# Decoupling between gravitationally bounded systems and the cosmic expansion

Yi Wang<EMAIL_ADDRESS>Zun Wang<EMAIL_ADDRESS>Department of Physics,
The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon,
Hong Kong, P.R.China  Jockey Club Institute for Advanced Study, The Hong Kong
University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong,
P.R.China

###### Abstract

Recently, it was hypothesized that some supermassive black holes (SMBHs) may
couple to the cosmic expansion. The mass of these SMBHs increase as the cubic
power of the cosmic scale factor, leaving the energy density of the SMBHs
unchanged when the universe expands. However, following general principles of
general relativity, namely, locality or junction conditions, we show that the
inner part of a gravitationally bounded system is unaware of the cosmic
expansion, since the outer solution can be smoothly replaced by an
asymptotically flat background. For the same reason, the direct reason that we
do not expand with the expansion of the universe is not that we are bound
states, but rather we are positioned in a greater gravitationally bounded
system, namely the local group.

##  1 Introduction

Since the late 1990s, accelerated cosmic expansion has been indicated from
supernova observations [1, 2], implying that the current universe is dominated
by an energy component with constant density and negative pressure, dubbed
dark energy (DE). In the last decades, numerous DE candidates have been come
up with, such as (i) the cosmological constant by the quantum vacuum
fluctuations, but the value of such vacuum energy predicted by most theories
is 120 orders of magnitude larger than DE, known as a fine-tuning problem;
(ii) Supersymmetry. However, supersymmetry must be broken below the scale of
the particle theory Standard Model, still leaving a fine-tuning of more than
50 orders of magnitude; (iii) Scalar field theories, such as slowly rolling
scalar fields. However, for these mechanisms to work, one still has to explain
why the bare cosmological constant is small. See, for example [3] for a review
of these proposals and references therein.

In the recent literature, black holes (BHs) are considered as one new
candidate as the source of DE [4, 5]. From observations, the mass of some BHs
increases with the volume of the cosmic expansion [6]. It was argued that this
may not be a coincidence of black hole local accretion rate, but instead the
expansion of BHs themselves coupling to the cosmic expansion, leading to a
constant energy density just as DE. While this appears to produce the correct
equation of state of DE, it also faces several doubts. For instance, the
cosmological coupling hypothesis is based only on statistical fitting results
from existing observations, with no theoretical support to explain the
coupling mechanism. Furthermore, it is not clear on how BHs can contribute
enough $\Omega_{\Lambda}\sim 0.7$ DE components, or how their perturbations
can maintain stability under negative pressure. Also, the original
cosmological constant problem of why the cosmological constant is small, is
left unexplained.

In addition to these doubts, a more direct issue is that, in general
relativity, the evolution of a system is only affected by the Riemann tensor
where the system is located, but not affected by the spacetime curvature
elsewhere. Within a gravitational bound state, say, a galaxy cluster or our
local group, the local Riemann tensor is not the one derived from the FRW
metric, but rather the one following from the gravitational bound state
conditions. Thus, expansion should not manifest itself in galaxy clusters or
our local group even for separation between free particles. To show this
explicitly, here we show that gravity deep inside bound states can be
described by a local effective theory, which do not exhibit the effects of
cosmic expansion. This applies to the earth-moon system, the solar system, or
the interior of galaxies. Therefore, BHs in galaxies, especially SMBHs at the
cores of galaxies, should only be subject to local gravitational effects and
cannot perceive the external expansion background, or even couple with it.
This holds unless the locality of general relativity is fundamentally broken,
invaliding junction conditions to connect solutions smoothly.

In this article, we investigate spherically symmetric gravitational solutions
in the Friedmann-Robertson-Walker (FRW) background [7]. Using the McVittie
solution [8, 9], we can clearly discern the equilibrium condition between the
effects of the gravitational force and cosmic expansion. Due to the extremely
small cosmological constant $\Lambda$, the dominant gravitational effect is
significantly enhanced by $r^{3}$ close to the system, completely canceling
out the background expansion. This indicates that gravitationally bounded
systems are not affected by the cosmic expansion background. To further verify
this, we construct models to connect the spherically symmetric solutions with
the FRW background using the timelike hypersurface shell $\Sigma$. Using
junction conditions [10, 11], we determine that the junction $\Sigma$
corresponds to the region where gravity and cosmic expansion are in
equilibrium. In the local gravitational system, the Hubble parameter is not
determined by the background, which violates the mechanism of cosmological
coupling.

Our paper is organized as follows: In section 2, we provide a brief review of
spherically symmetric solutions. In sections 3 and 4, we use a timelike shell
hypersurface to separate the interior spacetime from the exterior cosmic
background, thereby illustrating the lack of correlation between their
respective Hubble parameters. Finally, in section 5, we discuss our findings
and provide a summary of our results.

For the convention, we use $(+,-,-,-)$ and Planck units $(8\pi
G=c=\hbar=k_{B}=1)$ through this paper for convenience.

##  2 McVittie solution

In general relativity, we care about the spherical symmetric solution to
describe the spacetime outside the a star, galaxy cluster and so on. The
detailed solutions are summarized in Appendix A. Here, we introduce the
McVittie solution that represents such spherical gravitationally bounded
system embedded in an FRW background. Based on the Schwarzschild solution, the
metric reads

$\displaystyle ds^{2}$
$\displaystyle=\left(\frac{1-\frac{M}{2a(t)r}\sqrt{1+\kappa
r^{2}}}{1+\frac{M)}{2a(t)r}\sqrt{1+\kappa r^{2}}}\right)^{2}dt^{2}$ (2.1)
$\displaystyle-\left(\frac{a(t)}{1+\kappa
r^{2}}\right)^{2}\left(1+\frac{M}{2a(t)r}\sqrt{1+\kappa
r^{2}}\right)^{4}(dr^{2}+r^{2}d\Omega^{2})~{},$ (2.2)

where $M$ refers to the central object’s mass, $a(t)$ is the scale factor and
$d\Omega^{2}=d\theta^{2}+\sin^{2}\theta d\phi^{2}$. The parameter
$\kappa\in\\{-1,0,1\\}$ is related to the 3-space curvature of the FRW
spacetime.

