified charged particle v2 in 20–40% Pb–Pb collisions
is obtained by the average of the v2 measurements in the
20–30 and 30–40% centrality classes [
49
] weighted by the
corresponding Ncoll values. The v2 coefficients of prompt
D0 mesons and unidentified charged particles are
compatible within uncertainties as well as the ve←c obtained with
2
these two results. Therefore, the lower limit of the
systematic uncertainty from the B feed-down subtraction can be
positioned at the central values of the prompt D-meson v2
and v2e←c without strictly considering that the B-meson v2 is
expected to be lower than the D-meson v2.
As a consequence of the pT interval (2 < pT <
16 GeV/c) of the D0-meson v2 and pT-differential yield
measurements, the v2e←c is obtained in the range 2 < pT <
8 GeV/c. The fraction of electrons with pT > 2 GeV/c
that come from D0 mesons with pT < 2 GeV/c is
negligible according to PYTHIA simulations. The effect of the
pT upper limit of the D0-meson measurements is studied
by evaluating the ve←c with extrapolation of the pT and v2
2
distributions of D0 mesons up to 26 GeV/c. The transverse
momentum extrapolation is obtained from the power-law fit
function shown in the top panel of Fig. 2, while the impact
of the v2 of D0 mesons is estimated by explicitly setting its
value, in the interval 16 < pT < 26 GeV/c, to either zero,
or constant at high pT, or maximum value of the prompt
D0meson v2 (shown in Fig. 2). The highest relative difference
in these three scenarios, which increases from 0.3 to 40% in
the interval 2 < pT < 8 GeV/c, is assigned as a conservative
systematic uncertainty.
The effect of the mid-rapidity range of D0 mesons is
investigated by obtaining the ve←c using the D0-meson pT
dis2
tribution in the rapidity range |y| < 1.6 as input for the
simulation. The D0-meson v2 is considered to be the same in
this rapidity range, because no dependence on rapidity was
observed in ALICE results on leptons from heavy-flavour
hadron decays [
24, 36
] as discussed previously. The relative
difference of the obtained v2e←c with respect to the one using
the D0-meson pT distribution in the rapidity range |y| < 0.8
is negligible and thus no additional systematic uncertainty is
considered due to the rapidity effect.
In this analysis, the v2 and shape of the pT-differential
yields of charm hadrons are assumed to be the same as the
ones measured for D0 mesons. This is justified by the fact
that the v2 coefficients of D0, D+ and D∗+ mesons are
compatible within uncertainties in 30–50% Pb–Pb collisions at
√sNN = 2.76 TeV [
31
], also the prompt Ds+v2 is compatible
within uncertainties with the prompt non-strange D meson
v2 in 30–50% Pb–Pb collisions at √sNN = 5.02 TeV [
34
].
In addition, the ratios of the yields of D+/D0 and D∗+/D0
were observed to be constant within uncertainties in pp
collisions at √s = 7 TeV and no modification of the ratios was
observed within uncertainties in central and semi-central Pb–
Pb collisions at √sNN = 2.76 TeV [
51
]. A possible hint for
an enhancement of the Ds+/D0 ratio is observed in 0–10%
Pb–Pb collisions at √sNN = 2.76 TeV [
52
], but the
current uncertainties do not allow for a conclusion. The effect
of different decay kinematics of charm particles is estimated
by simulating the v2 of electrons from combined D, D∗, Ds ,
and Λc particle decays taking into account the fraction of
charm quarks that hadronise into these particles [
53
] and
using the same simulation input as used in the analysis (
pTdifferential yield and v2 of D0 mesons). The obtained ve←c
2
is compatible with the one using D0-meson decay and thus
no systematic uncertainty is considered due to this effect.
In order to exemplify the impact of a possible production
enhancement of Ds+ and Λc particles in Pb–Pb collisions
with respect to pp collisions, their fragmentation fractions
are increased by a factor 2 and 5, respectively, in the
simulation of the combined charm meson v2. The relative
difference of the obtained ve←c and the one using D0-meson
2
decay is negligible for pT < 3 GeV/c and its average is 5%
for pT > 3 GeV/c.
