Eur. Phys. J. C (2017) 77:339
DOI 10.1140/epjc/s10052-017-4890-x
Regular Article - Experimental Physics
Production of π
0
and η mesons up to high transverse momentum
in pp collisions at 2.76 TeV
ALICE Collaboration
⋆
CERN, 1211 Geneva 23, Switzerland
Received: 1 March 2017 / Accepted: 5 May 2017 / Published online: 22 May 2017
© CERN for the benefit of the ALICE collaboration 2017, corrected publication August 2017. This article is an open access publication
Abstract The invariantdifferential cross sections for inclu-
sive π
0
and η mesons at midrapidity were measured in
pp collisions at
√
s = 2.76 TeV for transverse momenta
0.4 < p
T
< 40 GeV/c and 0.6 < p
T
< 20 GeV/c, respec-
tively, using the ALICE detector. This large range in p
T
was achieved by combining various analysis techniques and
different triggers involving the electromagnetic calorime-
ter (EMCal). In particular, a newsingle-cluster,shower-shape
based method was developed for the identification of high-
p
T
neutral pions, which exploits that the showers originat-
ing from their decay photons overlap in the EMCal. Above
4GeV/c, the measured cross sections are found to exhibit a
similar power-law behavior with an exponent of about 6.3.
Next-to-leading-order perturbative QCD calculations differ
from the measured cross sections by about 30% for the π
0
,
and between 30–50% for the η meson, while generator-level
simulations with PYTHIA 8.2 describe the data to better than
10–30%, except at p
T
< 1GeV/c. The new data can there-
fore be used to further improve the theoretical description of
π
0
and η meson production.
1 Introduction
Measurements of identified hadron spectra in proton–proton
(pp) collisions are well suited to constrain predictions from
Quantum Chromodynamics (QCD) [
1]. Such predictions
are typically calculated in the pertubative approximation
of QCD (pQCD) based on the factorization of the elemen-
tary short-range scattering processes (such as quark–quark,
quark–gluon and gluon–gluon scatterings) involving large
momentum transfer (Q
2
) and long-range universal proper-
ties of QCD that need to be experimentally constrained. The
universal properties are typically modeled by parton distribu-
tion functions (PDFs), which describe the kinematic distribu-
tions of quarks and gluons within the proton in the collinear
The original version of this article was revised: in the original version
unfortunately the copyright holder was wrong.
⋆
e-mail:
alice-publications@cern.ch
approximation, and fragmentation functions (FFs), which
describe the probability for a quark or gluon to fragment
into hadrons of a certain type. The cross section for the pro-
duction of a given hadron of type H can be written as a sum
over parton types
E
d
3
σ
H
d p
=
a,b,c
f
a
(x
1
, Q
2
) ⊗ f
b
(x
2
, Q
2
)
⊗D
H
c
(z
c
, Q
2
) ⊗ d ˆσ
ab→cX
(Q
2
, x
1
, x
2
), (1)
where f
i
(x) denotes the proton PDF of parton i carrying a
fraction x of the proton’s longitudinal momentum, D
H
i
(z
i
)
the FF of parton i into hadron H carrying a fraction z
i
of
the parton’s momentum, and d ˆσ
ij→kX
the inclusive short-
distance scattering cross section of partons i and j into k (see
e.g. [2]).
Measurements of hadron production provide constraints
on thePDFsandFFs, which are crucial for pQCD predictions,
and at LHC energies probe rather low values of x ∼ 0.001
and z ∼ 0.1. The neutral pion (π
0
) is of special interest
because as the lightest hadron it is abundantly produced, and
at LHC collision energies belowa transversemomentum (p
T
)
of 20 GeV/c dominantly originates from gluon fragmenta-
tion. While the collision energy (
√
s) dependence of π
0
cross
sections has been useful for guiding the parametrization of
the FFs [
3], experimental data for neutral pions [4,5]atthe
LHC are not available above 20 GeV/c, where quark frag-
mentation starts to play a role. The new π
0
data presented in
this paper extend our previous measurement [
5] in pp colli-
sions at
√
s = 2.76 TeV to p
T
values of 40 GeV/c allowing
one to investigate the p
T
dependence of the π
0
cross sec-
tion at high transverse momentum. In addition, we present
the cross section of the η meson, which due to its strange
quark content provides access to the study of possible differ-
ences of fragmentation functions with and without strange
quarks [
6]. Furthermore, the η meson constitutes the second
most important source of decay photons and electrons after
the π
0
. Hence, π
0
and η meson spectra over a large p
T
range
are needed for a precise characterization of the decay pho-
123
339 Page 2 of 25 Eur. Phys. J. C (2017) 77 :339
ton (electron) background for direct photon (semileptonic
open charm and beauty) measurements.