For simplification, we consider the asymptotically spatially flat case with
$\kappa=0$ which fits most with the current cosmological data [12]. And we
could define a time-dependent mass parameter

$\displaystyle\mu(t)=\frac{M}{a(t)}~{}.$ (2.3)

Notice that the physical mass $M$ is fixed and won’t be diluted by the
universe expansion. The mass parameter $\mu(t)$ represents the mass inside the
radius $r_{c}=a(t)r$ at time $t$ in the comoving frame. Then the McVittie
solution becomes

$\displaystyle
ds^{2}=\left(\frac{1-\mu(t)/2r}{1+\mu(t)/2r}\right)^{2}dt^{2}-a^{2}(t)\left(1+\frac{\mu(t)}{2r}\right)^{4}(dr^{2}+r^{2}d\Omega^{2})~{}.$
(2.4)

We could obtain the Schwarzschild solution and FRW metric directly from the
McVittie solution (2.4) in the static spacetime $da(t)/dt=0$ and the massless
case $\mu(t)=0$. With a small mass parameter $\mu(t)\ll r$ by the universe
evolution, it leads to a perturbed FRW solution with $\phi=2\mu(t)$
perturbation potential.

In Croker et al. [6], one of the main ideas to attribute the source of DE to
BHs is a parameterized BH model with time-dependent mass in terms of the scale
factor $a(t)$, that

$\displaystyle m(a):=m(a_{0})\left(\frac{a}{a_{0}}\right)^{k}\ \ \ (a\geq
a_{0})~{},$ (2.5)

where $m(a)$ is the BH mass and $m(a_{0})$ is the mass of the BH at its
formation with the scale factor $a_{0}$. One question arises that what this
mass $m(a)$ refers to. In the current mechanism, the physical mass can’t be
affected by the cosmic expansion with $k=0$. If it refers to the mass from the
comoving observers which is estimated by the astronomical observations, the
parameter $k$ should be around $-1$ by (2.3).

However, in Farrah et al. [4, 5], their observations show that the offsets in
the mass of SMBHs increase apparently compared with the ones in stellar mass
reaching a factor of 7 between $z\sim 1$ and $z\sim 0$, and factor of 20
between $z\sim 2$ and $z\sim 0$. At $90\%$ confidence,

$\displaystyle k=2.96_{-1.46}^{+1.65}\ \ \ \mathrm{and}\ \ \
k=3.11_{-1.33}^{+1.19}~{},$ (2.6)

and excludes the $k=0$ case at $99.98\%$ confidence. This indicates that the
fitting result is not in agreement with any predictions for BH mass. It is
essential to figure out the mechanism of the “cosmological coupling” and
resolve its contradictions with solutions from the general relativity.

More intuitively, in general relativity, only the local Riemann tensor could
affect the evolution of the system. This means that for one SMBH in the
galaxy, it could only be affected by its own spacetime curvature, but cannot
perceive the outside cosmic expansion, or even couple with it. This will be
discussed more in the following section.

##  3 Schwarzschild solution in FRW background

The effect of the cosmic expansion is that two objects move away from each
other radially over time, which could be equivalent to one type of repulsive
force. It means that there will be some regions of the equilibrium between the
gravity and such repulsive force by the cosmic expansion. We can intuitively
figure it out from the asymptotically spatially flat McVittie solution (2.4)
in the Schwarzschild coordinates that

$\displaystyle x$ $\displaystyle=r\left(1+\frac{M}{2a(t)r}\right)^{2}a(t)\ \
\Rightarrow$ $\displaystyle ds^{2}$
$\displaystyle=\left(1-\frac{2M}{x}-H^{2}(t)x^{2}\right)dt^{2}+\frac{2H(t)x}{\sqrt{1-2M/x}}dxdt-(1-\frac{2M}{x})dx^{2}-x^{2}d\Omega^{2}~{},$
(3.1)

where $H(t)=\dot{a}/a$ is the Hubble parameter. Considering a small $x$ in the
local frame, the gravity potential term $2M/x$ will be the dominated effect in
the rate of $x^{3}$ compared with such small value of today’s Hubble parameter
$H\sim 2.19\times 10^{18}\mathrm{(s^{-1})}$. For the equilibrium region
between the gravity and cosmic expansion with radius $R_{e}$, we have

$\displaystyle\frac{2M}{R_{e}}=H^{2}(t)R_{e}^{2}\ \ \Rightarrow\ \
R_{e}=\left(\frac{2M}{H^{2}(t)}\right)^{1/3}~{}.$ (3.2)

Within this region with $R_{e}$, the local gravitationally bounded system
cannot be affected by the outside cosmic background.

Next, we construct one joint metric to show this picture more concretely as
shown in Figure.1. One timelike hypersurface $\Sigma$ is used to glue two
different solutions to form the new joint solution to describe the whole
spacetime. The inside solution $g^{-}$ is the Schwarzschild solution with
central fixed mass $M$ and the outside solution $g^{+}$ refers to the FRW
background. Then the junction $\Sigma=\Sigma^{-}\cap\Sigma^{+}$ should be a
dynamical shell between them.

Figure 1: The joint metric with inside Schwarzschild solution and outside FRW
background by junction $\Sigma$. The massless junction shell comoves with the
background, but the inside can’t perceive the outside cosmic expansion.