Finally, the D0-meson v2 systematic uncertainty from
data is summed in quadrature with other sources of
systematic uncertainty that affect significantly the v2e←c estimation,
which are the pT distribution of D0 mesons and the limited pT
interval of the D0-meson measurements. They are considered
as uncorrelated since the effect from the pT distribution of
D0 mesons is obtained with the BAMPS result and the effect
from the limited pT interval of the D0-meson measurements
is obtained by extrapolations. The term “from data” is
maintained later in this paper to distinguish all sources of
systematic uncertainty from the systematic uncertainty related to the
B feed-down subtraction of the D0-meson v2 measurement,
which is shown separately.
2.4 Elliptic flow of electrons from beauty-hadron decays
The v2 of electrons from beauty-hadron decays (v2e←b) is
obtained from Eq. 3 using the R, v2e←c+b and ve←c results
2
presented in their respective sections.
The three results are considered as statistically
independent. First, the factor R was measured in a different collision
system (pp collisions) or obtained with calculations. Second,
the v2e←c is obtained with a simulation using measurements
of D0 mesons reconstructed via the hadronic decay
channel D0 → K−π + in a different centrality class than in the
ve←c+b measurement.
2
Even though the systematic uncertainties of the R, v2e←c+b
and ve←c results might be partially correlated, especially
2
concerning the particle identification selection criteria, the
limited public information prevents a more accurate
treatment of these uncertainties. Therefore, they are assumed to
be uncorrelated as a conservative estimation. As an example
of the effect of a possible overestimation, if the systematic
uncertainties of the ve←c and ve←c+b results decrease by
2 2
30% in the interval 2 < pT < 8 GeV/c, the systematic
uncertainty from data of the ve←b result is expected to decrease
2
by approximately 24%.
Therefore, the statistical and systematic uncertainties of
the R, ve←c+b and ve←c results are propagated as
inde2 2
pendent variables. The ve←b systematic uncertainties from
2
data and from the B feed-down subtraction are
asymmetric as a consequence of the systematic uncertainty
asymmetry of the measurements used in this analysis. The
systematic uncertainty from data is evaluated according to the
method described in [
54
], where the positive and negative
deviations are obtained separately and their average is added
in quadrature. For verification, the alternative approach
presented in [
55
] is also applied in this analysis. No
significant difference between these methods is observed. Since
the asymmetry of the systematic uncertainty from the B
feeddown subtraction only comes from the v2e←c result, the limits
of the v2e←b systematic uncertainty are the deviations
resulting from the upper and lower limits of the v2e←c systematic
uncertainty.
3 Results
The relative contribution of electrons from beauty-hadron
decays to the yield of electrons from heavy-flavour hadron
decays at √s = 2.76 TeV obtained with POWHEG +
PYTHIA at NLO accuracy using EPS09 NLO nPDFs is
shown in the top panel of Fig. 3. The result is compared with
the R in pp collisions at √s = 2.76 TeV measured by the
ALICE collaboration using the electron-hadron azimuthal
correlation technique [
38,39
] and with the BAMPS result in
20–40% Pb–Pb collisions at √sNN = 2.76 TeV [40]. The
comparison shows that R is higher when in-medium effects
are present, which is consistent with the expectation of the
mass hierarchy of the energy loss of charm and beauty quarks
in the medium. The bottom panel of Fig. 3 shows the v2
of electrons from charm-hadron decays at mid-rapidity in
20–40% Pb–Pb collisions at √sNN = 2.76 TeV obtained
with a MC simulation with PYTHIA using as input the
pTdifferential yield and v2 distributions of D0 mesons in the
same collision system. A positive v2 of electrons from
charmhadron decays is found in all pT intervals, with a maximum
significance of 3.2σ−, where σ− is the combined statistical
and systematic uncertainties of the lower limit, in the interval
2 < pT < 3 GeV/c.
