2016 023 02 February

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

We present a Bayesian approach to particle identification (PID) within the
ALICE experiment. The aim is to more effectively combine the particle
identification capabilities of its various detectors. After a brief
explanation of the adopted methodology and formalism, the performance of the
Bayesian PID approach for charged pions, kaons and protons in the central
barrel of ALICE is studied. PID is performed via measurements of specific
energy loss ($\mathrm{d}E/\mathrm{d}x$) and time-of-flight. PID efficiencies
and misidentification probabilities are extracted and compared with Monte
Carlo simulations using high-purity samples of identified particles in the
decay channels
$\mathrm{K^{0}_{S}}\rightarrow\mathrm{\pi^{-}}\mathrm{\pi^{+}}$,
$\mathrm{\phi}\rightarrow\mathrm{K^{-}}\mathrm{K^{+}}$, and
$\mbox{$\mathrm{\Lambda}$}\rightarrow\mbox{$\mathrm{p}$}\mathrm{\pi^{-}}$ in
p–Pb collisions at $\sqrt{s_{\textsc{NN}}}=5.02\,\mathrm{TeV}$. In order to
thoroughly assess the validity of the Bayesian approach, this methodology was
used to obtain corrected $p_{\rm T}$ spectra of pions, kaons, protons, and
$\mathrm{D^{0}}$ mesons in pp collisions at $\sqrt{s}=7$ $\mathrm{TeV}$. In
all cases, the results using Bayesian PID were found to be consistent with
previous measurements performed by ALICE using a standard PID approach. For
the measurement of $\rm D^{0}\to K^{-}\pi^{+}$, it was found that a Bayesian
PID approach gave a higher signal-to-background ratio and a similar or larger
statistical significance when compared with standard PID selections, despite a
reduced identification efficiency. Finally, we present an exploratory study of
the measurement of $\rm\Lambda_{c}^{+}\to pK^{-}\pi^{+}$ in pp collisions at
$\sqrt{s}=7$ $\mathrm{TeV}$, using the Bayesian approach for the
identification of its decay products.

##  1 Introduction

Particle Identification (PID) provides information about the mass and flavour
composition of particle production in high-energy physics experiments. In the
context of ALICE (A Large Ion Collider Experiment) [1], identified particle
yields and spectra give access to the properties of the state of matter formed
at extremely high energy densities in ultra-relativistic heavy-ion collisions.
Modern experiments usually consist of a variety of detectors featuring
different PID techniques. Bayesian approaches to the problem of combining PID
signals from different detectors have already been used by several
experiments, e.g. NA27 [2], HADES [3] and BESII [4]. This technique was
proposed for ALICE during its early planning stages [5] and then used
extensively to prepare the ALICE Physics Performance Report [6, 7]. An
analogous method is also used to combine the PID signals from the different
layers of the ALICE Transition Radiation Detector.

The ALICE detector system is composed of a central part that covers the mid-
rapidity region $|\eta|<1$ (the ‘central barrel’), and a muon spectrometer
that covers the forward rapidity region $-4<\eta<-2.5$. The central barrel
detectors that have full coverage in azimuth ($\varphi$) are, from small to
large radii, the Inner Tracking System (ITS), the Time Projection Chamber
(TPC), the Transition Radiation Detector (TRD)111The TRD was completed during
the first Long Shutdown phase (2013–2015) and only had partial $\varphi$
coverage during the Run 1 data taking period (2009–2013). and the Time Of
Flight system (TOF). Further dedicated PID detectors with limited acceptance
in $\varphi$ and $\eta$ are also located in the central barrel. These are the
Electromagnetic Calorimeter (EMCal), the Photon Spectrometer (PHOS), and a
Cherenkov system for High-Momentum Particle Identification (HMPID).

The central barrel detectors provide complementary PID information and the
capability to separate particle species in different momentum intervals. At
low momenta ($p\lesssim 3$–$4\,\mathrm{GeV}/c$), a track-by-track separation
of pions, kaons and protons is made possible by combining the PID signals from
different detectors. At higher momenta, statistical unfolding based on the
relativistic rise of the TPC signal can be performed for PID. Given the wide
range of momenta covered, ALICE has the strongest PID capabilities of any of
the LHC experiments. More details about the identification possibilities of
the single detectors can be found in [1].

Several different PID methods were applied for analyses of data collected by
ALICE during the Run 1 data taking period of the LHC (2009–2013). A non-
exhaustive list of examples of PID in ALICE is given in the following. Results
were published on the transverse momentum ($p_{\rm T}$) distributions of
charged pion, kaon and proton production [8, 9, 10] in different collision
systems and centre-of-mass energies using the ITS, TPC, TOF and HMPID
detectors. Electron measurements from semileptonic heavy-flavour hadron decays
took advantage of the TPC, TOF, TRD and EMCal detectors [11, 12]. Neutral pion
production was studied via photon detection in the PHOS and the detection of
$\rm e^{+}e^{-}$ pairs from gamma conversions in the TPC. PID detectors were
also used extensively to improve the signal-to-background ratios when studying
the production of certain particles based on the reconstruction of their decay
products, such as $\mathrm{D}$ mesons [13], $\mathrm{\phi}$ and
$\mathrm{K^{*}}$ resonances [14]; in studies of particle correlations, such as
femtoscopy [15]; and to identify light nuclei [16]. In all analyses where PID
was used, selections were applied based on individual detector signals and
later combined.

In this paper we describe results obtained during Run 1 in
$\mathrm{p\kern-0.50003ptp}$ collisions at $\sqrt{s}=7\,\mbox{${\rm TeV}$}$,
Pb–Pb collisions at $\sqrt{s_{\textsc{NN}}}=2.76\,\mbox{${\rm TeV}$}$ and p–Pb
collisions at $\sqrt{s_{\textsc{NN}}}=5.02\,\mbox{${\rm TeV}$}$. In
particular, we focus on the hadron identification capabilities of the central
barrel detectors that had full azimuthal coverage during Run 1. These are the
ITS, TPC and TOF detectors, which are described in more detail below. The
other central barrel detectors are not discussed here.

The ITS is formed of six concentric cylindrical layers of silicon detectors:
two layers each of Silicon Pixel (SPD), Silicon Drift (SDD) and Silicon Strip
Detectors (SSD). The SDD and the SSD provide a read-out of the signal
amplitude, and thus contribute to the PID by measuring the specific energy
loss ($\mathrm{d}E/\mathrm{d}x$) of the traversing particle. A truncated mean
of the (up to) four signals is calculated, resulting in a relative
$\mathrm{d}E/\mathrm{d}x$ resolution of approximately 12% [1].

The TPC [17] is the main tracking device of ALICE. Particle identification is
performed by measuring the specific energy loss ($\mathrm{d}E/\mathrm{d}x$) in
the detector gas222 A Ne-CO2-based gas mixture of $\sim$90$\,\mathrm{m}^{3}$
in Run 1. in up to 159 read-out pad rows. A truncated mean that rejects the
40% largest cluster charges is built, resulting in a Gaussian
$\mathrm{d}E/\mathrm{d}x$ response. The $\mathrm{d}E/\mathrm{d}x$ resolution
ranges between 5–8% depending on the track inclination angle and drift
distance, the energy loss itself, and the centrality in p–Pb and Pb–Pb
collisions due to the differing detector occupancy.

The TOF detector [18] is based on Multigap Resistive Plate Chamber technology.
It measures the flight times of particles with an intrinsic resolution of
$\sim$80 ps. The expected flight time for each particle species is calculated
during the reconstruction, and then PID is performed via a comparison between
the measured and expected times.

Other forward-rapidity detectors are also relevant to the data analyses
presented in this paper. The V0 plastic scintillator arrays, V0A (covering
$2.8<\eta<5.1$) and V0C ($-3.7<\eta<-1.7$), are required in the minimum-bias
trigger. The V0 signals are also used to determine the centrality of p–Pb and
Pb–Pb collisions. The T0 detector is a quartz Cherenkov detector that is used
for start-time estimation with a resolution of $\sim$40 ps in pp collisions
and 20–25 ps in Pb–Pb collisions.

A thorough understanding of the detector response is crucial for any particle
identification method. In the case of $\mathrm{d}E/\mathrm{d}x$, this means a
well parameterised description of the average energy loss (according to the
Bethe-Bloch formula [19]) and a reliable estimate of the signal resolution.
For the TOF measurement, the start-time information, start-time resolution,
track reconstruction resolution, and intrinsic detector resolution need to be
known [18].

Combining the PID signals of the individual detectors using a Bayesian
approach [20] makes effective use of the full PID capabilities of ALICE.
However, using combined probabilities to perform particle identification may
result in unintuitive, non-trivial track selections. It is therefore important
to benchmark the Bayesian PID method, compare efficiencies in data and Monte
Carlo, and validate that this technique does not introduce a systematic bias
with respect to previously published results. This paper focuses on the
verification of the Bayesian PID approach on the basis of various data
analyses.

Section 2 describes the Bayesian approach (2.1), the definitions of efficiency
and contamination in the context of PID (2.2), the extraction and application
of prior distributions (2.3), and different strategies for using the resulting
probabilities (2.4). Section 3 presents benchmark analyses of high-purity
samples of pions, kaons, and protons from the two-prong decays of
$\mathrm{K^{0}_{S}}$ mesons, $\mathrm{\phi}$ mesons and $\Lambda$ baryons.
Section 4 presents validations of the Bayesian approach for two full analyses:
the measurement of the transverse momentum spectra of pions, kaons and protons
(4.1), and the analysis of $\rm D^{0}\to K^{-}\pi^{+}$ (4.2). Section 5
illustrates the application of the Bayesian PID approach to maximise the
statistical significance when analysing the production of
$\mathrm{\Lambda_{c}^{+}}$ baryons. Finally, a conclusion and outlook are
given in Section 6.

##  2 Bayesian PID in ALICE

Simple selections based on the individual PID signals of each detector do not
take full advantage of the PID capabilities of ALICE. An example of this is
illustrated in Fig. 1, which shows the separation of the expected TPC and TOF
signals for pions, kaons and protons with transverse momenta in the range
$2.5<p_{\rm T}<3$ $\mathrm{GeV}/c$. Clearly, the separation in the two-
dimensional plane (the peak-to-peak distance) of e.g. pions and kaons is
larger than the separation of each individual one-dimensional projection. A
natural way of combining the information of independent detectors is to
express the signals in terms of probabilities. An additional advantage of this
method is that detectors with non-Gaussian responses can also be included in a
straightforward way. A Bayesian approach makes use of the full PID
capabilities by folding the probabilities with the expected abundances
(priors) of each particle species. This section outlines the standard
‘$\mathrm{n_{\sigma}}$’ PID approach, before presenting the method used to
combine the signals from the different detectors when adopting a Bayesian PID
approach.

Figure 1: Combined particle identification in the TPC and TOF for data from
Pb–Pb collisions at $\sqrt{s_{\textsc{NN}}}=2.76\,\mathrm{TeV}$, shown as a
two-dimensional plot. The PID signals are expressed in terms of the deviation
from the expected response for pions in each detector.

