2015 152 18 June

Nuclear modification factor of charged pions, kaons, and protons

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

Transverse momentum ($p_{\rm{T}}$) spectra of pions, kaons, and protons up to
$p_{\rm{T}}=20\text{\,GeV/$c$}$ have been measured in Pb–Pb collisions at
$\sqrt{s_{\rm NN}}=2.76\text{\,TeV}$ using the ALICE detector for six
different centrality classes covering 0-80%. The proton-to-pion and the kaon-
to-pion ratios both show a distinct peak at $p_{\rm{T}}\approx
3\text{\,GeV/$c$}$ in central Pb–Pb collisions that decreases for more
peripheral collisions. For $p_{\rm{T}}>10\text{\,GeV/$c$}$, the nuclear
modification factor is found to be the same for all three particle species in
each centrality interval within systematic uncertainties of 10–20%. This
suggests there is no direct interplay between the energy loss in the medium
and the particle species composition in the hard core of the quenched jet. For
$p_{\rm{T}}<10\text{\,GeV/$c$}$, the data provide important constraints for
models aimed at describing the transition from soft to hard physics.

##  1 Introduction

In ultra-relativistic heavy-ion collisions, a strongly-interacting deconfined
medium of quarks and gluons is created. Experimental evidence for this state
of matter has been found both at the Relativistic Heavy-Ion Collider (RHIC)
[1, 2, 3, 4] as well as at the LHC [5, 6, 7, 8, 9]. Transverse momentum
($p_{\rm{T}}$) spectra probe many different properties of this medium. At low
$p_{\rm{T}}$ ($\lesssim 2\text{\,GeV/$c$}$) the spectra provide information on
bulk production, while at high $p_{\rm{T}}$ ($\gtrsim 10\text{\,GeV/$c$}$)
transport properties of the medium can be studied via jet quenching [10, 11,
12]. The microscopic QCD processes are different at low and high $p_{\rm{T}}$,
and it is an open question if additional physics processes occur in the
intermediate $p_{\rm{T}}$ region ($2\lesssim p_{\rm{T}}\lesssim
10\text{\,GeV/$c$}$). In this paper, the centrality evolution of the
transverse momentum spectra of pions, kaons, and protons as a function of
$p_{\rm{T}}$ for Pb–Pb collisions at $\sqrt{s_{\rm NN}}=2.76\text{\,TeV}$ is
presented. The focus is on intermediate and high $p_{\rm{T}}$, where these
measurements allow comparison between baryons and mesons, strange and non-
strange particles, and the search for particle mass-dependent effects.

For inclusive charged particle $p_{\rm{T}}$ spectra, jet quenching leads to a
suppression of high-$p_{\rm{T}}$ particle production at the RHIC [13, 14, 15]
and over an extended $p_{\rm{T}}$ range, up to $100\text{\,GeV/$c$}$, at the
LHC [6, 16, 17, 18]. The microscopic mechanism of jet quenching is not
completely understood, and one of the main goals of the experimental programs
at the RHIC and the LHC is to identify additional signatures associated with
the jet quenching to constrain theoretical modeling. Particle identification
(PID) is of fundamental interest since, due to the color Casimir factor,
gluons interact two times stronger with the medium than quarks [19, 20] and it
is known from e+e- studies of 3-jet events that gluons are more likely to
fragment to leading baryons than quarks are [21]. In addition, some models for
jet quenching predict large particle-species-dependent effects [22, 23, 24].
Measurements at the RHIC, in particular for baryons, have so far been
inconclusive due to the limited $p_{\rm{T}}$-range and the large systematic
and statistical uncertainties [25, 26, 27].

In the intermediate transverse momentum regime, the baryon-to-meson ratios,
e.g. the proton yield divided by the pion yield, measured by experiments at
the RHIC revealed a, so far, not well understood enhancement [28, 29, 30].
This so-called “baryon anomaly” could indicate the presence of new
hadronization mechanisms such as parton recombination [31, 32, 33] that could
be significantly enhanced and/or extended out to higher $p_{\rm{T}}$ at the
LHC due to larger mini-jet production [34]. In recombination models, the
enhancement at intermediate $p_{\rm{T}}$ is an effect of the coalescence of
lower $p_{\rm{T}}$ quark-like particles that leads to a larger production of
baryons than mesons. In a model without new intermediate $p_{\rm{T}}$ physics,
the rise of the baryon-to-meson ratio is due to hydrodynamics and the decrease
is solely a consequence of the growing importance of fragmentation.

In a recent letter [35] ALICE reported the charged pions, kaons, and proton
$p_{\rm{T}}$ spectra for $\rm pp$ and the most central and most peripheral
Pb–Pb collisions. The main observation was that, within statistical and
systematic uncertainties, the nuclear modification factor is the same for
$p_{\rm{T}}>10\text{\,GeV/$c$}$ for all three particle species. This suggests
that there are no significant particle-species-dependent effects related to
the energy loss. In this paper, the analysis used to obtain the measurements
at high $p_{\rm{T}}$ is presented in full detail, and the results for all
centrality classes are included. Recent measurements at low and intermediate
$p_{\rm{T}}$ of identified particle production and correlations in p–Pb
collisions have revealed phenomena typically associated with fluid-like
behavior in heavy-ion collisions [36, 37, 38]. This raises questions if
hydrodynamics and/or recombination can also be applied to describe these small
systems [39, 40, 41]. The centrality evolution studies for Pb–Pb collisions
can therefore also be seen as a possible experimental interconnection between
the smallest and the largest QCD bulk systems.

The outline of this paper is as follows. In Sec. 2, the data analysis is
described. The method using the energy loss in the TPC for particle
identification is laid out first and then the procedure using the Cherenkov
angle measured by the HMPID is presented. In Sec. 3, the final spectra are
presented, and the particle ratios and nuclear modification factors are
discussed and compared with theoretical calculations and results from previous
experiments at lower center-of-mass energies.

##  2  Data analysis

The results reported in this paper have been obtained with the central barrel
of the ALICE detector, which has full azimuthal coverage around midrapidity,
$|\eta|<0.8$ [42]. Different Particle IDentification (PID) devices are used
for the identification of $\pi^{\pm},\rm K^{\pm},\text{and }\rm p(\bar{p})$
(see Table 4 for exact $p_{\rm{T}}$ ranges). Ordering by $p_{\rm{T}}$, from
lowest to highest, the results are obtained using the specific energy loss,
${\rm d}E/{\rm d}x$, in the silicon Inner Tracking System (ITS), the ${\rm
d}E/{\rm d}x$ in the Time Projection Chamber (TPC), the time-of-flight
measured by the Time-Of-Flight (TOF) detector, the Cherenkov angle measured by
the High Momentum Particle Identification Detector (HMPID), and the TPC ${\rm
d}E/{\rm d}x$ in the relativistic rise region. The general performance of
these devices is reported in [43]. Detailed description of the lower
$p_{\rm{T}}$ analyses and the resulting $\pi^{\pm},\rm K^{\pm},\text{and }\rm
p(\bar{p})$ $p_{\rm{T}}$ spectra in Pb–Pb collisions are already published
[44]. In this section, the method used to extract these $p_{\rm{T}}$ spectra
in the HMPID and the TPC ${\rm d}E/{\rm d}x$ relativistic rise analysis is
described in detail.

Due to the limited acceptance of the HMPID, the analysis has been performed
with the larger 2011 dataset where a centrality trigger was used, restricting
the HMPID results to 0-50% central Pb–Pb collisions.

###  2.1  TPC dE/dx relativistic rise analysis

The relativistic rise of the ${\rm d}E/{\rm d}x$ in the TPC, where the average
energy loss increases as $\log{\beta\gamma}$ ($3\ll\beta\gamma\ll 1000$),
allows ALICE to extend the PID of $\pi^{\pm},\rm K^{\pm},\text{and }\rm
p(\bar{p})$ up to $p_{\rm{T}}=20\text{\,GeV/$c$}$. This section will focus on
details of this analysis.

####  2.1.1 Event and track selection

The event and track selection follows closely that of the inclusive charged
particle analysis [16]. The same spectrum normalization is adopted so that the
systematic uncertainties related to event and track selection are common,
allowing a precise comparison between the nuclear modification factors for
inclusive and identified charged particles. The analysis with PID described
here has additional systematic uncertainties related to the particle
identification that we will describe in Sec. 2.1.9.

A total of $11\times 10^{6}$ Pb–Pb collision events recorded in 2010 are used
in this analysis. The online (offline) trigger for minimum bias interactions
in Pb–Pb collisions requires signals in two (three) out of the three following
detector elements: the Silicon Pixel Detector (SPD) layers of the ITS and the
two forward scintillators (V0) located on opposite sides of the interaction
point. The centrality is determined from the measured amplitude in the V0
detector [45].

Primary tracks are reconstructed in the ALICE TPC [46] from clusters in up to
159 pad rows, where each cluster consists of a group of cells covering a few
neighboring pads and time bins. The tracks used in the analysis are restricted
to $|\eta|<0.8$ in order to be fully contained in the TPC active volume.
Furthermore, tracks are required to have at least one hit in one of the two
innermost SPD layers of the ITS, and the distance of closest approach to the
primary vertex is required to be less than 2 cm along the beam axis and less
than 7 standard deviations in the transverse plane
(${\approx}350\,\mu\text{m}$ for tracks with $p_{\rm{T}}=2\text{\,GeV/$c$}$,
decreasing slightly with $p_{\rm{T}}$). The resulting relative $p_{\rm{T}}$
resolution for these tracks is better than 5% at
$p_{\rm{T}}=20\text{\,GeV/$c$}$ [16]. The $p_{\rm{T}}$ spectra have been
corrected for this resolution using an unfolding procedure for
$p_{\rm{T}}>10\text{\,GeV/$c$}$ [16, 47]. This correction is smaller than 2%
at $p_{\rm{T}}=20\text{\,GeV/$c$}$.

####  2.1.2 Particle identification at large transverse momentum

Figure 1: (Color online) The ${\rm d}E/{\rm d}x$ as a function of the momentum
$p$ at mid-rapidity $|\eta|<0.2$ for 0-5% (left panel) and 60-80% (right
panel) Pb–Pb collisions. In each momentum bin, the ${\rm d}E/{\rm d}x$ spectra
have been normalized to have unit integrals and only bins with more than 0.1%
of the counts are shown (making electrons not visible in this plot except at
very low momentum). The curves show the final $\langle{\rm d}E/{\rm
d}x\rangle$ responses for pions, kaons, and protons. Figure 2:  Separation in
number of standard deviations ($S_{\sigma}$) as a function of momentum
between: pions and protons (upper panels), pions and kaons (middle panels),
and kaons and protons (lower panels). Results are shown for 0-5% (left panels)
and 40-60% (middle panels) Pb–Pb; and pp (right panels) collisions. Because
the TPC response is track-length dependent, the separation is better for
tracks at forward pseudorapidities (solid lines) than for those at smaller
$\eta$ (dashed lines). The degradation in separation power in more central
collisions is expected from occupancy effects – in the most peripheral
collisions an average of $149$ clusters are assigned to tracks with
$p_{\rm{T}}>2\text{\,GeV/$c$}$, while in the most central collisions only
$127$ clusters are assigned.

Figure 1 shows the ${\rm d}E/{\rm d}x$ as a function of momentum $p$ in 0-5%
central Pb–Pb collisions. It is evident that particle identification in the
relativistic rise region requires precise knowledge of the $\langle{\rm
d}E/{\rm d}x\rangle$ response and resolution $\sigma$. To quantify this, and
to motivate the detailed studies in the following, the final response
functions are used to estimate the separation power, where, for example, the
charged pion-to-kaon separation in number of standard deviations,
$S_{\sigma}$, is

$S_{\sigma}=\frac{\left\langle\frac{{\rm d}E}{{\rm
d}x}\right\rangle_{\pi^{+}+\pi^{-}}-\left\langle\frac{{\rm d}E}{{\rm
d}x}\right\rangle_{{\rm K}^{+}+{\rm
K}^{-}}}{0.5\left(\sigma_{\pi^{+}+\pi^{-}}+\sigma_{{\rm K}^{+}+{\rm
K}^{-}}\right)},$ (1)

that is, the absolute $\langle{\rm d}E/{\rm d}x\rangle$ difference normalized
to the arithmetic average of the resolutions. Fig. 2 shows that the separation
power between particle species is only a few standard deviations, making PID
very challenging, requiring optimization of the ${\rm d}E/{\rm d}x$ signal
itself and the use of external PID constraints to calibrate the response. In
the following, these analysis aspects will be covered in detail.

####  2.1.3 The ${\rm d}E/{\rm d}x$ calibration

The ${\rm d}E/{\rm d}x$ is obtained as a truncated mean, where the average is
performed considering only the 60% lowest cluster charge values to remove the
tail of the Landau like cluster charge distribution. It is customary to use
the notation ${\rm d}E/{\rm d}x$ and talk about the Bethe–Bloch curve, even if
the ${\rm d}E/{\rm d}x$ used in the analysis is only the truncated mean and
does not contain energy losses deposited as sub-ionization-threshold
excitations or the full ionization from delta-electrons, discussed in detail
in [48]. While the Bethe–Bloch specific energy loss depends only on
$\beta\gamma=p/m$, the one obtained from the detected truncated mean also
depends on other parameters such as the actual cluster sample length, i.e.,
the pad length and/or track inclination over the pad. In the following, we
shall refer to the relationship between the two types of specific energy
losses as _the transfer function_ and it is this relationship that is
optimized in the ${\rm d}E/{\rm d}x$ calibration, and used also as input for
the analysis strategy discussed later.

