2015 082 28 March

Coherent $\rho^{0}$ photoproduction

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

We report the first measurement at the LHC of coherent photoproduction of
$\rho^{0}$ mesons in ultra-peripheral Pb–Pb collisions. The invariant mass and
transverse momentum distributions for $\rho^{0}$ production are studied in the
$\pi^{+}\pi^{-}$ decay channel at mid-rapidity. The production cross section
in the rapidity range $|y|<$ 0.5 is found to be
$\mathrm{d}\sigma/\mathrm{d}y=425\pm 10\,(\mathrm{stat.})$
${}^{+42}_{-50}\,(\mathrm{sys.})$ mb. Coherent $\rho^{0}$ production is
studied with and without requirement of nuclear breakup, and the fractional
yields for various breakup scenarios are presented. The results are compared
with those from lower energies and with model predictions.

##  1 Introduction

Charged particle beams at the LHC generate an electromagnetic field which can
be regarded as a beam of quasi–real photons; thus at the LHC, besides hadronic
interactions, also photonuclear and photon–photon interactions occur.
Collisions in which the impact parameter exceeds the sum of the radii of the
incoming beam particles are called ultra–peripheral collisions (UPC). In UPC
the cross section for hadronic processes is strongly suppressed, while the
cross sections for two–photon and photonuclear interactions remain large. This
is particularly the case for heavy ions, because the intensity of the photon
flux grows with the square of the ion charge, $Z$. A number of reviews of UPC
are available; e.g., [1, 2]. The ALICE Collaboration has previously studied
exclusive photoproduction of $J/\psi$ in ultra-peripheral Pb–Pb and p–Pb
collisions [3, 4, 5].

Exclusive photoproduction of $\rho^{0}$ vector mesons,
$\mathrm{Pb+Pb}\rightarrow\mathrm{Pb+Pb}+\rho^{0}$, can be described as the
fluctuation of a quasi-real photon into a virtual $\rho^{0}$ vector meson,
which then scatters elastically off the target nucleus. Two cases can be
distinguished. When the interaction involves the complete target nucleus, the
process is called coherent. In this case the target nucleus normally remains
intact. If the virtual $\rho^{0}$ vector meson scatters off only one of the
nucleons in the target, then the process is called incoherent and in this case
the target nucleus normally breaks up, emitting neutrons at very forward
rapidities. For coherent processes, the size of the lead ion restricts the
mean transverse momentum of the vector meson to be about 60 MeV/$c$
corresponding to a de Broglie wavelength of the nuclear size, while it is of
the order of 500 MeV/$c$ for incoherent processes.

Because of the strong electromagnetic fields in ultra-peripheral collisions of
heavy ions, multiple photons may be exchanged in a single event. The
additional photons can lead to excitation of the nuclei. The dominant process
is the excitation to a Giant Dipole Resonance [6]. As these photonuclear
processes occur on a different time scale, they are assumed to be independent,
so the probabilities factorize. The excited nucleus typically decays by the
emission of neutrons at very forward rapidities. The signature of these
processes is thus a $\rho^{0}$ vector meson with very low transverse momentum
which may be accompanied by a few neutrons at very forward rapidities but no
other particles.

Photoproduction of $\rho^{0}$ vector mesons on nuclear targets has been
studied in fixed target experiments with lepton beams [7], and more recently
in ultra-peripheral collisions by the STAR Collaboration at RHIC at
$\sqrt{s_{\rm NN}}=$ 62 [8], 130 [9], and $200$ GeV [10]. STAR has also
observed coherent photoproduction of the $\rho^{0}(1700)$ [11].

The $\rho^{0}$ vector meson gives the dominant contribution to the hadronic
structure of the photon. For proton targets, the process
$\gamma+p\rightarrow\rho^{0}+p$ contributes about 10% to 20% of the total
$\gamma+p$ cross section, depending on energy [12]. Scaling from a nucleon
target to a nuclear target is often done using the Glauber model assuming
Vector Meson Dominance [13]. The large value of
$\sigma(\gamma+\mathrm{p}\rightarrow\rho^{0}+\mathrm{p})$ means that for heavy
nuclei one may reach the limit where the target appears like a black disk and
the total $\rho^{0}+A$ cross section approaches $2\pi R_{A}^{2}$ ($R_{A}$ is
the nuclear radius). The situation may, however, be more complicated for
several reasons. The cross section
$\sigma(\gamma+\mathrm{p}\rightarrow\rho^{0}+\mathrm{p})$ has contributions
both from Reggeon and Pomeron exchange, and its energy dependence is therefore
not monotonic. Furthermore, the nuclear medium might modify the Reggeon and
Pomeron components differently. There may also be interference between the
$\rho$ and $\rho^{\prime}$ production amplitudes, and these amplitudes may be
affected by the nuclear environment in a different way [14]. A detailed
discussion of models for photoproduction of $\rho^{0}$ on complex nuclei based
on data from fixed target experiments can be found in [13].

The cross sections measured by STAR [9, 10, 8] at RHIC were found to be about
a factor two less than that predicted by the calculation of Ref. [15], while
in agreement with STARLIGHT [16]. The reason for the difference between these
two models, which both use the Glauber model to obtain the $\gamma$-nucleus
cross section, will be discussed below. The many issues associated with
calculating the photonuclear $\rho^{0}$ cross section and the discrepancies
between models thus call for more data. In particular, it is important to
establish if the trends seen at lower energies persist at higher energies.

Moreover, the total cross section for exclusive $\rho^{0}$ production is very
large at LHC energies, with the models mentioned above predicting that it
could be between 50–100% of the total hadronic inelastic cross section. It
could thus constitute a significant background, e.g. at the trigger level, to
low multiplicity peripheral hadronic interactions and to other types of ultra-
peripheral collisions. It therefore has to be well understood. The high
statistics in the $\rho^{0}$ sample allows the predictions for exclusive
$\rho^{0}$ production accompanied by nuclear fragmentation to be tested with
good precision.

This paper presents the first measurement of the cross section for coherent
photoproduction of $\rho^{0}$ vector mesons in Pb–Pb collisions at the LHC.
The $\rho^{0}$ is reconstructed using the $\pi^{+}\pi^{-}$ decay channel in
the rapidity range $|y|<$ 0.5. The rapidity interval corresponds to a
$\gamma$-nucleon center of mass energy in the range $36\leq W_{\gamma N}\leq
59$ GeV with $\langle W_{\gamma N}\rangle=$ 48 GeV, about a factor of 4 higher
than in any previous measurement [10]. The cross section is measured for the
cases of no neutron emission and for at least one emitted neutron. The new
data presented in this paper will hopefully help to clarify some of the
theoretical uncertainties mentioned above.