###  2.1 PID signals in ALICE

The response of each detector can be expressed in terms of its raw signal,
$S$. One of the simplest ways of performing PID is to directly select based on
$S$. Examples of $S$ include the flight-time information from the TOF
detector, $t_{\mathrm{TOF}}$, and the specific energy loss
$\mathrm{d}E/\mathrm{d}x$ in detector gas or silicon, respectively measured by
the TPC and the ITS. A more advantageous approach would be to use a
discriminating variable, $\xi$, which makes use of the expected detector
response $R$:

$\xi=f(S,R),$ (1)

where $R$ can have functional dependences on the properties of the particle
tracks, typically the momentum $p$, the charge $Z$, or the track length $L$.
The detector response functions are usually complex parameterisations
expressing an in-depth knowledge of subtle detector effects.

For a detector with a Gaussian response, $R$ is given by the expected average
signal $\hat{S}(H_{i})$ for a given particle species $H_{i}$ and the expected
signal resolution $\sigma$. The index $i$ usually refers to electrons, muons,
pions, kaons or protons, but may also include light nuclei such as deuterons,
tritons, ${}^{3}\mathrm{He}$ nuclei and ${}^{4}\mathrm{He}$ nuclei. The most
commonly used discriminating variable for PID is the $\mathrm{n_{\sigma}}$
variable, defined as the deviation of the measured signal from that expected
for a species $H_{i}$, in terms of the detector resolution:

$\mathrm{n}_{\sigma_{\scriptstyle\alpha}^{\scriptstyle
i}}=\frac{S_{\alpha}-\hat{S}(H_{i})_{\alpha}}{\sigma_{\alpha}^{i}},$ (2)

where $\rm\alpha=(ITS,TPC,...)$. The resolution is given here as
$\sigma_{\alpha}^{i}$, as it depends both on the detector and the species
being measured. In the following, $\sigma_{\alpha}^{i}$ is simply referred to
as ‘$\sigma$’.

The $\mathrm{n_{\sigma}}$ PID approach corresponds to a ‘true/false’ decision
on whether a particle belongs to a given species. A certain identity is
assigned to a track if this value lies within a certain range around the
expectation (typically 2 or 3$\sigma$). Depending on the detector separation
power, a track can be compatible with more than one identity.

For a given detector $\alpha$ with a Gaussian response, it is possible to
define the conditional probability that a particle of species $H_{i}$ will
produce a signal $S$ as

$P(S|H_{i})=\frac{1}{\sqrt{2\pi}\sigma}e^{-\frac{1}{2}\mathrm{n_{\sigma}}^{2}}=\frac{1}{\sqrt{2\pi}\sigma}e^{-\frac{(S-\hat{S}(H_{i}))^{2}}{2\sigma^{2}}}.$
(3)

In the case of a non-Gaussian response, the probability is described by an
alternative parameterisation appropriate to the detector. The advantage of
using probabilities is that the probabilities from different detectors,
$P_{\alpha}$, with and without Gaussian responses, can then be combined as a
product:

$P(\vec{S}|H_{i})=\prod_{\alpha=\mathrm{ITS,TPC,...}}P_{\alpha}(S_{\alpha}|H_{i}),$
(4)

where $\vec{S}=(S_{\mathrm{ITS}},S_{\mathrm{TPC}},...)$.

The probability estimate $P(\vec{}S|H_{i})$ (either for a single detector, or
combined over many) can be interpreted as the conditional probability that the
set of detector signals $\vec{}S$ will be seen for a given particle species
$H_{i}$. However, the variable of interest is the conditional probability that
the particle is of species $H_{i}$, given some measured detector signal (i.e.
$P(H_{i}|\vec{}S)$). The relation between the two for a combined set of
detectors can be expressed using Bayes’ theorem [20]:

$P(H_{i}|\vec{S})=\frac{P(\vec{S}|H_{i})C(H_{i})}{\sum_{k=e,\mu,\pi,...}P(\vec{S}|H_{k})C(H_{k})}.$
(5)

Here, $C(H_{i})$ is an a priori probability of measuring the particle species
$H_{i}$, also known as the _prior_ , and the conditional probability
$P(H_{i}|\vec{S})$ is known as the _posterior_ probability.

The priors (which are discussed in more detail in Section 2.3) serve as a
‘best guess’ of the true particle yields per event. When such a definition is
adopted for the priors, a selection based on the Bayesian probability
calculated with Eq. 5 then corresponds to a request on the purity (defined as
the ratio between the number of correctly identified particles and the total
selected). Additionally, priors can be used to reject certain particle species
that are not relevant to a given analysis. Most commonly in the context of the
ALICE central barrel, the prior for muons is set to zero. Due to the
similarity between the pion and muon mass, the two species are almost
indistinguishable over a broad momentum range; the efficiency of detecting a
pion would thus be reduced if muons were not neglected. At the same time, this
influences the number of particles wrongly identified as pions, since the true
abundance of muons (roughly 2% of all particles, estimated using Monte Carlo
simulations) is neglected. This case is further discussed in the following
sections.

###  2.2 PID efficiency and contamination

In order to obtain the physical quantity of interest (typically a cross
section or a spectrum) from a raw yield, it is necessary to (a) compute the
efficiency due to other selections applied before PID, and (b) compute the
efficiency of the PID strategy. The PID efficiency is defined as the
proportion of particles of a given species that are identified correctly by
the PID selections. Both kinds of efficiency are usually estimated via Monte
Carlo techniques. To precisely compute the efficiency of a given PID strategy,
it is of utmost importance that an accurate description of the actual signals
present in the data is provided by the Monte Carlo simulation. Special care
must be given to the ‘tuning’ of Monte Carlo simulations to reproduce all of
the features and dependences observed in data for PID signals.

It is possible to define a $\mathrm{\epsilon}_{\mathrm{PID}}$ matrix that
contains the probability to identify a species _i_ as a species _j_. If only
pions, kaons and protons are considered, the $3\times 3$
$\mathrm{\epsilon}_{\mathrm{PID}}$ matrix is defined as

$\mathrm{\epsilon}_{\mathrm{PID}}=\begin{pmatrix}\epsilon_{\pi\pi}&\epsilon_{\pi\mathrm{K}}&\epsilon_{\pi\mathrm{p}}\\\
\epsilon_{\mathrm{K}\pi}&\epsilon_{\mathrm{K}\mathrm{K}}&\epsilon_{\mathrm{Kp}}\\\
\epsilon_{\mathrm{p}\pi}&\epsilon_{\mathrm{p}\mathrm{K}}&\epsilon_{\mathrm{pp}}\end{pmatrix},$
(6)

where the diagonal elements $\epsilon_{ii}$ are the PID efficiencies, and the
non-diagonal elements ($\epsilon_{ij}$, $i\neq j$) represent the probability
of misidentifying a species _i_ as a different species _j_.

The abundance vectors for pions, kaons and protons are defined as

$\vec{A}_{\mathrm{meas}}=\begin{pmatrix}\pi_{\mathrm{meas}}\\\
\mathrm{K}_{\mathrm{meas}}\\\
\mathrm{p}_{\mathrm{meas}}\end{pmatrix}{\text{~{}and~{}~{}}}\vec{A}_{\mathrm{true}}=\begin{pmatrix}\pi_{\mathrm{true}}\\\
\mathrm{K}_{\mathrm{true}}\\\ \mathrm{p}_{\mathrm{true}}\end{pmatrix},$ (7)

where the elements of $\vec{A}_{\mathrm{meas}}$ $(\vec{A}_{\mathrm{true}})$
represent the measured (true) abundances of each species. The diagonal
elements $\epsilon_{ii}$ of the PID matrix are then defined as

$\epsilon_{ii}=\frac{N_{i\text{ identified as }i}}{A_{\text{true}}^{i}}.$ (8)

Techniques to estimate the matrix elements are discussed in Section 3. The
abundance vectors $\vec{A}_{\mathrm{meas}}$ and $\vec{A}_{\mathrm{true}}$ are
linked by the following relation:

$\begin{pmatrix}\pi_{\mathrm{meas}}\\\ \mathrm{K}_{\mathrm{meas}}\\\
\mathrm{p}_{\mathrm{meas}}\end{pmatrix}=\begin{pmatrix}\epsilon_{\pi\pi}&\epsilon_{\pi\mathrm{K}}&\epsilon_{\pi\mathrm{\mathrm{p}}}\\\
\epsilon_{\mathrm{K}\pi}&\epsilon_{\mathrm{K}\mathrm{K}}&\epsilon_{\mathrm{K}\mathrm{\mathrm{p}}}\\\
\epsilon_{\mathrm{p}\pi}&\epsilon_{\mathrm{p}\mathrm{K}}&\epsilon_{\mathrm{p}\mathrm{\mathrm{p}}}\end{pmatrix}^{\intercal}\cdot\begin{pmatrix}\pi_{\mathrm{true}}\\\
\mathrm{K}_{\mathrm{true}}\\\ \mathrm{p}_{\mathrm{true}}\end{pmatrix}.$ (9)

Inverting the $\mathrm{\epsilon}_{\mathrm{PID}}^{\intercal}$ matrix, the
physical quantities are then extracted via:

$\vec{A}_{\mathrm{true}}=(\mathrm{\epsilon}_{\mathrm{PID}}^{\intercal})^{-1}\times\vec{A}_{\mathrm{meas}}.$
(10)

The $\mathrm{\epsilon}_{\mathrm{PID}}$ matrix elements have functional
dependences on many variables, primarily $p_{\rm T}$ and collision system.
Other second-order dependences (for example pseudorapidity, event
multiplicity, and centrality) can also be studied depending on the specific
track selections and PID strategies applied.

The contamination of the species _j_ due to a different species _i_ $(c_{ji})$
is the number of particles belonging to species _i_ that are wrongly
identified as _j_ $(N_{i~{}\text{identified as}~{}j})$, divided by the total
number of identified _j_ particles $(A_{\mathrm{meas}}^{j})$ [7]:

$c_{ji}=\frac{N_{i~{}\text{identified as }j}}{A_{\mathrm{meas}}^{j}},i\neq j.$
(11)

Contamination should not be confused with the misidentification probabilities
defined in Eq. 6, which do not depend on the real abundances. The connection
between contamination and misidentification is:

$c_{ji}=\frac{\epsilon_{ij}A_{\mathrm{true}}^{i}}{\epsilon_{jj}A_{\mathrm{true}}^{j}+\sum_{j\neq
k}{\epsilon_{jk}A_{\mathrm{true}}^{k}}}.$ (12)

There is usually a trade-off between efficiency and contamination. Both depend
on the PID strategy (e.g. choice of detectors), the detector response, and the
priors used, all of which are momentum-dependent. The contamination is
additionally driven by the real abundances.

An accurate estimate of the contamination $c_{ji}$ depends on the real
abundances, and it must be determined with data-driven techniques (or with
Monte Carlo simulations with abundances corresponding to what is found in the
data).

Although the PID matrix elements are independent of the real abundances, they
still depend on the choice of priors. They are therefore evaluated
consistently as long as the same set of priors is used both in the data
analysis and for the Monte Carlo simulations, provided that the detector
responses are simulated correctly. In addition, a choice of priors that lies
closer to the true abundances allows the best compromise to be found between
the maximisation of the efficiency and the minimisation of the contamination
probabilities. Considering that any systematic uncertainties in the detector
response will be amplified if the efficiency is low or if the contamination
probabilities are large, the method becomes more effective as the priors tend
closer to reality. An extreme example of this would be the identification of
pions and muons using equal priors for all species, as the two species are
difficult to distinguish from each other
($\varepsilon_{\pi\pi}\approx\varepsilon_{\mu\mu}\approx 0.5$ and
$\varepsilon_{\pi\mu}\approx\varepsilon_{\mu\pi}\approx 0.5$). In such a case,
even a small discrepancy in the description of the detector response in Monte
Carlo would cause a fluctuation in $\varepsilon_{ij}$, leading to a large
uncertainty in the estimate of the pion yield; a choice of priors
corresponding to the true abundances would prevent this from happening.