The new measurement of the π
0
cross section is a result
of five analyses using data from various ALICE detector
systems and different identification techniques. The decay
photons are either measured directly in the Electromagnetic
Calorimeter (EMCal), the Photon Spectrometer (PHOS) or
via the photon conversion method (PCM). In the PCM mea-
surement, the photons are reconstructed via their conversions
into e
+
e
−
pairs within the detector material, where the e
+
e
−
pairs are reconstructed with the charged-particle trackingsys-
tems. The π
0
is reconstructed statistically using the invariant
mass technique. At high p
T
, where the decay photons are too
close together to be resolved individually, the π
0
can still be
measured via the characteristic shape of their energy depo-
sition in the EMCal. We combine statistically independent
analyses where (1) both photons are individually resolved
in the EMCal (EMC), (2) one photon is identified in the
EMCal and one is reconstructed via its conversion to e
+
e
−
(PCM–EMC), and (3) the photon pair’s energy is merged in
the EMCal (mEMC). Finally, the previously published mea-
surements based on methods where both photons are recon-
structed with (4) PHOS or (5) PCM are included as well [
5].
The addition of the EMCal based measurements extends the
p
T
reach from 12 to 40 GeV/c, the highest p
T
for identified
hadrons achieved so far. The η meson cross section that was
previously not available at
√
s = 2.76 TeV is measured in the
range from 0.6to20GeV/c using the PCM, PCM-EMC and
EMC methods. Consequently, the η/π
0
ratio is measured in
the same p
T
range.
The article is organized as follows: Sect.
2 briefly
describes the experimental setup. Section
3 describes the data
samples and event selection. Section
4 describes the neutral
meson reconstruction techniques and corresponding correc-
tions for the cross section measurements. Section
5 discusses
the systematic uncertainties of the various measurements.
Section
6 presents the data and comparison with calculations
and Sect.
7 provides a summary.
2 ALICE detector
A detailed description of the ALICE detector systems and
their performance can be found in Refs. [
7,8]. The new
measurements primarily use the Electromagnetic Calorime-
ter (EMCal), the Inner Tracking System (ITS), and the Time
Projection Chamber (TPC) at mid-rapidity, which are posi-
tioned within a 0.5 T solenoidal magnetic field. Two forward
scintillator arrays (V0A and V0C) subtending a pseudora-
pidity (η) range of 2.8 <η<5.1 and −3.7 <η<−1.7,
respectively, provided the minimum bias trigger, which will
be further discussed in the next section.
The ITS [
7] consists of two layers of Silicon Pixel Detec-
tors (SPD) positioned at a radial distance of 3.9 and 7.6 cm,
two layers of Silicon Drift Detectors (SDD) at 15.0 and
23.9cm, and two layers of Silicon Strip Detectors (SSD)
at 38.0 and 43.0 cm from the beamline. The two SPD lay-
ers cover a pseudorapidity range of |η| < 2 and |η| < 1.4,
respectively. The SDD and the SSD subtend |η| < 0.9 and
|η| < 1.0, respectively. The primary vertex can be recon-
structed with a precision of σ
z(xy)
= A/
(dN
ch
/dη)
β
⊕ B,
where A ≈ 600 (300) µm, for the longitudinal (z) and trans-
verse (xy) directions, respectively, B ≈ 40 µm and β ≈ 1.4.