##  2 The ALICE experiment and the UPC trigger

A full description of the ALICE detectors and their performance can be found
in [17, 18]; here, only the components relevant for this analysis will be
briefly described. The Inner Tracking System (ITS) and Time Projection Chamber
(TPC) are used to measure and identify the tracks of the decay products of the
$\rho^{0}$ vector meson. The ITS consists of six layers of silicon detectors
covering the full azimuthal angle. The two innermost layers form the Silicon
Pixel Detector (SPD) with a pseudorapidity acceptance of $|\eta|<1.4$. The SPD
also provides trigger information at the lowest level. Two layers of silicon
drift and two of silicon strip detectors complement the ITS, and all six
layers have an acceptance of $|\eta|<0.9$. The TPC is the main tracking
detector of ALICE. It has a Ne–CO2–N2 gas mixture contained in a large –
almost 90 m3 – cylindrical drift detector with a central membrane at high
voltage and two readout planes, composed of multi-wire proportional chambers,
at the end caps. It covers the full azimuth and $|\eta|<0.9$ for full length
tracks. It also provides a measurement of the ionization energy loss,
d$E/$d$x$, which allows the identification of particles. The TPC and ITS are
situated inside a large solenoid magnet providing a B = 0.5 T field.

The measurement of neutrons emitted at forward rapidities is performed with a
set of two neutron Zero Degree Calorimeters (ZDC) located 114 m away on each
side of the interaction point. The ZDC has a 99% detection probability for
neutrons with $|\eta|>8.8$[19]. Figure 1 illustrates the capabilities of the
ZDC to separate the emission of zero, one or several neutrons at zero degrees.
The sample appearing in this figure was obtained from events fulfilling the
event selection described in Section 3.

Figure 1: Energy deposit in the Zero-Degree Calorimeters. The curves
correspond to Gaussian fits for 0, 1, 2, 3, or 4 neutrons entering the
calorimeter. The plot is for events satisfying the requirements (i)–(vi)
described in the text.

In addition to the SPD, this analysis uses the Time of Flight (TOF) and VZERO
detectors for triggering. TOF is a large cylindrical barrel surrounding the
TPC. It has 18 sectors in azimuth, each made of multigap resistive plate
chambers distributed in five gas-tight modules, with a total of 152928 read-
out channels and an intrinsic time resolution better than 50 ps. The
pseudorapidity acceptance is the same as for the TPC. The VZERO consists of
two arrays of scintillators called VZERO-A and VZERO-C, covering the
pseudorapidity ranges $2.8<\eta<5.1$ (VZERO-A) and $-3.7<\eta<-1.7$ (VZERO-C).
Its time resolution, better than 500 ps [20], allows beam-beam collisions to
be distinguished from beam-gas collisions.

The data used for this analysis were collected during the 2010 Pb–Pb run of
the LHC at an energy of $\sqrt{s_{\rm NN}}=2.76$ TeV. Two different triggers
were used. At the beginning of the run, when the luminosity was low, the
trigger requirement was at least two hits in the TOF detector. When the
luminosity was increased the trigger selection was strengthened to improve the
purity by additionally requiring at least two hits in the outer layer of the
SPD, and no activity in any of the VZERO arrays.

The luminosity is determined from the cross section for triggering on at least
one neutron in the ZDC detectors [19]. This cross section has been determined
from a van der Meer scan [21] to be $371.4\pm
0.6\,(\mathrm{stat.})^{+24}_{-19}\,(\mathrm{syst.})$ b [18]. The integrated
luminosities for the two samples are $48^{+3}_{-2}$ mb-1 (TOF trigger only)
and $214^{+14}_{-11}$ mb-1 (SPD+TOF+VZERO trigger).

##  3 Track and event selection

In addition to the trigger selection, the events used for the analysis are
required to fulfill the following requirements:

  1. i)

a primary vertex has to be identified within 10 cm of the nominal interaction
point position, along the beam direction;

  2. ii)

the event is required to have exactly two tracks reconstructed in the TPC and
ITS satisfying the track selections discussed below;

  3. iii)

the VZERO arrays are required to be empty (the difference between the offline
and online VZERO selection will be discussed below);

  4. iv)

the energy loss in the TPC has to be consistent with that for pions within $4$
standard deviations from the Bethe-Bloch expectations, i.e.,
$\Delta\sigma_{\pi^{+}}^{2}+\Delta\sigma_{\pi^{-}}^{2}<16$ (see Fig. 2);

  5. v)

the track pairs used to define the coherent signal have to have a transverse
momentum below $150$ MeV/$c$ and rapidity $|y|<$ 0.5, the latter requirement
being imposed to avoid edge effects;

  6. vi)

the track pairs used to define the coherent signal are required to have tracks
of opposite charge.

The background estimated from like-sign pairs ($\pi^{+}\pi^{+}$ and
$\pi^{-}\pi^{-}$) is below 2% and it is subtracted from the final sample bin-
by-bin in invariant mass.

The track selection requires that each track has at least 70 space points, out
of a maximum of 159, in the TPC and a $\chi^{2}$ per degree of freedom from
the Kalman fit procedure better than 4. Each track has at least one hit in the
SPD with a $\chi^{2}$ per ITS hit less than 36. The distance of closest
approach between the track and the primary vertex has to be less than 2 cm
along the beam direction and less than $0.0182+0.035/p^{1.01}_{T}$ cm ($p_{\rm
T}$ in GeV/c) in the plane perpendicular to the beam direction. These track
selection cuts are based on studies of the detector performance [18].

Three other track selections are used in order to estimate systematic errors.
These differ from the default track selection described above in the following
ways: (a) accepting tracks reconstructed only in the ITS in addition to
combined ITS-TPC tracks satisfying the default track selection; (b) using only
TPC information and accepting tracks having at least 50 space points in the
TPC; (c) using the default track cuts with stronger requirements on TPC
variables. The latter requirements meant that the tracks had to pass at least
120 of the 159 TPC pad rows and have a cluster in more than 80% of the crossed
pad rows. For the cross section calculation, the mean of the results of the
four different track selection methods is used. The systematic error related
to the track selection is estimated from the deviation from the mean. This
contributes ${}^{+3.7}_{-3.0}$% to the systematic error.

The momentum resolution of the ALICE central barrel tracking system [18]
translates into a resolution in transverse momentum of single
$\pi^{+}\pi^{-}$–pairs better than 4 MeV/c in the kinematic range studied
here. Similarly, the resolution in invariant mass varies between 2 MeV/$c^{2}$
($M_{\pi\pi}=0.4$ GeV/$c^{2}$) and 6 MeV/$c^{2}$ ($M_{\pi\pi}=1.5$
GeV/$c^{2}$).

Figure 2: Identification of $\pi^{+/-}$ from the TPC d$E$/d$x$. The $x$– and
$y$–axes show the deviation of the measured energy loss from the Bethe-Bloch
(BB) expectations for positive and negative tracks, respectively. The scale is
such that one unit corresponds to one standard deviation. The circle,
corresponding to $4\sigma$, shows the selection used. The entries in the upper
right corner are from $e^{+}e^{-}$ pairs produced in two-photon interactions.
The plot is for events satisfying the requirements (i)–(iii) and (v) – (vi)
described in the text.