In cases where the detector responses are well separated between different
species, the priors do not need to correspond to the true abundances, and
could even be flat. The differences between different choices can then be used
to provide an estimate of the systematic uncertainties depending on the
current knowledge of the detector response. The influence of the choice of
priors is further discussed as part of the analyses presented in Section 4.

The combination of probabilities can also be used to identify and reduce the
level of unphysical background that may arise in PID analyses due to track
misassociation between detectors. For example, the fraction of TPC tracks that
are not correctly associated with the corresponding TOF hit increases with the
multiplicity of the event, and depends on the spatial matching window used in
the reconstruction to associate a TOF hit to a track. In ALICE this effect
only plays a role in Pb–Pb and p–Pb collisions, and even in the most central
Pb–Pb collisions it remains below 10% for tracks with momentum above 1
$\mathrm{GeV}/c$. In these cases, a mismatch probability can be defined based
on e.g. the measured flight time being uncorrelated with the track
reconstructed with the ITS and TPC due to the TOF hit being produced by
another particle.

###  2.3 Priors in ALICE

As discussed in Section 2.1, an analysis using the Bayesian approach is
expected to be moderately dependent on the choice of priors. Separate sets of
priors were evaluated for each collision system. They were evaluated by means
of an iterative procedure on data taken in 2010 and 2013 from
$\mathrm{p\kern-0.50003ptp}$, Pb–Pb, and p–Pb collisions at
$\sqrt{s}=7\,\mbox{${\rm TeV}$}$, $\sqrt{s_{\textsc{NN}}}=2.76\,\mbox{${\rm
TeV}$}$ and $\sqrt{s_{\textsc{NN}}}=5.02$ ${\rm TeV}$, respectively, and were
computed as a function of transverse momentum. Priors were also determined as
a function of centrality for Pb–Pb collisions, and of the multiplicity class
(based on the signal in the V0A detector) for p–Pb data. All of the priors
were obtained at mid-rapidity, $|\eta|<0.8$.

The absolute normalisation of the priors is arbitrary, and was chosen so as to
normalise all of the priors to the abundance of pions. The value of the priors
for pions is thereby set to unity for all $p_{\rm T}$. Flat priors (i.e. 1 for
all species) are applied at the beginning of the iterative procedure. Bayesian
posterior probabilities $P_{n}(H_{i}|S)$ are computed using the priors
obtained in step $n$, as defined in Eq. 5. These probabilities are then used
in turn as weights to fill identified $p_{\rm T}$ spectra $Y(H_{i},p_{\rm T})$
for the step $n+1$ starting from the inclusive (unidentified) measured $p_{\rm
T}$ spectra:

$Y_{n+1}(H_{i},p_{\rm T})=\sum_{S}P_{n}(H_{i}|S),$ (13)

where the summation is performed for all signals $S$ induced by particles of a
given $p_{\rm T}$ in the sample. It is then possible to obtain a new set of
priors $C_{n+1}$ from the relative ratios of the identified spectra according
to

$C_{n+1}(H_{i},p_{\rm T})=\frac{Y_{n+1}(H_{i},p_{\rm
T})}{Y_{n+1}(H_{\pi},p_{\rm T})}.$ (14)

The procedure is then iterated, and the extracted prior values converge
progressively with each iteration. The values of the priors are shown in the
left panel of Fig. 2 for the K$/\pi$ ratio obtained using data from p–Pb
collisions. The convergence of this procedure is illustrated in the right-hand
panel, as a ratio of the priors for successive steps. A satisfactory
convergence is obtained after 6–7 iterations.

Figure 2: An example of the iterative prior extraction procedure for p–Pb data
(for the 10–20% V0A multiplicity class). The extracted K$/\pi$ ratio of the
priors is shown as a function of $p_{\rm T}$ at each step of the iteration
(left) and as a ratio of the value between each successive step (right). Step
0 refers to the initial ratio, which is set to 1.

A set of priors was obtained for global tracks, defined as tracks
reconstructed in both the ITS and TPC. This set is referred to in the
following as $C(H_{i})_{\rm TPC}$ (the “standard priors”). This set of priors
is then propagated to other detectors using “propagation factors”
$F_{\alpha}$, which are detector-specific and dependent on transverse
momentum. In some cases these multiplicative factors can also be charge-
dependent (this is true for EMCal, for example). $F_{\alpha}$, which is
obtained for each detector via Monte Carlo, takes into account the particles
reaching the outer detectors, as well as the acceptances of the outer
detectors and their corresponding energy thresholds. The abundances measured
by TOF and TPC will differ due to these effects. The requirement of a given
detector therefore changes the priors. For an outer detector $\alpha$, the
priors for a track with momentum $p_{\rm T}$ are determined as

$C(H_{i})_{\alpha}(p_{\rm T})=F_{\alpha}(p_{\rm T})\times C(H_{i})_{\rm
TPC}(p_{\rm T}).$ (15)

Priors are currently propagated for TRD, TOF, EMCal and HMPID. Priors were
also generated for tracks that are obtained using only ITS hits. These were
used for the spectrum analysis at low momentum [9]. In the analyses presented
in this paper, the propagation procedure of priors from TPC to TOF was tested
extensively.

Since the priors correspond to relative particle abundances, it is possible to
directly compare the priors obtained from the iterative procedure with the
abundances measured by ALICE [8, 10, 21]. Comparisons between the priors and
the measured p$/\pi$ and K$/\pi$ ratios are shown in Fig. 3 for
$\mathrm{p\kern-0.50003ptp}$ and Pb–Pb collisions at $\sqrt{s}=7$ TeV and
$\sqrt{s_{\textsc{NN}}}=2.76$ TeV, respectively, and in Fig. 4 for p–Pb
collisions at $\sqrt{s_{\textsc{NN}}}=5.02$ TeV. In some cases the priors
cover a larger range than the measurements made by ALICE.

In order to make these comparisons, the priors were corrected by several
factors to take into account the different selections used in the physics
analyses and in the priors computation. Since the standard priors are provided
for the TPC case, only the tracking efficiency correction was applied.
Additional conversions from pseudorapidity intervals (used for the priors) to
rapidity intervals (used for the measurement) were also applied, as well as an
average feed-down correction derived from the Pb–Pb analysis [10]. This feed-
down mainly applies to protons from the decays of $\Lambda$ baryons.

The priors (open symbols) and the measured abundances (filled symbols) are
consistent with one another within roughly 10% over a wide momentum range for
all centrality ranges (for Pb–Pb collisions) and V0A multiplicity classes (for
p–Pb collisions). The choice to use feed-down corrections evaluated in a given
system leads to better agreement at low momenta in Pb–Pb collisions than in
p–Pb collisions. However, at high momenta, where the PID performance is better
exploited, the results are independent of this correction. The overall level
of agreement is satisfactory, as the priors represent a realistic description
of the various particle abundances.

Figure 3: The proton/pion ratio (left) and kaon/pion ratio (right), as
measured by ALICE [8, 10] using TPC and TOF (filled symbols), compared with
the standard priors as described in the text (open symbols) for Pb–Pb and
$\mathrm{p\kern-0.50003ptp}$ collisions. For Pb–Pb, the results are reported
for different centrality classes. Particle ratios are calculated for mid-
rapidity, $|y|<0.5$. The double ratios (the measured abundances divided by the
Bayesian priors) are shown in the lower panels. Figure 4: The proton/pion
ratio (left) and kaon/pion ratio (right), as measured by ALICE [21] using TPC
and TOF (filled symbols), compared with the standard priors obtained with an
iterative procedure (open symbols) for p–Pb collisions for different V0A
multiplicity classes. Particle ratios are calculated for mid-rapidity,
$|y|<0.5$ with respect to the centre-of-mass system. The double ratios (the
measured abundances divided by the Bayesian priors) are shown in the lower
panels.

It is also important to test whether there is any dependence of the final
result on the set of priors used. To perform these tests, it is possible to
use alternative sets of priors as well as flat priors, which essentially
combine the probabilities from the different detectors without weighting them
with Bayesian priors. Slightly different sets of priors can be obtained by
varying the track selection parameters. An example of a systematic check on
the dependence on varying the set of priors is discussed in Section 4.2 for
the $\mathrm{D^{0}}$ case.

###  2.4 Bayesian PID strategies

Once the Bayesian probability for each species (p, K, $\pi$, etc.) has been
calculated for a given track, the PID selection may be applied with a variety
of selection criteria. The three criteria applied in this paper are:

  * •

Fixed threshold: The track is accepted as belonging to a species if the
probability for this is greater than some pre-defined value. As an example,
the choice of a 50% threshold means that a particle will only be accepted as a
kaon if its Bayesian probability of being a kaon is greater than 50%. Note
that this strategy is not necessarily exclusive, as a threshold of less than
50% could lead to multiple possible identities. As already discussed, a
selection on the Bayesian probability corresponds to a purity requirement of
the signal if the priors reflect the true particle abundances.

  * •

Maximum probability: The track is accepted as the most likely species (i.e.
the species with the highest probability).

  * •

Weighted: All tracks reaching the PID step of the analysis are accepted, with
a weight different from unity applied to their yield. The weight is defined as
the product of the Bayesian probabilities obtained for the tracks involved
(e.g. in $\rm D^{0}\to K^{-}\pi^{+}$, this is the kaon probability of the
negative track multiplied by the pion probability of the positive track). The
final result is corrected for the average weight determined in Monte Carlo
simulations in the same way as is done for the PID efficiency in other
methods.

The fixed threshold method is compared with $\mathrm{n_{\sigma}}$ PID as part
of the benchmark analysis (see Section 3). The maximum probability method is
used in the single-particle spectrum analysis described in Section 4.1 and for
the $\mathrm{\Lambda_{c}^{+}}$ baryon analysis in Section 5. Finally, all
three of the aforementioned methods are tested for the analysis of $\rm
D^{0}\to K^{-}\pi^{+}$ in Section 4.2.

##  3 Benchmark analysis on two-prong decay channels

High-purity samples of identified particles were selected via the study of
specific decay channels. These samples served as a baseline for validating the
Monte Carlo tools that are normally used to estimate the efficiencies and
misidentification probabilities (i.e. the $\mathrm{\epsilon}_{\mathrm{PID}}$
matrix discussed in Section 2) of the Bayesian PID approach. The methodology
developed in this section was also applied to the $\mathrm{n_{\sigma}}$ PID
approach, providing an important cross-check.

###  3.1 Description of the method

The following decays were used to obtain high-purity samples of three
different species:

  * •

$\mathrm{K^{0}_{S}}\to\mathrm{\pi^{-}}\mathrm{\pi^{+}}$ to study charged
pions;

  * •

$\mbox{$\mathrm{\Lambda}$}\to\mbox{$\mathrm{p}$}\mathrm{\pi^{-}}$ (and
respective charge conjugates) to study protons; and

  * •

$\mathrm{\phi}\to\mathrm{K^{-}}\mathrm{K^{+}}$ to study charged kaons.