Each of the up to 159 clusters used to reconstruct a track contains
information on the ionization energy loss in the TPC. To equalize the gain,
each individual readout channel has been calibrated using ionization clusters
produced by the decay of radioactive krypton, ${}^{86}_{36}{\rm Kr}$, released
into the TPC gas [46].

In $\rm pp$ collisions the cluster integrated charge is used for calculating
the ${\rm d}E/{\rm d}x$. The integrated charge is corrected for the tails of
the charge distribution that are below the readout threshold. Due to the large
probability for overlapping clusters in Pb–Pb collisions, the maximum charge
in the cluster is used to calculate the ${\rm d}E/{\rm d}x$ in this case. The
maximum charge is the largest charge in a cluster cell (pad and time bin). The
maximum charge has to be corrected for the drift-length dependent reduction
due to diffusion and the dependence on the relative pad position of the
induced signal (the measured maximum charge is largest if the cluster center
is also the pad center, and smallest if it is between two pads).

The performance and stability of the ${\rm d}E/{\rm d}x$ transfer function,
with respect to gain variations, is improved in the following two ways.
Reconstructed space points where the charge is deposited on a single pad, that
are not used for track fitting, are included in the ${\rm d}E/{\rm d}x$
calculation. An attempt is made, to identify clusters below the readout
threshold. If a row has no cluster assigned to the track but clusters were
assigned in both neighboring rows, it is assumed that the cluster charge was
below the readout threshold and a virtual cluster is assigned with charge
corresponding to the lowest reconstructed charge cluster on the track. This
virtual cluster is then included in the calculation of the truncated mean.
This is similar to the strategy adopted by ALEPH, but without changing the
truncation range [49].

Figure 3: The ${\rm d}E/{\rm d}x$ as a function of $\eta$ for electrons on the
Fermi Plateau (upper panel) and MIP pions (middle panel); the selection
criteria are described in the text. The solid round markers indicate the
average, $\langle{\rm d}E/{\rm d}x\rangle$, and the height of the boxes is
given by the standard deviation, $\sigma$. The lower panel shows the ratio
between the Plateau and MIP $\langle{\rm d}E/{\rm d}x\rangle$. The statistical
uncertainty is smaller than the marker sizes. These results were obtained for
$\rm pp$ collisions at $\sqrt{s}=$2.76 TeV.

The $\eta$ dependence of the ${\rm d}E/{\rm d}x$ is sensitive to corrections
for the track-length and the diffusion. There is also a small correction for
the direct drift-length dependent signal attenuation, due to absorption, of
ionization electrons by Oxygen [46]. At $\eta=0$ the ionization electrons
drift the full 250 cm to the readout chambers and, as a result, the signal is
spread out, due to diffusion, making threshold effects more prominent than for
tracks with $\eta=0.8$. At the same time, the sampled track length is longer
for track with $\eta=0.8$ than with $\eta=0$. The ${\rm d}E/{\rm d}x$
calibration is validated using pions in the Minimum Ionizing Particle (MIP)
regime and electrons in the Fermi Plateau region. A clean sample of MIP pions
is selected via tracks with momenta $0.4<p<0.6\text{\,GeV/$c$}$ and energy
loss $0.8<({\rm d}E/{\rm d}x)/\langle{\rm d}E/{\rm d}x\rangle_{\rm MIP}<1.2$.
A clean electron sample is obtained in the same momentum range via centrality
dependent ${\rm d}E/{\rm d}x$ cuts (as $S_{\sigma}$ depends on centrality) and
by rejecting kaons using Time-Of-Flight (TOF) information: $0.9<\beta_{\rm
TOF}<1.1$. For both samples it is found that the $\eta$-dependence of the
$\langle{\rm d}E/{\rm d}x\rangle$ is negligible. We note that one expects
these two classes of tracks to have different sensitivity to threshold
corrections. The result of the validation test for pp collisions is shown in
Fig. 3, which displays the $\langle{\rm d}E/{\rm d}x\rangle$ response as a
function of $\eta$ for electrons (upper panel) and pions (middle panel).

####  2.1.4 Division into homogenous samples

Figure 4: Number of clusters used in the ${\rm d}E/{\rm d}x$ calculation for
$p_{\rm{T}}>2\text{\,GeV/$c$}$ without (squares) and with (circles) the
geometric cut. Results are presented for $\rm pp$ (upper panel) and central
Pb–Pb (lower panel) collisions at $\sqrt{s_{\rm NN}}=$ 2.76 TeV. The minimum
number of clusters on a track is 70.

From studies of the transfer function, one expects a significant track-length
dependence. For the “stiff” high-$p_{\rm{T}}$ tracks used in this analysis,
the track-length in the transverse bending plane is rather similar, but there
is a significant $\eta$ dependence and the effect of this on the ${\rm
d}E/{\rm d}x$ resolution is visible in Fig. 3 for the pion MIPs. This
motivates performing the analysis in $|\eta|$ intervals: $|\eta|<0.2$,
$0.2\leq|\eta|<0.4$, $0.4\leq|\eta|<0.6$ and $0.6\leq|\eta|<0.8$ and then
combining the results.

Furthermore, tracks close to and/or crossing the TPC sector boundaries have
significantly fewer clusters assigned. Because the analyzed tracks are
“stiff”, those tracks close to the sector boundaries can be easily rejected
using a geometric cut in the azimuthal track angle $\varphi$, which excludes
approximately 10% of the tracks for $p_{\rm{T}}>6\text{\,GeV/$c$}$. Figure 4
shows the effect of the geometric cut on the distribution of the number of
clusters per track. The cases before and after the $\varphi$ cut are shown for
$\rm pp$ (upper panel) and central Pb–Pb (lower panel) collisions. The large
difference between the distributions for $\rm pp$ and central Pb–Pb is an
occupancy effect and essentially independent of $p_{\rm{T}}$. The cut
significantly improves the ${\rm d}E/{\rm d}x$ performance by rejecting tracks
with less information (fewer clusters) in regions where the calibration is
more sensitive to complex edge behaviors that can have larger effects on
“stiff” tracks. This also simplifies the analysis because in each $|\eta|$
interval, a single resolution parameter is sufficient to describe individual
particles species (e.g., all pions) in a given momentum bin.

####  2.1.5 Obtaining the high-$p_{\rm{T}}$ yields

Figure 5: (Color online) Four-Gaussian fits (line) to the ${\rm d}E/{\rm d}x$
spectra (markers) for tracks having momentum in the range
3.4–$3.6\text{\,GeV/$c$}$ (upper figure) and 8.0–$9.0\text{\,GeV/$c$}$ (lower
figure) with $|\eta|<0.2$. In each panel, the signals of pions (rightmost
Gaussian), kaons, and protons (leftmost Gaussian) are shown as red, green, and
blue dashed areas, respectively. The contribution of electrons is small
($<1\%$) and therefore not visible in the figure. Results for all six Pb–Pb
centrality classes are presented. The ${\rm d}E/{\rm d}x$ spectra have all
been normalized to have unit integrals.

Since, as already mentioned, the event and track selection scheme is identical
to the one used for the inclusive charged particle spectra [16], and each
charged track has an associated TPC ${\rm d}E/{\rm d}x$ measurement, the
charged pion, kaon, and (anti)proton yields measured in this analysis are
normalized to the inclusive charged particle spectra 111The $\varphi$ cut
described in Sec. 2.1.4 was not applied in the inclusive charged particle
analysis, but as this cut is a geometric cut it is independent of particle
species type and therefore does not affect this normalization.. This
highlights the unique direct correspondence between the two analyses and
guarantees that the results are fully consistent even at the level of
statistical uncertainties. The analysis of the ${\rm d}E/{\rm d}x$ spectra is
therefore aimed at extracting the relative yields of $\pi^{\pm},\rm
K^{\pm},\text{and }\rm p(\bar{p})$, referred to as the particle fractions in
the following.

In a narrow momentum and $|\eta|$ interval, the ${\rm d}E/{\rm d}x$
distribution can be described by a sum of four Gaussians ($\pi$, ${\rm K}$,
$p$, and $e$), see e.g. Fig. 5, and the requirements for the analysis to be
able to extract the yields with high precision is that the means and widths of
the Gaussians are constrained. Additional external track samples such as
protons from $\Lambda$ decays are used to obtain the constraints. The method
presented in the following has been benchmarked using Monte Carlo (MC)
simulations and the closure tests, comparing reconstructed output with
generated input, for all yields show less than 2% systematic deviations. From
studies comparing test beam data results with the ALICE specific MC
implementation of the energy-loss in the TPC, the MC is known to be precise
and to take into account all important detector effects [50], with the limit
that the test beam data was recorded under controlled conditions (fixed track
topology and large gas gain) and that ion tail effects are not included in the
MC simulations.

####  2.1.6 Measurement of the TPC response: parameterization of the
Bethe–Bloch and resolution curves

The first step of the analysis is to extract the response parameterizations
used to constrain the fits. The Bethe–Bloch curve is parameterized as follows:

$\left\langle\frac{{\rm d}E}{{\rm
d}x}\right\rangle=a\left[\frac{1+(\beta\gamma)^{2}}{(\beta\gamma)^{2}}\right]^{e}+\frac{b}{c}\log\left[\frac{(1+\beta\gamma)^{c}}{1+d^{\prime}(1+\beta\gamma)^{c}}\right],$
(2)

where $a,b,c,d$, and $e$ are free parameters (the variable $d^{\prime}$ is
used to simplify the expression and is defined as $d^{\prime}=\exp[c(a-d)/b]$
where $d$ is the $\langle{\rm d}E/{\rm d}x\rangle$ in the Fermi Plateau
regime, $\beta\gamma\gtrsim 1000$).

For $d^{\prime}\ll 1$, as is the case here, the parameterization has a simple
behavior in different regions of $\beta\gamma$. For small $\beta\gamma$,
$\beta\gamma\ll 3$–$4$, $\left\langle\frac{{\rm d}E}{{\rm
d}x}\right\rangle\approx\frac{a}{(\beta\gamma)^{2e}}$ , while on the
logarithmic rise: $\left\langle\frac{{\rm d}E}{{\rm d}x}\right\rangle\approx
a+b\log\left(1+\beta\gamma\right)$. The parameterization has been motivated by
demanding this behavior in the discussed $\beta\gamma$ limits, while at the
same time requiring that each parameter has a clear meaning. It uses
$1+\beta\gamma$ to ensure that the logarithmic term is always positive.

The relative resolution, $\sigma/\langle{\rm d}E/{\rm d}x\rangle$, as a
function of $\langle{\rm d}E/{\rm d}x\rangle$ is parameterized with a second-
degree polynomial, which was found to describe the data well:

$\sigma/\langle{\rm d}E/{\rm d}x\rangle=a_{0}+a_{1}\langle{\rm d}E/{\rm
d}x\rangle+a_{2}\langle{\rm d}E/{\rm d}x\rangle^{2}.$ (3)

The TPC response (Bethe–Bloch and resolution curves) is determined for each
$\eta$ region. Due to the deterioration of the TPC ${\rm d}E/{\rm d}x$
performance with increasing multiplicity, the curves differ significantly and
have to be extracted separately for $\rm pp$ and each Pb–Pb centrality class.

Figure 6: (Color online) ${\rm d}E/{\rm d}x$ spectra for secondary pions (top
panel) and protons (bottom panel) identified via the reconstruction of the
weak decay topology of ${\rm K_{S}^{0}}$ and $\Lambda$, respectively. A narrow
invariant-mass cut reducing statistics was applied to select clean samples
(but the pion sample still contains a small visible proton background). The
curves are single Gaussian fits to the data and the reduced $\chi^{2}$ is
calculated in the range indicated by the fit curves only. Figure 7: (Color
online) ${\rm d}E/{\rm d}x$ spectra for secondary pions (open triangles) and
protons (full circles) identified via the reconstruction of the weak decay
topology of ${\rm K_{S}^{0}}$ and $\Lambda$, respectively. The spectra have
been normalized to have the same integrals. The spectrum for primary pions
(full triangles) is obtained by requiring $\beta_{\rm TOF}>1$. Results for
peripheral (upper panel) and central (lower panel) Pb–Pb collisions are shown.
The tracks were chosen in the momentum (pseudorapidity) interval
$5<p<7\text{\,GeV/$c$}$ ($0.6\leq|\eta|<0.8$). Note that most spectra also
contain a well-understood background.

The parameters $a,b,d,$ and $e$ are well determined using external PID
information. Secondary pion (proton) tracks identified via the reconstruction
of the weak decay topology of ${\rm K_{S}^{0}}$ ($\Lambda$) and data samples
with TOF enhanced ($\beta_{\rm TOF}>1$) primary pions are used. The $V^{0}$
selection used in this analysis is similar to the one used in the dedicated
analysis [51]. To verify that the ${\rm d}E/{\rm d}x$ response is Gaussian,
narrow invariant-mass cuts were applied to $\rm pp$ data where the $V^{0}$
reconstruction is cleanest. Figure 6 shows single Gaussian fits to the pion
and proton peaks for such data and we note that the reduced $\chi^{2}$ value
is in the expected range for a valid fit model. In the following,
$10\text{\,MeV/$c^{2}$}$ wide invariant-mass cuts around the peaks was used to
select signal and reject background as a compromise between statistics and
purity. Using this information, the Bethe–Bloch function is constrained in the
$\beta\gamma$ interval of 3–60. Figure 7 shows examples of the TPC ${\rm
d}E/{\rm d}x$ spectra for these samples in the momentum ($\eta$) range:
5–$7\text{\,GeV/$c$}$ ($0.6\leq|\eta|<0.8$) for the most central and most
peripheral Pb–Pb collisions analyzed. In this case, the proton candidate
samples from the $\Lambda$ decay are not pure samples, and have some
contamination of pions since the invariant mass peak region still contains
considerable combinatorial background. This contamination is seen in the
asymmetry towards the higher value of ${\rm d}E/{\rm d}x$ in the proton
sample. In the case of the pion samples from the $K_{S}^{0}$ decay, proton
contamination creates the asymmetry towards the lower value of ${\rm d}E/{\rm
d}x$ in the spectra. Hence, in these cases, to obtain the mean ${\rm d}E/{\rm
d}x$ and resolution for each particle species, the asymmetric tail of the
Gaussians were not considered.
The Fermi Plateau is fixed using electron-positron pairs from photon
conversions (a photon conversion is reconstructed similar to a V0 decay and
identified from the low invariant mass). The same information is used to
measure the ${\rm d}E/{\rm d}x$ resolution as a function of $\langle{\rm
d}E/{\rm d}x\rangle$. The relative resolution around the MIP222The resolution
depends on centrality and track length and is worse in central events and for
smaller $|\eta|$. is ${\approx}5.5$–$7.5\%$ and improves with increasing
$\langle{\rm d}E/{\rm d}x\rangle$ (primary ionization) in the relativistic
rise region to ${\approx}4.5$–$5.5\%$. These data samples are henceforth
referred to as the external PID data.