The ionization energy loss for the selected tracks is shown in Fig. 2. The
scale on both axes is in units of the number of standard deviations from the
Bethe-Bloch expectation in the TPC; in this way the dependence on track
momentum is removed. Pions can be clearly identified by the $4\sigma$ circle
centered on $(0,0)$, while the events above and to the right of the pions are
mostly $e^{+}e^{-}$ pairs from $\gamma\gamma$ $\rightarrow$ $e^{+}e^{-}$. This
figure shows that any possible contamination from kaons or protons in the
sample is negligible. There could, however, be a contamination from muons from
the process $\gamma\gamma\rightarrow\mu^{+}\mu^{-}$, which cannot be
distinguished from pions using the energy loss. This contribution can be
estimated from the number of $e^{+}e^{-}$ pairs in the data sample, as the
cross sections for $\gamma\gamma\rightarrow\mu^{+}\mu^{-}$ and
$\gamma\gamma\rightarrow e^{+}e^{-}$ are about the same at midrapidity for
invariant masses well above threshold. It can also be calculated from
STARLIGHT [22, 23]. Both methods give an expected number of muon pairs of
about 5%, which is not corrected for, but added to the systematic error. The
contribution from $\gamma\gamma\rightarrow\pi^{+}\pi^{-}$ is expected to be
much smaller than from $\gamma\gamma\rightarrow\mu^{+}\mu^{-}$. The
$\pi^{+}\pi^{-}$ cross section is reduced by the form factor of the pion, see
e.g. [24], so this contribution is not considered.

##  4 Data analysis

Using the event and track selection described in the previous section, the
four–momenta of the two tracks are constructed and pair variables are
extracted. The resulting distribution of the pair transverse momentum is shown
in Fig. 3 for events with $0.4$ $\leq$ $M_{\pi\pi}$ $\leq$ $1.1$ GeV/$c^{2}$
and $|y|<$ 0.5. A peak at low transverse momentum ($p_{\rm T}<0.15$ GeV/$c$),
corresponding to coherent production, is clearly seen. The distribution is
compared with the corresponding distributions from STARLIGHT [16, 23] events
for coherent and incoherent $\rho^{0}$ production, processed through the
detector response simulation based on GEANT 3. The coherent peak is shifted to
slightly lower $p_{\rm T}$ in data than that predicted by STARLIGHT. A similar
trend has been observed by STAR at lower energies [25]. The shape of the
coherent peak in the $p_{\rm T}$ distribution is determined by the nuclear
form factor. The form factor used in STARLIGHT is consistent with what is
obtained from elastic electron-nucleus scattering, which probes the charge
content of the nucleus. Since the $\rho^{0}$ couples to both neutrons and
protons, a possible explanation of this difference could thus be the presence
of a “neutron skin”. The effect, however, appears larger than what the current
limit on the difference between neutron and proton radius in
${}^{208}\mathrm{Pb}$ (0.3 fm) allows [26], and is thus not fully understood.
Data also show a dip around $p_{T}=0.12$ GeV/$c$, which is not present in the
model. The absence of this dip in the model can be understood from the fact
that in STARLIGHT the transverse momentum of the photon is considered, and
this reduces the dip one would expect from the form factor of the target
nucleus alone. In a Glauber calculation, the transverse momentum distribution
is determined from a Fourier transform of the nuclear profile function, see
e.g. [2], and the direct dependence on the form factor is only an
approximation; this could also contribute to explaining the difference between
STARLIGHT and data. The high-$p_{\rm T}$ tail of the distribution is very well
described by the incoherent $p_{\rm T}$ spectrum from STARLIGHT.

The transverse momentum distribution for coherent production may also be
parameterized as an exponential,
$\mathrm{d}N/\mathrm{d}t\propto\mathrm{exp}(bt)$ where $t=-p_{T}^{2}$. Fitting
the ALICE data to such a function gives $b=428\pm 6(\mathrm{stat.})\pm
15(\mathrm{syst.})$ GeV2/$c^{2}$. The systematic error has been obtained as
the difference in slope between STARLIGHT events and STARLIGHT events
processed through the full detector simulation. The ALICE result can be
compared with the corresponding measurement by STAR, where $b=388\pm 24$
GeV2/$c^{2}$ was found [10]. The STAR and ALICE results are consistent within
errors if one takes into consideration that $b$ is expected to be
$\approx$4–8% larger for a lead nucleus than for a gold nucleus because of the
difference in size (one expects $b\propto R^{2}$). The fit was performed for
$|t|>0.002$ GeV2/$c^{2}$ to avoid interference effects at very low $p_{T}$
[10].

Figure 3: Transverse momentum distributions for $\pi^{+}\pi^{-}$–pairs. The
dashed (red) and dash-dotted (blue) histograms show the normalized $p_{\rm T}$
distribution from STARLIGHT passed through the detector response simulation
for coherent and incoherent $\rho^{0}$ production, respectively. The solid
(black) histogram is the sum of the two.

The final sample of coherent $\rho^{0}\to\pi^{+}\pi^{-}$ candidates is
corrected for acceptance and efficiency in invariant mass bins. The event
sample used to determine the corrections has uniform distributions in
invariant mass, rapidity, transverse momentum, and azimuthal angle over the
ranges $2m_{\pi}$ $\leq$ $M_{\pi\pi}$ $\leq$ $1.5$ GeV/$c^{2}$, $|y|$ $\leq$
$1.0$, $p_{\rm T}$ $\leq$ $0.15$ GeV/$c$, and $0$ $\leq$ $\phi$ $\leq$ $2\pi$.
Using a flat distribution in transverse momentum is justified over the narrow
range $p_{\rm T}$ $\leq$ $0.15$ GeV/$c$, where the acceptance and efficiency
are constant. All models predict only a very small variation of the cross
section over the range $|y|<$ 0.5 (see Fig. 5 below) so also for rapidity a
uniform input distribution is justified. The advantage of using a flat input
distribution in invariant mass is to obtain sufficient statistics in the tails
of the distribution. If one were to use a $\rho^{0}$–shape as input, one would
need enormous statistics to cover the high and low invariant mass ranges. The
$\rho^{0}$ candidates are assumed to be transversely polarized. This is
expected from helicity conservation and has been confirmed by photoproduction
measurements [10, 27]. This polarization translates into a
$\mathrm{d}n_{\pi}/\mathrm{d}\Omega\propto\sin^{2}(\theta)$ angular
distribution of the $\pi^{+}\pi^{-}$ decay products in their center of mass
system ($\theta$ is here measured relative to the direction of flight of the
$\rho^{0}$ in the $\gamma$-nucleon center of mass system). All generated
samples serve as input to a full detector simulation using GEANT 3 for the
propagation of particles through the detector. Selection criteria are applied
in the same way as done for real events. The variation of the detector
configuration during the data taking period is included in the detector
response simulations. The product of acceptance and efficiency varies from
about 2% at the low end of the studied invariant mass interval ($M_{\pi\pi}=$
0.6 GeV/$c^{2}$) to about 12% at the high end ($M_{\pi\pi}=$ 1.5 GeV/$c^{2}$).

Figure 4: Invariant mass distribution for pions corrected for acceptance and
efficiency. The solid (blue) curve corresponds to a fit to the Söding
parameterization Eq. 1, and the dashed (green) curve shows the resonant
contribution only. The dot-dashed (red) curve shows the fit to the Ross-
Stodolsky parameterization Eq. 3. The parameters of the fit are given in the
text.