The first two cases are true $\mathrm{V^{0}}$ decays, comprising two charged
prongs originating from a secondary vertex displaced from the interaction
point, whereas the daughters of the $\mathrm{\phi}$ meson originate from the
primary interaction vertex due to its shorter lifetime. For conciseness, all
of these are referred to as $\mathrm{V^{0}}$ decays in this paper.

Here we report results based on the p–Pb data set, testing the PID method
using both TPC and TOF. The p–Pb data sample is less affected by background
uncertainties than the Pb–Pb sample when performing fits of the invariant mass
spectra, due to the smaller amount of combinatorial background. This is
especially true for the $\mathrm{\phi}$ analysis.

Different track selection criteria were applied in order to select daughter
particles coming either from the primary vertex (for the $\mathrm{\phi}$ case)
or from a secondary vertex (for the $\mathrm{K^{0}_{S}}$ and
$\mathrm{\Lambda}$ cases). For a given $\mathrm{V^{0}}$, a fit of the
combinatorial invariant mass distribution allows the background to be
subtracted and the yield of $\mathrm{V^{0}}$ decays to be extracted. The
estimated yield is considered to be a pure sample of a given species (a
precise measurement of the total number of particles of a given species in a
given data set). This estimation was done without applying any PID selections.
Then the exercise was repeated applying PID selections on each of the two
prongs, selecting between pions, kaons and protons. The comparison with the
number of positively identified secondary prongs determines the efficiency and
the misidentification with respect to the values estimated when not applying
PID.

Figure 5 shows examples of the fitting procedure for the $\mathrm{K^{0}_{S}}$
invariant masses for $2<p_{\rm T}^{\pi}<3\,\mathrm{GeV}/c$. From left to
right, the panels show the analysis without PID and then requiring the
identification of a positive pion, kaon, or proton, respectively. The
$\mathrm{K^{0}_{S}}$ signal (and background) fitted in the latter three cases,
compared with the results without applying PID, allow the extraction of the
identification efficiency and misidentification probabilities.

Figure 5: $\mathrm{V^{0}}$ fits to extract the yield and background for
$\mathrm{K^{0}_{S}}\to\mathrm{\pi^{-}}\mathrm{\pi^{+}}$ in p–Pb collisions at
$\sqrt{s_{\textsc{NN}}}=5.02$ TeV. From left to right: no PID selections
applied and selecting pions, kaons and protons using a specific PID strategy
(here, Bayesian probability $>$ 0.2). The yield estimated from the second plot
from the left (compared with the no-PID yield result) gives a measure of the
PID efficiency for the pions, while the remaining ones give information about
misidentification.

In order to reduce the background for the $\mathrm{\phi}$ analysis, before
starting the procedure, one of the two decay tracks was ‘tagged’ using a PID
selection requiring compatibility with the kaon hypothesis and then the PID
selection under study is applied on the other track. The tagging was performed
with a 2$\sigma$ selection on a combination of the TPC and TOF signals.

The TPC and TOF signals are combined as $|\mathrm{n}_{\sigma}^{\rm
Comb}(j)|=\sqrt{(\mathrm{n}_{\sigma}^{\rm TPC}(j)^{2}+\mathrm{n}_{\sigma}^{\rm
TOF}(j)^{2})/2}$. The same method was also applied on the simulated sample in
order to check the agreement between Monte Carlo and data on the estimated
quantities. This serves as a validation for the Monte Carlo estimation of the
efficiency of a given PID strategy, as well as for the subsequent corrections
required in order to extract physics results.

###  3.2 Comparison of PID efficiencies between data and Monte Carlo

The PID matrix elements obtained for different Bayesian probability thresholds
are presented here. An example for the highest purity case considered in this
work (Bayesian probability greater than 80%) is shown in Fig. 6. Each plot
represents a row of the $\mathrm{\epsilon}_{\mathrm{PID}}$ matrix for a given
species $i$, with the $i=j$ points corresponding to the PID efficiencies
($\epsilon_{ii}$) and the $i\neq j$ points corresponding to the
misidentification probabilities ($\epsilon_{ij}$). The matrix was evaluated
separately for positively and negatively charged tracks. As no difference was
found between the two cases, the results shown here were averaged over both
charges. For Monte Carlo, the PID hypothesis was tested both via the true
particle identity available in the simulation and by applying the same
procedure as for the data.

Figure 6: $\mathrm{\epsilon}_{\mathrm{PID}}$ matrix elements in p–Pb
collisions after selection with a Bayesian probability greater than 80%.
Comparisons with Monte Carlo (open symbols) are also shown. Figure 7:
$\mathrm{\epsilon}_{\mathrm{PID}}$ matrix elements in p–Pb collisions after
selection with a 2$\sigma$ selection on the combined TPC and TOF signal.
Comparisons with Monte Carlo (open symbols) are also shown.

As can be seen from Fig. 6, the efficiencies and misidentification
probabilities can be evaluated very precisely. The agreement between data and
Monte Carlo is good, both in shape and absolute value. The general features of
the PID strategies are also described well, and behave as expected: using a
high threshold maximises the purity, but also sharply reduces the efficiency.
Nevertheless, even for $P\geq 80\%$, where the efficiency estimate is more
sensitive to the description of the detector responses in the simulations, the
agreement with Monte Carlo remains within 5% below 3 $\mathrm{GeV}/c$.

The analysis was repeated using 2$\sigma$ and 3$\sigma$ selections on the
combined TOF and TPC signals, as discussed above, to identify the three hadron
species. The result is shown in Fig. 7 for the 2$\sigma$ case. As expected,
the $\mathrm{\epsilon}_{\mathrm{PID}}$ matrix elements have different values
from the 80% Bayesian probability threshold (given that the $\rm
n_{\sigma}^{Comb}$ selection is somewhat more inclusive), and the probability
of misidentification increases accordingly. The agreement between Monte Carlo
and data for the misidentification probabilities is worse in the
$\mathrm{n_{\sigma}}$ case than in the Bayesian case for kaons misidentified
as pions. However, there remains a good agreement between Monte Carlo and data
overall. The efficiencies are below the values expected from a perfectly
Gaussian signal; a Monte Carlo or data-driven evaluation of the PID strategy
efficiency is therefore mandatory. The non-Gaussian tail of the TOF signal
[18], caused by charge induction on pairs of neighbouring readout pads, plays
a significant role in this discrepancy. The mismatch fraction is also not
negligible in p–Pb collisions, being $\sim$2% above 1 $\mathrm{GeV}/c$.

Figure 8: Data/Monte Carlo ratios of PID efficiencies for pions, kaons and
protons in p–Pb collisions, extracted using different Bayesian probability
thresholds. Figure 9: Data/Monte Carlo ratios of PID efficiencies for pions,
kaons and protons in p–Pb collisions, extracted using 2- and 3$\sigma$
selections on the combined TPC and TOF signal.

For a more detailed comparison, the ratios between data and Monte Carlo are
presented in Figs. 8 and 9 for efficiencies obtained using different Bayesian
probability thresholds, and a 2$\sigma$ or 3$\sigma$ PID selection,
respectively. The agreement is very similar (within $\sim$5%) for both
methods. A larger difference is seen for kaons when using a very high Bayesian
probability threshold (corresponding to a “high purity” strategy). However,
such an approach could still be beneficial in physics analyses where an
efficiency correction is not needed (such as analyses investigating Bose-
Einstein correlations [15] or the flow of identified particles [22]). The
uncertainties reported in these plots are purely statistical. Apart from the
case of kaons extracted from $\mathrm{\phi}$ decays, the statistical
uncertainties on the Monte Carlo simulations give the largest contribution to
the uncertainties shown here. The $\mathrm{\phi}$-meson invariant mass plots
are affected by a larger combinatorial background in the data sample when PID
is not requested (i.e. in the denominator of the efficiency). As the ratios of
data to Monte Carlo for both Bayesian and $\mathrm{n_{\sigma}}$ PID are close
to unity in Figs. 8 and 9, it can be concluded that the systematic
uncertainties from the PID procedure are well under control in both cases.

In summary, the $\mathrm{V^{0}}$ analysis technique described in this section
serves not only as a validation of the quality of the Monte Carlo description
of the various detector responses, but can also be used in data and
simulations to validate different PID strategies and track selections for any
kind of analysis. Finally, it provides a tool to investigate the systematic
uncertainties that arise due to the PID selection.

##  4 Bayesian approach applied to physics analyses

In this section we present validations of the Bayesian PID approach for two
analyses already published by the ALICE Collaboration in pp collisions at
$\sqrt{s}=7$ TeV: identified pion, kaon and proton spectra [8] and $\rm
D^{0}\to K^{-}\pi^{+}$ [13]. While the previous papers remain the proper
references for the extraction of the physical quantities such as cross
sections, and for theory comparisons, this paper shows the results obtained by
applying the Bayesian approach to the PID part of those analyses.

###  4.1 Identified hadron spectra

The consistency of the Bayesian PID technique was tested using the tools
described in the previous sections to obtain the $p_{\rm T}$ spectra of pions,
kaons and protons. This analysis used a data sample of $1.2\times 10^{8}$
inelastic $\mathrm{p\kern-0.50003ptp}$ collisions at $\sqrt{s}=7$
$\mathrm{TeV}$ that was collected in 2010.

The results are compared here with similar measurements that were already
reported in [8]. In the quoted paper, different PID techniques were used
depending on the detectors involved in different $p_{\rm T}$ ranges
($\mathrm{n_{\sigma}}$ for ITS only and for the combined TPC and TOF signals,
and unfolding techniques for TOF and HMPID separately). Charged kaon spectra
were also measured via the identification of their decays (measurement of the
kink topology). Full details of the original analysis, including the event
selection criteria (which were also used here) and the procedure used to merge
the various PID techniques and detectors, can be found in [8].

The efficiency, detector acceptance, and other correction factors, were
estimated using Monte Carlo samples that simulated the detector conditions
run-by-run. The simulation was based on the PYTHIA6.4 event generator [23]
using the Perugia0 tune [24], with events propagated through the detector
using GEANT3 [25].

Only the TPC and TOF detectors were used for PID. The particle species were
identified using the maximum probability method outlined in Section 2.4. The
identification of charged hadrons used different detector combinations in
different momentum ranges, as shown in Table 1. Although a Bayesian approach
does not necessarily require such a division, it was chosen in order to make a
closer comparison with the analysis presented in [8]. In particular, the TOF
efficiency drops very steeply at low momentum due to the acceptance, meaning
that the systematic uncertainty on the TOF efficiency would become dominant
and make the comparison difficult.

Hadron | TPC | TPC–TOF
---|---|---
$\pi$ | 0.2 $\leq p_{\rm T}\leq$ 0.5 | 0.5 $\leq p_{\rm T}\leq$ 2.5
K | 0.3 $\leq p_{\rm T}\leq$ 0.45 | 0.45 $\leq p_{\rm T}\leq$ 2.5
p | 0.5 $\leq p_{\rm T}\leq$ 0.8 | 0.8 $\leq p_{\rm T}\leq$ 2.5
Table 1: PID detectors and transverse momentum ranges (in $\mathrm{GeV}/c$)
used for the analysis of identified hadron spectra.