The inside junction $\Sigma^{-}$ in the comoving coordinates
$(t,r,\theta,\delta)$ is

$\displaystyle
ds_{-}^{2}=\left(1-\frac{2M}{R}\right)dt^{2}-\frac{dr^{2}}{\left(1-\frac{2M}{R}\right)}-R^{2}d\Omega^{2}~{},$
(3.3)

and the outside junction $\Sigma^{+}$ in FRW spacetime with coordinates
$(\tau,l,\theta,\delta)$ behaves as

$\displaystyle ds_{+}^{2}=d\tau^{2}-a^{2}(\tau)l_{s}^{2}d\Omega^{2}$ (3.4)

in FRW spacetime with the scale factor $a(\tau)$. The junction shell $\Sigma$
is massless which means that it should be in sync with the FRW background with
fixed value $l=l_{s}$ at $\Sigma$, and for the inside solution, it match with
the boundary at $r=R$. We summarize more details on junction conditions
calculation in Appendix B. Follow the junction conditions, the joint metric
exists with such conditions

$\displaystyle R$ $\displaystyle=\left(\frac{2M}{H^{2}(\tau)}\right)^{1/3}$
(3.5) $\displaystyle t$
$\displaystyle=\int_{\tau_{0}}^{\tau}(1-H^{2}R^{2})^{-1}d\tau~{}.$ (3.6)

We notice that the position of the junction $R(\tau)$ just match with the
equilibrium region between gravity and cosmic expansion in (3.2)

$\displaystyle
R(\tau)=R_{e}(\tau)=\left(\frac{2M}{H^{2}(\tau)}\right)^{1/3}~{},$ (3.7)

which consistent with the conclusion by the locality of general relativity.
The position of the junction shell $\Sigma$ depends on the Hubble parameter of
FRW background, but within the junction, the inside spacetime curvature is
only affected by the gratatinally bounded system itself. If we place a pair of
test particles in the interior spacetime, they will only perceive the local
Schwarzschild background and no cosmic expansion effect will be detected. For
the case where the internal spacetime is also an expansion solution, we will
discuss this in the next section.

##  4 McVittie solution in FRW background

In this section, we replace the interior spacetime with McVittie solution
which Hubble parameter could be different from the one of FRW background. A
timelike junction shell junction $\Sigma$ intersects with both solution at
$\Sigma^{\pm}$. The inside McVittie solution is described with scale factor
$b(t)$ in comoving coordinates $(t,r,\theta,\delta)$. For the outside FRW
background, the scale factor is still $a(\tau)$ with $(\tau,l,\theta,\delta)$
coordinates.

Figure 2: The joint metric with inside McVittie solution and outside FRW
background. The inside scale factor is $b(t)$, which could be different from
the outside one $a(\tau)$. The inside gravitationally bounded system still
couldn’t perceive the outside cosmic expansion even though the inside
spacetime is also the expanding solution.

The McVittie solution could be written in the isotropic form as

$\displaystyle
ds_{-}^{2}=\left(\frac{1-\frac{M}{2Rb(t)}}{1+\frac{M}{2Rb(t)}}\right)^{2}dt^{2}-b^{2}(t)\left(1+\frac{M}{2Rb(t)}\right)^{4}(dr^{2}+R^{2}d\Omega^{2})~{}.$
(4.1)

On the outside

$\displaystyle ds_{+}^{2}=d\tau^{2}-a^{2}(\tau)l_{s}^{2}d\Omega^{2}~{}.$ (4.2)

Follow the junction conditions at $\Sigma$, the matched metric reads

$\displaystyle
R^{2}b^{2}(t)\left(1+\frac{M}{2Rb(t)}\right)^{2}=a^{2}(\tau)l_{s}^{2}$ (4.3)
$\displaystyle\left(\frac{1-\frac{M}{2Rb(t)}}{1+\frac{M}{2Rb(t)}}\right)^{2}\dot{t}^{2}-\dot{R}^{2}b^{2}(t)\left(1+\frac{M}{2Rb(t)}\right)^{4}-1=0~{},$
(4.4)

and $K_{\mu\nu}^{-}=K_{\mu\nu}^{+}$ must be satisfied, where any functions
satisfy $\dot{A}\equiv dA/d\tau$ for convenience. Then we could figure out the
position of such junction should satisfy

$\displaystyle R=\left(\frac{2M}{b(t)H^{2}(\tau)}\right)^{1/3}~{},$ (4.5)

which depends on the interior physical mass and the scale factors for two
sides. This also matches with the equilibrium region between potential terms
of gravity and cosmic expansion in McVittie solution just like (3.7). In
particular, we could let $b(t)=1$ to simplify this to the case in the last
section. This means that the joint metric satisfying Einstein field equation
could have a nonuniform distribution of the Hubble parameters. Even though the
interior spacetime is also an expanding solution, the gravitationally bounded
system still cannot perceive the outside cosmic expansion.

##  5 Discussion and summary

We considered two interior spherically symmetric solutions to be joined with
the cosmic background, following the corresponding junction conditions for the
joint solution. The junction $\Sigma$ is dynamically determined by the Hubble
parameters of both sides and indicates the equilibrium region between gravity
and cosmic expansion. For the interior static Schwarzschild solution combined
with the FRW background, such an equilibrium region is related to

$\displaystyle R_{e}\sim\left(\frac{2M}{H^{2}(\tau)}\right)^{1/3}~{}.$ (5.1)

Our results show that local gravitationally bounded systems cannot be affected
by the cosmic background. For BHs within galaxies, they cannot perceive the
outside cosmological expansion. On scales larger than that between galaxies,
gravity is weak enough for the cosmic expansion to manifest.

Our calculation, though simple, clarifies some issues that was usually not
properly interpreted. For example, why our body, or the solar system does not
expand with the cosmic expansion? The conventional explanation is that they
are bounded systems and the cosmic expansion is too weak to separate them.
However, our work shows that this is not the direct reason111What is a “direct
reason”? An analogy may be helpful here: imagine that we are sitting in a
house. Outside the house (and only outside the house), wind is blowing
strongly. Why aren’t we blown away by the wind? The direct reason should be
that, there is no wind in the house at all, instead of calculating the
fraction force to show that it can balance the force by the wind if we were
outside the house. . Since us, and the solar system are deep inside our local
group, a gravitationally bounded system, even if our body or the solar system
were not bounded by additional forces but rather free particles, they will not
expand with the expansion of the universe since these free particles do not
perceive cosmic expansion at all. In explaining the decoupling from cosmic
expansion, only the largest gravitationally bounded system matters.

Having that said, if further observations confirm that the mass of BHs indeed
increases in coupling to the cosmic expansion, instead of coincidentally a
similar accretion rate, we need to understand how this coupling fits into the
theory of gravity, i.e. how general relativity should be modified for this to
happen.