The uncertainty in the trigger efficiency is obtained by comparing the
measured trigger efficiency with the one in the detector response simulation
in a data sample taken with a ZDC trigger [4]. The result is a trigger
efficiency uncertainty of ${}^{+3.8}_{-9.0}$%. In addition, a correction is
applied for the trigger dead time resulting from after pulses in the TOF. The
systematic error on this correction is estimated to be $\pm 1.3$%.

The invariant mass distribution of the $\rho^{0}$ candidates, corrected for
acceptance and efficiency and normalized by the luminosity to provide a cross
section, is shown in Fig. 4. It is well known that the shape of the $\rho^{0}$
in photoproduction deviates from a pure Breit-Wigner resonance [7, 9, 10, 8,
27]. Several different parameterizations exist to describe the shape, with one
of the most often used being a formula due to Söding, where a continuum
amplitude, $B$, is added to the Breit-Wigner resonance [28]:

$\frac{\mathrm{d}\sigma}{\mathrm{d}M_{\pi\pi}}=\left|A\frac{\sqrt{M_{\pi\pi}M_{\rho^{0}}\Gamma(M_{\pi\pi})}}{M^{2}_{\pi\pi}-M^{2}_{\rho^{0}}+iM_{\rho^{0}}\Gamma(M_{\pi\pi})}+B\right|^{2}\;.$
(1)

Here, $A$ is the amplitude of the Breit–Wigner function, $B$ is the amplitude
of the direct non–resonant $\pi^{+}\pi^{-}$ production, and the mass dependent
width is given by

$\Gamma(M_{\pi\pi})=\Gamma_{\rho^{0}}\frac{M_{\rho^{0}}}{M_{\pi\pi}}\left[\frac{M^{2}_{\pi\pi}-4m^{2}_{\pi}}{M^{2}_{\rho^{0}}-4m^{2}_{\pi}}\right]^{\frac{3}{2}}\;,$
(2)

with $m_{\pi}$ the mass of the pion. Eq. 1 was fitted to the measured
$M_{\pi\pi}$ distribution with $M_{\rho^{0}}$, $\Gamma_{\rho^{0}}$, $A$, and
$B$ as free parameters. The fit gives $M_{\rho^{0}}=761.6\pm
2.3\,(\mathrm{stat.})^{+6.1}_{-3.0}\,(\mathrm{syst.})$ MeV/$c^{2}$ and
$\Gamma_{\rho^{0}}=150.2\pm
5.5\,(\mathrm{stat.})^{+12.0}_{-5.0}\,(\mathrm{syst.})$ MeV/$c^{2}$, in
agreement with the values reported by the PDG [29]. The ratio of the
non–resonant and resonant amplitudes is found to be $|B/A|=0.50\pm
0.04\,(\mathrm{stat.})^{+0.10}_{-0.04}\,(\mathrm{syst.})$ (GeV/c2)-1/2. The
systematic errors are obtained by varying the fitting method ($\chi^{2}$ or
log likelihood minimization), track selection (as discussed above), and
fitting range.

The ratio $|B/A|$ is lower than what was found by STAR with Au targets,
$|B/A|=$ 0.81–0.89 (GeV/c2)-1/2 for $\langle W_{\gamma N}\rangle$ in the range
7–12 GeV [9, 10, 8]. The result from ZEUS with proton targets for $\langle
W_{\gamma N}\rangle$ in the range 55–90 GeV shows that $|B/A|$ varies with the
$\gamma$–proton momentum tranfer [27]. The average is $|B/A|=0.67\pm
0.02\,(\mathrm{stat.})\pm 0.04\,(\mathrm{syst.})$, while for momentum
transfers of the same order as for coherent production $|B/A|\approx$ 0.8. The
lower value of $|B/A|$ observed by ALICE may indicate that the non-resonant
contribution is more strongly absorbed in heavy nuclei at high energies, as
had been previously suggested [30].

Other parameterizations of the $\rho^{0}$ shape are possible, and as a cross
check the invariant mass distribution was also fit to a Ross-Stodolsky
function [27, 31]:

$\frac{\mathrm{d}\sigma}{\mathrm{d}M_{\pi\pi}}=f\;\left|\frac{\sqrt{M_{\pi\pi}M_{\rho^{0}}\Gamma(M_{\pi\pi})}}{M^{2}_{\pi\pi}-M^{2}_{\rho^{0}}+iM_{\rho^{0}}\Gamma(M_{\pi\pi})}\right|^{2}\left(\frac{M_{\rho^{0}}}{M_{\pi\pi}}\right)^{k}\;\;,$
(3)

with a slightly different definition of the mass dependent width

$\Gamma(M_{\pi\pi})=\Gamma_{\rho^{0}}\left[\frac{M^{2}_{\pi\pi}-4m^{2}_{\pi}}{M^{2}_{\rho^{0}}-4m^{2}_{\pi}}\right]^{\frac{3}{2}}\;\;.$
(4)

As can be seen in Fig. 4, this parameterization also described the observed
shape of the invariant mass distribution well and gave a $\rho^{0}$ mass
($M_{\rho^{0}}=769.2\pm 2.8\,(\mathrm{stat.})^{+8.0}_{-5.2}\,(\mathrm{syst.})$
MeV/$c^{2}$) and width ($\Gamma_{\rho^{0}}=156.9\pm
6.1\,(\mathrm{stat.})^{+17.3}_{-5.9}\,(\mathrm{syst.})$ MeV/$c^{2}$)
consistent with the PDG values. The deviation from a pure Breit-Wigner shape
is given by the parameter $k$, which was found to be $k=4.7\pm
0.2\,(\mathrm{stat.})^{+0.8}_{-0.6}\,(\mathrm{syst.})$. This can be compared
to the corresponding value for proton targets from ZEUS [27] and H1 [32] at
HERA. ZEUS finds $k=5.13\pm 0.13$ averaged over all momentum transfers and
$k\approx 6$ for $t=0$, while H1 reports $k=6.84\pm 1.00$ averaged over all
momentum transfers. The larger value of $k$ for proton targets again indicates
that the invariant mass distribution for Pb-targets deviates less from a pure
Breit-Wigner resonance, as was also found using the Söding formula.

As can be seen in the lower part of Fig. 4, there is a hint of a resonance
around 1.3 GeV/c2. This may be understood from two-photon production of the
$f_{2}(1270)$ meson followed by its decay into two pions,
$\gamma+\gamma\rightarrow f_{2}(1270)\rightarrow\pi^{+}\pi^{-}$. This meson is
a “standard candle” in two-photon interactions with a well known
$\gamma\gamma$ coupling, but it has so far not been observed in ultra-
peripheral collisions because of the large background from photonuclear
processes. The significance of the excess over the $\rho^{0}$ Breit-Wigner
distribution is estimated to be $4^{+2}_{-1}$, where the error comes from the
uncertainty in the skewness of the Breit-Wigner distribution (parameter $k$ in
the Ross-Stodolsky formula).