The TPC [
9]isalarge(90m
3
) cylindrical drift detector
filled with a Ne/CO
2
gas mixture. It covers a pseudorapidity
range of |η| < 0.9 over the full azimuthal angle for the maxi-
mum track length of 159 reconstructed space points. The ITS
and the TPC were aligned with respect to each other to a pre-
cision better than 100µm using tracks from cosmic rays and
proton–proton collisions [
10]. The combined information of
the ITS and TPC allows one to determine the momenta of
charged particles in the range of 0.05–100GeV/c with a reso-
lution between 1% at low p
T
and 10% at high p
T
. In addition,
the TPC provides particle identification via the measurement
of the specific energy loss (dE/dx) with a resolution of ≈5%.
The tracking detectors are complemented by the Transition
Radiation Detector (TRD) and a large time-of-flight (TOF)
detector. These detectors were used to estimate the system-
atic uncertainty resulting from the non-perfect knowledge of
the material in front of the EMCal.
The EMCal [
11] is a layered lead-scintillator sampling
calorimeter with wavelength shifting fibers for light col-
lection. The overall EMCal covers 107
◦
in azimuth and
−0.7 ≤ η ≤ 0.7 in pseudorapidity. The detector con-
sists of 12,288 cells (also called towers) with a size of
η ×ϕ = 0.0143 ×0.0143 corresponding to about twice
the effective Molière radius; the cells are read out individ-
ually. With a depth of 24.6cm,or≈20 radiation lengths,
2 × 2 cells comprise a physical module. The 3072 modules
are arranged in 10 full-sized and 2 one-third-sized super-
modules, consisting of 12 ×24 and 4 ×24 modules, respec-
tively, of which only the full-sized modules, corresponding
to an azimuthal coverage of 100
◦
, were readout for the data
recorded in 2011–2013.
1
The modules are installed with a
radial distance to the nominal collision vertex of 4.28 m at
the closest point, and assembled to be approximately pro-
jective in η. The scintillation light from each cell is col-
lected with wavelength shifting fibers that are connected to
a5× 5mm
2
active-area avalanche photodiode. The rela-
tive energy and position resolutions improve with rising inci-
dent energy of the particle [
12]. The energy resolution can
1
The detector was installed in its complete configuration by early 2012,
while 4 and 10 full-sized supermodules were present in 2010 and 2011,
respectively.
123
Eur. Phys. J. C (2017) 77 :339 Page 3 of 25 339
Table 1 Approximate trigger threshold and corresponding trigger rejection factor for EMCal triggers, as well as integrated luminosity for minimum
bias and various EMCal triggers
Year Trigger Trigger name Approx. threshold Trigger rejection factor (R
Trig
) L
int
(nb
−1
)
2011 MB
OR
INT1 0 1 0.524 ±0.010
EMCal L0 EMC1 3.4 GeV 1217 ±67 13.8 ±0.806
2013 MB
AND
INT7 0 1 0.335 ±0.013
EMCal L0 EMC7 2.0 GeV 126.0 ±4.31.19 ±0. 062
EMCal L1 (G2) EG2 3.5 GeV 1959 ±131 6.98 ±0. 542
EMCal L1 (G1) EG1 5.5 GeV 7743 ±685 47.1 ±4.57
be described by a constant and two energy dependent terms
parametrized as
σ
E
E
= A
2
⊕
B
2
E
⊕
C
2
E
2
% with A = 1.7 ±0.3,
B = 11.3 ±0.5, C = 4.8 ±0.8 and E in GeV. The position
resolution is linear as a function of 1/
√
E and parametrized
as 1.5mm+
5.3mm
√
E
with E in GeV. Starting with the highest
cell E
seed
> 0.5 GeV, the energy depositions from directly
adjacent EMCal cells with E
cell
> 0.1 GeV are combined to
form clusters representing the total energy and physical posi-
tion of incident particles [
8]. The clustering algorithm allows
only one local energy maximum in a cluster; if a second is
found a new cluster is initiated. Each cell is restricted to only
be part of one cluster. Individual cells were calibrated using
the π
0
mass peak position evaluated cell-by-cell, achieving
a relative variation of below 1%.