The PID efficiency is higher than 95% for pions and protons, while for kaons
it begins to decrease from 100% at 1 $\mathrm{GeV}/c$ to 75% at 2.5
$\mathrm{GeV}/c$. The misidentification percentage is below 5% for pions and
protons for all $p_{\rm T}$, and reaches 20% for kaons at $p_{\rm
T}=2.5\,\mathrm{GeV}/c$. In order to avoid the dependence of the corrections
on the relative abundances of each hadron species in the event generator, the
spectra were corrected for their respective PID efficiencies and for
contamination using the $\mathrm{\epsilon}_{\mathrm{PID}}$ matrix method
described in Section 2.2. A $4\times 4$ matrix (also including electrons) was
defined for each $p_{\rm T}$ interval. These matrices were then inverted and
used in Eq. 10 in order to obtain the spectra. In addition, the spectra were
corrected for the tracking, TPC–TOF matching and primary vertex determination
efficiencies. The contributions from secondary particles that were not removed
by a selection based on the distance of closest approach to the vertex were
determined using a data-driven method, as explained in [8], and were
subtracted from the final spectra.

Figure 10 compares the minimum-bias charged hadron spectra from
$\mathrm{p\kern-0.50003ptp}$ collisions at $\sqrt{s}=7$ $\mathrm{TeV}$
obtained from this analysis with the published result. A very good agreement
within the uncertainties can be observed between the $p_{\rm T}$ spectra
obtained using these different approaches. For this comparison, the
statistical uncertainties are shown for both analyses, while the systematic
uncertainties that are not only related to PID were only considered for the
results published in [8]. The ratios of the spectra, presented in the lower
panels of Fig. 10, show an agreement within $\pm 5\%$ for all species.

Figure 10: Identified particle spectra from the Bayesian analysis, compared
with the measurement reported by ALICE in pp collisions at 7 $\mathrm{TeV}$
[8].

A further check was performed testing the stability of the method against the
priors used. The analysis was repeated using flat priors, i.e. equal
probabilities for the four particle species that are included in the PID
matrix (electrons, pions, kaons and protons). The muon priors were set to
zero, their percentage being negligible (with standard priors, they are
estimated to be less than 2% with respect to all other particle species).
Despite considering quite an extreme case here in terms of varying the priors,
the pion and proton abundances were consistent with the result obtained with
standard priors within 3%. A decrease in the estimated pion abundance at
$p_{\rm T}>1\,\mathrm{GeV}/c$ resulted in a variation of up to 10% for kaons
in some $p_{\rm T}$ intervals. The observed variations can be interpreted as
being due to remaining uncertainties in the detector response; a naive set of
priors, such as a set of flat priors, is generally expected to amplify such
effects.

###  4.2 Analysis of $\rm D^{0}\to K^{-}\pi^{+}$

This section presents a comprehensive overview of a variety of Bayesian PID
strategies applied to the analysis of $\rm D^{0}\to K^{-}\pi^{+}$ (and charge
conjugates) in pp collisions at $\sqrt{s}=7$ ${\rm TeV}$. The analysis was
based on a data sample of roughly $3\times 10^{8}$ events collected during Run
1. The geometrical selections on the displaced decay vertex topology matched
those used in the ALICE measurement of $\rm D^{0}\to K^{-}\pi^{+}$ in pp
collisions reported in [13].

In order to make a detailed assessment of the Bayesian method, this analysis
compares the results obtained using each of the PID strategies outlined in
Section 2.4. In each case, the PID method relied on selecting an oppositely
charged pair of tracks corresponding to a kaon and a pion. The TPC and TOF
detectors were used in conjunction with one another. For tracks without TOF
information, the PID was based on information from the TPC only.

For the fixed-threshold method, probability thresholds of 40%, 50%, 70%, and
80% were tested. Note that in the case of the 40% threshold, there is the
possibility that a daughter track may be compatible with both the kaon and
pion hypothesis; in such cases, the track was accepted as possibly belonging
to either species. For the maximum-probability and fixed-threshold methods,
once the daughter tracks were analysed, the candidate was accepted or rejected
according to the following criteria:

  * •

if both daughters were identified as possible kaons, the candidate was
accepted both as a $\mathrm{D^{0}}$ and a $\mathrm{\overline{D}^{0}}$;

  * •

if one daughter was identified as a kaon and the other as a pion, the
candidate was accepted as a $\mathrm{D^{0}}$ if the negative track was a kaon
and the positive track was a pion, and vice-versa for
$\mathrm{\overline{D}^{0}}$;

  * •

if neither daughter was identified as a kaon, the candidate was rejected;

  * •

if either daughter was not compatible with the kaon or the pion hypothesis,
the candidate was rejected.

The weighted method was implemented as defined in Section 2.4, whereby the
invariant mass distributions were filled for each candidate with weights
$W_{i}$. These weights are defined as

$\displaystyle W_{\mathrm{D^{0}}}=P_{\mathrm{K^{-}}}$ $\displaystyle\times
P_{\mathrm{\pi^{+}}},\text{ and}$ (16) $\displaystyle
W_{\mathrm{\overline{D}^{0}}}=P_{\mathrm{K^{+}}}$ $\displaystyle\times
P_{\mathrm{\pi^{-}}},$

where $P_{i}$ corresponds to the Bayesian probability assigned to each track
for a given species $i$. In this case, the PID efficiency from Monte Carlo
corresponded to the average weight that was assigned to simulated
$\mathrm{D^{0}}$ mesons in each $p_{\rm T}$ interval.

Once the invariant mass distributions in each $p_{\rm T}$ interval had been
obtained, the yields were fitted using a Gaussian function for the signal and
an exponential function to estimate the background. The raw signal was
extracted according to the integral of the fit to the signal distribution. In
order to ensure the stability of the fitting procedure, the width and mean of
the Gaussian functions were kept the same in each $p_{\rm T}$ interval for all
PID methods. To do this, the fit parameters were first determined for the
$\mathrm{n_{\sigma}}$ PID method in each $p_{\rm T}$ interval, and then fixed
to those values in the fitting procedure for each other PID method.

Example invariant mass distributions obtained without PID, with
$\mathrm{n_{\sigma}}$ PID, and with Bayesian PID using the maximum-probability
strategy are shown in Fig. 11, with a logarithmic scale on the vertical axis.
There is a clearly visible increase in the signal-to-background ratio when
using $\mathrm{n_{\sigma}}$ PID as compared to the analysis without PID, and a
further increase when applying a Bayesian selection with the maximum-
probability strategy. Due to the large background and low statistical
significance, it was not possible to extract a stable yield for $1<p_{\rm
T}<2$ $\mathrm{GeV}/c$ without PID. For this reason, the results obtained
without PID are excluded for this $p_{\rm T}$ interval in the following
comparisons.

Figure 11: A comparison of the invariant mass distributions in three $p_{\rm
T}$ intervals for $\mathrm{D^{0}}$ candidates obtained without PID, with
$\mathrm{n_{\sigma}}$ PID, and with Bayesian PID using the maximum probability
condition. Due to the low statistical significance, it was not possible to
extract a stable signal without PID for $1<p_{\rm T}<2\,\mathrm{GeV}/c$,
therefore this fit and its results are not shown.

Full comparisons of the signal-to-background ratio and significance obtained
for different PID strategies are shown in Fig. 12. The statistical
significance is defined as the signal divided by the square root of the sum of
the signal and background. The signal-to-background ratio increases
significantly for all $p_{\rm T}$ when using the $\mathrm{n_{\sigma}}$ PID
approach, as compared to not making a PID selection. A similar increase, of a
factor of at least 2, was seen in each of the Bayesian methods when compared
with $\mathrm{n_{\sigma}}$ PID.

As expected, the statistical significance of the signal was higher for the
$\mathrm{n_{\sigma}}$ PID than when no PID selection was applied. At low
$p_{\rm T}$, all but the strictest Bayesian selections (i.e. 80% probability
threshold) gave a further increase in significance over the
$\mathrm{n_{\sigma}}$ PID method, while at higher $p_{\rm T}$ the significance
of these methods became similar to that of $\mathrm{n_{\sigma}}$ PID. The 80%
probability threshold yielded a lower statistical significance than
$\mathrm{n_{\sigma}}$ PID for $p_{\rm T}>3\,\mathrm{GeV}/c$, whereas the
performance of the two methods is equivalent for $p_{\rm T}\leq
3\,\mathrm{GeV}/c$.

Figure 12: (Left) Signal-to-background ratio and (right) statistical
significance as a function of $p_{\rm T}$ for various methods of particle
identification. Note that the increase in significance at $8<p_{\rm
T}<12\,\mathrm{GeV}/c$ is an effect of the width of the $p_{\rm T}$ interval
increasing from 1 to 4 $\mathrm{GeV}/c$.

The efficiencies for each particle identification method were obtained using
charm-enriched Monte Carlo simulations, as described in [13]. The PID
efficiency was defined as the proportion of simulated D mesons that passed the
PID selection criteria, having already passed the other selections. In the
case of the weighted Bayesian PID method, as previously mentioned, the PID
efficiency corresponded to an average weight for true $\mathrm{D^{0}}$
candidates, and for the purposes of corrections was used in the same way as
the other PID efficiencies. The PID efficiencies obtained for each method are
shown in Fig. 13.

Figure 13: A comparison of the PID efficiencies for $\rm D^{0}\to
K^{-}\pi^{+}$ obtained using various PID strategies, as a function of $p_{\rm
T}$.

When a stricter PID selection was applied (for example, an 80% probability
threshold as compared to a 70% threshold), the PID efficiency fell
correspondingly. All of the Bayesian methods gave a lower PID efficiency than
the $\mathrm{n_{\sigma}}$ method. The observed significances and efficiencies
highlight a benefit and a potential drawback in using a strict Bayesian PID
strategy: while a tighter PID selection gives a yield of higher purity, it
also requires a greater reliance on the Monte Carlo simulation to give an
accurate correction due to the reduced PID efficiency. However, it is
important to note that this is not necessarily inherent to the Bayesian PID
method. For example, a very narrow $\mathrm{n_{\sigma}}$ selection (e.g. at
0.5$\sigma$) would also yield a lower efficiency, leading to a similar degree
of reliance on the Monte Carlo simulations; even a 2$\sigma$ selection reduces
the PID efficiency to 80%.

The corrected yields obtained using each particle identification method are
compared in Fig. 14. In each case, the ratio shown is the corrected yield
divided by that obtained using $\mathrm{n_{\sigma}}$ PID. As the candidates
selected by each of the Bayesian methods are a subset of those selected by the
$\mathrm{n_{\sigma}}$ approach, the uncertainties on the corrected yields are
assumed to be fully correlated and so almost cancel out in the ratio.

Figure 14: Ratios of corrected yields obtained using various Bayesian PID
methods to that obtained using $\mathrm{n_{\sigma}}$ PID, for (left) fixed
probability thresholds, and (right) maximum probability and weighted Bayesian
PID, and no PID. The 5% systematic uncertainty on the $\mathrm{n_{\sigma}}$
PID method is shown as a blue box at $0.5\,\mathrm{GeV}/c$.

It was found that there is a relatively good agreement between the Bayesian
PID method and the $\mathrm{n_{\sigma}}$ PID method, even when very different
probability thresholds are applied. Averaging over $p_{\rm T}$, the fixed
probability threshold methods give a systematic difference between 5 and 9%,
increasing for the lower probability thresholds. For the weighted and maximum-
probability methods, the average deviations from $\mathrm{n_{\sigma}}$ are 3%
and 7%, respectively. In every case this difference is of a similar order to
the systematic uncertainty of the $\mathrm{n_{\sigma}}$ PID approach
(${\sim}5\%$) [13].