The normalized yield of $\rho^{0}$s ($N_{\mathrm{yield}}$) is obtained by
integrating the resonant part of Eq. 1 (obtained by setting $B=0$ and taking
the other parameters from the fit) from $2m_{\pi}$ to 1.5 GeV/c2. The
systematic error on the number of extracted $\rho^{0}$s is obtained by varying
the fitting method ($\chi^{2}$ or log likelihood minimization) and fitting
range, resulting in an error of ${}^{+0.8}_{-1.4}$%. The uncertainty in the
track selection gives an additional error of ${}^{+3.7}_{-3.0}$% as discussed
above. Both Eq. 1 and 3 describe the observed shape equally well (the
integrated yield differ by less than 0.5%), so no additional systematic error
was added to the yield because of the choice of fitting function.

It is worth noting that the shape of the resonant contribution (shown by the
dashed curve in Fig. 4) is quite different from the shape of the measured
$\pi^{+}\pi^{-}$ invariant mass distribution. However, the integrated yield
between $2m_{\pi}$ and 1.5 GeV/c2 does not deviate by more than around 1% if
the non-resonant amplitude is included in the integration.

The number of extracted $\rho^{0}$s is corrected for the following 3
contributions: incoherent events with $p_{\rm T}<$ 0.15 GeV/c
($f_{\mathrm{incoh}}$), events which have one or more additional SPD tracklets
($f_{\mathrm{SPD}}$), and the number of coherent $\rho^{0}$ events lost by the
VZERO offline timing requirement ($f_{\mathrm{VZERO}}$).

The number of incoherent events with $p_{\rm T}<$ 0.15 GeV/c is estimated in
two different ways: first fitting the sum of two exponentials in $p_{\rm
T}^{2}$ to the $p_{\rm T}$ distributions and integrating the fitted functions
over the interval chosen for the coherent selection ($p_{\rm T}<$ 0.15 GeV/c),
and second using the fit to the STARLIGHT templates shown in Fig. 3. The
correction for incoherent events is found to be 5.1% in both cases with an
uncertainty estimated from using different track selections of $\pm$0.7%.

The track selection (a) above allows one to check the events for any
additional activity in the ITS, for example from tracks with low momenta,
which do not reach the TPC, using SPD tracklets, defined as any combination of
hits from the two SPD layers. Rejecting events with one or more extra
tracklets, not associated with the two good tracks coming from the primary
vertex, removes 3.0% of the events in the signal region. Since true UPC events
should have no additional tracks, the extracted yield is corrected for this.
In the Monte Carlo samples of coherently produced $\rho^{0}$s, the same cut
removes only 0.5% of the events which is taken as the systematic error
associated with this cut.

The events selected by the SPD+TOF+VZERO trigger are required to have no
online signal in the VZERO detector. A similar cut is also applied offline to
the events triggered by TOF only. The VZERO offline selection is further
refined using the timing information. This selection has been tuned to work
well for hadronic interactions, which typically have a non-zero signal in the
VZERO on both sides. In the ultra-peripheral events studied here, where the
VZERO is required to be empty, the offline selection is less reliable, and a
coherent signal can be observed in the events with 2 tracks rejected by the
offline VZERO requirement. The increase in the coherent signal when the
offline VZERO selection is not used amounts to 10.0%. The systematic error of
this number is obtained from the estimated contamination from hadronic events
following from this looser cut. This contamination is determined from the
fraction of the events which have a signal in the ZDCs, resulting in a
systematic error of ${}^{+0.0}_{-3.1}$%.

The corrected number of coherent $\rho^{0}$s is then obtained from

$N_{\rho}^{coh}=\frac{N_{\mathrm{yield}}}{1+f_{\mathrm{incoh}}+f_{\mathrm{SPD}}+f_{\mathrm{VZERO}}}\;,$
(5)

with $f_{\mathrm{incoh}}=0.051\pm 0.007$, $f_{\mathrm{SPD}}=0.030\pm 0.005$,
and $f_{\mathrm{VZERO}}=-0.100^{+0.031}_{-0.000}$. From this number the
differential cross section is calculated as

$\frac{\mathrm{d}\sigma}{\mathrm{d}y}=\frac{N_{\rho}^{coh}}{\mathrm{L}_{int}\cdot\Delta
y}\;.$ (6)

The systematic errors discussed above are summarized in Table 1. They have
been evaluated for the SPD+TOF+VZERO trigger sample, which contains more than
80% of the total integrated luminosity. The total error is obtained by adding
the individual errors following the description in [33]. The two trigger
samples, with appropriate errors, are compared as a cross check. They use
different trigger combinations and were taken under quite different running
conditions, with the typical hadronic minimum bias interaction rate being
around 10 Hz during the early part of the run when the TOF only trigger was
used and around 200 Hz during the later part of the run when the SPD+TOF+VZERO
trigger was used. The correction factor for trigger dead time due to after
pulses was thus very different for the two samples ($\approx$1 during the
early part and $\approx$5 during the later part).

Variable | Systematic error
---|---
Luminosity | ${}^{+6.5\%}_{-5.1\%}$
Trigger efficiency | ${}^{+3.8\%}_{-9.0\%}$
Trigger dead time correction |  $\pm 1.3$%
Signal extraction | ${}^{+0.8\%}_{-1.4\%}$
Track selection | ${}^{+3.7\%}_{-3.0\%}$
Particle ID | ${}^{+0.0\%}_{-5.0\%}$
Incoherent contribution |  $\pm 0.7$%
SPD tracklets |  $\pm 0.5$%
VZERO offline selection | ${}^{+0.0\%}_{-3.1\%}$
Total | ${}^{+9.2\%}_{-11.2\%}$
Table 1:  Summary of the systematic error in the cross section calculation.
The numbers are for the SPD+TOF+VZERO trigger sample. For a discussion of the
TOF only trigger sample and the separation between correlated and uncorrelated
errors of the two samples, see the text.

To make a comparison of the cross sections measured under the different
trigger conditions, the systematic errors are separated into correlated and
uncorrelated errors for the two trigger samples. The fully correlated errors
are those related to luminosity, incoherent contribution, trigger efficiency,
and particle identification. The fully uncorrelated errors are those related
to the VZERO offline selection (different VZERO thresholds were used for the
two data samples), the cut on SPD tracklets, and trigger dead time. The errors
related to the signal extraction and track selection are found to be partly
correlated, but are decorrelated for the comparison. This gives a cross
section $\mathrm{d}\sigma/\mathrm{d}y=466^{+25}_{-25}$ mb for the sample taken
with the TOF only trigger and $\mathrm{d}\sigma/\mathrm{d}y=414^{+14}_{-16}$
mb for the sample taken with the SPD+TOF+VZERO trigger. The error is obtained
from the squared sum of the statistical and uncorrelated systematic error. The
difference of 12% corresponds to 1.8 standard deviations. The final cross
section is obtained as the weighted mean of the cross sections of the two
samples. The weighting procedure provides a total error, including both the
statistical and uncorrelated systematic components. The uncorrelated component
is separated from the total error by subtracting in quadrature the error
obtained in the case when only the statistical errors are used for the
weighting. The uncorrelated systematic error is then added in quadrature to
the correlated systematic error to obtain the total systematic error. The
final result is $\mathrm{d}\sigma/\mathrm{d}y=425\pm
10\,(\mathrm{stat.})^{+42}_{-50}\,(\mathrm{syst.})$ mb.