3 Data samples and event selection
The data presented in this paper were recorded during the
2011 and 2013 periods with pp collisions at
√
s = 2.76 TeV.
Various EMCal triggers were employed and, while the major-
ity of the minimum bias data were recorded in 2011, the
2013 running period took advantage of higher threshold
EMCal triggers to collect a notable high-p
T
data sample.
For the pp data collected in 2011, the minimum bias trig-
ger (MB
OR
) required a hit in either V0 detector or a hit in the
SPD, while it required hits in both V0 detectors for the data
collected in 2013 (MB
AND
). The respective cross sections
were determined based on van-der-Meer scans, and found
to be σ
MB
AND
= 47.7 ± 0.9 mb with σ
MB
AND
/σ
MB
OR
=
0.8613 ± 0.0006 and σ
MB
AND
/σ
inel
= 0.760
+0.052
−0.028
[
13].
For the normalisation of the 2013 data, for which there
was no vdM scan, the uncertainty σ
MB
AND
was conserva-
tively increased to 4%, to account for possible variations of
the MB
AND
trigger efficiency between 2011 and 2013. The
resulting uncertainty due to the luminosity determination is
2.5% for both datasets together.
The EMCal issues triggers at two different levels, Level 0
(L0) and Level 1 (L1). The events accepted at L0 are further
processed at L1. The L0 decision, issued latest 1.2 µsafter
the collision, is based on the analog charge sum of 2×2 adja-
cent cells evaluated with a sliding window algorithm within
each physical Trigger Region Unit (TRU) spanning 4 × 24
cells in coincidence with a minimum bias trigger. The L1
trigger decision, which must be taken within 6.2 µsafterthe
collision, can incorporate additional information from dif-
ferent TRUs, as well as other triggers or detectors. The data
presented in this paper used the photon (EG) trigger at L1,
which extends the 2 ×2 sliding window search across neigh-
boring TRUs, resulting in a ≈30% larger trigger area than
the L0 trigger.
In 2011, only the L0 trigger was used with one thresh-
old (EMC1), while in 2013, one L0 (EMC7) and two L1
triggers (EG1, EG2) with different thresholds were used, as
summarized in Table
1. The lower L1 trigger threshold in
2013 was set to approximatelymatch the L0 threshold in 2011
for consistency. In case an event was associated with several
triggers, the trigger with the lowest threshold was retained.
However, the thresholds are configured in the hardware
via analog values, not actual units of energy. Their transfor-
mation into energy values directly depends on the energy cal-
ibration of the detector. For a reliable normalization of each
trigger, the Trigger Rejection Factor (R
Trig
) is used. The R
Trig
takes into account a combination of the efficiency, accep-
tance and the downscaling of the respective triggers. It can
be obtained from the ratio R of the number of clusters recon-
structed in EMCal triggered events to those in minimum bias
events at high cluster energy E where R should be approxi-
mately constant (plateau region), assuming the trigger does
not affect the cluster reconstruction efficiency, but only the
overall rate of clusters. To reduce the statistical uncertain-
ties on the normalization for the higher threshold triggers,
R
Trig
was always estimated with respect to the trigger with
the next lower threshold in the EMCal or the respective min-
imum bias trigger if no lower EMCal trigger was available.
By consecutively multiplying the individual rejection factors
up to the minimum bias trigger, the final R
Trig
was obtained
with respect to the minimum bias trigger. The energy depen-
dence of the ratios between cluster spectra of the relevant trig-
ger combinations (EMC1/INT1, EMC7/INT7, EG2/EMC7
and EG1/EG2) are shown in Fig.