In the relativistic rise region, the analysis is very stable because in this
region $\langle{\rm d}E/{\rm d}x\rangle\approx a+b\log{\beta\gamma}$, so the
${\rm d}E/{\rm d}x$ separation between particle species, e.g., protons and
pions, is constant: $\langle{\rm d}E/{\rm d}x\rangle_{\rm p}-\langle{\rm
d}E/{\rm d}x\rangle_{\pi}\approx a+b\log(p/m_{\rm
p})-(a+b\log(p/m_{\pi}))\approx b\log(m_{\pi}/m_{\rm p})$. So as long as all
particle species are in this $\beta\gamma$ regime a simple extrapolation can
be applied. For $\beta\gamma\gtrsim 100$ the pions ($p\gtrsim
14\text{\,GeV/$c$}$) start to approach the Fermi Plateau region and the
$\langle{\rm d}E/{\rm d}x\rangle$ dependence on $\beta\gamma$ is more complex.
To address this, a two dimensional fit to the ${\rm d}E/{\rm d}x$ vs $p$
distribution is performed. All the parameters of the resolution function and
the parameters $a,b,d,$ and $e$ of Eq. 2 are fixed. The parameter $c$ and the
yields of $\pi^{+}+\pi^{-}$, ${\rm K}^{+}+{\rm K}^{-}$ and ${\rm
p}+{\rm\bar{p}}$ in different momentum intervals are free parameters. This fit
method works fine if the corrections to the logarithmic rise, due to the
transition to the Plateau, are small, which restricts the current analysis to
$p_{\rm{T}}<20\text{\,GeV/$c$}$. With higher statistics and the use of cosmic
muons as additional constraints, we expect to be able to extend the method up
to $50\text{\,GeV/$c$}$.

There is a final subtle point that should be mentioned here. The systematic
uncertainty on the yields from the ${\rm d}E/{\rm d}x$ method alone is rather
large for particles with ionization energy loss close to 1 MIP, but additional
information from other analyses can be used to constrain the results. One
would like to avoid using the actual lower $p_{\rm{T}}$ $\pi^{\pm},\rm
K^{\pm},\text{and }\rm p(\bar{p})$ measurements, as this will introduce a
direct bias in the final combined spectra (Sec. 3). Instead, the neutral kaon
yields are used to constrain the charged kaons in Pb–Pb collisions333The
assumption is that the invariant $p_{\rm{T}}$ spectra are the same. The
charged kaon fraction ($f_{{\rm K}^{+}+{\rm K}^{-}}$) is obtained working
backwards through Eq. 5 and Eq.4.. The two dimensional fit is applied again,
but the parameter $e$, which mainly affects the proton $\langle{\rm d}E/{\rm
d}x\rangle$, is now allowed to vary while the other parameters, $a$–$d$, are
constrained and the charged kaon yield in the fit is also restricted to be
consistent with the neutral kaon yield (the pion and proton yields are free).
The effect of this refit is largest in central collisions at low $p_{\rm{T}}$
($<4\text{\,GeV/$c$}$) and decreases with centrality; at $3\text{\,GeV/$c$}$
the effect on the extracted kaon yield is 10% ($<1$%) for 0-5% (60-80%)
collision centrality.

Figure 8: (Color online) Final Bethe–Bloch (upper figure) and resolution (lower figure) curves obtained as described in the text. Results are shown for $\rm pp$ (left panels) and 0-5% Pb–Pb (right panels) collisions. The Bethe–Bloch curve is shown in the region relevant for pions, kaons, and protons in this analysis. The external PID data samples of pions, protons and electrons are used to obtain the parameterizations, these data are plotted as markers. The shaded areas represent the systematic uncertainty of the parameterizations. Parameter | Pb–Pb 0-5% | Pb–Pb 60-80% | $\rm pp$
---|---|---|---
$a$ | 33.9–35.4 | 32.9–33.1 | 32.5–33.3
$b$ | 7.66–7.89 | 8.58–9.01 | 8.52–8.77
$c$ | 2.18–7.18 | 1.25–2.38 | 1.65–43.0
$d$ | 78.0–78.5 | 80.0–80.6 | 80.6–80.7
$e$ | 1.22–1.30 | 1.37–1.39 | 1.43–1.55
Table 1:  Parameters obtained for the Bethe–Bloch function (Eq. 2) for central
and peripheral Pb–Pb collisions and $\rm pp$ collisions. Results are given as
the range found for the four $|\eta|$ intervals.

Figure 8 shows the final parameterizations of the Bethe–Bloch and resolution
curves for $\rm pp$ and the most central Pb–Pb collisions. The values obtained
for the external PID data are also shown. Table 1 shows the values of the
parameters of Eq. 2 for different centrality classes and $\rm pp$ collisions.
All parameters except $c$ are close for the four $|\eta|$ intervals and
similar across systems. As previously mentioned, the parameter $c$ is related
to the transition in the logarithmic rise to the Plateau and the large
difference mainly reflects that the parameter is statistically not well
constrained for some of the datasets. For the $\rm pp$ dataset, where the
largest variation is observed, we obtain similar results within statistical
uncertainties if $c=2$ is used for all $|\eta|$-slices .

The separation power, $S_{\sigma}$, obtained with the final parameterizations
for $\rm pp$, 0-5% Pb–Pb, and 40-60% Pb–Pb collisions are shown in Fig. 2. As
expected, the performance is the best for low multiplicity events and
decreases as the multiplicity increases and the separation is better for the
longest tracks ($0.6\leq|\eta|<0.8$). For $p>6.0\text{\,GeV/$c$}$ the
$S_{\sigma}$ separation is nearly constant as expected because of the
logarithmic relativistic rise (as $\sigma\propto\langle{\rm d}E/{\rm
d}x\rangle$ a small decrease of the separation is observed). The separation
power plays an important role in the determination of the systematic
uncertainties described in Sec. 2.1.9.

####  2.1.7 Extraction of the particle fractions

All the following results are for the sum of positive and negative pions,
kaons, and protons. Positive and negative yields were found to be comparable
at the 5% level or better for all six centrality classes and $\rm pp$
collisions.

Having determined the Bethe–Bloch and resolution curves as described in the
previous section, it is now straightforward to fit the ${\rm d}E/{\rm d}x$
spectra using the sum of four Gaussian distributions for pions, kaons,
protons, and electrons. For each momentum interval, the $\langle{\rm d}E/{\rm
d}x\rangle$ position and width of each Gaussian are fixed. Figure 5 shows
examples of these fits for the momentum intervals 3.4–$3.6\text{\,GeV/$c$}$
and 8–$9\text{\,GeV/$c$}$. The electrons are hardly visible in any of the fits
as the yield is below 1% of the total. For $p_{\rm{T}}>10\text{\,GeV/$c$}$, it
is no longer possible to separate electrons from pions, and the relative
fraction of electrons is assumed to remain constant above this $p_{\rm{T}}$.
There is a small contamination of primary muons in the pions due to the
similar mass (and therefor similar $\langle{\rm d}E/{\rm d}x\rangle$).
High-$p_{\rm{T}}$ muons are predominantly the result of semi-leptonic decays
of hadrons containing heavy quarks and for those decays one expects muon and
electron branching ratios to be similar, so the electron yield (fraction) is
subtracted from the pions to correct for the muon contamination. This
correction changes the pion yield by less than 1% in the full $p_{\rm{T}}$
range in agreement with MC simulations based on the PYTHIA generator [52].
Since this ${\rm d}E/{\rm d}x$ analysis is not optimized for electrons and the
contamination is extrapolated to high $p_{\rm{T}}$, half of the correction is
assigned as a systematic uncertainty. The contamination of (anti)deuterons in
the (anti)proton sample is negligible ($<1\%$).

Figure 9: (Color online) Uncorrected particle fractions as a function of
momentum (upper figure) and as a function of $p_{\rm{T}}$ (lower figure) for
$|\eta|<0.2$ (full markers) and $0.6\leq|\eta|<0.8$ (empty markers). Charged
pions, kaons, and (anti)protons are plotted with circles, squares, and
triangles, respectively. The error bars indicate the statistical uncertainty.
Results for six centrality classes are presented.

The particle fractions, i.e., the contribution of charged pions
($f^{\prime}_{\pi^{+}+\pi^{-}}$), kaons ($f^{\prime}_{{\rm K}^{+}+{\rm
K}^{-}}$), and (anti)protons ($f^{\prime}_{{\rm p}+{\rm\bar{p}}}$) to the
yield of inclusive charged particles, obtained as a function of momentum, are
plotted in Fig. 9 (upper figure) as a function of centrality for the two
extreme $|\eta|$ intervals. One observes a significant $\eta$ dependence of
pion and proton fractions for $p<10\text{\,GeV/$c$}$.

The extracted fractions as a function of transverse momentum are obtained bin-
by-bin using a weighting procedure

$f_{\rm id}(\langle p_{\rm{T}}\rangle_{i})=\sum_{j}f^{\prime}_{\rm id}(\langle
p\rangle_{j}){\rm R}(\langle p\rangle_{i},\langle p_{\rm{T}}\rangle_{j}),$ (4)

where $f_{\rm id}$ ($f^{\prime}_{\rm id}$) is given in bins of $p_{\rm{T}}$
($p$) and $\rm R$ is a response matrix reflecting the relation between $p$ and
$p_{\rm{T}}$ bins. This averaging introduces some smoothing of the fractions
as neighboring $p_{\rm{T}}$ fractions have contributions from the same $p$
fractions, but the analysis is done in narrow $|\eta|$ intervals so only a few
momentum bins contribute and the fractions depend only weakly on $p$;
therefore, we consider the systematic effect of this procedure negligible. The
fractions $f_{\rm id}$ are shown in the lower panel of Fig. 9. The
transformation has little effect for $|\eta|<0.2$, as expected, but we now
observe that for $0.6\leq|\eta|<0.8$ the results are consistent with particle
ratios being constant at midrapidity. We find that all four pseudo-rapidity
intervals are consistent and the final fractions used to obtain the spectra in
the next section are computed as the weighted average of the four
pseudorapidity intervals.

####  2.1.8 Spectra

The invariant yields are obtained from the particle fractions using the
relation

$\frac{{\rm d}^{2}N_{\rm id}}{{\rm d}p_{\rm{T}}{\rm d}y}={\rm J}_{\rm
id}\frac{\epsilon_{\rm ch}}{\epsilon_{\rm id}}f_{\rm id}\times\frac{{\rm
d}^{2}N_{\rm ch}}{{\rm d}p_{\rm{T}}{\rm d}\eta}.$ (5)

The first expression on the right hand side is the input from the PID
analysis, where ($\epsilon_{\rm ch}$) $\epsilon_{\rm id}$ is the efficiency
for (inclusive) identified charged particles and ${\rm J}_{\rm id}$ is the
Jacobian correction (from pseudorapidity $\eta$ to rapidity $y$) and $f_{\rm
id}$ is the fractional yield. The second expression is the fully corrected
transverse momentum spectrum of inclusive charged particles that has already
been published by ALICE [16].

The relative efficiency correction, $\epsilon_{\rm ch}/\epsilon_{\rm id}$, was
found to be consistent within $\pm 3\%$ for all centrality classes and $\rm
pp$ collisions, and for event generators: PYTHIA [52], PHOJET [53], and HIJING
[54]. Thus, an average correction was used and a systematic uncertainty of 3%
was assigned. At high $p_{\rm{T}}$ the correction is nearly constant and on
the order of 0.95. It is below 1 because the inclusive charged particle
spectra contain weakly decaying baryons such as $\Sigma^{+}$ that are not
reconstructed with the charged particle selection for primary particles. The
proton and pion spectra have been corrected for feed-down from weak decays
using MC simulations for the relative fraction of secondaries scaled to those
extracted from Distance-of-Closest-Approach MC template fits to data [44]. For
$p_{\rm{T}}$ $\approx$ 2 (3) GeV/$c$, the correction is approximately 0.3%
($4$%) for the pion (proton) yield and decreasing with increasing
$p_{\rm{T}}$. Scaling between data and MC has a limited precision and could be
different at higher $p_{\rm{T}}$. To be conservative, half of the correction
is therefore assigned as a systematic uncertainty. This contribution to the
systematic uncertainty is still small, as shown in Table 2.

Figure 10: (Color online) Correction factors as a function of $p_{\rm{T}}$.
These are applied to the fractions of pions (left panels), kaons (middle
panels), and protons (right panels). Results are presented for peripheral
(upper figure) and central (lower figure) Pb–Pb collisions. The correction to
the pion fraction due to the muon contamination is not drawn, but is $\leq
1\%$. Only pions and protons are corrected for feed-down.