In addition to the $\rho^{0}$ cross section, the cross section for two-photon
production of $e^{+}e^{-}$ pairs in the range $0.6\leq M_{ee}\leq 2.0$ GeV/c2
and $|\eta_{1,2}|<$ 0.9 ($\eta_{1,2}$ are the pseudorapidities of the two
tracks) was measured. The analysis is similar to the one for $\rho^{0}$ but
the PID requirement was modified to accept electrons rather than pions. The
detector efficiency is determined using STARLIGHT events processed through the
full ALICE detector simulation. The result is $\sigma(0.6\leq M_{ee}\leq
2.0\;\mathrm{GeV},|\eta_{1,2}|<0.9)=9.8\pm
0.6\,(\mathrm{stat.})^{+0.9}_{-1.2}\,(\mathrm{syst.})$ mb, which is in good
agreement with the STARLIGHT [22] prediction for the same selection in
invariant mass and pseudorapidity ($\sigma=$ 9.7 mb). The cross sections for
the individual trigger samples are $11.8\pm
1.6\,(\mathrm{stat.})^{+1.1}_{-1.4}\,(\mathrm{syst.})$ mb (TOF only trigger)
and $9.4\pm 0.7\,(\mathrm{stat.})^{+0.9}_{-1.1}\,(\mathrm{syst.})$ mb
(SPD+TOF+VZERO trigger).

As discussed above, photoproduction of vector mesons may occur in interactions
where additional photons are exchanged between the nuclei, leading to neutron
emission in the forward region. These neutrons may be detected in the ALICE
ZDCs. Four Gaussian distributions centered around each peak with means and
variances constrained to $x_{n}=nx_{1}$ and $\sigma_{n}=\sqrt{n}\sigma_{1}$
have been fitted to the ZDC energy distribution shown in Fig. 1. Here, $x_{1}$
and $\sigma_{1}$ are the position and width of the peak corresponding to one
neutron, and $n$ is the number of neutrons. In order to separate different
cases of neutron emission, the minima between the first three Gaussians are
used. The minimum between zero and one-neutron emission lies at half the
energy per nucleon and it is roughly three sigma away from the adjacent peaks.
A given event is considered to have no neutron in the ZDC if the energy
registered in the calorimeter is less than $600$ GeV, one neutron if the
energy lies between $600$ GeV and $2000$ GeV and more than one neutron if the
energy is above $2000$ GeV.

The events are divided into different groups as follows: no neutrons emitted
in any direction (0n0n), at least one neutron emitted in any direction (Xn),
at least one neutron emitted in one direction and no neutron emitted in the
other direction (0nXn), at least one neutron emitted in both directions
(XnXn).

The corrections applied in obtaining the cross section from the measured yield
are independent of the ZDC signal. The fractional yield for each fragmentation
selection thus reflects the relative $\rho^{0}$ production cross section. The
only exception to this is the correction for the incoherent contribution
($f_{\mathrm{incoh}}$), which is expected to be higher when a signal is
required in the ZDCs. This correction is thus calculated for each ZDC
selection separately, using the same method as described above.

Figure 5: The cross section for coherent photoproduction of $\rho^{0}$,
$\mathrm{d}\sigma/\mathrm{d}y$, in ultra-peripheral collisions for the three
models compared with the ALICE result.

##  5 Results and discussion

The coherent $\rho^{0}$ photoproduction cross section,
$\mathrm{d}\sigma/\mathrm{d}y$, is shown and compared with model predictions
in Fig. 5. The measured cross section is in agreement with STARLIGHT [16] and
the calculation by Gonçalves and Machado (GM) [34], while the GDL (Glauber-
Donnachie-Landshoff) prediction [15, 35] is about a factor of 2 higher than
data. The calculation by GM is based on the Color Dipole model, while
STARLIGHT and GDL use the photon-proton cross section
$\sigma(\gamma+\mathrm{p}\rightarrow\rho^{0}+\mathrm{p})$ constrained from
data as input. In STARLIGHT, the $\gamma$-nucleon cross section is given by
the parameterization $\sigma=5.0\,W_{\gamma N}^{0.20}+26.0\,W_{\gamma
N}^{-1.23}\,\mu\mathrm{b}$ ($W_{\gamma N}$ in GeV), while GDL use the
Donnachie-Landshoff model [36] for the total $\rho N$ cross section. All
calculations use the Glauber model to scale the cross section from
$\gamma$-nucleon to $\gamma$-nucleus.

The STAR Collaboration has published the total coherent $\rho^{0}$
photoproduction cross section at three different energies [9, 10, 8]. To be
able to compare the current result to those, one has to integrate
$\mathrm{d}\sigma/\mathrm{d}y$ over the whole phase space, which can only be
done using models. The extrapolation factor from $|y|<0.5$ to all rapidities
is calculated as the mean of the values obtained from the STARLIGHT (10.6) and
GM (9.1) models, and the deviation of the two from the mean ($\approx 8$%) is
added to the systematic error. This gives
$\sigma(\mathrm{Pb+Pb}\rightarrow\mathrm{Pb+Pb}+\rho^{0})=4.2\pm
0.1(\mathrm{stat.})^{+0.5}_{-0.6}(\mathrm{syst.})$ b at $\sqrt{s_{\rm
NN}}=2.76$ TeV. The total cross section as a function of $\sqrt{s_{\rm NN}}$
is shown in Fig. 6, where the results from ALICE and STAR Collaborations are
compared with the STARLIGHT and GDL calculations. The total cross section
increases by about a factor of 5 between the top RHIC energy and $\sqrt{s_{\rm
NN}}=2.76$ TeV.

The cross section and its energy dependence is well described by STARLIGHT,
while the GDL calculation overpredicts the cross section by about a factor of
2. The agreement with STARLIGHT is somewhat surprising since its Glauber
calculation does not include the elastic part of the total cross section,
which is included in the GDL model. It has been argued that coherent
$\rho^{0}$ production off heavy nuclei may probe the onset of the Black Body
Limit, in which the total $\rho^{0}$–nucleus cross section approaches $2\pi
R_{A}^{2}$ at high energies [15]. The results from STAR and ALICE do not
favour this picture. The cross section is instead reduced by about a factor of
2 compared with the GDL model [35], independent of energy, indicating that
further work is needed to understand this process. It should be noted that
none of the models in Fig. 5 include cross terms such as
$\rho+\mathrm{N}\rightarrow\rho^{\prime}+\mathrm{N}$.

Figure 6: Excitation function for coherent and exclusive $\rho^{0}$
production. The results from ALICE and STAR[9, 10, 8] are compared with the
STARLIGHT and GDL predictions for Pb–Pb and Au–Au.

The photonuclear cross section,
$\sigma(\gamma+\mathrm{Pb}\rightarrow\rho^{0}+\mathrm{Pb})$, in STARLIGHT is
almost energy independent for $W_{\gamma N}>10$ GeV. The increase in the Pb–Pb
cross section, $\sigma(\mathrm{Pb+Pb}\rightarrow\mathrm{Pb+Pb}+\rho^{0})$,
with $\sqrt{s_{\rm NN}}$ is thus almost entirely due to the increase in the
photon flux at higher collision energies.