1.AtlowE, there is a
minimum at roughly the threshold of the lower-level trig-
ger for EG2/EMC7 and EG1/EG2, while at high E there
is a pronounced plateau for every trigger combination. The
123
339 Page 4 of 25 Eur. Phys. J. C (2017) 77 :339
Fig. 1 Energy dependence of ratios between cluster spectra for
EMC1/INT1, EMC7/INT7, EG2/EMC7 and EG1/EG2. The trigger
names INT1 and INT7 denote the minimum bias triggers MB
OR
and
MB
AND
respectively. The trigger names EMC1, EMC7, EG2 and EG1
denote the EMCal triggers at L0 in 2011 and 2013, and the EMCal trig-
gers at L1 in 2013 with increasing threshold respectively. The individ-
ual trigger rejection factors and their respective fit ranges in the plateau
region are indicated as well. The final rejection factors with respect to
the minimum bias trigger are given in Table
1
averages above the threshold in the plateau region, which
represent R
Trig
for the respective trigger combinations, are
indicated by a line whose width represents the respective
statistical uncertainty. The corresponding systematic uncer-
tainties were obtained by varying the range for the fit of
the plateau region. Finally, the values for the average trig-
ger rejection factors above the threshold with respect to the
corresponding minimum bias triggers are given in Table
1.
For the PCM–EMC and EMC analyses, all available triggers
were used, while for mEMC only the EMC1, EG2 and EG1
triggers were included. The collected integrated luminosities
for minimum bias and EMCal triggers
L
int
=
N
trig
σ
MB
R
trig
, (2)
where σ
MB
refers to σ
MB
OR
for 2011 and σ
MB
AND
for 2013,
are summarized in Table
1. The statistical uncertainties on
R
Trig
are treated as systematic uncertainties on the integrated
luminosity.
Monte Carlo (MC) samples were generated using
PYTHIA8 [
14] and PHOJET [15]. The correction factors
obtained independently from the two MC samples were
found to be consistent, and hence combined. For mesons with
p
T
> 5GeV/c, as in the triggered or merged cluster analyses,
PYTHIA6 [
16] simulations enriched with jets generated in
bins of the hard scattering (p
T,hard
) were used. All MC sim-
ulations were obtained for a full ALICE detector description
using the GEANT3 [
17] framework and reconstructed with
the same algorithms as for the data processing.
The different triggers of the EMCal affect the proper-
ties of the reconstructible mesons, like the energy asym-
metry (α =
E
1
−E
2
E
1
+E
2
) of the decay photons, and hence sig-
nificantly alter the reconstruction efficiency above the trig-
ger threshold in the trigger turn-on region. The efficiency
biases κ
Trig
induced by the triggers were simulated using the
approximate thresholds and their spread for different TRUs.
The bias was defined as the ratio of the π
0
or η reconstruc-
tion efficiency in triggered events over that in minimum bias
events. Figure
2 shows the p
T
dependence of κ
Trig
for dif-
ferent triggers and reconstruction methods for the π
0
and η
meson. While κ
Trig
is unity for the mEMC analysis in the
considered kinematic range, it is significantly below one for
the PCM–EMC and EMC neutral meson reconstruction, and
reaches ≈1 only at about twice the trigger threshold. The
corresponding correction factors are found to be larger for
the PCM–EMC compared to the EMC method, and larger
for the η than the π
0
meson. This is a consequence of the
much lower energy threshold imposed on the photons recon-
structed with PCM, which leads to wider opening angle and
asymmetry distributions of the reconstructible mesons. At
low p
T
, κ
Trig
also exhibits the effect of the trigger on sub-
leading particles, for which the efficiency in triggered events
is strongly reduced. However, the various triggers are only
used if the meson momentum is at least 1.5 times the trig-
ger threshold, thus the effect on the subleading particles is
negligible.
In the offline analysis, only events with a reconstructed
vertex with |z
vtx
| < 10 cm with respect to the nominal inter-
action vertex position along the beam direction were used.
The finite primary vertex reconstruction efficiency for the
MB
OR
(MB
AND
) trigger of about 0.92 (0.98) is taken into
account in the normalization of the respective minimum bias
triggers. Furthermore, only events with exactly one recon-
structed vertex were accepted to remove pileup from in- and
out-of-bunch collisions. While the in-bunch pileup is negli-
gible after the vertex selection, the out-of-bunch pileup accu-
mulating in the TPC due to its readout time of 90ms, needs
to be subtracted statistically for the mesons measured with
PCM, as described in Ref. [
5]. For the π
0
(η) mesons recon-
structed with PCM the out-of-bunch pileup correction ranges
from 20% (9%) at low p
T
to about 3% above 4 GeV/c. Anal-
yses involving the EMCal are not affected because contri-
butions of clusters from different bunch crossings are sup-
pressed by a suitable selection of clusters within a certain
time window around the main bunch crossing.