The efficiency and feed-down corrections are plotted in Fig. 10 as a function
of $p_{\rm{T}}$ for central and peripheral Pb–Pb collisions. The Jacobian
correction from $\eta$ to $y$, which has to be included for the lower
$p_{\rm{T}}$ bins, is also shown and the largest effect is observed for
protons, as expected. At $p_{\rm{T}}$ $\approx 3\text{\,GeV/$c$}$, the
correction is ${\approx}5\%$, ${\approx}1\%$, and ${\ll}1$% for protons,
kaons, and pions, respectively.

####  2.1.9 Systematic uncertainties

The systematic uncertainty on the invariant yields has three main components:
event and track selection, efficiency correction of the fractions, and the
fraction extraction. Contributions from the event and track selection are
taken directly from the inclusive charged particle result [16]. The systematic
uncertainties for the corrections have been covered in the previous sections
and are summarized in Table 2.

Figure 11: (Color online) Upper figure: Relative variation of the width
parameterizations with respect to the measured values in different ${\rm
d}E/{\rm d}x/\langle{\rm d}E/{\rm d}x_{\rm MIP}\rangle$ intervals. Lower
figure: Relative variation of the Bethe–Bloch $\langle{\rm d}E/{\rm
d}x\rangle$ parameterization with respect to the measured values in different
${\rm d}E/{\rm d}x/\langle{\rm d}E/{\rm d}x_{\rm MIP}\rangle$ intervals. The
distributions were constructed using all the available data, six centrality
classes and $\rm pp$ collisions with four sub-samples ($|\eta|$ intervals)
each.

The systematic uncertainty on the fractions is mainly due to the uncertainties
in the parameterization of the Bethe–Bloch and resolution curves used to
constrain the fits. This systematic uncertainty can be due to calibration
effects such that, for example, the $\langle{\rm d}E/{\rm d}x\rangle$ does not
depend on $\beta\gamma$ alone, it can be related to the parameterizations not
being able to describe the data properly, or it can be due to the statistical
precision of the external PID data sets. To evaluate the uncertainty due to
these effects, the deviation of the fitted curves from the actual measured
means and widths of the ${\rm d}E/{\rm d}x$ spectra obtained from the analysis
of the external pion, proton, and electron samples are used. Figure 11 shows
the relative variations; all the available data were used for constructing the
distributions, i.e., each of the six centrality classes and $\rm pp$
collisions have four sub-samples of tracks at different $|\eta|$. It was found
that the precision of all these data sets is similar, so the final variation
in systematic uncertainties for the same observable for different centrality
classes and $\rm pp$ collisions is caused by the different separation power
shown in Fig. 2. The results for the width (Fig. 11 upper panel) are shown for
$\rm p+\bar{p}$, $\pi^{+}+\pi^{-}$, and $e^{+}+e^{-}$, corresponding to the
different samples and covering different $\langle{\rm d}E/{\rm
d}x\rangle/\langle{\rm d}E/{\rm d}x_{\rm MIP}\rangle$ ranges. In a given
$\langle{\rm d}E/{\rm d}x\rangle/\langle{\rm d}E/{\rm d}x_{\rm MIP}\rangle$
interval, the standard deviation of the distribution was taken as the
systematic uncertainty associated with the extraction of the widths. An
analogous analysis was done for the Bethe–Bloch curve, an example of which is
shown in the lower panel of Fig. 11.

In peripheral collisions, an additional contribution originating from the
statistical uncertainty in the fits to the external PID data has to be taken
into account for the Bethe–Bloch curve. The total systematic uncertainty is
assigned as the quadratic sum of both contributions and is the band shown
around the parameterizations in Fig. 8.

Figure 12:  (Color online). An example of the systematic uncertainty
estimation in 0-5% Pb–Pb and $\rm pp$ collisions for $3.4<p\leq
3.6\text{\,GeV/$c$}$. Upper figure: From left to right: the variation of
extracted fractional yields for pions (left panel), kaons (middle panel), and
protons (right panel) when the fixed values for the $\langle{\rm d}E/{\rm
d}x\rangle$ and the resolution are randomly varied. Lower figure: the
corresponding variation of the particle ratios.

The propagation of the uncertainties to the particle fractions is done by
refitting the ${\rm d}E/{\rm d}x$ spectra, while randomly varying the
constrained parameters, $\langle{\rm d}E/{\rm d}x\rangle$ and $\sigma$, within
the uncertainty for the parameterizations assuming a Gaussian variation
centered at the nominal value. For each $p_{\rm{T}}$ bin, all the $\langle{\rm
d}E/{\rm d}x\rangle$ and $\sigma$ values are randomly varied and refitted 1000
times resulting in fraction distributions like those shown in Fig. 12. The
systematic uncertainties assigned to the particle fractions are the standard
deviation of the associated distributions. By using the same method for the
particle ratios (Fig. 12 lower panel), the correlation in the fit between the
extracted yields for the two different particle species are directly taken
into account. At high $p_{\rm{T}}$, the variation becomes dominated by
statistical fluctuations due to the limited amount of data. But, as the
fractions are nearly constant there (see Fig. 9) and the separation is also
nearly constant (see Fig. 2), a constant absolute systematic uncertainty is
assigned for $p_{\rm{T}}>8\text{\,GeV/$c$}$.

A summary of the different contributions to the systematic uncertainty is
shown in Table 2 for all centrality classes and for two representative
$p_{\rm{T}}$ regions. For pions, the dominant contribution comes from the
event and track selection, which amounts to 7–8% over the whole $p_{\rm{T}}$
range while the PID systematic uncertainty stays between 1–2%. For kaons and
protons, the PID systematic uncertainty is the largest. The systematic
uncertainty decreases with increasing separation and is smaller where the
fractions are larger, see Fig. 9. For protons at
$p_{\rm{T}}=3\text{\,GeV/$c$}$, the two effects largely compensate (the
fractional yields increase for more central collisions) to keep the systematic
uncertainty nearly constant. For kaons, at the same $p_{\rm{T}}$, there is a
strong centrality dependence because the fractional yields also are lower for
more central collisions. For the lower multiplicity intervals ($\rm pp$ and
60-80% centrality) this trend is broken because of the significant statistical
uncertainty in the parameterized curves.

At high $p_{\rm{T}}$ (${\approx}10\text{\,GeV/$c$}$) the PID systematic
uncertainty for kaons stays between 7–8% for Pb–Pb collisions and is around 5%
for $\rm pp$ collisions. For protons, the contribution is 16–20% (except for
60-80% Pb–Pb collisions where it is 29% due to a much larger statistical
uncertainty in the fits to the external PID data).

|  $\pi^{+}+\pi^{-}$ |  ${\rm K^{+}+K^{-}}$ |  ${\rm p+\bar{p}}$ |  $\rm K/\pi$ |  $\rm p/\pi$
---|---|---|---|---|---
$p_{\rm{T}}$ (GeV/$c$) | 2.0 | 10 | 3.0 | 10 | 3.0 | 10 | 3.0 | 10 | 3.0 | 10
Pb–Pb collisions (0-5%)
(a) | 8.4% | 8.1% | 8.2% | 8.1% | 8.2% | 8.1% | -
(b) |  $<0.1$% | - | 2.1% | 1.5% |  $<0.1$% | 2.1% | 1.5%
(c) | 0.1% | 1.7% | - | 0.6% | 1.7% | 0.6% | 1.7%
(d) | 1.5% | 2.2% | 18% | 8.4% | 9.8% | 17% | 22% | 10% | 11% | 16%
Pb–Pb collisions (5-10%)
(a) | 8.4% | 8.2% | 8.2% | 8.2% | 8.2% | 8.2% | -
(b) |  $<0.1$% | - | 2.1% | 1.5% |  $<0.1$% | 2.1% | 1.5%
(c) | 0.2% | 1.5% | - | 0.6% | 1.5% | 0.6% | 1.5%
(d) | 1.4% | 2.2% | 16% | 8.0% | 9.5% | 16% | 18% | 10% | 9.8% | 15%
Pb–Pb collisions (10-20%)
(a) | 8.3% | 8.1% | 8.2% | 8.1% | 8.2% | 8.1% | -
(b) |  $<0.1$% | - | 2.2% | 1.8% |  $<0.1$% | 2.2% | 1.8%
(c) | 0.3% | 1.3% | - | 0.6% | 1.3% | 0.6% | 1.3%
(d) | 1.5% | 2.3% | 16% | 8.9% | 10% | 20% | 16% | 11% | 9.2% | 18%
Pb–Pb collisions (20-40%)
(a) | 8.4% | 8.2% | 8.2% | 8.2% | 8.2% | 8.2% | -
(b) |  $<0.1$% | - | 2.1% | 1.6% |  $<0.1$% | 2.1% | 1.6%
(c) | 0.2% | 1.3% | - | 0.5% | 1.3% | 0.5% | 1.3%
(d) | 1.5% | 2.2% | 15% | 8.4% | 10% | 17% | 16% | 11% | 10% | 17%
Pb–Pb collisions (40-60%)
(a) | 8.7% | 8.5% | 8.6% | 8.5% | 8.6% | 8.5% | -
(b) |  $<0.1$% | - | 1.9% | 1.6% |  $<0.1$% | 1.9% | 1.6%
(c) | 0.3% | 1.1% | - | 0.5% | 1.1% | 0.5% | 1.1%
(d) | 1.4% | 2.1% | 14% | 8.0% | 11% | 17% | 15% | 10% | 11% | 17%
Pb–Pb collisions (60-80%)
(a) | 10% | 9.7% | 9.8% | 9.7% | 9.8% | 9.7% | -
(b) |  $\leq 0.1$% | - | 2.0% | 1.8% |  $\leq 0.1$% | 2.0% | 1.8%
(c) | 0.3% | 0.8% | - | 0.4% | 0.8% | 0.4% | 0.8%
(d) | 1.4% | 2.4% | 16% | 7.1% | 20% | 29% | 16% | 8.9% | 18% | 22%
pp collisions
(a) | 7.4% | 7.6% | 7.4% | 7.6% | 7.4% | 7.6% | -
(b) |  $\leq 0.1$% | - | 2.0% | 1.8% |  $\leq 0.1$% | 2.0% | 1.8%
(c) | 0.4% | 0.6% | - | 0.5% | 0.6% | 0.5% | 0.6%
(d) | 1.1% | 1.7% | 16% | 5.7% | 24% | 17% | 16% | 6.8% | 25% | 13%
(e) | 3.0% | 4.2%
Table 2:  Summary of the systematic uncertainties for the charged pion, kaon,
and (anti)proton spectra and for the particle ratios. The different
contributions are (a) event and track selection, (b) feed-down correction, (c)
correction for muons, (d) parameterization of Bethe–Bloch and resolution
curves, and (e) efficiency correction (same for all systems). Note that ${\rm
K}/\pi=({\rm K^{+}+K^{-}})/(\pi^{+}+\pi^{-})$ and ${\rm p}/\pi=({\rm
p+\bar{p}})/(\pi^{+}+\pi^{-})$.

###  2.2 HMPID analysis of Pb-Pb data

Figure 13: Cherenkov angle measured in the HMPID as a function of the momentum
$p$ in 0-10% central Pb–Pb collisions. The solid lines represent the
theoretical curves for each particle species. The $z$-axis indicated by the
color scale is logarithmic.

The HMPID is used in order to constrain the uncertainty of the charged pion,
kaon, and (anti)proton measurements in the transition region between the TOF
and TPC relativistic rise methods (in the region around
$p_{\rm{T}}=3\text{\,GeV/$c$}$). Thus, it both improves the precision of the
measurement and validates the other methods in the region where they have the
worst PID separation.

The HMPID [55] detector consists of seven identical proximity focusing RICH
(Ring Imaging Cherenkov) counters. Photon and charged particle detection is
provided by a Multi-Wire Proportional Chamber (MWPC) coupled to a CsI
photocathode segmented into pads of size $0.8{\times}0.84$ cm2 (the
probability to obtain an amplified signals for an incident photon, the quantum
efficiency, is $\approx$ 25% for $\lambda_{\rm{ph}}$ = 175 nm). The
amplification gas is CH4 at atmospheric pressure with an anode-cathode gap of
2 mm; the operational voltage is 2050 V corresponding to a gain of
${\approx}4\times$104. It is located at about 5 m from the beam axis, covering
a limited acceptance of $|\eta|<0.5$ and $1.2^{\circ}<\varphi<58.5^{\circ}$.

The HMPID analysis uses the 2011 Pb–Pb data with around $7.8\times 10^{6}$
central triggered events (0-10% centrality) and $5\times 10^{6}$ semi-central
triggered events (10-50% centrality444To match centrality classes with the
high-$p_{\rm{T}}$ analysis only spectra for 0-40% will be shown in this paper.
Results for 20-30%, 30-40%, and 40-50% are available on HepData.). The event
and track selection is similar to the one described in Sec. 2.1.1, but in
addition it is required that the tracks are propagated and matched to a
primary ionization cluster in the MWPC gap of the HMPID detector (denoted
matched cluster in the following). The matching efficiency, including spurious
matches, is ${\approx}95\%$ (see $\varepsilon_{\text{match}}$ below). The
matching criteria are tightened to reject the fake cluster-track matches,
which account for ${\approx}30$–$40\%$ (see $C_{\text{distance}}$ later), so
that only tracks matched with their corresponding primary ionization cluster
are identified. The PID in the HMPID is done by measuring the Cherenkov angle,
$\theta_{\rm{Ch}}$ [55], given by

$\cos\theta_{\rm{Ch}}=\frac{1}{n\beta}\Rightarrow\theta_{\rm{Ch}}=\arccos\left(\frac{\sqrt{p^{2}+m^{2}}}{np}\right),$
(6)

where $n$ is the refractive index of the radiator used (liquid C6F14 with $n$
= 1.29 at temperature $T=20\,^{\circ}\text{C}$ for photons with energy 6.68
eV). Figure 13 shows the Cherenkov angle as a function of the momentum for
central Pb–Pb collisions.