## Acknowledgement

We thank Tingqi Cai, Chao Chen, Jinbo Jiang, Tao Liu and Mian Zhu for helpful
discussions and comments. This work was supported in part by the National Key
R$\&$D Program of China (2021YFC2203100), the NSFC Excellent Young Scientist
Scheme (Hong Kong and Macau) Grant No. 12022516, and by the RGC of Hong Kong
SAR, China Grant No. 16306422.

##  Appendix A Detailed solutions of spherically symmetric distribution

###  A.1 Schwarzschild solution

The static spherically symmetric metric is

$\displaystyle
ds^{2}=e^{\nu(r)}dt^{2}-e^{\lambda(r)}dr^{2}-r^{2}(d\theta^{2}+\sin^{2}{\theta}d\phi^{2})~{},$
(1.1)

where the coefficients $\nu(r)$ and $\lambda(r)$ only depends on $r$.

Then, we consider a spherically symmetric galaxy cluster composed by non-
relativistic gas without charge and spin, where the energy density
$\rho=\rho(r)$ and pressure $p=p(r)$ are only functions of $r$ with equation
of state $p=p(\rho)$.

The Einstein field equations in the static spacetime

$\displaystyle R_{\mu\nu}-\frac{1}{2}Rg_{\mu\nu}=T_{\mu\nu}~{},$ (1.2)

where $T_{\mu\nu}$ refers to the energy-momentum tensor assumed to be the form
of the perfect fluid tensor with 4-velocity $u_{\mu}$ as $T_{\mu\nu}=\rho
u_{\mu}u_{\nu}+p(u_{\mu}u_{\nu}-g_{\mu\nu})$. Only consider the nonzero terms
on the diagonal, we could get three independent nonlinear differential
equations,

$\displaystyle\rho+3p$
$\displaystyle=e^{-\lambda}\left[\nu^{\prime\prime}+\frac{1}{2}\nu^{\prime}\left(\nu^{\prime}-\lambda^{\prime}+\frac{4}{r}\right)\right]$
(1.3) $\displaystyle\rho-p$
$\displaystyle=e^{-\lambda}\left[-\nu^{\prime\prime}-\frac{1}{2}\nu^{\prime}\left(\nu^{\prime}-\lambda^{\prime}\right)+\frac{2\lambda^{\prime}}{r}\right]$
(1.4) $\displaystyle\rho-p$
$\displaystyle=e^{-\lambda}\left[\frac{1}{2r}(\lambda^{\prime}-\nu^{\prime})-\frac{1}{r^{2}}\right]+\frac{1}{r^{2}}~{},$
(1.5)

where any functions satisfies $A^{\prime}\equiv\partial A(r)/\partial r$ for
convenience. Here, the fourth component equation on $T_{33}$ is ignored due to
the similarity to $T_{22}$ component with additional $\sin^{2}{\theta}$
coefficient. Then we could get the expressions of energy density $\rho(r)$ and
the pressure $p(r)$ respectively

$\displaystyle\rho(r)$
$\displaystyle=\frac{e^{\lambda}}{r^{2}}\left(\lambda^{\prime}r-1\right)+\frac{1}{r^{2}}$
(1.6) $\displaystyle p(r)$
$\displaystyle=\frac{e^{-\lambda}}{r^{2}}\left(\nu^{\prime}r+1\right)-\frac{1}{r^{2}}~{},$
(1.7)

and one constraint equation on $\lambda$ and $\nu$

$\displaystyle\frac{e^{\lambda}}{r^{2}}=\frac{1}{2}\left[-\nu^{\prime\prime}+\frac{(\lambda^{\prime}+\nu^{\prime})}{r}+\frac{1}{2}\nu^{\prime}(\lambda^{\prime}-\nu^{\prime})+\frac{2}{r^{2}}\right]~{}.$
(1.8)

Consider a bounded and constant energy density distribution for
simplification, this should describe the exterior Schwarzschild metric. So we
could follow that form to define a general mass function $m=m(r)$, which
satisfies $g_{rr}\equiv\left(1-\frac{2m(r)}{r}\right)^{-1}$. Then from (1.6)
we could get the expression of the solution of spherically symmetric
distribution with given $\rho(r)$ and $p(r)$,

$\displaystyle g_{rr}$
$\displaystyle=-e^{\lambda}=-\left(1-\frac{2m(r)}{r}\right)^{-1}$ (1.9)
$\displaystyle g_{tt}$
$\displaystyle=e^{\nu}=\exp{\left[\int_{0}^{r}\left(\frac{2m(r^{\prime})+p(r^{\prime})r^{\prime
3}}{r^{\prime 2}-2m(r^{\prime})r^{\prime}}\right)dr^{\prime}\right]}~{},$
(1.10)

where the mass function is defined as

$\displaystyle m(r)=\int_{0}^{r}\frac{1}{2}\rho(r^{\prime})r^{\prime
2}dr^{\prime}~{}.$ (1.11)

For the special case, if such galaxy cluster is only bounded in $0<r<R$, this
could lead to the Schwarzschild metric in Schwarzschild coordinates
$(t,r,\theta,\phi)$ with fixed mass function $m(r)=M$. For the interior
solution $(0<r<R)$, its line element is

$\displaystyle ds^{2}$
$\displaystyle=\frac{1}{4}\left(3\sqrt{1-\frac{2M}{R}}-\sqrt{1-\frac{2Mr^{2}}{R^{3}}}\right)^{2}dt^{2}$
$\displaystyle-\left(1-\frac{2Mr^{2}}{R^{3}}\right)^{-1}dr^{2}-r^{2}(d\theta^{2}+\sin^{2}\theta
d\phi^{2})~{}.$ (1.12)

For the exterior solution $(r>R)$, the line elements becomes

$\displaystyle
ds^{2}=\left(1-\frac{2M}{r}\right)dt^{2}-\left(1-\frac{2M}{r}\right)^{-1}dr^{2}-r^{2}(d\theta^{2}+\sin^{2}\theta
d\phi^{2})~{},$ (1.13)

which matches with the interior solution at the surface $r=R$ with the same
line element [13, 14]. Furthermore, the junction conditions need to be applied
to match their extrinsic curvature.