The v2 coefficients of electrons from beauty-hadron
decays in 20–40% Pb–Pb collisions at √sNN = 2.76 TeV
obtained with different approaches of the factor R (top panel
of Fig. 3) are shown in Fig. 4. The result computed with the
coefficient R in pp collisions is an estimation of the
minimum value, as discussed previously. The v2 of electrons
from beauty-hadron decays in 20–40% Pb–Pb collisions at
√sNN = 2.76 TeV is compatible with zero within
approximately 1σ of the total uncertainty, obtained by summing
in quadrature the different uncertainty contributions, in all
pT intervals and different R coefficients. However, the large
statistical and systematic uncertainties prevent a definite
conclusion. The result is consistent with the measured v2 of
nonprompt J/ψ mesons from B-hadron decays in 10–60% Pb–Pb
collisions at √sNN = 2.76 TeV [
27
], which is also
compatible with zero within uncertainties.
Figure 5 shows the v2 of electrons from charm- and
beauty-hadron decays, inclusive [
36
] and separated, in 20–
40% Pb–Pb collisions at √sNN = 2.76 TeV. The v2 of
electrons from beauty-hadron decays is lower than the v2
of electrons from charm-hadron decays, although they are
compatible within uncertainties. The average of the v2
coefficients of electrons from charm- and beauty-hadron decays
obtained in the interval 2 < pT < 8 GeV/c are listed in
Table 1. Because of the asymmetric uncertainties, the average
is obtained numerically with an iterative sum of the likelihood
functions parametrised by variable-width Gaussians [
55,56
].
The standard deviation, which is the combination of
statistical and systematic uncertainties, is assumed to vary linearly.
The maximum value of the summed likelihood function
corresponds to the average v2, while the points at which the
function is −0.5 correspond to the lower and upper limits of
the total uncertainty.
R from ALICE
R from POWHEG+PYTHIA(EPS09NLO)
R from BAMPS
Fig. 5 Elliptic flow of electrons from charm- and beauty-hadron
decays, inclusive [36] and separated, in 20–40% Pb–Pb collisions at
√sNN = 2.76 TeV. The vertical error bars represent the statistical
uncertainties and the horizontal error bars indicate the bin widths. The
empty and filled boxes represent the systematic uncertainties from data
and from the B feed-down subtraction, respectively, in the D0-meson
v2 measurement [
32
]
4 Conclusions
We presented a method to subtract the contribution of charm
quarks in the elliptic flow of electrons from heavy-flavour
hadron decays. The v2 of electrons from charm-hadron
decays was estimated using a MC simulation of D0-meson
decays into electrons with PYTHIA, based on measurements
of the pT-differential yield and v2 of D0 mesons in Pb–
Pb collisions at √sNN = 2.76 TeV by ALICE. A positive
v2 of electrons from charm-hadron decays is found with a
maximum significance of 3.2σ− in the interval 2 < pT <
3 GeV/c. The computed v2 of electrons from charm-hadron
decays was then subtracted from the v2 of electrons from
←b0.25
e 2
v
0.2
izontal error bars indicate the bin widths. The empty and filled boxes
represent the systematic uncertainties from data and from the B
feeddown subtraction, respectively, in the D0-meson v2 measurement [
32
]
Table 1 Average of the v2 coefficients of electrons from charm- and
beauty-hadron decays obtained in the transverse momentum interval
2 < pT < 8 GeV/c in 20–40% Pb–Pb collisions at √sNN = 2.76 TeV.
The reported errors are the combined statistical and systematic
uncertainties. See text for more details
Result
e ← c
e ← b
e ← b
e ← b
R approach –
ALICE
BAMPS
POWHEG+PYTHIA(EPS09NLO)
Average v2
0.150+0.034
−0.028
0.014+0.039
−0.042
−0.010+0.047
−0.052
0.032+0.028
−0.030
heavy-flavour hadron decays in 20–40% Pb–Pb collisions at
√sNN = 2.76 TeV measured by the ALICE collaboration.