The model by GM, although in agreement with the current result, has been
criticized for using the Color Dipole model for a soft probe like the
$\rho^{0}$ [35]. A recent publication shows that the calculation indeed has
large uncertainties arising from the choice of $\rho^{0}$ wave function and
dipole cross section [37].

The number of events satisfying the different fragmentation scenarios as well
as the ratio to the total number of events are shown in Table 2. The table
also shows the expected fractions from the STARLIGHT [38] and GDL [35] models.
These models assume that the probabilities for exchange of multiple photons in
a single event factorize in impact parameter space. One should note that some
of the fractions are correlated: the sum of (0n0n) and (Xn) should be 100%,
and the sum of (0nXn) and (XnXn) should be equal to (Xn). This is the case
within errors, but the sum is not exact, since the incoherent contribution is
subtracted for each selection separately. The results in Table 2 are
consistent with both the STARLIGHT and GDL calculations within three standard
deviations.

Selection | Number of events | Fraction | STARLIGHT | GDL
---|---|---|---|---
All events | 7293 | 100 % |  |
0n0n | 6175 | 84.7$\pm$0.4(stat.)${}_{-1.9}^{+0.4}$(syst.) % | 79 % | 80 %
Xn | 1174 | 16.1$\pm$0.4(stat.)${}_{-0.5}^{+2.2}$(syst.) % | 21 % | 20 %
0nXn | 958 | 13.1$\pm$0.4(stat.)${}_{-0.3}^{+0.9}$(syst.) % | 16 % | 15 %
XnXn | 231 | 3.2$\pm$0.2(stat.)${}_{-0.1}^{+0.4}$(syst.) % | 5.2 % | 4.5 %
Table 2:  The number of events that satisfy various selections on the number
of neutrons detected in the ZDCs. 0n0n corresponds to no neutrons emitted in
any direction; Xn to at least one neutron emitted in any direction; 0nXn to no
neutrons in one direction and at least one neutron in the other direction;
XnXn to at least one neutron in both directions. For the relative yield the
systematic error is estimated, as explained in the text.

##  6 Conclusions

The first LHC measurement on coherent photoproduction of $\rho^{0}$ in Pb–Pb
collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV has been presented. Comparisons
with model calculations show that the measured cross section is in agreement
with the predictions by STARLIGHT [16] and Gonçalves and Machado (GM) [34],
despite the idiosyncrasies in these models mentioned above. The Glauber-
Donnachie-Landshoff (GDL) model [15, 35] overpredicts the cross section by
about a factor of two. Comparisons with results from Au–Au collisions at RHIC
energies indicate that this factor of two difference is independent of
collision energy in the range $\sqrt{s_{\rm NN}}=62.4$–$2760$ GeV. In a recent
preprint, it is argued that inelastic nuclear shadowing combined with the
inclusion of intermediate states with higher mass in the $\gamma$–vector meson
transtition could explain the discrepancy [39]. Regardless of whether this is
the correct explanation or not, it indicates that non-trivial corrections to
the $\rho^{0}$ photoproduction cross section may become important at high
photon energies.

The relative yields for different fragmentation scenarios are found to be in
agreement with predictions from the STARLIGHT and GDL models. This is
important not only to confirm the assumptions in the two models but also
because some experiments, e.g. PHENIX [40], have relied on a ZDC signal to
trigger on ultra-peripheral collisions. To be able to relate such measurements
to a photonuclear cross section, it is imperative that the probabilities for
exchange of multiple photons are well understood.

The total cross section is found to be about half the total hadronic inelastic
cross section. This is an increase of about a factor of 5 from Au–Au
collisions at $\sqrt{s_{\rm NN}}=200$ GeV, where the fraction was about 10%.
If the increase of the coherent $\rho^{0}$ photoproduction cross section
continues to follow STARLIGHT, one can expect it to exceed the total hadronic
production cross section of heavy ions such as lead or gold at a $\sqrt{s_{\rm
NN}}$ of about 20 TeV.

## Acknowledgements

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

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##  Appendix A The ALICE Collaboration

J. Adamorg39&D. Adamováorg82&M.M. Aggarwalorg86&G. Aglieri Rinellaorg36&M.
Agnelloorg110&N. Agrawalorg47&Z. Ahammedorg130&S.U. Ahnorg67&I.
Aimoorg93,org110&S. Aiolaorg135&M. Ajazorg16&A. Akindinovorg57&S.N.
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Vinogradovorg99&L. Vinogradovorg129&Y. Vinogradovorg98&T. Virgiliorg31&V.
Vislaviciusorg34&Y.P. Viyogiorg130&A. Vodopyanovorg65&M.A. Völklorg92&K.
Voloshinorg57&S.A. Voloshinorg133&G. Volpeorg36,org134&B. von Hallerorg36&I.
Vorobyevorg91&D. Vranicorg96,org36&J. Vrlákováorg40&B. Vulpescuorg69&A.
Vyushinorg98&B. Wagnerorg18&J. Wagnerorg96&H. Wangorg56&M. Wangorg7,org112&Y.
Wangorg92&D. Watanabeorg126&M. Weberorg36&S.G. Weberorg96&J.P. Wesselsorg53&U.
Westerhofforg53&J. Wiechulaorg35&J. Wikneorg22&M. Wildeorg53&G. Wilkorg76&J.
Wilkinsonorg92&M.C.S. Williamsorg104&B. Windelbandorg92&M. Winnorg92&C.G.
Yaldoorg133&Y. Yamaguchiorg125&H. Yangorg56&P. Yangorg7&S. Yanoorg46&Z.
Yinorg7&H. Yokoyamaorg126&I.-K. Yooorg95&V. Yurchenkoorg3&I. Yushmanovorg99&A.
Zaborowskaorg132&V. Zaccoloorg79&A. Zamanorg16&C. Zampolliorg104&H.J.C.
Zanoliorg118&S. Zaporozhetsorg65&A. Zarochentsevorg129&P. Závadaorg59&N.
Zaviyalovorg98&H. Zbroszczykorg132&I.S. Zguraorg61&M. Zhalovorg84&H.
Zhangorg18,org7&X. Zhangorg73&Y. Zhangorg7&C. Zhaoorg22&N. Zhigarevaorg57&D.
Zhouorg7&Y. Zhouorg79,org56&Z. Zhouorg18&H. Zhuorg18,org7&J. Zhuorg112,org7&X.
Zhuorg7&A. Zichichiorg12,org28&A. Zimmermannorg92&M.B.
Zimmermannorg53,org36&G. Zinovjevorg3&M. Zyzakorg42