The measurement of the single photon $\theta_{\rm{Ch}}$ angle in the HMPID
requires knowledge of the track impact position and angle. These are estimated
from the track extrapolation from the central tracking devices up to the
radiator volume, where the Cherenkov photons are emitted. Only one matched
cluster is associated to each extrapolated track, selected as the closest
cluster to the extrapolated track point on the cathode plane, with a charge
above ${\approx}120$ ADC. The cut on the charge excludes clusters from
electronic noise ($\sigma_{pedestal}\approx 1$ ADC) and photons. The matching
efficiency is defined for tracks extrapolated to the HMPID acceptance as

$\varepsilon_{\text{match}}=\frac{N(\text{Extrapolated with matched
cluster})}{N(\text{Extrapolated})}.$ (7)

This efficiency is ${\approx}95\%$ and independent of momentum, particle
species, and event multiplicity.

Figure 14: (Color online) Distribution of the $X$ (left panel) and $Y$ (right
panel) residuals between the matched cluster position and the closest
extrapolated track point at the HMPID chamber plane (HMPID module 2), for
positive and negative tracks with $p_{\rm{T}}>1.5\text{\,GeV/$c$}$ in Pb–Pb
collisions (0-50% centrality). The histograms have been scaled to have a
similar maximum value. The small shift between positive and negative tracks in
the $Y$ residuals is due to a radial residual misalignment and an imperfect
estimate of the energy loss in the material traversed by the track and is not
corrected for in the calculation of the residual distance.  Figure 15: (Color
online) The distance cut correction, $C_{\text{distance}}$, as a function of
$p_{\rm{T}}$ for positive (red) and negative (blue) tracks, respectively, in
Pb–Pb collisions (0-50% centrality).

In Fig. 14, the residuals distribution between the track extrapolation and the
matched cluster position in local chamber coordinates, $X$ and $Y$, for tracks
with $p_{\rm{T}}>1.5\text{\,GeV/$c$}$ is shown. The distributions have a
resolution of $\sigma_{res}\approx~{}2~{}\text{cm}$. To reject fake cluster-
match associations in the detector, mainly the situation when there is no
correct signal to match as for example the particle was absorbed or deflected
in the material between the TPC and the HMPID detector, a selection on the
distance, $\sqrt{X^{2}+Y^{2}}$, computed on the cathode plane between the
track extrapolation and the matched cluster is applied. This distance has to
be less than 5 cm. This represents the best compromise between the loss of
statistics and the probability of an incorrect association, where the latter
becomes negligible (${<}0.1\%$) even in the most central collisions, as
estimated from MC simulations. The distance cut leads to a correction factor

$C_{\text{distance}}=\frac{N(\text{Extrapolated with matched cluster distance
$<5$ cm})}{N(\text{Extrapolated with matched cluster})},$ (8)

for each momentum bin and does not depend on event multiplicity. Fig. 15 shows
this correction factor as a function of $p_{\rm{T}}$ for positive and negative
tracks integrated over the centrality classes (0-50%).

Figure 16: (Color online) Fit to the $\theta_{\rm{Ch}}$-distributions of pions
(upper panel) and protons (lower panel) obtained in MC simulations for two
different momentum bins. The histograms have been scaled to have a similar
maximum value.

Starting from the photon cluster coordinates on the photocathode, a back-
tracking algorithm calculates the corresponding emission angle. The Cherenkov
photons are selected by the Hough Transform Method (HTM) [56], which for each
track transforms the coordinates of photon hits into emission angles. The
angle interval with the most hit candidates is selected and $\theta_{\rm{Ch}}$
is computed as the weighted mean of the single photon angles. In central Pb–Pb
collisions, where the total number of signals in the HMPID chambers is large,
it is possible that the angle is constructed based on hits not corresponding
to the Cherenkov photons associated with the track. This results in a
significant reduction of the PID efficiency in the most central collisions.
Figure 16 gives an example of the same effect in MC simulations. The response
function consists of a Gaussian distribution for correctly assigned rings
(signal) plus a distribution strongly increasing with the Cherenkov angle for
incorrectly assigned rings (background). The signals from other tracks and
photons in the same event are uniformly distributed on the chamber plane, and
so the background rises with $\theta_{\rm{Ch}}$ since the probability of
finding background clusters increases. The background contribution decreases
with increasing track momentum because higher momentum tracks give rise to a
larger number of Cherenkov photons and have a smaller inclination angle,
producing rings that are more likely to be fully contained inside the
acceptance. As a result of this, the probability of incorrectly associating an
angle computed from background clusters to the track decreases. The shoulder
in the distribution starting at 0.7 rad is a boundary effect due to the finite
geometrical acceptance of the chamber.

Figure 17: (Color online) Distributions of the Cherenkov angle measured in the
HMPID for positive tracks having $p_{\rm{T}}$ in the range
2.6–$2.7\text{\,GeV/$c$}$ (upper figure) and in the range
3.8–$4.0\text{\,GeV/$c$}$ (lower figure), for six different centrality
classes, 0-5%, 5-10%, 10-20%, 20-30%, 30-40%, and 40-50%. The histograms have
been scaled to have a similar maximum value. The shoulder in the distributions
starting at 0.7 rad is a boundary effect due to the finite chamber geometrical
acceptance.

Figure 17 gives examples of the reconstructed Cherenkov angle distributions in
two narrow $p_{\rm{T}}$ intervals for different centrality classes; the
reconstructed angle distribution is fitted with a sum of three Gaussian
distributions, corresponding to the signals from pions, kaons, and protons,
plus a distribution associated with the misidentified tracks that is modeled
with a 6th-degree polynomial function that minimizes the reduced $\chi^{2}$ of
the fit.

Figure 18: (Color online) Mean Cherenkov angle (upper panel) and standard
deviation (lower panel) values for pions, kaons, and protons obtained by the
three-Gaussian fitting procedure as a function of $p_{\rm{T}}$ for 0-5% and
40-50% centrality Pb–Pb collisions. The data points from the two different
centrality classes overlap such that the difference is smaller than the size
of the symbols used. Figure 19: (Color online) Comparison of the mean
Cherenkov angle values obtained by the three-Gaussian fitting procedure and
those evaluated from the V0s study for pions (left panel) and protons (right
panel) in the most central Pb–Pb collisions.

The fitting is performed in 2 steps. In the first step, the initial parameters
are based on the expected values. For the signal, the means
$\langle\theta_{\rm{Ch}}\rangle_{i}$ are obtained from Eq. 6, tuning the
refractive index to match the observed Cherenkov angles, and the sigma values
$\sigma_{i}$ are taken from the MC distribution in the given transverse
momentum bin. The initial shape of the 6th-degree polynomial background is
taken from MC simulations. Furthermore, the signal parameters are constrained
to the ranges: [$\langle\theta_{\rm{Ch}}\rangle_{i}$ \-
$\sigma_{i}$,$\langle\theta_{\rm{Ch}}\rangle_{i}$ \+ $\sigma_{i}$] for the
means, and [$\sigma_{i}$ \- 0.1$\cdot\sigma_{i}$, $\sigma_{i}$ \+
0.1$\cdot\sigma_{i}$] for the widths. After this first step, the $p_{\rm{T}}$
dependence of each parameter is fitted with a continuous function. In the
second step, the fitting is repeated with only the yields as free parameters
and constraining the mean and sigma values to the continuous functions. The
means and widths constrained in this way are all found to be independent of
centrality as shown in Fig. 18 for 0-5% and 40-50% centrality classes. In Fig.
19, a comparison is shown between the mean values of the Cherenkov angle
obtained from the fitting procedure with those obtained using a clean sample
of protons and pions identified from $\Lambda$ and $\rm{K}^{0}_{S}$ decays.

Figure 20: (Color online) Identification efficiency for pions (upper panel)
and protons (lower panel) selected exploiting V0 decay properties, compared
with the MC results for primary tracks for 0-5% and 40-50% centrality classes.

To correct for the incorrectly assigned Cherenkov rings, a PID efficiency is
used. This efficiency has to be derived from a dataset containing identified
particles of a single species, so one can use MC or $V^{0}$ daughters. For
such a clean set of particles that passes the distance cut, e.g. MC pions as
in Fig. 16, the PID efficiency is

$\varepsilon_{\text{PID}}=\frac{N(\text{signal})}{N(\text{signal and
background})},$ (9)

where the signal is the integral of the Gaussian fit function. The PID
efficiency has been evaluated from MC simulations that reproduce the
background observed in the data well. A data-driven cross check of the
efficiency has been performed using a clean sample of $V^{0}$ daughter tracks.
The comparison between data and MC is shown in Fig. 20 for 0-5% and 40-50%
centrality classes, and shows good agreement. We also observe that, as
expected, the efficiency decreases for more central collisions due to the
occupancy effects mentioned above. The maximum value of the PID efficiency is
${\approx}80\%$ at $p_{\rm{T}}\sim 6\text{\,GeV/$c$}$ in the 40-50% centrality
class. As an additional check of the PID efficiency, the ratio between the raw
yields extracted from the fit (signal) corrected by the PID efficiency and the
total entries in the original histogram (signal and background) has been
evaluated for each $p_{\rm{T}}$ bin for all centralities. The ratio is
consistent with unity when the systematic uncertainties listed in Table 3 are
taken into account.

The systematic uncertainty for the HMPID analysis has contributions from
tracking and PID. These uncertainties have been estimated by individually
changing the track selection cuts and the parameters of the fit function used
to extract the raw yields. The means of the Gaussian functions have been
changed by $\pm\sigma$. Similarly, the widths of the Gaussian functions have
been varied by $\pm 10\%$, accounting for the maximum expected variation of
the resolution as a result of the different running conditions of the detector
during data acquisition that can have an impact on the performance. When the
means are changed, the widths are fixed to the default value, and vice versa.
The parameter variation is performed for all three particles species. In
addition, the uncertainty on the association of the track to the matched
cluster is obtained by varying the value of the distance cut required for the
match by $\pm$1 cm. These contributions do not vary with the collision
centrality. To estimate the uncertainty due to the incomplete knowledge of the
shape of the background distribution, an alternative background function,
depending on tan($\theta$) and derived from geometrical considerations in case
of orthogonal tracks [55], has been used:

$f(\theta)=a+b\times\tan\theta+c\times[\tan\theta(1+\tan^{2}\theta)]^{d},$
(10)

where $a,b,c$, and $d$ are free parameters. The corresponding systematic
uncertainty reaches a maximum value at low momenta for the most central
collisions ($\approx$ 15% for pions and $\approx$ 8% for kaons and protons).
The systematic uncertainty decreases with $p_{\rm{T}}$ because, as previously
explained, the background contribution decreases with increasing track
momentum. A summary of the different contributions to the systematic
uncertainty for the HMPID Pb–Pb analysis is given in Table 3.

Effect | $\pi^{\pm}$ | K± | p and $\rm\overline{p}$
---|---|---|---
$p_{\rm{T}}$ range (GeV/$c$) | 2.5 | 4 | 2.5 | 4 | 2.5 | 4
PID | 6% | 12% | 6% | 12% | 4% | 5%
Tracking efficiency | 6% | 6% | 7%
Distance cut correction | 6% | 2% | 6% | 2% | 4% | 2%
Background (Pb-Pb 0-5%) | 10% | 4% | 5% | 3% | 5% | 3%
Background (Pb-Pb 5-10%) | 7% | 4% | 3% | 2% | 3% | 2%
Background (Pb-Pb 10-20%) | 6% | 4% | 3% | 2% | 3% | 2%
Background (Pb-Pb 20-30%) | 5% | 3% | 3% | 2% | 2% | 2%
Background (Pb-Pb 30-40%) | 3% | 1% | 2% | 1% | 2% | 1%
Background (Pb-Pb 40-50%) | 2% | 1% | 2% | 1% | 2% | 1%
Table 3: Main sources of systematic uncertainties for the HMPID Pb–Pb
analysis.

##  3 Results and discussion

The measurement of charged pion, kaon, and (anti)proton transverse momentum
spectra has been performed via several independent analyses, each one focusing
on a sub-range of the total $p_{\rm{T}}$ distribution, using individual
detectors and specific techniques to optimize the signal extraction (see Table
4). The results were combined in the overlapping ranges using a weighted
average with the independent systematic uncertainties as weights (a $3\%$
common systematic uncertainty due to the TPC tracking is added directly to the
combined spectrum). The statistical uncertainties are much smaller and
therefore neglected in the combination weights. For
$p_{\rm{T}}>4\text{\,GeV/$c$}$ only the TPC ${\rm d}E/{\rm d}x$ relativistic
rise analysis is used for all species. Figure 21 shows the ratio of individual
spectra to the combined spectrum for the 0-5%, 20-40%, and 60-80% central
Pb–Pb data, illustrating the compatibility between the different analyses. In
the centrality intervals where the HMPID measurements are available, they
improve the systematic uncertainty of the kaon and proton yields by
approximately a factor of two in the $p_{\rm{T}}$ region where it is later
observed that the peaks of the kaon-to-pion and the proton-to-pion ratios are
located (see Fig. 25 and Fig. 26). We note that the final charged pion spectra
are consistent with the neutral pion spectra scaled by a factor of two within
statistical and systematic uncertainties [57].