###  A.2 Solutions in isotropic coordinates

Here we derive the form of isotropic coordinate for solutions under
spherically symmetric distribution. Like (1.1), the metric could be defined as

$\displaystyle
ds^{2}=e^{\alpha(r)}dt^{2}-e^{\beta(r)}(dr^{2}+r^{2}d\theta^{2}+r^{2}\sin^{2}\theta
d\phi^{2})~{},$ (1.14)

where parameters $\alpha(r)$ and $\beta(r)$ are only functions of $r$. From
the Einstein field equation, we could get three independent nonlinear
differential equations

$\displaystyle\rho+3p$
$\displaystyle=e^{-\beta}\left(\alpha^{\prime\prime}+\frac{\alpha^{\prime
2}}{2}+\frac{\alpha^{\prime}\beta^{\prime}}{2}+\frac{2\beta^{\prime}}{r}\right)$
(1.15) $\displaystyle\rho-p$
$\displaystyle=e^{-\beta}\left(-2\beta^{\prime\prime}-\alpha^{\prime\prime}-\frac{\alpha^{\prime
2}}{2}+\frac{\alpha^{\prime}\beta^{\prime}}{2}-\frac{2\beta^{\prime}}{r}\right)$
(1.16) $\displaystyle\rho-p$
$\displaystyle=-\frac{1}{2}e^{-\beta}\left(2\beta^{\prime\prime}+\frac{2\alpha^{\prime}}{r}+\beta^{\prime
2}+\alpha^{\prime}\beta^{\prime}+\frac{6\beta^{\prime}}{r}\right)~{}.$ (1.17)

Then the energy density $\rho(r)$ and pressure $p(r)$ could be expressed as

$\displaystyle\rho(r)$
$\displaystyle=-e^{-\beta}\left(\beta^{\prime\prime}+\frac{2\beta^{\prime}}{r}+\frac{\beta^{\prime
2}}{4}\right)$ (1.18) $\displaystyle p(r)$
$\displaystyle=e^{-\beta}\left(\frac{\alpha^{\prime}}{r}+\frac{\beta^{\prime}}{r}+\frac{\alpha^{\prime}\beta^{\prime}}{2}+\frac{\beta^{\prime
2}}{4}\right)~{}.$ (1.19)

Notice that the energy density is on parameter $\beta(r)$ from the
differential equation. If we consider the Schwarzschild case with the constant
and bounded $(0<r<R)$ energy density distribution without the singularity, the
general solution is

$\displaystyle\beta=\log{\left[\frac{12}{\rho(Ar^{2}+A^{-1})^{2}}\right]}~{}.$
(1.20)

And from the constraint by A.3 and A.4, the general form of $\alpha$ should be

$\displaystyle\alpha=2\log{\left[\frac{1}{(1+A^{2}r^{2})}-B\right]^{2}}+C~{},$
(1.21)

where $A$, $B$ and $C$ could be arbitrary constant for the above expressions
which could be evaluated by the given boundary conditions. At the distribution
boundary $r=R$, the pressure should be zero $p(R)=0$ and $g_{\mu\nu}$,
$\partial g_{\mu\nu}$ should be continuous here. Finally, we could get the
exterior isotropic solution $(r>R)$

$\displaystyle
ds^{2}=\left(\frac{1-m/2r}{1+m/2r}\right)^{2}dt^{2}-(1+m/2r)^{4}dr^{2}-r^{2}d\Omega^{2}~{},$
(1.22)

and the interior isotropic solution $(0<r<R)$

$\displaystyle ds^{2}$
$\displaystyle=\left[\frac{m^{2}r^{2}+4R^{4}-4mR(r^{2}+R^{2})}{(m+2R)(mr^{2}+2R^{3})}\right]^{2}dt^{2}$
$\displaystyle-\left[\frac{(m+2R)^{3}}{8(mr^{2}+R^{3})}\right]^{2}dr^{2}-r^{2}d\Omega^{2}~{},$
(1.23)

which match with each other at the boundary $r=R$.

##  Appendix B Junction conditions

In the previous literature, there are several junction conditions with
different degrees of constraints. In this work we choose the commonly used
Israel junction conditions to glue two spacetime solutions [15]. The
requirement is that their metric and the extrinsic curvature $K$ should match
with each other at the junction $\Sigma$, where $K$ is defined as

$\displaystyle
K_{\mu\nu}=(n_{c}\Gamma^{c}_{ab}-\partial_{a}n_{b})e^{a}_{\mu}e^{b}_{\nu}~{},$
(2.1)

where $e^{a}_{\mu}=\partial x^{a}/\partial y^{\mu}$ and $n$ refers to the
normal vector to the junction.

There are connections between the inside spacetime and the FRW comoving time
$\tau$ with $t=t(\tau)$ and $r=r(\tau)$ so the inside one $\Sigma^{-}$ could
be in the same form as $\Sigma^{+}$ that

$\displaystyle
ds_{-}^{2}=\left[\left(1-\frac{2M}{r}\right)\dot{t}^{2}-\frac{\dot{r}^{2}}{\left(1-\frac{2M}{r}\right)}\right]d\tau^{2}-r^{2}d\Omega^{2}~{}.$
(2.2)

At the junction shell, the first condition requires

$\displaystyle R(\tau)$ $\displaystyle=a(\tau)l_{s}$ (2.3)
$\displaystyle\left(1-\frac{2M}{R}\right)^{2}\dot{t}^{2}$
$\displaystyle-\left(1-\frac{2M}{R}\right)-\dot{R}^{2}=0~{}.$ (2.4)

For the second condition to match the extrinsic curvature normal to $\Sigma$,
we only care about the independent $K_{\tau\tau}$ and $K_{\theta\theta}$
components since $K_{\delta\delta}=\sin^{2}\theta K_{\theta\theta}$. For the
inside junction $K^{-}$ in Schwarzschild solution,

$\displaystyle K^{-}_{\tau\tau}$
$\displaystyle=\sum(n_{c}\Gamma_{ab}^{c}-\partial_{a}n_{b})e_{\tau}^{a}e_{\tau}^{b}$
$\displaystyle=\frac{2M\dot{t}}{R^{2}}+\frac{\ddot{t}}{\dot{R}}\left(1-\frac{2M}{R}\right)+\frac{(\ddot{R}+M/R)}{\dot{t}\left(1-\frac{2M}{R}\right)}~{},$
(2.5) $\displaystyle K^{-}_{\theta\theta}$
$\displaystyle=\partial_{\tau}t\Gamma_{\theta\theta}^{r}=-\left(1-\frac{2M}{R}\right)R\dot{t}~{}.$
(2.6)