4 Neutral meson reconstruction
Neutral mesons decaying into two photons fulfill
M =
2E
1
E
2
(1 − cos θ
12
) (3)
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Eur. Phys. J. C (2017) 77 :339 Page 5 of 25 339
Fig. 2 Efficiency bias κ
Trig
induced by different triggers (EMC1, EMC7 and EG1) for neutral pions (left panel)andη mesons (right panel)for
PCM–EMC (open symbols)andEMC(closed symbols)
where M is the reconstructed mass of the meson, E
1
and
E
2
are the measured energies of two photons, and θ
12
is the
opening angle between the photons measured in the labo-
ratory frame. Photon candidates are measured either by a
calorimeter or by PCM. Neutral meson candidates are then
obtained by correlating photon candidates measured either
by EMC, PHOS or PCM exclusively, or by a combination
of them (PCM–EMC). The corresponding π
0
and η meson
measurements are described in Sect.
4.1. The typical opening
angle θ
12
decreases with increasing p
T
of the meson due to
the larger Lorentz boost. For π
0
mesons with p
T
above 5–6
GeV/c, the decay photons become close enough so that their
electromagnetic showers overlap in neighboring calorimeter
cells of the EMCal. At p
T
above 15 GeV/c, the clustering
algorithm can no longer efficiently distinguish the individual
showers in the EMCal, and π
0
mesons can be measured by
inspecting the shower shape of single clusters, referred to as
“merged” clusters and explained in Sect.
4.2.
To be able to directly compare the reconstruction perfor-
mances of the various measurement techniques and triggers,
the invariant differential neutral meson cross sections were
expressed as
E
d
3
σ
dp
3
=
N
rec
p
T
p
T
κ
Trig
ε
1
L
int
1
BR
(4)
with the inverse of the normalized efficiency
1
ε
=
1
2π A y
P
ε
rec
(5)
and integrated luminosity (see Eq.
2). The measured cross
sections were obtained by correcting the reconstructed meson
yield N
rec
for reconstruction efficiency ε
rec
, purity P and
acceptance A, efficiency bias κ
Trig
, integrated luminos-
ity L
int
,aswellasforthep
T
and y interval ranges, p
T
and y, respectively, and the γγ decay branching ratio BR.
For invariant mass methods, the effect of reconstructed pho-
ton impurities on the meson purity are significantly reduced
due to the subtraction of the combinatorial background, and
hence the resulting meson impurities were neglected. For the
mEMC method, the π
0
purity correction was obtained from
MC simulations tuned to data. In the case of neutral pions, the
contribution from secondary π
0
s was subtracted from N
rec
before applying the corrections. The contribution from weak
decays was estimated for the different methods by simulat-
ing the decays of the K
0
S
and using their measured spec-
tra [
18], taking into account the reconstruction efficiencies,
as well as resolution and acceptance effects for the respec-
tive daughter particles The contribution from neutral pions
produced by hadronic interactions in the detector material
was estimated based on the full detector simulations using
GEANT3. Finally, the results were not reported at the center
of the p
T
intervals used for the measurements, but following
the prescription in Ref. [
19] at slightly lower p
T
values, in
order to take into account the effect of the finite bin width
p
T
. The correction was found to be less than 1% in every
p
T
interval for the π
0
, and between 1–4% for the η meson.
4.1 Invariant mass analyses
Applying Eq.
3, the invariant mass distribution is obtained
by correlating all pairs of photon candidates per event. The
neutral meson yield is then statistically extracted using the
distinct mass line shape for identification of the signal and
a model of the background. In the following, only the new
measurements are described. Details of the PCM and PHOS
π
0
measurements can be found in Refs. [
4,5].
123