Figure 21: (Color online). The ratio of individual spectra to the combined spectrum as a function of $p_{\rm{T}}$ for pions (upper panels), kaons (middle panels), and protons (lower panels). From left-to-right the columns show 0-5%, 20-40%, and 60-80% (where there are no HMPID results). Only the $p_{\rm{T}}$ range where the analyses overlap is shown. For $p_{\rm{T}}>4\text{\,GeV/$c$}$, no combination is done and the TPC ${\rm d}E/{\rm d}x$ relativistic rise results are used directly, which gives rise to a small discontinuity for protons at this $p_{\rm{T}}$. The ITS+TPC+TOF spectra are the results published in [44]. The statistical and independent systematic uncertainties are shown as vertical error bars and as a band, respectively, and only include those on the individual spectra. | ITS+TPC+TOF | HMPID | TPC ${\rm d}E/{\rm d}x$ rel. rise
---|---|---|---
$\pi^{\pm}$ | 0.1 – 3.0 | 1.5 – 4.0 | 2.0 – 20.0
K± | 0.2 – 3.0 | 1.5 – 4.0 | 3.0 – 20.0
p($\bar{\rm p})$ | 0.3 – 4.6 | 1.5 – 6.0 | 3.0 – 20.0
K/$\pi$ | 0.2 – 3.0 | 1.5 – 4.0 | 3.0 – 20.0
p/$\pi$ | 0.3 – 3.0 | 1.5 – 4.0 | 3.0 – 20.0
Table 4: The $p_{\rm{T}}$ ranges (GeV/$c$) used in the combination of the most
central results. In $\rm pp$ and peripheral Pb–Pb collisions the separation
power is different and in some cases the $p_{\rm{T}}$ ranges therefore change
a little.

The final combined transverse momentum distributions for the three particle
species are shown in Fig. 22. For $p_{\rm{T}}<3\text{\,GeV/$c$}$, a hardening
of the spectra is observed going from peripheral to central events. This
effect is mass dependent and is characteristic of hydrodynamic flow as
discussed in [44]. For high $p_{\rm{T}}$ ($>10\text{\,GeV/$c$}$) the spectra
follow a power-law shape as expected from perturbative QCD (pQCD)
calculations. In the following, the high-$p_{\rm{T}}$ results are first
discussed before going on to the intermediate $p_{\rm{T}}$ region.

Figure 22:  (Color online). Transverse momentum spectra of charged pions (left
panel), kaons (middle panel), and (anti)protons (right panel) measured in
Pb–Pb and $\rm pp$ collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV. The systematic
and statistical error are plotted as color boxes and vertical error bars (hard
to see), respectively. The spectra have been scaled by the factors listed in
the legend for clarity.

###  3.1 The high-$p_{\rm{T}}$ results

Figure 23:  (Color online). The nuclear modification factor $R_{\rm AA}$ as a
function of $p_{\rm{T}}$ for different particle species. Results for different
collision centralities are shown. Statistical and PID systematic uncertainties
are plotted as vertical error bars and boxes around the points, respectively.
The total normalization uncertainty ($\rm pp$ and Pb–Pb) is indicated in each
panel by the vertical scale of the box centered at $p_{\rm{T}}$ =
$1\text{\,GeV/$c$}$ and $R_{\rm AA}$ = 1 [16].

To study jet quenching at high $p_{\rm{T}}$, the nuclear modification factor,
$R_{\rm AA}$, is constructed. The $R_{\rm AA}$ is

$R_{\rm AA}=\frac{{\rm d}^{2}N_{\rm id}^{\rm AA}/{\rm d}y{\rm
d}p_{\rm{T}}}{\langle T_{\rm AA}\rangle{\rm d}^{2}\sigma_{\rm id}^{\rm
pp}/{\rm d}y{\rm d}p_{\rm{T}}},$ (11)

where $N_{\rm id}^{\rm AA}$ and $\sigma^{\rm pp}_{\rm id}$ are the charged
particle yield in nucleus-nucleus (A–A) collisions and the cross section in
$\rm pp$ collisions, respectively, and $\langle T_{\rm AA}\rangle$ is the
nuclear overlap function. The latter is obtained from a Glauber model [58] and
is related to the average number of binary nucleon-nucleon collisions ($N_{\rm
coll}$) and the inelastic nucleon-nucleon cross section as $\langle T_{\rm
AA}\rangle=\langle N_{\rm coll}\rangle/\sigma^{\rm NN}_{\rm inel}$.

Figure 23 shows the $R_{\rm AA}$ for all centrality classes. The results show
that for all centrality classes any particle species dependence of the nuclear
modification for $p_{\rm{T}}>10\text{\,GeV/$c$}$ is small, compared with the
large suppression ($R_{\rm AA}\ll 1$). This suggests that jet quenching does
not produce signatures that affect the particle species composition for the
leading particles. The results presented in this paper are all done at the
particle level, while for some models that motivated these studies the
predictions are done for jets, e.g. the Sapeta–Wiedemann model [22]. It is not
obvious how to compare the results presented here with such calculations. In
the following we therefore discuss how inclusive $p_{\rm{T}}$ spectra compare
with inclusive jet $p_{\rm{T}}$ spectra. In particular, it is examined if the
results are likely to be affected by a quenched jet fragmentation bias (if
quenched jets emit less high-$p_{\rm{T}}$ particles than unquenched ones) or a
surface bias (if unquenched jets from the surface dominate).

At the LHC, by studying dijets in Pb–Pb collisions and selecting on the dijet
asymmetry, one can study samples with large asymmetries where one knows, based
on comparisons with $\rm pp$ results, that at least the subleading jet has
suffered a large energy loss [8, 9]. The study of the Fragmentation Functions
(FFs) for these quenched jets has shown that for charged tracks with
$p_{\rm{T}}>4\text{\,GeV/$c$}$ they are similar to those observed in $\rm pp$
collisions for subleading jets with $p_{\rm{T,jet}}>50\text{\,GeV/$c$}$ [59],
in agreement with what one also finds for inclusive jets [60]. This rules out
a large fragmentation bias (for lower jet $p_{\rm{T}}$ see below) and suggests
that any surface bias is the same as for inclusive jets. To understand the jet
$p_{\rm{T}}$ covered by the results presented here, one can now, thanks to the
similarity of the FFs in $\rm pp$ and Pb–Pb collisions, rely on NLO pQCD
calculations for $\rm pp$ collisions. The FFs found to best describe the
inclusive charged particle spectra [61] are the Kretzer distributions [62].
NLO pQCD calculations using the Kretzer FFs suggest that more than half of the
particles with $p_{\rm{T}}$ between 10 and $20\text{\,GeV/$c$}$ are from gluon
jets and that the typical jet $p_{\rm{T}}$ is roughly a factor of 2-3 larger
than the hadron $p_{\rm{T}}$ ($\langle z\rangle=p_{\rm T,hadron}/p_{\rm
T,jet}\approx 0.4$) [61]555The publication contains only calculations for
$\sqrt{s}=900\text{\,GeV}$ and $\sqrt{s}=7\text{\,TeV}$ that have been
averaged as an approximate estimate for the energy of
$\sqrt{s}=2.76\text{\,TeV}$ shown here since the energy dependence is not that
strong.. The conclusions for jets with $p_{\rm{T,jet}}>50\text{\,GeV/$c$}$ is
therefore expected to be directly applicable also for the highest-$p_{\rm{T}}$
particles studied here. ALICE has studied charged jets in Pb–Pb collisions
where it was found that requiring minimum one track with
$p_{\rm{T}}>10\text{\,GeV/$c$}$ in a jet gives the same fragmentation bias of
the jet reconstruction efficiency in Pb–Pb collisions as in PYTHIA for
$20<p_{\rm{T,ch.\ jet}}<110\text{\,GeV/$c$}$ [63], so there is no evidence
even for lower $p_{\rm{T}}$ jets that there is a different fragmentation bias
in Pb–Pb collisions than in $\rm pp$ collisions. The results in Fig. 23
therefore indicate that for jets with final $p_{\rm{T}}$ of order $25$ to
$50\text{\,GeV/$c$}$, jet quenching does not produce large particle-species-
dependent effects in the hard core of the jet where leading particle
production mainly occurs.

To be able to set stronger constraints, one needs theoretical modeling. As the
$R_{\rm AA}$ for charged pions, kaons, and protons reported here for
$p_{\rm{T}}>10\text{\,GeV/$c$}$ are all compatible to the $R_{\rm AA}$ for
inclusive charged particles [16] and neutral pions [57] we refer to these
papers for comparisons with models without large particle-species-dependent
effects. When compared with models which include large particle-species-
dependent effects, the results indicate that the jet quenching mechanism does
not involve direct exchange of quantum numbers with the medium, and there are
also no indications of a modified color structure of the fragmentation [22] or
that the probe is excited to other color states [23]. Models in which the
hadronization of jet fragments occurs in the medium also appear to be ruled
out [24]. It seems that the medium quenches the jet as a whole rather than
directly interacting with its fragments. Such a picture has recently been
proposed [64], arguing that the medium typically cannot resolve the structure
inside the hard core of the jet such that all fragments lose energy
coherently.

Figure 24:  (Color online). The nuclear modification factor $R_{\rm AA}$ as a
function of $p_{\rm{T}}$ for charged pions, compared with PHENIX results for
neutral pions [65]. Results for different collision centralities are shown.
Statistical and PID systematic uncertainties are plotted as vertical error
bars and boxes around the points, respectively.

In Fig. 24, the $R_{\rm AA}$ for charged pions, the most precise measurement
in this work and the one least sensitive to radial flow, is compared with the
$R_{\rm AA}$ for neutral pions measured by PHENIX [65] at the RHIC666The
results have been obtained from the tables at the PHENIX website and the 5-10%
data set has been constructed from the 0-5% and 0-10%.. The ALICE results are
systematically below the PHENIX values for $p_{\rm{T}}<10\text{\,GeV/$c$}$ but
consistent within systematic uncertainties for larger $p_{\rm{T}}$. We note
that the relative centrality evolution is similar at the two center-of-mass
energies. In [66], a simple study of the $R_{\rm AA}$ at
$p_{\rm{T}}=10\text{\,GeV/$c$}$ found that the energy loss is ${\approx}40\%$
larger at the LHC than at the RHIC in all centrality classes (it scales as
$\sqrt{{\rm d}N/{\rm d}\eta}$ for a fixed initial geometry).

Figure 25:  (Color online). Charged kaon to charged pion ratio as a function
of transverse momentum (solid markers). The upper figure shows the full
$p_{\rm{T}}$-range with the $\rm pp$ results (open markers) overlaid in the
most central and the most peripheral centrality class. In the lower figure the
Pb–Pb results for $p_{\rm{T}}<8\text{\,GeV/$c$}$ are compared with EPOS model
2.17-3 (line). The systematic and statistical error are plotted as color boxes
and vertical error bars, respectively.

Figure 26:  (Color online). (Anti)proton to charged pion ratio as a function
of transverse momentum (solid markers). The upper figure shows the full
$p_{\rm{T}}$-range with the $\rm pp$ results (open markers) overlaid in the
most central and the most peripheral centrality class. In the lower figure the
Pb–Pb results for $p_{\rm{T}}<8\text{\,GeV/$c$}$ are compared with EPOS model
2.17-3 (line). The systematic and statistical error are plotted as color boxes
and vertical error bars, respectively. Figure 27:  (Color online). The
integrated particle ratios for $p_{\rm{T}}>10\text{\,GeV/$c$}$ in $\rm pp$ and
Pb–Pb collisions as a function of the number of participants. Left panel: the
kaon-to-pion ratio. Right panel: the proton-to-pion ratio scaled by a factor
of 3 for clarity. Statistical and PID systematic uncertainties are plotted as
vertical error bars and boxes around the points, respectively. Note that this
kaon-to-pion (proton-to-pion) “high-$p_{\rm{T}}$” ratio is ${\approx}4$
(${\approx}2$) times larger than the bulk ratio [44].

The proton-to-pion and the kaon-to-pion ratios as a function of $p_{\rm{T}}$
are shown in Fig. 25 and Fig. 26. The similarity at high $p_{\rm{T}}$ for the
$R_{\rm AA}$ implies that the particle ratios there are also the same in $\rm
pp$ and Pb–Pb collisions. Since the particle ratios are independent of
$p_{\rm{T}}$ in this region, we use the integrated particle ratios for
$p_{\rm{T}}>10\text{\,GeV/$c$}$ to elucidate the precision with which the
suppression of pions, kaons, and protons is similar, see Fig. 27. The
advantage of using particle ratios is that the results for heavy-ion
collisions can be shown separately from the $\rm pp$ results. Furthermore, in
the ratios the systematic uncertainty associated with the inclusive charged
particle $p_{\rm{T}}$ spectra normalization cancels. All the steps in the
high-$p_{\rm{T}}$ ${\rm d}E/{\rm d}x$ analysis discussed in Sec. 2.1 are done
independently for each centrality class (using disjunct datasets) so one does
not expect any direct correlations of the results. We conclude that all kaon-
to-pion (proton-to-pion) ratios as a function of $N_{\text{part}}$ are
consistent within the systematic uncertainty of ${\approx}10~{}\%$
(${\approx}20\%$). Measurements with improved precision using Run 2 and Run 3
LHC data could reveal possible subtle particle-species differences.

###  3.2 The intermediate $p_{\rm{T}}$ results

In the following, the intermediate $p_{\rm{T}}$ regions in Fig. 25 and Fig.
26, where the proton-to-pion and the kaon-to-pion ratios are enhanced, are
discussed.