And for the outside one $K^{+}$ in FRW spacetime,

$\displaystyle K^{+}_{\tau\tau}$
$\displaystyle=(a\Gamma_{\tau\tau}^{l}\partial_{\tau}n^{+}_{\tau})e_{\tau}^{\tau}e_{\tau}^{\tau}=0$
(2.7) $\displaystyle K^{+}_{\theta\theta}$
$\displaystyle=(a\Gamma_{\theta\theta}^{l}-0)e_{\theta}^{\theta}e_{\theta}^{\theta}=-al_{s}=-R~{}.$
(2.8)

Under the requirement $K_{\mu\nu}^{-}=K_{\mu\nu}$, from (2.3) to (2.6) with
four independent equations, we could get

$\displaystyle R(\tau)$ $\displaystyle=\left(\frac{2M}{H^{2}}\right)^{1/3}$
(2.9) $\displaystyle t(\tau)$
$\displaystyle=\int_{\tau_{0}}^{\tau}(1-H^{2}r^{2})^{-1}d\tau~{},$ (2.10)

where $H=\dot{a}/a(\tau)$ refers to the Hubble parameter outside.

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2012-012 J/$\psi$ suppression at forward rapidity in Pb-Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=2.76$ TeV

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

The ALICE experiment has measured the inclusive J/$\psi$ production in Pb-Pb
collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV down to zero transverse
momentum in the rapidity range $2.5<y<4$. A suppression of the inclusive
J/$\psi$ yield in Pb-Pb is observed with respect to the one measured in pp
collisions scaled by the number of binary nucleon-nucleon collisions. The
nuclear modification factor, integrated over the 0%–80% most central
collisions, is $0.545\pm 0.032\rm{(stat.)}\pm 0.083\rm{(syst.)}$ and does not
exhibit a significant dependence on the collision centrality. These features
appear significantly different from measurements at lower collision energies.
Models including J/$\psi$ production from charm quarks in a deconfined
partonic phase can describe our data.

Ultra-relativistic collisions of heavy nuclei aim at producing nuclear matter
at high temperature and pressure. Under such conditions Quantum Chromodynamics
predicts the existence of a deconfined state of partonic matter, the quark-
gluon plasma (QGP). Among the possible probes of the QGP, heavy quarks are of
particular interest since they are expected to be produced in the primary
partonic scatterings and to coexist with the surrounding medium. Therefore,
the measurement of quarkonium states and hadrons with open heavy flavor is
expected to provide essential information on the properties of the strongly-
interacting system formed in the early stages of heavy-ion collisions [1]. In
particular, according to the color-screening model [2], measuring the in-
medium dissociation probability of the different quarkonium states is expected
to provide an estimate of the initial temperature of the system. In the past
two decades, J/$\psi$ production in heavy-ion collisions was intensively
studied at the Super Proton Synchrotron (SPS) and at the Relativistic Heavy
Ion Collider (RHIC), from approximately $20$ to $200$ GeV center of mass
energy per nucleon pair ($\sqrt{s_{\mathrm{NN}}}$). At the SPS, a strong
J/$\psi$ suppression was found in the most central Pb-Pb collisions [3]. The
observed suppression is larger than the one expected from Cold Nuclear Matter
(CNM) effects, which include nuclear absorption and (anti-) shadowing. The
dissociation of excited $\rm{c\overline{c}}$ states like $\chi_{\rm{c}}$ and
$\psi\rm{(2S)}$, which in pp collisions constitute about 40% of the inclusive
J/$\psi$ yield [1], is one possible interpretation of the observed
suppression. A J/$\psi$ suppression was also observed at RHIC, in central Au-
Au collisions [4, 5], at a level similar to the one observed at the SPS when
measured at mid-rapidity although it is larger at forward rapidity. Several
models [6, 7, 8, 9] attempt to reproduce the RHIC data by adding to the direct
J/$\psi$ production a regeneration component from deconfined charm quarks in
the medium, which counteracts the J/$\psi$ dissociation in a QGP. A
quantitative description of these final-state effects is however difficult at
the present time because of the lack of precision in the CNM effects and in
the open charm cross section determination. The measurement of charmonium
production is especially promising at the Large Hadron Collider (LHC) where
the high-energy density of the medium and the large number of c$\bar{\rm{c}}$
pairs produced in central Pb-Pb collisions should help to disentangle between
the different suppression and regeneration scenarios. At the LHC, a
suppression of inclusive J/$\psi$ with high transverse momentum was observed
in central Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV with respect
to peripheral collisions or pp collisions at the same energy by ATLAS [10] and
CMS [11], respectively.

In this Letter, we report ALICE results on inclusive J/$\psi$ production in
Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV at forward rapidity,
measured via the $\mu^{+}\mu^{-}$ decay channel. Our measurement encloses the
low transverse momentum region that is not accessible to other LHC experiments
and thus complements their observations. The J/$\psi$ corrected yield in Pb-Pb
collisions is combined with the one measured in pp collisions at the same
center-of-mass energy [12] to form the J/$\psi$ nuclear modification factor
$R_{\rm{AA}}$. The results are presented as a function of collision centrality
and rapidity ($y$), and in intervals of transverse momentum ($p_{\rm{t}}$).