In effect, the difference of the corrected yield from the
$\mathrm{n_{\sigma}}$ result represents the systematic uncertainty due to the
choice of Bayesian PID method. Therefore it can be concluded that the PID
systematic uncertainties for the Bayesian approach are not much larger than
those from the $\mathrm{n_{\sigma}}$ approach. The observed deviations also
contain systematic contributions related to the yield extraction procedure.

A final check was made to ensure that the results remained independent of the
choice of the prior probability distribution used. Ideally, the requirement of
an external input should guide the measurement, and fluctuations in these
priors should not have a substantial effect on the final result that is
obtained. In order to test this, two modified sets of priors were prepared,
with the proportion of kaons scaled up and down by 10% for all $p_{\rm T}$. An
analysis using these modified sets of priors was then performed and compared
to the analysis with the standard priors. The corrected yields using the
modified priors were divided by the yields using the standard set of priors
for each Bayesian analysis method. It was found that the average deviations
from unity remained within roughly 2% for each set of alternative priors with
all of the Bayesian PID strategies. The smallest deviations were observed for
the maximum probability and weighted methods, and for lower fixed probability
thresholds.

In conclusion, since the corrected yield is largely independent of the choice
of PID method, and considering the improvement in signal-to-background ratio
and (at low $p_{\rm T}$) significance, we conclude that the Bayesian PID
method is a valid choice for the analysis of $\rm D^{0}\to K^{-}\pi^{+}$.
However, it must be noted that although the stricter Bayesian methods give a
purer signal, they also create an increased reliance on the Monte Carlo
simulations to correct for the lower efficiencies, as well as introducing a
greater dependence on the choice of priors in those $p_{\rm T}$ intervals that
have lower statistical significance.

##  5 Application of Bayesian PID for $\mathrm{\Lambda_{c}^{+}}$ analysis

In this section we present an exploratory study of $\rm\Lambda_{c}^{+}\to
pK^{-}\pi^{+}$ in pp collisions at $\sqrt{s}=7$ ${\rm TeV}$ using a Bayesian
PID approach. This decay channel suffers from a high level of combinatorial
background, even in the relatively low-multiplicity environment of a pp
collision. Due to the short decay length of the $\mathrm{\Lambda_{c}^{+}}$
($c\tau=59.9\,\mbox{$\mu{\rm m}$}$ [26]) and current limitations in the
spatial resolution of the ITS, topological and geometrical selections alone
are not sufficient to reduce this background and extract a signal. This means
that a robust PID strategy is required to select $\mathrm{\Lambda_{c}^{+}}$
candidates.

Here we compare analyses of $\rm\Lambda_{c}^{+}\to pK^{-}\pi^{+}$ using the
$\mathrm{n_{\sigma}}$ approach, a Bayesian approach using the maximum-
probability criterion, and an alternative “minimum-$\sigma$” approach that
mimics the Bayesian strategy. This analysis used ${\sim}3\times 10^{8}$ events
from pp collisions at $\sqrt{s}=7\,\mathrm{TeV}$ collected during Run 1.

Both the TPC and TOF responses were used for the $\mathrm{n_{\sigma}}$
approach. A 3$\sigma$ selection was applied on the TOF signal for kaons, pions
and protons at all $p_{\rm T}$, while in the TPC a $p_{\rm T}$-dependent
$\mathrm{n_{\sigma}}$ selection (between 2 and 3$\sigma$) was applied for
protons and kaons, and a 3$\sigma$ selection was applied for pions at all
$p_{\rm T}$. If the track had a valid TOF signal, only this was used for the
PID; otherwise the TPC response was used. For the Bayesian PID method, the TPC
and TOF responses were combined; in cases where the TOF signal was not
available, only the TPC response was used.

The minimum-$\sigma$ strategy serves as a middle ground between the
$\mathrm{n_{\sigma}}$ analysis and the Bayesian approach. It is also based on
the deviation from the expected detector signal, but in this case only the
species resulting in the smallest $\mathrm{n_{\sigma}}$ value is chosen for
each track, making this an exclusive selection. The TPC and TOF responses are
combined by adding their respective $\mathrm{n_{\sigma}}$ values in
quadrature. The potential benefit of this approach is that it uses similar
logic to the Bayesian approach, without requiring the input of any priors.

In order to build $\mathrm{\Lambda_{c}^{+}}$ candidates, triplets of tracks
were reconstructed and selected, based on PID and topological selections.
Pairs of oppositely charged tracks were reconstructed from the set of selected
tracks, and a secondary (decay) vertex was computed. Selections were applied
to each pair based on the distance of closest approach between the two tracks,
and the distance between the primary and the secondary vertex of the
reconstructed pair. A third track was then associated to each selected pair to
form a triplet. The secondary vertex of the triplet was calculated and the
$\mathrm{\Lambda_{c}^{+}}$ candidates were selected using:

  * •

the quality of the reconstructed vertex, which was determined using the
quadratic sum of the distances of the single tracks from the calculated
secondary vertex;

  * •

the distance between the primary and the secondary vertex of the triplet
(decay length); and

  * •

the cosine of the pointing angle. The pointing angle is the angle between the
momentum vector of the reconstructed $\mathrm{\Lambda_{c}^{+}}$ candidate and
the $\mathrm{\Lambda_{c}^{+}}$ flight line reconstructed from the line joining
the primary and secondary vertices.

Figure 15: Invariant mass spectra of $\rm\Lambda_{c}^{+}\to pK^{-}\pi^{+}$
using $\mathrm{n_{\sigma}}$ PID, minimum-$\sigma$ PID and Bayesian PID for
(left) $2<p_{\rm T}<6$ $\mathrm{GeV}/c$ and (right) $3<p_{\rm T}<4$
$\mathrm{GeV}/c$. Due to the low statistical significance, it was not possible
to extract a stable signal for $\mathrm{n_{\sigma}}$ PID for $3<p_{\rm
T}<4\,\mathrm{GeV}/c$, therefore this fit and its results are not shown.

The invariant mass plots for pK$\pi$ candidates with $2<p_{\rm T}<6$
$\mathrm{GeV}/c$ are shown in the left-hand panel of Fig. 15 for the standard
$\mathrm{n_{\sigma}}$ PID approach (top), the alternative minimum-$\sigma$
approach (middle) and Bayesian PID (bottom). Over this $p_{\rm T}$ interval,
the statistical significance determined from the yield extraction (as defined
in Section 4.2) is $4.4\pm 1.0$ for $\mathrm{n_{\sigma}}$ PID, $5.1\pm 1.0$
for minimum-$\sigma$ PID and $6.0\pm 1.1$ for Bayesian PID. In addition, the
signal-to-background ratio is three times higher in the Bayesian case than for
$\mathrm{n_{\sigma}}$ PID, with a background that is reduced by a factor of
approximately seven. On the other hand, the Bayesian PID method yields fewer
$\mathrm{\Lambda_{c}^{+}}$ candidates in the peak, indicating a lower
selection efficiency.

The equivalent invariant mass distributions for $3<p_{\rm T}<4$
$\mathrm{GeV}/c$ are shown in the right-hand panel of Fig. 15. In this case,
the $\mathrm{n_{\sigma}}$ PID approach yields an insufficient statistical
significance to extract a stable yield. As with the $p_{\rm T}$-integrated
case, the statistical significance improves when using the other two methods
($2.7\pm 1.0$ for minimum-$\sigma$ and $4.4\pm 1.1$ for Bayesian PID), and we
again find a marked improvement in the signal-to-background ratio for these
two approaches. From this we conclude that the Bayesian approach represents
the best candidate PID method for future measurements of the
$\mathrm{\Lambda_{c}^{+}}$ production cross section.

##  6 Conclusions and outlook

A Bayesian method for particle identification has been presented and validated
for a variety of analyses. A comparison between different PID selection
methods in ALICE was performed, with a focus on testing the suitability of
Bayesian PID techniques. A selection based on the Bayesian probability can be
interpreted as a request on the purity, and therefore the main benefit of
these techniques is that they increase the purity of the extracted signal by
combining information from different detectors via a relatively simple
technique.

The iterative procedure used to extract the prior probabilities (corresponding
to the relative particle abundances) was outlined for
$\mathrm{p\kern-0.50003ptp}$ collisions at $\sqrt{s}=7\,\mathrm{TeV}$, p–Pb
collisions at $\sqrt{s_{\textsc{NN}}}=5.02\,\mathrm{TeV}$ and Pb–Pb collisions
at $\sqrt{s_{\textsc{NN}}}=2.76\,\mathrm{TeV}$. In each collision system, and
for every centrality and multiplicity class studied in Pb–Pb and p–Pb
collisions, the extracted priors were found to be consistent with the true
particle abundances seen in data.

The ability of Monte Carlo simulations to compute efficiencies and
misidentification probabilities was tested via high-purity samples of pions,
kaons and protons from the two-prong decays
$\mathrm{K^{0}_{S}}\to\mathrm{\pi^{-}}\mathrm{\pi^{+}}$,
$\mbox{$\mathrm{\Lambda}$}\to\mbox{$\mathrm{p}$}\mathrm{\pi^{-}}$, and
$\mathrm{\phi}\to\mathrm{K^{-}}\mathrm{K^{+}}$ in p–Pb collisions at
$\sqrt{s_{\textsc{NN}}}=5.02\,\mathrm{TeV}$. Equivalent analyses were also
performed using $\mathrm{n_{\sigma}}$ PID. It was found that the variation in
the result when using Bayesian PID as opposed to $\mathrm{n_{\sigma}}$ PID was
on the order of 5% in each case.

Comparisons between the Bayesian approach and PID methods used in measurements
already published by ALICE in pp collisions at $\sqrt{s}=7\,\mathrm{TeV}$ were
performed for the analysis of the $p_{\rm T}$-differential yields of
identified pions, kaons and protons. In this case, the previous analysis used
a combination of $\mathrm{n_{\sigma}}$ PID, unfolding methods and spectra
obtained with kinks. A simple maximum-probability Bayesian PID method was used
in this analysis. When compared, the results from $\mathrm{n_{\sigma}}$ PID
and Bayesian PID were found to be consistent with one another within
uncertainties.

A detailed comparison of different Bayesian PID strategies was performed for
the analysis of $\rm D^{0}\to K^{-}\pi^{+}$ in pp collisions at
$\sqrt{s}=7\,\mathrm{TeV}$. Through the use of different probability
thresholds, the trade-off between selecting a purer sample and having a
stronger dependence on the description of the detectors in Monte Carlo
simulations was demonstrated. An increase in the signal-to-background ratio
over the $\mathrm{n_{\sigma}}$ PID method was seen for all $p_{\rm T}$ for all
of the tested Bayesian strategies. The statistical significance was found to
be similar or greater than $\mathrm{n_{\sigma}}$ PID for all of the Bayesian
methods other than a strict 80% probability threshold. In every case, the
corrected yield was found to be stable against the choice of PID method when
comparing with the $\mathrm{n_{\sigma}}$ PID method used for $\mathrm{D^{0}}$
mesons. The dependence on the choice of priors was also investigated, and it
was found that the uncertainty on the corrected yield due to the choice of
priors was within ${\sim}2\%$. We conclude that the systematic uncertainties
arising from the choice of Bayesian PID method are of a similar order to those
of the $\mathrm{n_{\sigma}}$ approach.