## Affiliation notes

0Deceased

idp5852480Also at: University of Kansas, Lawrence, Kansas, United States

## Collaboration Institutes

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

org2Benemérita Universidad Autónoma de Puebla, Puebla, Mexico

org3Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine

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

org5Budker Institute for Nuclear Physics, Novosibirsk, Russia

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

org7Central China Normal University, Wuhan, China

org8Centre de Calcul de l’IN2P3, Villeurbanne, France

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

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

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

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

org13Chicago State University, Chicago, Illinois, USA

org14China Institute of Atomic Energy, Beijing, China

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

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

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

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

org19Department of Physics, Aligarh Muslim University, Aligarh, India

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

org21Department of Physics, Sejong University, Seoul, South Korea

org22Department of Physics, University of Oslo, Oslo, Norway

org23Dipartimento di Elettrotecnica ed Elettronica del Politecnico, Bari,
Italy

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

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

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

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

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

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

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

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

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

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

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

org35Eberhard Karls Universität Tübingen, Tübingen, Germany

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

org37Faculty of Engineering, Bergen University College, Bergen, Norway

org38Faculty of Mathematics, Physics and Informatics, Comenius University,
Bratislava, Slovakia

org39Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Prague, Czech Republic

org40Faculty of Science, P.J. Šafárik University, Košice, Slovakia

org41Faculty of Technology, Buskerud and Vestfold University College,
Vestfold, Norway

org42Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-
Universität Frankfurt, Frankfurt, Germany

org43Gangneung-Wonju National University, Gangneung, South Korea

org44Gauhati University, Department of Physics, Guwahati, India

org45Helsinki Institute of Physics (HIP), Helsinki, Finland

org46Hiroshima University, Hiroshima, Japan

org47Indian Institute of Technology Bombay (IIT), Mumbai, India

org48Indian Institute of Technology Indore, Indore (IITI), India

org49Inha University, Incheon, South Korea

org50Institut de Physique Nucléaire d’Orsay (IPNO), Université Paris-Sud,
CNRS-IN2P3, Orsay, France

org51Institut für Informatik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

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

org53Institut für Kernphysik, Westfälische Wilhelms-Universität Münster,
Münster, Germany

org54Institut Pluridisciplinaire Hubert Curien (IPHC), Université de
Strasbourg, CNRS-IN2P3, Strasbourg, France

org55Institute for Nuclear Research, Academy of Sciences, Moscow, Russia

org56Institute for Subatomic Physics of Utrecht University, Utrecht,
Netherlands

org57Institute for Theoretical and Experimental Physics, Moscow, Russia

org58Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovakia

org59Institute of Physics, Academy of Sciences of the Czech Republic, Prague,
Czech Republic

org60Institute of Physics, Bhubaneswar, India

org61Institute of Space Science (ISS), Bucharest, Romania

org62Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico

org63Instituto de Física, Universidad Nacional Autónoma de México, Mexico
City, Mexico

org64iThemba LABS, National Research Foundation, Somerset West, South Africa

org65Joint Institute for Nuclear Research (JINR), Dubna, Russia

org66Konkuk University, Seoul, South Korea

org67Korea Institute of Science and Technology Information, Daejeon, South
Korea

org68KTO Karatay University, Konya, Turkey

org69Laboratoire de Physique Corpusculaire (LPC), Clermont Université,
Université Blaise Pascal, CNRS–IN2P3, Clermont-Ferrand, France

org70Laboratoire de Physique Subatomique et de Cosmologie, Université
Grenoble-Alpes, CNRS-IN2P3, Grenoble, France

org71Laboratori Nazionali di Frascati, INFN, Frascati, Italy

org72Laboratori Nazionali di Legnaro, INFN, Legnaro, Italy

org73Lawrence Berkeley National Laboratory, Berkeley, California, United
States

org74Lawrence Livermore National Laboratory, Livermore, California, United
States

org75Moscow Engineering Physics Institute, Moscow, Russia

org76National Centre for Nuclear Studies, Warsaw, Poland

org77National Institute for Physics and Nuclear Engineering, Bucharest,
Romania

org78National Institute of Science Education and Research, Bhubaneswar, India

org79Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

org80Nikhef, National Institute for Subatomic Physics, Amsterdam, Netherlands

org81Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United
Kingdom

org82Nuclear Physics Institute, Academy of Sciences of the Czech Republic, Řež
u Prahy, Czech Republic

org83Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States

org84Petersburg Nuclear Physics Institute, Gatchina, Russia

org85Physics Department, Creighton University, Omaha, Nebraska, United States

org86Physics Department, Panjab University, Chandigarh, India

org87Physics Department, University of Athens, Athens, Greece

org88Physics Department, University of Cape Town, Cape Town, South Africa

org89Physics Department, University of Jammu, Jammu, India

org90Physics Department, University of Rajasthan, Jaipur, India

org91Physik Department, Technische Universität München, Munich, Germany

org92Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg,
Heidelberg, Germany

org93Politecnico di Torino, Turin, Italy

org94Purdue University, West Lafayette, Indiana, United States

org95Pusan National University, Pusan, South Korea

org96Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum
für Schwerionenforschung, Darmstadt, Germany

org97Rudjer Bošković Institute, Zagreb, Croatia

org98Russian Federal Nuclear Center (VNIIEF), Sarov, Russia

org99Russian Research Centre Kurchatov Institute, Moscow, Russia

org100Saha Institute of Nuclear Physics, Kolkata, India

org101School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom

org102Sección Física, Departamento de Ciencias, Pontificia Universidad
Católica del Perú, Lima, Peru

org103Sezione INFN, Bari, Italy

org104Sezione INFN, Bologna, Italy

org105Sezione INFN, Cagliari, Italy

org106Sezione INFN, Catania, Italy

org107Sezione INFN, Padova, Italy

org108Sezione INFN, Rome, Italy

org109Sezione INFN, Trieste, Italy

org110Sezione INFN, Turin, Italy

org111SSC IHEP of NRC Kurchatov institute, Protvino, Russia

org112SUBATECH, Ecole des Mines de Nantes, Université de Nantes, CNRS-IN2P3,
Nantes, France

org113Suranaree University of Technology, Nakhon Ratchasima, Thailand

org114Technical University of Split FESB, Split, Croatia

org115The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy
of Sciences, Cracow, Poland

org116The University of Texas at Austin, Physics Department, Austin, Texas,
USA

org117Universidad Autónoma de Sinaloa, Culiacán, Mexico

org118Universidade de São Paulo (USP), São Paulo, Brazil

org119Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

org120University of Houston, Houston, Texas, United States

org121University of Jyväskylä, Jyväskylä, Finland

org122University of Liverpool, Liverpool, United Kingdom

org123University of Tennessee, Knoxville, Tennessee, United States

org124University of the Witwatersrand, Johannesburg, South Africa

org125University of Tokyo, Tokyo, Japan

org126University of Tsukuba, Tsukuba, Japan

org127University of Zagreb, Zagreb, Croatia

org128Université de Lyon, Université Lyon 1, CNRS/IN2P3, IPN-Lyon,
Villeurbanne, France

org129V. Fock Institute for Physics, St. Petersburg State University, St.
Petersburg, Russia

org130Variable Energy Cyclotron Centre, Kolkata, India

org131Vinča Institute of Nuclear Sciences, Belgrade, Serbia

org132Warsaw University of Technology, Warsaw, Poland

org133Wayne State University, Detroit, Michigan, United States

org134Wigner Research Centre for Physics, Hungarian Academy of Sciences,
Budapest, Hungary

org135Yale University, New Haven, Connecticut, United States

org136Yonsei University, Seoul, South Korea

org137Zentrum für Technologietransfer und Telekommunikation (ZTT),
Fachhochschule Worms, Worms, Germany