The observation of the large proton-to-pion ratio at intermediate $p_{\rm{T}}$
at the RHIC generated numerous speculations that the degrees of freedom in the
medium are constituent quark-like and that they recombine when hadronizing to
give rise to distinct meson and baryon properties. As the $\phi$ meson has a
similar mass to a proton, it is crucial in testing these ideas and results at
the RHIC indeed seemed to confirm this picture [67], while at LHC the picture
appears to be more complicated [68, 69]. Some of the models developed to
describe results at the RHIC have been extended to the LHC energies. One can,
in general, separate recombination models into two classes. In soft models,
recombination only occurs for soft thermal radially-flowing partons. In [68]
ALICE showed calculations for such a model [31] and the prediction is that at
the LHC energies the particle ratios in central collisions are similar to
those measured at the highest RHIC energy. In hard recombination models, jet
fragments can recombine with both partons from the medium and other jets. At
LHC energies, the mini-jet activity is much larger than at RHIC energies,
which motivated predictions for central collisions of particle ratios an order
of magnitude larger ($p/\pi\sim 10$–$20$) than the peak values reported here
and persisting out to much higher $p_{\rm{T}}$ [34]. The failure of hard
recombination is in qualitative agreement with the picture where the jet
interacts with the medium as a whole so that the hard fragments of the jet
cannot recombine with partons in the medium or in another jet.

EPOS [70] is a full MC generator which contains both soft and hard physics. It
incorporates a hydrodynamical phase and additional hadronization processes at
intermediate $p_{\rm{T}}$ where the interaction between bulk matter and
quenched jets is considered [71]. This interaction introduces a baryon-meson
effect, where fully quenched jets are allowed to hadronize with flowing medium
quarks. When we study the full set of ratios at all centralities (Fig. 25 and
Fig. 26) EPOS generally reproduces the centrality dependence well, even for
very peripheral events, where it is known that pure hydrodynamical
calculations fail to describe the data [44]. However, EPOS overpredicts the
magnitude of both the proton-to-pion and the kaon-to-pion peak; it is
therefore critical to understand how important the additional hadronization
processes are, relative to the hydrodynamic flow, when all parameters have
been tuned.

Figure 28: (Color online) ALICE (circles) results from $\sqrt{s_{\rm
NN}}=2.76\text{\,TeV}$ Pb–Pb collisions compared with STAR and PHENIX results
for $\sqrt{s_{\rm NN}}=200\text{\,GeV}$ Au–Au collisions. Left panel: the
proton-to-pion ratio. Right panel: the kaon-to-pion ratio.

Figure 28 shows a comparison of particle ratios with results from STAR [25]
and PHENIX [27] at the RHIC measured in Au–Au collision at $\sqrt{s_{\rm
NN}}=200\text{\,GeV}$. In both cases, the results have been averaged for both
charge signs for pions and protons. We use the STAR feeddown-corrected data
for this comparison 777Values taken from
https://drupal.star.bnl.gov/STAR/files/starpublications/65/data.html for
protons and a similar feed-down correction has been assumed for anti-protons..
The proton-to-pion peak at the LHC is approximately 20% larger than at the
RHIC, which is consistent with an increased average radial flow velocity. At
high $p_{\rm{T}}$, the systematic uncertainties of the STAR data are very
large and it was noted in a later publication that they might even be
underestimated [26]. Interestingly, there is no evidence for a peak in the
kaon-to-pion ratio measured by PHENIX, which is similar to the ALICE data
points for $p_{\rm{T}}\leq 3\text{\,GeV/$c$}$, but continues to rise in the
few data points above this $p_{\rm{T}}$.

Careful modeling of $p_{\rm{T}}$ spectra and azimuthal flow is needed to
answer the question of whether there are additional hadronization processes
such as soft recombination at the LHC888We note that in a recent preprint it
is shown that soft recombination together with pQCD+quenching can give a good
description of pion, kaon, and (anti)proton spectra in central heavy-ion
collisions both at the RHIC and the LHC for
$1.5<p_{\rm{T}}<10\text{\,GeV/$c$}$ [72].. Since the multiplicity evolution of
particle ratios in p–Pb collisions is similar to what is observed for Pb–Pb
collisions [37] it would be interesting to include those results in the
modeling, in particular, since there is no indication of jet quenching [73]
which conceptually simplifies the problem.

##  4 Conclusion

We have reported the centrality dependent measurement of charged pions, kaons
and (anti)protons at large transverse momenta in Pb–Pb collisions at the LHC.
When combined with previously published data at lower $p_{\rm{T}}$, the new
results provide a comprehensive dataset of pion, kaon, and (anti)proton
$p_{\rm{T}}$ spectra with unprecedented systematic precision and $p_{\rm{T}}$
reach. The spectra are sensitive to physics mechanisms that differentiate
between baryons and mesons, strange and non-strange, or heavy and light
hadrons.

At high $p_{\rm{T}}$ ($p_{\rm{T}}>10\text{\,GeV/$c$}$), particle ratios and
nuclear modification factors allow the study of effects related to jet
quenching. The measurements in this $p_{\rm{T}}$ range do not show any
difference in the nuclear modification factor for pions, kaons, and protons. A
comparison of the present results with jet measurements and theoretical
calculations establishes that jet quenching does not introduce large species-
dependent modifications for leading particles. Instead, at high $p_{\rm{T}}$,
for all 6 centrality classes and the $\rm pp$ data analyzed here, the same
kaon-to-pion and proton-to-pion ratios are obtained within a systematic
precision of ${\approx}10$–20%.

At intermediate $p_{\rm{T}}$, calculations are needed to determine whether
models containing only hydrodynamics and jet quenching can provide a good
description across many observables of the available experimental results or
if additional processes such as recombination are needed. Since the initial
geometry of the collision directly affects both the flow and the energy loss,
the centrality dependence presented in this paper is important for
constraining both the low-$p_{\rm{T}}$ hydrodynamics and the high-$p_{\rm{T}}$
jet quenching in the calculations.

The results in this paper, taken together with the wealth of other high
$p_{\rm{T}}$ and jet results from the LHC, point toward a need for further
development of a microscopic QCD-based picture that explains in detail the
relation between the jet, the medium, and the energy loss.

## Acknowledgements

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: State
Committee of Science, World Federation of Scientists (WFS) and Swiss Fonds
Kidagan, Armenia, Conselho Nacional de Desenvolvimento Científico e
Tecnológico (CNPq), Financiadora de Estudos e Projetos (FINEP), Fundação de
Amparo à Pesquisa do Estado de São Paulo (FAPESP); National Natural Science
Foundation of China (NSFC), the Chinese Ministry of Education (CMOE) and the
Ministry of Science and Technology of China (MSTC); Ministry of Education and
Youth of the Czech Republic; Danish Natural Science Research Council, the
Carlsberg Foundation and the Danish National Research Foundation; The European
Research Council under the European Community’s Seventh Framework Programme;
Helsinki Institute of Physics and the Academy of Finland; French CNRS-IN2P3,
the ‘Region Pays de Loire’, ‘Region Alsace’, ‘Region Auvergne’ and CEA,
France; German Bundesministerium fur Bildung, Wissenschaft, Forschung und
Technologie (BMBF) and the Helmholtz Association; General Secretariat for
Research and Technology, Ministry of Development, Greece; Hungarian Orszagos
Tudomanyos Kutatasi Alappgrammok (OTKA) and National Office for Research and
Technology (NKTH); Department of Atomic Energy and Department of Science and
Technology of the Government of India; Istituto Nazionale di Fisica Nucleare
(INFN) and Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche
”Enrico Fermi”, Italy; MEXT Grant-in-Aid for Specially Promoted Research,
Japan; Joint Institute for Nuclear Research, Dubna; National Research
Foundation of Korea (NRF); Consejo Nacional de Cienca y Tecnologia (CONACYT),
Direccion General de Asuntos del Personal Academico(DGAPA), México, Amerique
Latine Formation academique - European Commission (ALFA-EC) and the EPLANET
Program (European Particle Physics Latin American Network); Stichting voor
Fundamenteel Onderzoek der Materie (FOM) and the Nederlandse Organisatie voor
Wetenschappelijk Onderzoek (NWO), Netherlands; Research Council of Norway
(NFR); National Science Centre, Poland; Ministry of National
Education/Institute for Atomic Physics and National Council of Scientific
Research in Higher Education (CNCSI-UEFISCDI), Romania; Ministry of Education
and Science of Russian Federation, Russian Academy of Sciences, Russian
Federal Agency of Atomic Energy, Russian Federal Agency for Science and
Innovations and The Russian Foundation for Basic Research; Ministry of
Education of Slovakia; Department of Science and Technology, South Africa;
Centro de Investigaciones Energeticas, Medioambientales y Tecnologicas
(CIEMAT), E-Infrastructure shared between Europe and Latin America (EELA),
Ministerio de Economía y Competitividad (MINECO) of Spain, Xunta de Galicia
(Consellería de Educación), Centro de Aplicaciones Tecnológicas y Desarrollo
Nuclear (CEADEN), Cubaenergía, Cuba, and IAEA (International Atomic Energy
Agency); Swedish Research Council (VR) and Knut $\&$ Alice Wallenberg
Foundation (KAW); Ukraine Ministry of Education and Science; United Kingdom
Science and Technology Facilities Council (STFC); The United States Department
of Energy, the United States National Science Foundation, the State of Texas,
and the State of Ohio; Ministry of Science, Education and Sports of Croatia
and Unity through Knowledge Fund, Croatia. Council of Scientific and
Industrial Research (CSIR), New Delhi, India

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##  Appendix A The ALICE Collaboration