The subtraction was weighted by the relative contribution of
electrons from beauty-hadron decays to the yield of electrons
from heavy-flavour hadron decays. Since this observable is
not measured in Pb–Pb collisions, three different approaches
were used as estimations in the analysis. The resulting v2 of
electrons from beauty-hadron decays in 20–40% Pb–Pb
collisions at √sNN = 2.76 TeV from the subtraction is compatible
with zero within approximately 1σ of the total uncertainty
in all pT intervals and different approaches of the relative
contribution of electrons from beauty-hadron decays to the
yield of electrons from heavy-flavour hadron decays.
However, the large statistical and systematic uncertainties prevent
a definite conclusion. The v2 of electrons from beauty-hadron
decays is found to be lower than the v2 of electrons from
charm-hadron decays.
5 Outlook
In the presented method, the elliptic flow of electrons from
beauty-hadron decays can be determined by using three
observables that have largely been measured at the LHC and
RHIC. Based on available results of these observables, the
procedure was applied using measurements performed by the
ALICE collaboration. The method demonstrated to be
effective; however, the current statistical and systematic
uncertainties of the ALICE results prevent a definite conclusion
whether the collective motion of the medium constituents
influences beauty quarks. A better accuracy of the results
on heavy-flavour particles has been achieved in
measurements in Pb–Pb collisions at √sNN = 5.02 TeV [
34
] and it
is expected to be further improved with the ALICE upgrade,
which is foreseen to start in 2019.
In particular, the upgrade of the Inner Tracking System
(ITS) detector will improve the determination of the distance
of closest approach to the primary vertex, momentum
resolution and readout rate capabilities [
57
]. These improvements
will allow for more precise measurements of D mesons down
to low transverse momenta and for reducing the systematic
uncertainties from data and from the B feed-down
subtraction. The latter will be possible with the direct measurement
of the fraction of prompt D mesons and D mesons from
Bmeson decays, which is expected to be accessible with
relative statistical and systematic uncertainties smaller than 1
and 5% [
57
], respectively, for prompt D0 mesons. In addition,
the ITS upgrade will enable the tracking of electrons down
to approximately 0.05 GeV/c and enhance the capability to
separate prompt from displaced electrons [
57
], improving
the reconstruction of electrons that do not originate from
heavy-flavour hadron decays needed for the background
subtraction. Moreover, the systematic uncertainty of the elliptic
flow of electrons from beauty-hadron decays can be further
improved by taking into account correlations among different
contributions.
The capability of the heavy-flavour measurements will
also enhance with the increase of luminosity. For instance,
the current relative statistical uncertainty of the D-meson v2
measurement in Pb–Pb collisions is 10% for an integrated
luminosity of 0.1 nb−1, while it is expected to be 0.2% for
a scenario with an integrated luminosity of 10 nb−1 [
57
].
Also the elliptic flow coefficients of Ds and Λc particles are
expected to be achievable with a relative statistical
uncertainty of 8 and 20% [
57
], respectively.
Therefore, the presented method can be used to extract
the elliptic flow of electrons from beauty-hadron decays with
better precision with future measurements of the three needed
observables.
Acknowledgements We would like to thank Carsten Greiner and
Florian Senzel for providing the BAMPS results, as well as Francesco Prino
for fruitful discussions. We are grateful for the support of the Deutsche
Forschungsgemeinschaft (DFG) through the Research Training Group
“GRK 2149: Strong and Weak Interactions—from Hadrons to Dark
Matter”; Bundesministerium für Bildung und Forschung (BMBF) under
the project number 05P15PMCA1; Conselho Nacional de
Desenvolvimento Científico e Tecnológico (CNPq); and Fundação de Amparo à
Pesquisa do Estado de São Paulo (FAPESP).
Open Access This article is distributed under the terms of the Creative
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ons.org/licenses/by/4.0/), which permits unrestricted use, distribution,
and reproduction in any medium, provided you give appropriate credit
to the original author(s) and the source, provide a link to the Creative
Commons license, and indicate if changes were made.
Funded by SCOAP3.
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