The ALICE detector is described in [13]. At forward rapidity ($2.5<y<4$) the
production of quarkonium states is measured in the muon spectrometer 111In the
ALICE reference frame, the muon spectrometer covers a negative $\eta$ range
and consequently a negative $y$ range. We have chosen to present our results
with a positive $y$ notation. down to $p_{\rm{t}}=0$. The spectrometer
consists of a ten interaction length thick absorber filtering the muons in
front of five tracking stations comprising two planes of cathode pad chambers
each, with the third station inside a dipole magnet with a 3 Tm field
integral. The tracking apparatus is completed by a triggering system made of
four planes of resistive plate chambers downstream of a 1.2 m thick iron wall,
which absorbs secondary hadrons escaping from the front absorber and low
momentum muons coming mainly from $\pi$ and K decays. In addition, the silicon
pixel detector (SPD) and scintillator arrays (VZERO) were used in this
analysis. The VZERO counters, two arrays of 32 scintillator tiles each, cover
$2.8\leq\eta\leq 5.1$ (VZERO-A) and $-3.7\leq\eta\leq-1.7$ (VZERO-C). The SPD
consists of two cylindrical layers covering $|\eta|\leq 2.0$ and $|\eta|\leq
1.4$ for the inner and outer layers, respectively. All these detectors have
full azimuthal coverage. The minimum bias (MB) trigger requirement used for
this analysis consists of a logical AND of the three following conditions: (i)
a signal in two readout chips in the outer layer of the SPD, (ii) a signal in
VZERO-A, (iii) a signal in VZERO-C, providing a high triggering efficiency for
hadronic interactions. The beam induced background was further reduced by
timing cuts on the signals from the VZERO and from the zero degree
calorimeters (ZDC). The contribution from electromagnetic processes was
removed with a cut on the energy deposited in the neutron ZDCs. The centrality
determination is based on a fit of the VZERO amplitude distribution as
described in [14]. A cut corresponding to the most central 80% of the nuclear
cross section was applied; for these events the MB trigger is fully efficient.
A data sample of 17.7 $\times$ 106 Pb-Pb collisions collected in 2010
satisfying all the above conditions is used in the following analysis. It
corresponds to an integrated luminosity $\mathcal{L}_{\rm int}\approx 2.9$
$\mu$b-1. This data sample was further divided into five centrality classes
from 0%–10% (central collisions) to 50%–80% (peripheral collisions).

J/$\psi$ candidates are formed by combining pairs of opposite-sign (OS) tracks
reconstructed in the geometrical acceptance of the muon spectrometer.

Figure 1: (Color online) Invariant mass spectrum of $\mu^{+}\mu^{-}$ pairs
(solid black circles) with $p_{\rm{t}}\geq 0$ and $2.5<y<4$ in the 0%–80% most
central Pb-Pb collisions.

To reduce the combinatorial background, the reconstructed tracks in the muon
tracking chambers are required to match a track segment in the muon trigger
system. The resulting invariant mass distribution of OS muon pairs for the
0%–80% most central Pb-Pb collisions is shown in Fig. 1, where a J/$\psi$
signal above the combinatorial background is clearly visible. The J/$\psi$ raw
yield was extracted by using two different methods. The OS dimuon invariant
mass distribution was fitted with a Crystal Ball (CB) function to reproduce
the J/$\psi$ line shape, and a sum of two exponentials to describe the
underlying continuum. The CB function connects a Gaussian core with a power-
law tail [15] at low mass to account for energy loss fluctuations and
radiative decays. At high transverse momenta ($p_{\rm{t}}\geq 3\ {\rm
GeV}/c$), the sum of two exponentials does not describe correctly the
underlying continuum; it was replaced by a third order polynomial.
Alternatively, the combinatorial background was subtracted using an event-
mixing technique. The resulting mass distribution was fitted with a CB
function and an exponential or a first order polynomial to describe the
remaining background. The event mixing was preferred to the like-sign
subtraction technique since it is less sensitive to correlated signal pairs
present in the like-sign spectra and gives better statistical precision. The
$\psi\rm{(2S)}$ was not included in the signal line shape since its
contribution is negligible. The width of the J/$\psi$ mass peak depends on the
resolution of the spectrometer which can be affected by the detector occupancy
that increases with centrality. This effect, evaluated by embedding simulated
J/$\psi\rightarrow\mu^{+}\mu^{-}$ decays into real events, was found to be
less than 2%. This conclusion was confirmed by a direct measurement of the
tracking chamber resolution versus centrality using reconstructed tracks.
Therefore, the same CB line shape can be used for all centrality classes. The
parameters of the CB tails were fixed to the values obtained either in
simulations or in pp collisions where the signal to background ratio is much
higher. For each of these choices, the mean and width of the CB Gaussian part
were fixed to the value obtained by fitting the mass distribution in the
centrality range 0%–80%. In addition, a variation of the width of $\pm$ 1
standard deviation was applied to account for uncertainties (varying the mean
has turned out to have a negligible effect in comparison). The raw J/$\psi$
yield in each centrality class was determined as the average of the results
obtained with the two fitting approaches and the various CB parametrizations,
while the corresponding systematic uncertainties were defined as the RMS of
these results. It was also checked that every individual result differs from
the mean value by less than three RMS. The raw J/$\psi$ yield in our Pb-Pb
sample is $2350\pm 139\rm{(stat.)}\pm 189\rm{(syst.)}$. The invariant mass
resolution is around 78 MeV/$c^{2}$, in very good agreement with the embedded
J/$\psi$ simulations. The signal to background ratio integrated over $\pm\ 3\
\sigma$ of the mass resolution varies from 0.1 for central collisions to 1.5
for peripheral collisions.

The measured number of J/$\psi$ ($N_{\rm{J/}\psi}^{i}$) was normalized to the
number of events in the corresponding centrality class ($N_{\rm{events}}^{i}$)
and further corrected for the branching ratio (BR) of the dimuon decay
channel, the acceptance $A$ and the efficiency $\epsilon^{i}$ of the detector.
The inclusive J/$\psi$ yield in each centrality class $i$ for our measured
$p_{\rm{t}}$ and $y$ ranges ($\Delta p_{\rm{t}}$, $\Delta y$) is then given
by:

$\displaystyle Y_{\rm{J/}\psi}^{i}(\Delta p_{\rm{t}},\Delta
y)=\frac{N_{\rm{J/}\psi}^{i}}{{\rm
BR}_{\rm{J/}\psi\rightarrow\mu^{+}\mu^{-}}N_{\rm{events}}^{i}A\epsilon^{i}}.$
(1)