In summary, a good level of consistency is seen in both of the full analyses
considered in Sections 4.1 and 4.2 with respect to previously reported
results. Because of this, we conclude that the validity of the Bayesian PID
approach has been successfully assessed.

Furthermore, the improved performance of the Bayesian PID approach in certain
scenarios will prove beneficial for future analyses. The case of the
$\mathrm{\Lambda_{c}^{+}}$ baryon was presented as an example where a simple
$\mathrm{n_{\sigma}}$ approach is unable to yield a stable signal, while the
Bayesian approach is able to combine information from the different detectors
effectively without the need to develop a complex variable-$\sigma$ selection.
This presents a promising option for a more comprehensive study of the
$\mathrm{\Lambda_{c}^{+}}$ production cross section in
$\mathrm{p\kern-0.50003ptp}$ and p–Pb collisions.

The analyses presented here are currently limited to charged hadrons detected
in the TPC and TOF detectors. However, the method can be extended to other
particle species and detectors within the ALICE central barrel, and we expect
to further test and refine these techniques in future. In particular, it will
be possible to examine the performance of the Bayesian approach for electron
identification with the TRD at full azimuthal coverage in Run 2.

## 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; National Research,
Development and Innovation Office (NKFIH), Hungary; 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; Japan Society
for the Promotion of Science (JSPS) KAKENHI and MEXT, 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; Pontificia Universidad Católica
del Perú.

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##  Appendix A The ALICE Collaboration

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Kisiel133, G. Kiss135, J.L. Klay6, C. Klein53, J. Klein35, C. Klein-Bösing54,
S. Klewin94, A. Kluge35, M.L. Knichel94, A.G. Knospe118,122, C. Kobdaj114, M.
Kofarago35, T. Kollegger97, A. Kolojvari131, V. Kondratiev131, N.
Kondratyeva75, E. Kondratyuk111, A. Konevskikh56, M. Kopcik115, P.
Kostarakis89, M. Kour91, C. Kouzinopoulos35, O. Kovalenko77, V. Kovalenko131,
M. Kowalski117, G. Koyithatta Meethaleveedu47, I. Králik59, A. Kravčáková40,
M. Krivda59,101, F. Krizek84, E. Kryshen86,35, M. Krzewicki42, A.M. Kubera20,
V. Kučera84, C. Kuhn55, P.G. Kuijer82, A. Kumar91, J. Kumar47, L. Kumar88, S.
Kumar47, P. Kurashvili77, A. Kurepin56, A.B. Kurepin56, A. Kuryakin99, M.J.
Kweon50, Y. Kwon137, S.L. La Pointe110, P. La Rocca28, P. Ladron de Guevara11,
C. Lagana Fernandes120, I. Lakomov35, R. Langoy41, C. Lara52, A. Lardeux15, A.
Lattuca26, E. Laudi35, R. Lea25, L. Leardini94, G.R. Lee101, S. Lee137, F.
Lehas82, R.C. Lemmon83, V. Lenti103, E. Leogrande57, I. León Monzón119, H.
León Vargas64, M. Leoncino26, P. Lévai135, S. Li7,70, X. Li14, J. Lien41, R.
Lietava101, S. Lindal22, V. Lindenstruth42, C. Lippmann97, M.A. Lisa20, H.M.
Ljunggren33, D.F. Lodato57, P.I. Loenne18, V. Loginov75, C. Loizides74, X.
Lopez70, E. López Torres9, A. Lowe135, P. Luettig53, M. Lunardon29, G.
Luparello25, T.H. Lutz136, A. Maevskaya56, M. Mager35, S. Mahajan91, S.M.
Mahmood22, A. Maire55, R.D. Majka136, M. Malaev86, I. Maldonado Cervantes63,
L. MalininaIV,66, D. Mal’Kevich58, P. Malzacher97, A. Mamonov99, V. Manko80,
F. Manso70, V. Manzari103,35, M. Marchisone126,65,26, J. Mareš60, G.V.
Margagliotti25, A. Margotti104, J. Margutti57, A. Marín97, C. Markert118, M.
Marquard53, N.A. Martin97, J. Martin Blanco113, P. Martinengo35, M.I.
Martínez2, G. Martínez García113, M. Martinez Pedreira35, A. Mas120, S.
Masciocchi97, M. Masera26, A. Masoni105, A. Mastroserio32, A. Matyja117, C.
Mayer117, J. Mazer125, M.A. Mazzoni108, D. Mcdonald122, F. Meddi23, Y.
Melikyan75, A. Menchaca-Rocha64, E. Meninno30, J. Mercado Pérez94, M. Meres38,
Y. Miake128, M.M. Mieskolainen45, K. Mikhaylov66,58, L. Milano35,74, J.
Milosevic22, A. Mischke57, A.N. Mishra48, D. Miśkowiec97, J. Mitra132, C.M.
Mitu62, N. Mohammadi57, B. Mohanty79,132, L. Molnar113,55, L. Montaño
Zetina11, E. Montes10, D.A. Moreira De Godoy54, L.A.P. Moreno2, S. Moretto29,
A. Morreale113, A. Morsch35, V. Muccifora72, E. Mudnic116, D. Mühlheim54, S.
Muhuri132, M. Mukherjee132, J.D. Mulligan136, M.G. Munhoz120, R.H.
Munzer93,36,53, H. Murakami127, S. Murray65, L. Musa35, J. Musinsky59, B.
Naik47, R. Nair77, B.K. Nandi47, R. Nania104, E. Nappi103, M.U. Naru16, H.
Natal da Luz120, C. Nattrass125, S.R. Navarro2, K. Nayak79, R. Nayak47, T.K.
Nayak132, S. Nazarenko99, A. Nedosekin58, L. Nellen63, F. Ng122, M.
Nicassio97, M. Niculescu62, J. Niedziela35, B.S. Nielsen81, S. Nikolaev80, S.
Nikulin80, V. Nikulin86, F. Noferini104,12, P. Nomokonov66, G. Nooren57,
J.C.C. Noris2, J. Norman124, A. Nyanin80, J. Nystrand18, H. Oeschler94, S.
Oh136, S.K. Oh67, A. Ohlson35, A. Okatan69, T. Okubo46, L. Olah135, J.
Oleniacz133, A.C. Oliveira Da Silva120, M.H. Oliver136, J. Onderwaater97, C.
Oppedisano110, R. Orava45, M. Oravec115, A. Ortiz Velasquez63, A. Oskarsson33,
J. Otwinowski117, K. Oyama94,76, M. Ozdemir53, Y. Pachmayer94, D. Pagano26, P.
Pagano30, G. Paić63, S.K. Pal132, J. Pan134, A.K. Pandey47, V. Papikyan1, G.S.
Pappalardo106, P. Pareek48, W.J. Park97, S. Parmar88, A. Passfeld54, V.
Paticchio103, R.N. Patra132, B. Paul100, H. Pei7, T. Peitzmann57, H. Pereira
Da Costa15, D. Peresunko80,75, C.E. Pérez Lara82, E. Perez Lezama53, V.
Peskov53, Y. Pestov5, V. Petráček39, V. Petrov111, M. Petrovici78, C. Petta28,
S. Piano109, M. Pikna38, P. Pillot113, L.O.D.L. Pimentel81, O. Pinazza104,35,
L. Pinsky122, D.B. Piyarathna122, M. Płoskoń74, M. Planinic129, J. Pluta133,
S. Pochybova135, P.L.M. Podesta-Lerma119, M.G. Poghosyan85,87, B.
Polichtchouk111, N. Poljak129, W. Poonsawat114, A. Pop78, S. Porteboeuf-
Houssais70, J. Porter74, J. Pospisil84, S.K. Prasad4, R. Preghenella104,35, F.
Prino110, C.A. Pruneau134, I. Pshenichnov56, M. Puccio26, G. Puddu24, P.
Pujahari134, V. Punin99, J. Putschke134, H. Qvigstad22, A. Rachevski109, S.
Raha4, S. Rajput91, J. Rak123, A. Rakotozafindrabe15, L. Ramello31, F. Rami55,
R. Raniwala92, S. Raniwala92, S.S. Räsänen45, B.T. Rascanu53, D. Rathee88,
K.F. Read85,125, K. Redlich77, R.J. Reed134, A. Rehman18, P. Reichelt53, F.
Reidt94,35, X. Ren7, R. Renfordt53, A.R. Reolon72, A. Reshetin56, K.
Reygers94, V. Riabov86, R.A. Ricci73, T. Richert33, M. Richter22, P.
Riedler35, W. Riegler35, F. Riggi28, C. Ristea62, E. Rocco57, M. Rodríguez
Cahuantzi11,2, A. Rodriguez Manso82, K. Røed22, E. Rogochaya66, D. Rohr42, D.
Röhrich18, F. Ronchetti72,35, L. Ronflette113, P. Rosnet70, A. Rossi35,29, F.
Roukoutakis89, A. Roy48, C. Roy55, P. Roy100, A.J. Rubio Montero10, R. Rui25,
R. Russo26, E. Ryabinkin80, Y. Ryabov86, A. Rybicki117, S. Saarinen45, S.
Sadhu132, S. Sadovsky111, K. Šafařík35, B. Sahlmuller53, P. Sahoo48, R.
Sahoo48, S. Sahoo61, P.K. Sahu61, J. Saini132, S. Sakai72, M.A. Saleh134, J.
Salzwedel20, S. Sambyal91, V. Samsonov86, L. Šándor59, A. Sandoval64, M.
Sano128, D. Sarkar132, N. Sarkar132, P. Sarma44, E. Scapparone104, F.
Scarlassara29, C. Schiaua78, R. Schicker94, C. Schmidt97, H.R. Schmidt34, S.
Schuchmann53, J. Schukraft35, M. Schulc39, Y. Schutz35,113, K. Schwarz97, K.
Schweda97, G. Scioli27, E. Scomparin110, R. Scott125, M. Šefčík40, J.E.
Seger87, Y. Sekiguchi127, D. Sekihata46, I. Selyuzhenkov97, K. Senosi65, S.
Senyukov3,35, E. Serradilla10,64, A. Sevcenco62, A. Shabanov56, A.
Shabetai113, O. Shadura3, R. Shahoyan35, M.I. Shahzad16, A. Shangaraev111, A.
Sharma91, M. Sharma91, M. Sharma91, N. Sharma125, A.I. Sheikh132, K.
Shigaki46, Q. Shou7, K. Shtejer9,26, Y. Sibiriak80, S. Siddhanta105, K.M.
Sielewicz35, T. Siemiarczuk77, D. Silvermyr33, C. Silvestre71, G.
Simatovic129, G. Simonetti35, R. Singaraju132, R. Singh79, S. Singha79,132, V.
Singhal132, B.C. Sinha132, T. Sinha100, B. Sitar38, M. Sitta31, T.B. Skaali22,
M. Slupecki123, N. Smirnov136, R.J.M. Snellings57, T.W. Snellman123, J.
Song96, M. Song137, Z. Song7, F. Soramel29, S. Sorensen125, R.D.de Souza121,
F. Sozzi97, M. Spacek39, E. Spiriti72, I. Sputowska117, M. Spyropoulou-
Stassinaki89, J. Stachel94, I. Stan62, P. Stankus85, E. Stenlund33, G.
Steyn65, J.H. Stiller94, D. Stocco113, P. Strmen38, A.A.P. Suaide120, T.
Sugitate46, C. Suire51, M. Suleymanov16, M. SuljicI,25, R. Sultanov58, M.
Šumbera84, S. Sumowidagdo49, A. Szabo38, A. Szanto de ToledoI,120, I.
Szarka38, A. Szczepankiewicz35, M. Szymanski133, U. Tabassam16, J.
Takahashi121, G.J. Tambave18, N. Tanaka128, M. Tarhini51, M. Tariq19, M.G.
Tarzila78, A. Tauro35, G. Tejeda Muñoz2, A. Telesca35, K. Terasaki127, C.
Terrevoli29, B. Teyssier130, J. Thäder74, D. Thakur48, D. Thomas118, R.
Tieulent130, A.R. Timmins122, A. Toia53, S. Trogolo26, G. Trombetta32, V.
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L. Valencia Palomo70, S. Vallero26, J. Van Der Maarel57, J.W. Van Hoorne35, M.
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A. Vinogradov80, L. Vinogradov131, Y. VinogradovI,99, T. Virgili30, V.
Vislavicius33, Y.P. Viyogi132, A. Vodopyanov66, M.A. Völkl94, K. Voloshin58,
S.A. Voloshin134, G. Volpe32,135, B. von Haller35, I. Vorobyev36,93, D.
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Wang57, M. Wang7,113, D. Watanabe128, Y. Watanabe127, M. Weber35,112, S.G.
Weber97, D.F. Weiser94, J.P. Wessels54, U. Westerhoff54, A.M. Whitehead90, J.
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Windelband94, M. Winn94, H. Yang57, P. Yang7, S. Yano46, Z. Yasin16, Z. Yin7,
H. Yokoyama128, I.-K. Yoo96, J.H. Yoon50, V. Yurchenko3, I. Yushmanov80, A.
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S. Zaporozhets66, N. Zardoshti101, A. Zarochentsev131, P. Závada60, N.
Zaviyalov99, H. Zbroszczyk133, I.S. Zgura62, M. Zhalov86, H. Zhang18, X.
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Zhou7, Y. Zhou81, Z. Zhou18, H. Zhu18, J. Zhu7,113, A. Zichichi27,12, A.
Zimmermann94, M.B. Zimmermann54,35, G. Zinovjev3, M. Zyzak42