J. Adamorg40&D. Adamováorg83&M.M. Aggarwalorg87&G. Aglieri Rinellaorg36&M.
Agnelloorg111&N. Agrawalorg48&Z. Ahammedorg132&S.U. Ahnorg68&I.
Aimoorg94,org111&S. Aiolaorg137&M. Ajazorg16&A. Akindinovorg58&S.N.
Alamorg132&D. Aleksandrovorg100&B. Alessandroorg111&D. Alexandreorg102&R.
Alfaro Molinaorg64&A. Aliciorg105,org12&A. Alkinorg3&J.R.M. Almarazorg119&J.
Almeorg38&T. Altorg43&S. Altinpinarorg18&I. Altsybeevorg131&C. Alves Garcia
Pradoorg120&C. Andreiorg78&A. Andronicorg97&V. Anguelovorg93&J.
Anielskiorg54&T. Antičićorg98&F. Antinoriorg108&P. Antonioliorg105&L.
Aphecetcheorg113&H. Appelshäuserorg53&S. Arcelliorg28&N. Armestoorg17&R.
Arnaldiorg111&I.C. Arseneorg22&M. Arslandokorg53&B. Audurierorg113&A.
Augustinusorg36&R. Averbeckorg97&M.D. Azmiorg19&M. Bachorg43&A.
Badalàorg107&Y.W. Baekorg44&S. Bagnascoorg111&R. Bailhacheorg53&R.
Balaorg90&A. Baldisseriorg15&F. Baltasar Dos Santos Pedrosaorg36&R.C.
Baralorg61&A.M. Barbanoorg111&R. Barberaorg29&F. Barileorg33&G.G.
Barnaföldiorg136&L.S. Barnbyorg102&V. Barretorg70&P. Bartaliniorg7&K.
Barthorg36&J. Bartkeorg117&E. Bartschorg53&M. Basileorg28&N. Bastidorg70&S.
Basuorg132&B. Bathenorg54&G. Batigneorg113&A. Batista Camejoorg70&B.
Batyunyaorg66&P.C. Batzingorg22&I.G. Beardenorg80&H. Beckorg53&C.
Beddaorg111&N.K. Beheraorg48,org49&I. Belikovorg55&F. Belliniorg28&H. Bello
Martinezorg2&R. Bellwiedorg122&R. Belmontorg135&E. Belmont-Morenoorg64&V.
Belyaevorg76&G. Bencediorg136&S. Beoleorg27&I. Berceanuorg78&A.
Bercuciorg78&Y. Berdnikovorg85&D. Berenyiorg136&R.A. Bertensorg57&D.
Berzanoorg36,org27&L. Betevorg36&A. Bhasinorg90&I.R. Bhatorg90&A.K.
Bhatiorg87&B. Bhattacharjeeorg45&J. Bhomorg128&L. Bianchiorg122&N.
Bianchiorg72&C. Bianchinorg135,org57&J. Bielčíkorg40&J. Bielčíkováorg83&A.
Bilandzicorg80&R. Biswasorg4&S. Biswasorg79&S. Bjelogrlicorg57&J.T.
Blairorg118&F. Blancoorg10&D. Blauorg100&C. Blumeorg53&F. Bockorg93,org74&A.
Bogdanovorg76&H. Bøggildorg80&L. Boldizsárorg136&M. Bombaraorg41&J.
Bookorg53&H. Borelorg15&A. Borissovorg96&M. Borriorg82&F. Bossúorg65&E.
Bottaorg27&S. Böttgerorg52&P. Braun-Munzingerorg97&M. Bregantorg120&T.
Breitnerorg52&T.A. Brokerorg53&T.A. Browningorg95&M. Brozorg40&E.J.
Bruckenorg46&E. Brunaorg111&G.E. Brunoorg33&D. Budnikovorg99&H.
Bueschingorg53&S. Bufalinoorg111&P. Buncicorg36&O. Buschorg93,org128&Z.
Butheleziorg65&J.B. Buttorg16&J.T. Buxtonorg20&D. Caffarriorg36&X. Caiorg7&H.
Cainesorg137&L. Calero Diazorg72&A. Calivaorg57&E. Calvo Villarorg103&P.
Cameriniorg26&F. Carenaorg36&W. Carenaorg36&F. Carnesecchiorg28&J. Castillo
Castellanosorg15&A.J. Castroorg125&E.A.R. Casulaorg25&C. Cavicchioliorg36&C.
Ceballos Sanchezorg9&J. Cepilaorg40&P. Cerelloorg111&J. Cerkalaorg115&B.
Changorg123&S. Chapelandorg36&M. Chartierorg124&J.L. Charvetorg15&S.
Chattopadhyayorg132&S. Chattopadhyayorg101&V. Chelnokovorg3&M. Cherneyorg86&C.
Cheshkovorg130&B. Cheynisorg130&V. Chibante Barrosoorg36&D.D.
Chinellatoorg121&P. Chochulaorg36&K. Choiorg96&M. Chojnackiorg80&S.
Choudhuryorg132&P. Christakoglouorg81&C.H. Christensenorg80&P.
Christiansenorg34&T. Chujoorg128&S.U. Chungorg96&Z. Chunhuiorg57&C.
Cicaloorg106&L. Cifarelliorg12,org28&F. Cindoloorg105&J. Cleymansorg89&F.
Colamariaorg33&D. Colellaorg36,org33,org59&A. Colluorg25&M. Colocciorg28&G.
Conesa Balbastreorg71&Z. Conesa del Valleorg51&M.E. Connorsorg137&J.G.
Contrerasorg11,org40&T.M. Cormierorg84&Y. Corrales Moralesorg27&I. Cortés
Maldonadoorg2&P. Corteseorg32&M.R. Cosentinoorg120&F. Costaorg36&P.
Crochetorg70&R. Cruz Albinoorg11&E. Cuautleorg63&L. Cunqueiroorg36&T.
Dahmsorg92,org37&A. Daineseorg108&A. Danuorg62&D. Dasorg101&I.
Dasorg51,org101&S. Dasorg4&A. Dashorg121&S. Dashorg48&S. Deorg120&A. De
Caroorg31,org12&G. de Cataldoorg104&J. de Cuvelandorg43&A. De Falcoorg25&D. De
Gruttolaorg12,org31&N. De Marcoorg111&S. De Pasqualeorg31&A.
Deistingorg97,org93&A. Delofforg77&E. Dénesorg136&G. D’Erasmoorg33&D. Di
Bariorg33&A. Di Mauroorg36&P. Di Nezzaorg72&M.A. Diaz Corcheroorg10&T.
Dietelorg89&P. Dillensegerorg53&R. Diviàorg36&Ø. Djuvslandorg18&A.
Dobrinorg57,org81&T. Dobrowolskiorg770&D. Domenicis Gimenezorg120&B.
Dönigusorg53&O. Dordicorg22&T. Drozhzhovaorg53&A.K. Dubeyorg132&A.
Dublaorg57&L. Ducrouxorg130&P. Dupieuxorg70&R.J. Ehlersorg137&D. Eliaorg104&H.
Engelorg52&B. Erazmusorg36,org113&I. Erdemirorg53&F. Erhardtorg129&D.
Eschweilerorg43&B. Espagnonorg51&M. Estienneorg113&S. Esumiorg128&J.
Eumorg96&D. Evansorg102&S. Evdokimovorg112&G. Eyyubovaorg40&L.
Fabbiettiorg37,org92&D. Fabrisorg108&J. Faivreorg71&A. Fantoniorg72&M.
Faselorg74&L. Feldkamporg54&D. Feleaorg62&A. Felicielloorg111&G.
Feofilovorg131&J. Ferenceiorg83&A. Fernández Téllezorg2&E.G. Ferreiroorg17&A.
Ferrettiorg27&A. Festantiorg30&V.J.G. Feuillardorg70,org15&J.
Figielorg117&M.A.S. Figueredoorg124,org120&S. Filchaginorg99&D.
Finogeevorg56&E.M. Fioreorg33&M.G. Fleckorg93&M. Florisorg36&S.
Foertschorg65&P. Fokaorg97&S. Fokinorg100&E. Fragiacomoorg110&A.
Francesconorg30,org36&U. Frankenfeldorg97&U. Fuchsorg36&C. Furgetorg71&A.
Fursorg56&M. Fusco Girardorg31&J.J. Gaardhøjeorg80&M. Gagliardiorg27&A.M.
Gagoorg103&M. Gallioorg27&D.R. Gangadharanorg74&P. Ganotiorg88&C. Gaoorg7&C.
Garabatosorg97&E. Garcia-Solisorg13&C. Gargiuloorg36&P. Gasikorg92,org37&M.
Germainorg113&A. Gheataorg36&M. Gheataorg62,org36&P. Ghoshorg132&S.K.
Ghoshorg4&P. Gianottiorg72&P. Giubellinoorg36,org111&P. Giubilatoorg30&E.
Gladysz-Dziadusorg117&P. Glässelorg93&D.M. Goméz Coralorg64&A. Gomez
Ramirezorg52&P. González-Zamoraorg10&S. Gorbunovorg43&L. Görlichorg117&S.
Gotovacorg116&V. Grabskiorg64&L.K. Graczykowskiorg134&K.L. Grahamorg102&A.
Grelliorg57&A. Grigorasorg36&C. Grigorasorg36&V. Grigorievorg76&A.
Grigoryanorg1&S. Grigoryanorg66&B. Grinyovorg3&N. Grionorg110&J.F. Grosse-
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Guernaneorg71&B. Guerzoniorg28&K. Gulbrandsenorg80&H. Gulkanyanorg1&T.
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Hetlandorg38&T.E. Hildenorg46&H. Hillemannsorg36&B. Hippolyteorg55&R.
Hosokawaorg128&P. Hristovorg36&M. Huangorg18&T.J. Humanicorg20&N.
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Ilkivorg77&M. Inabaorg128&M. Ippolitovorg76,org100&M. Irfanorg19&M.
Ivanovorg97&V. Ivanovorg85&V. Izucheevorg112&P.M. Jacobsorg74&S.
Jadlovskaorg115&C. Jahnkeorg120&H.J. Jangorg68&M.A. Janikorg134&P.H.S.Y.
Jayarathnaorg122&C. Jenaorg30&S. Jenaorg122&R.T. Jimenez Bustamanteorg97&P.G.
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Kaminorg53&J.H. Kangorg138&V. Kaplinorg76&S. Karorg132&A. Karasu Uysalorg69&O.
Karavichevorg56&T. Karavichevaorg56&L. Karayanorg93,org97&E. Karpechevorg56&U.
Kebschullorg52&R. Keidelorg139&D.L.D. Keijdenerorg57&M. Keilorg36&K.H.
Khanorg16&M.M. Khanorg19&P. Khanorg101&S.A. Khanorg132&A. Khanzadeevorg85&Y.
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Patraorg132&B. Paulorg101&T. Peitzmannorg57&H. Pereira Da Costaorg15&E.
Pereira De Oliveira Filhoorg120&D. Peresunkoorg100,org76&C.E. Pérez
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Petráčekorg40&V. Petrovorg112&M. Petroviciorg78&C. Pettaorg29&S.
Pianoorg110&M. Piknaorg39&P. Pillotorg113&O. Pinazzaorg105,org36&L.
Pinskyorg122&D.B. Piyarathnaorg122&M. Płoskońorg74&M. Planinicorg129&J.
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## Affiliation notes

0Deceased

idp25091132Also at: M.V. Lomonosov Moscow State University, D.V. Skobeltsyn
Institute of Nuclear, Physics, Moscow, Russia

idp26170716Also at: University of Kansas, Lawrence, Kansas, United States

## Collaboration Institutes

org1A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute)
Foundation, Yerevan, Armenia

org2Benemérita Universidad Autónoma de Puebla, Puebla, Mexico

org3Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine

org4Bose Institute, Department of Physics and Centre for Astroparticle Physics
and Space Science (CAPSS), Kolkata, India

org5Budker Institute for Nuclear Physics, Novosibirsk, Russia

org6California Polytechnic State University, San Luis Obispo, California,
United States

org7Central China Normal University, Wuhan, China

org8Centre de Calcul de l’IN2P3, Villeurbanne, France

org9Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana,
Cuba

org10Centro de Investigaciones Energéticas Medioambientales y Tecnológicas
(CIEMAT), Madrid, Spain

org11Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City
and Mérida, Mexico

org12Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche
“Enrico Fermi”, Rome, Italy

org13Chicago State University, Chicago, Illinois, USA

org14China Institute of Atomic Energy, Beijing, China

org15Commissariat à l’Energie Atomique, IRFU, Saclay, France

org16COMSATS Institute of Information Technology (CIIT), Islamabad, Pakistan

org17Departamento de Física de Partículas and IGFAE, Universidad de Santiago
de Compostela, Santiago de Compostela, Spain

org18Department of Physics and Technology, University of Bergen, Bergen,
Norway

org19Department of Physics, Aligarh Muslim University, Aligarh, India

org20Department of Physics, Ohio State University, Columbus, Ohio, United
States

org21Department of Physics, Sejong University, Seoul, South Korea

org22Department of Physics, University of Oslo, Oslo, Norway

org23Dipartimento di Elettrotecnica ed Elettronica del Politecnico, Bari,
Italy

org24Dipartimento di Fisica dell’Università ’La Sapienza’ and Sezione INFN
Rome, Italy

org25Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy

org26Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy

org27Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy

org28Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Bologna, Italy

org29Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Catania, Italy

org30Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Padova, Italy

org31Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo
Collegato INFN, Salerno, Italy

org32Dipartimento di Scienze e Innovazione Tecnologica dell’Università del
Piemonte Orientale and Gruppo Collegato INFN, Alessandria, Italy

org33Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari,
Italy

org34Division of Experimental High Energy Physics, University of Lund, Lund,
Sweden

org35Eberhard Karls Universität Tübingen, Tübingen, Germany

org36European Organization for Nuclear Research (CERN), Geneva, Switzerland

org37Excellence Cluster Universe, Technische Universität München, Munich,
Germany

org38Faculty of Engineering, Bergen University College, Bergen, Norway

org39Faculty of Mathematics, Physics and Informatics, Comenius University,
Bratislava, Slovakia

org40Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Prague, Czech Republic

org41Faculty of Science, P.J. Šafárik University, Košice, Slovakia

org42Faculty of Technology, Buskerud and Vestfold University College,
Vestfold, Norway

org43Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-
Universität Frankfurt, Frankfurt, Germany

org44Gangneung-Wonju National University, Gangneung, South Korea

org45Gauhati University, Department of Physics, Guwahati, India

org46Helsinki Institute of Physics (HIP), Helsinki, Finland

org47Hiroshima University, Hiroshima, Japan

org48Indian Institute of Technology Bombay (IIT), Mumbai, India

org49Indian Institute of Technology Indore, Indore (IITI), India

org50Inha University, Incheon, South Korea

org51Institut de Physique Nucléaire d’Orsay (IPNO), Université Paris-Sud,
CNRS-IN2P3, Orsay, France

org52Institut für Informatik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

org53Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

org54Institut für Kernphysik, Westfälische Wilhelms-Universität Münster,
Münster, Germany

org55Institut Pluridisciplinaire Hubert Curien (IPHC), Université de
Strasbourg, CNRS-IN2P3, Strasbourg, France

org56Institute for Nuclear Research, Academy of Sciences, Moscow, Russia

org57Institute for Subatomic Physics of Utrecht University, Utrecht,
Netherlands

org58Institute for Theoretical and Experimental Physics, Moscow, Russia

org59Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovakia

org60Institute of Physics, Academy of Sciences of the Czech Republic, Prague,
Czech Republic

org61Institute of Physics, Bhubaneswar, India

org62Institute of Space Science (ISS), Bucharest, Romania

org63Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico

org64Instituto de Física, Universidad Nacional Autónoma de México, Mexico
City, Mexico

org65iThemba LABS, National Research Foundation, Somerset West, South Africa

org66Joint Institute for Nuclear Research (JINR), Dubna, Russia

org67Konkuk University, Seoul, South Korea

org68Korea Institute of Science and Technology Information, Daejeon, South
Korea

org69KTO Karatay University, Konya, Turkey

org70Laboratoire de Physique Corpusculaire (LPC), Clermont Université,
Université Blaise Pascal, CNRS–IN2P3, Clermont-Ferrand, France

org71Laboratoire de Physique Subatomique et de Cosmologie, Université
Grenoble-Alpes, CNRS-IN2P3, Grenoble, France

org72Laboratori Nazionali di Frascati, INFN, Frascati, Italy

org73Laboratori Nazionali di Legnaro, INFN, Legnaro, Italy

org74Lawrence Berkeley National Laboratory, Berkeley, California, United
States

org75Lawrence Livermore National Laboratory, Livermore, California, United
States

org76Moscow Engineering Physics Institute, Moscow, Russia

org77National Centre for Nuclear Studies, Warsaw, Poland

org78National Institute for Physics and Nuclear Engineering, Bucharest,
Romania

org79National Institute of Science Education and Research, Bhubaneswar, India

org80Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

org81Nikhef, Nationaal instituut voor subatomaire fysica, Amsterdam,
Netherlands

org82Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United
Kingdom

org83Nuclear Physics Institute, Academy of Sciences of the Czech Republic, Řež
u Prahy, Czech Republic

org84Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States

org85Petersburg Nuclear Physics Institute, Gatchina, Russia

org86Physics Department, Creighton University, Omaha, Nebraska, United States

org87Physics Department, Panjab University, Chandigarh, India

org88Physics Department, University of Athens, Athens, Greece

org89Physics Department, University of Cape Town, Cape Town, South Africa

org90Physics Department, University of Jammu, Jammu, India

org91Physics Department, University of Rajasthan, Jaipur, India

org92Physik Department, Technische Universität München, Munich, Germany

org93Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg,
Heidelberg, Germany

org94Politecnico di Torino, Turin, Italy