Affiliation Notes

I Deceased
II Also at: Georgia State University, Atlanta, Georgia, United States
III Also at Department of Applied Physics, Aligarh Muslim University, Aligarh,
India
IV Also at: M.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute
of Nuclear, Physics, Moscow, Russia

Collaboration Institutes

1 A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute)
Foundation, Yerevan, Armenia
2 Benemérita Universidad Autónoma de Puebla, Puebla, Mexico
3 Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine
4 Bose Institute, Department of Physics and Centre for Astroparticle Physics
and Space Science (CAPSS), Kolkata, India
5 Budker Institute for Nuclear Physics, Novosibirsk, Russia
6 California Polytechnic State University, San Luis Obispo, California, United
States
7 Central China Normal University, Wuhan, China
8 Centre de Calcul de l’IN2P3, Villeurbanne, France
9 Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana,
Cuba
10 Centro de Investigaciones Energéticas Medioambientales y Tecnológicas
(CIEMAT), Madrid, Spain
11 Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City
and Mérida, Mexico
12 Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche “Enrico
Fermi”, Rome, Italy
13 Chicago State University, Chicago, Illinois, USA
14 China Institute of Atomic Energy, Beijing, China
15 Commissariat à l’Energie Atomique, IRFU, Saclay, France
16 COMSATS Institute of Information Technology (CIIT), Islamabad, Pakistan
17 Departamento de Física de Partículas and IGFAE, Universidad de Santiago de
Compostela, Santiago de Compostela, Spain
18 Department of Physics and Technology, University of Bergen, Bergen, Norway
19 Department of Physics, Aligarh Muslim University, Aligarh, India
20 Department of Physics, Ohio State University, Columbus, Ohio, United States
21 Department of Physics, Sejong University, Seoul, South Korea
22 Department of Physics, University of Oslo, Oslo, Norway
23 Dipartimento di Fisica dell’Università ’La Sapienza’ and Sezione INFN Rome,
Italy
24 Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy
25 Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy
26 Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy
27 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Bologna, Italy
28 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Catania, Italy
29 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Padova, Italy
30 Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo
Collegato INFN, Salerno, Italy
31 Dipartimento di Scienze e Innovazione Tecnologica dell’Università del
Piemonte Orientale and Gruppo Collegato INFN, Alessandria, Italy
32 Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari,
Italy
33 Division of Experimental High Energy Physics, University of Lund, Lund,
Sweden
34 Eberhard Karls Universität Tübingen, Tübingen, Germany
35 European Organization for Nuclear Research (CERN), Geneva, Switzerland
36 Excellence Cluster Universe, Technische Universität München, Munich,
Germany
37 Faculty of Engineering, Bergen University College, Bergen, Norway
38 Faculty of Mathematics, Physics and Informatics, Comenius University,
Bratislava, Slovakia
39 Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Prague, Czech Republic
40 Faculty of Science, P.J. Šafárik University, Košice, Slovakia
41 Faculty of Technology, Buskerud and Vestfold University College, Vestfold,
Norway
42 Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-
Universität Frankfurt, Frankfurt, Germany
43 Gangneung-Wonju National University, Gangneung, South Korea
44 Gauhati University, Department of Physics, Guwahati, India
45 Helsinki Institute of Physics (HIP), Helsinki, Finland
46 Hiroshima University, Hiroshima, Japan
47 Indian Institute of Technology Bombay (IIT), Mumbai, India
48 Indian Institute of Technology Indore, Indore (IITI), India
49 Indonesian Institute of Sciences, Jakarta, Indonesia
50 Inha University, Incheon, South Korea
51 Institut de Physique Nucléaire d’Orsay (IPNO), Université Paris-Sud, CNRS-
IN2P3, Orsay, France
52 Institut für Informatik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany
53 Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany
54 Institut für Kernphysik, Westfälische Wilhelms-Universität Münster,
Münster, Germany
55 Institut Pluridisciplinaire Hubert Curien (IPHC), Université de Strasbourg,
CNRS-IN2P3, Strasbourg, France
56 Institute for Nuclear Research, Academy of Sciences, Moscow, Russia
57 Institute for Subatomic Physics of Utrecht University, Utrecht, Netherlands
58 Institute for Theoretical and Experimental Physics, Moscow, Russia
59 Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovakia
60 Institute of Physics, Academy of Sciences of the Czech Republic, Prague,
Czech Republic
61 Institute of Physics, Bhubaneswar, India
62 Institute of Space Science (ISS), Bucharest, Romania
63 Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico
64 Instituto de Física, Universidad Nacional Autónoma de México, Mexico City,
Mexico
65 iThemba LABS, National Research Foundation, Somerset West, South Africa
66 Joint Institute for Nuclear Research (JINR), Dubna, Russia
67 Konkuk University, Seoul, South Korea
68 Korea Institute of Science and Technology Information, Daejeon, South Korea
69 KTO Karatay University, Konya, Turkey
70 Laboratoire de Physique Corpusculaire (LPC), Clermont Université,
Université Blaise Pascal, CNRS–IN2P3, Clermont-Ferrand, France
71 Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-
Alpes, CNRS-IN2P3, Grenoble, France
72 Laboratori Nazionali di Frascati, INFN, Frascati, Italy
73 Laboratori Nazionali di Legnaro, INFN, Legnaro, Italy
74 Lawrence Berkeley National Laboratory, Berkeley, California, United States
75 Moscow Engineering Physics Institute, Moscow, Russia
76 Nagasaki Institute of Applied Science, Nagasaki, Japan
77 National Centre for Nuclear Studies, Warsaw, Poland
78 National Institute for Physics and Nuclear Engineering, Bucharest, Romania
79 National Institute of Science Education and Research, Bhubaneswar, India
80 National Research Centre Kurchatov Institute, Moscow, Russia
81 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
82 Nikhef, Nationaal instituut voor subatomaire fysica, Amsterdam, Netherlands
83 Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom
84 Nuclear Physics Institute, Academy of Sciences of the Czech Republic, Řež u
Prahy, Czech Republic
85 Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States
86 Petersburg Nuclear Physics Institute, Gatchina, Russia
87 Physics Department, Creighton University, Omaha, Nebraska, United States
88 Physics Department, Panjab University, Chandigarh, India
89 Physics Department, University of Athens, Athens, Greece
90 Physics Department, University of Cape Town, Cape Town, South Africa
91 Physics Department, University of Jammu, Jammu, India
92 Physics Department, University of Rajasthan, Jaipur, India
93 Physik Department, Technische Universität München, Munich, Germany
94 Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
95 Purdue University, West Lafayette, Indiana, United States
96 Pusan National University, Pusan, South Korea
97 Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum
für Schwerionenforschung, Darmstadt, Germany
98 Rudjer Bošković Institute, Zagreb, Croatia
99 Russian Federal Nuclear Center (VNIIEF), Sarov, Russia
100 Saha Institute of Nuclear Physics, Kolkata, India
101 School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom
102 Sección Física, Departamento de Ciencias, Pontificia Universidad Católica
del Perú, Lima, Peru
103 Sezione INFN, Bari, Italy
104 Sezione INFN, Bologna, Italy
105 Sezione INFN, Cagliari, Italy
106 Sezione INFN, Catania, Italy
107 Sezione INFN, Padova, Italy
108 Sezione INFN, Rome, Italy
109 Sezione INFN, Trieste, Italy
110 Sezione INFN, Turin, Italy
111 SSC IHEP of NRC Kurchatov institute, Protvino, Russia
112 Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria
113 SUBATECH, Ecole des Mines de Nantes, Université de Nantes, CNRS-IN2P3,
Nantes, France
114 Suranaree University of Technology, Nakhon Ratchasima, Thailand
115 Technical University of Košice, Košice, Slovakia
116 Technical University of Split FESB, Split, Croatia
117 The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of
Sciences, Cracow, Poland
118 The University of Texas at Austin, Physics Department, Austin, Texas, USA
119 Universidad Autónoma de Sinaloa, Culiacán, Mexico
120 Universidade de São Paulo (USP), São Paulo, Brazil
121 Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil
122 University of Houston, Houston, Texas, United States
123 University of Jyväskylä, Jyväskylä, Finland
124 University of Liverpool, Liverpool, United Kingdom
125 University of Tennessee, Knoxville, Tennessee, United States
126 University of the Witwatersrand, Johannesburg, South Africa
127 University of Tokyo, Tokyo, Japan
128 University of Tsukuba, Tsukuba, Japan
129 University of Zagreb, Zagreb, Croatia
130 Université de Lyon, Université Lyon 1, CNRS/IN2P3, IPN-Lyon, Villeurbanne,
France
131 V. Fock Institute for Physics, St. Petersburg State University, St.
Petersburg, Russia
132 Variable Energy Cyclotron Centre, Kolkata, India
133 Warsaw University of Technology, Warsaw, Poland
134 Wayne State University, Detroit, Michigan, United States
135 Wigner Research Centre for Physics, Hungarian Academy of Sciences,
Budapest, Hungary
136 Yale University, New Haven, Connecticut, United States
137 Yonsei University, Seoul, South Korea
138 Zentrum für Technologietransfer und Telekommunikation (ZTT),
Fachhochschule Worms, Worms, Germany