The product $A\epsilon$ was determined from Monte Carlo simulations. The
generated J/$\psi$ $p_{\rm{t}}$ and $y$ distributions were extrapolated from
existing measurements [16], including shadowing effects from EKS98
calculations [17]. As the measured J/$\psi$ polarization in pp collisions at
$\sqrt{s}=7$ TeV is compatible with zero [18], and J/$\psi$ mesons produced
from charm quarks in the medium are expected to be unpolarized, we presume
J/$\psi$ production is unpolarized. For the tracking chambers, the time-
dependent status of each electronic channel during the data taking period was
taken into account as well as the residual misalignment of the detection
elements. The efficiencies of the muon trigger chambers were determined from
data and were then applied in the simulations [19]. Finally, the dependence of
the efficiency on the detector occupancy was included using the embedding
technique. For J/$\psi$ mesons emitted at $2.5<y<4$ and $p_{\rm{t}}\geq 0$, a
run-averaged value of $A\epsilon=0.176$ with a 8% relative systematic
uncertainty was obtained. A $8\%\pm 2\%({\rm syst.})$ relative decrease of the
efficiency was observed when going from peripheral to central collisions.

The J/$\psi$ yield measured in Pb-Pb collisions in centrality class $i$ is
combined with the inclusive J/$\psi$ cross section measured in pp collisions
at the same energy to form the nuclear modification factor $R_{\rm{AA}}$
defined as:

$\displaystyle R_{\rm{AA}}^{i}=\frac{Y_{\rm{J/}\psi}^{i}(\Delta
p_{\rm{t}},\Delta y)}{\langle
T_{\rm{AA}}^{i}\rangle\times\sigma_{\rm{J/}\psi}^{\rm{pp}}(\Delta
p_{\rm{t}},\Delta y)}.$ (2)

The inclusive J/$\psi$ cross section in pp collisions
$\sigma_{\rm{J/}\psi}^{\rm{pp}}(\Delta p_{\rm{t}},\Delta y)$ was measured
using the same apparatus and analysis technique within the corresponding
$p_{\rm{t}}$ and $y$ range [12]. The reference value
$\sigma_{\rm{J/}\psi}^{\rm{pp}}$ used for the calculation of $R_{\rm{AA}}$
integrated over $p_{\rm{t}}$ and $y$ is $3.34\pm 0.13\rm{(stat.)}\pm
0.24\rm{(syst.)}\pm 0.12\rm{(lumi.)}^{+0.53}_{-1.07}\rm{(pol.)}\;\mu b$. The
centrality intervals used in this analysis, the average number of
participating nucleons $\langle N_{\rm{part}}\rangle$ and average value of the
nuclear overlap function $\langle T_{\rm{AA}}\rangle$ derived from a Glauber
model calculation [14] are summarized in Table 1.

Table 1:  The average number of participating nucleons $\langle N_{\rm{part}}\rangle$ without and with $\langle N_{\rm{coll}}\rangle$ weighting, the mid-rapidity charged-particle density d$N_{\rm{ch}}^{\rm{w}}/$d$\eta|_{\eta=0}$ with $\langle N_{\rm{coll}}\rangle$ weighting and the average value of the nuclear overlap function $\langle T_{\rm{AA}}\rangle$ for the centrality classes expressed in percentages of the nuclear cross section [14]. Centrality | $\langle N_{\rm{part}}\rangle$ | $\langle N_{\rm{part}}^{\rm{w}}\rangle$ | $\frac{{\rm d}N_{\rm{ch}}^{\rm{w}}}{\rm{d}\eta|_{\eta=0}}$ |  $\langle T_{\rm{AA}}\rangle$ (mb-1)
---|---|---|---|---
0%–10% | 356$\pm$4 | 361$\pm$4 | 1463$\pm$60 | 23.5$\pm$1.0
10%–20% | 260$\pm$4 | 264$\pm$4 |  979$\pm$37 | 14.4$\pm$0.6
20%–30% | 186$\pm$4 | 189$\pm$4 |  658$\pm$23 | 8.74$\pm$0.37
30%–50% | 107$\pm$3 | 117$\pm$3 |  369$\pm$13 | 3.87$\pm$0.18
50%–80% |  32$\pm$2 |  47$\pm$2 |  110$\pm$5 | 0.72$\pm$0.05
0%–80% | 139$\pm$3 | 264$\pm$4 | – | 7.03$\pm$0.27

Since our most peripheral bin is rather large, the variables $\langle
N_{\rm{part}}^{\rm{w}}\rangle$ and the charged-particle density measured at
mid-rapidity ${\rm d}N_{\rm{ch}}^{\rm{w}}/{\rm d}\eta|_{\eta=0}$ were weighted
by the number of binary collisions $\langle N_{\rm{coll}}\rangle$. Indeed in
absence of nuclear matter effects, the J/$\psi$ production cross section in
nucleus-nucleus is expected to scale with $\langle N_{\rm{coll}}\rangle$. The
weighted values are given in Table 1 and are used for the ALICE data points in
the following figures. All systematic uncertainties entering the $R_{\rm{AA}}$
calculation are listed in Table 2. In the figures below, the point to point
uncorrelated systematic uncertainties are represented as boxes at the position
of the data points while the statistical ones are indicated by vertical bars.
Correlated systematic uncertainties are quoted directly on the figures.

Table 2:  Summary of the systematic uncertainties entering the $R_{\rm{AA}}$ calculation. The type I (II) stands for correlated (uncorrelated) uncertainties. The centrality dependence for the type II is given as a range. source | value | type
---|---|---
signal extraction | 5%–12% | II
input MC parametrization | 5% | I
tracking efficiency | 5% and 0%–1% | I and II
trigger efficiency | 4% and 0%–2% | I and II
matching efficiency | 2% | I
$T_{\rm{AA}}$ | 4%–8% | II
$\sigma_{\rm{J/}\psi}^{\rm{pp}}$ at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV | 9% | I

The inclusive J/$\psi$ $R_{\rm{AA}}$ measured by ALICE at
$\sqrt{s_{\mathrm{NN}}}=2.76$ TeV in the range $2.5<y<4$ and $p_{\rm{t}}\geq
0$ is shown in Fig. 2 as a function of ${\rm d}N_{\rm{ch}}/{\rm
d}\eta|_{\eta=0}$ (left) and $N_{\rm{part}}$ (right). The charged-particle
density closely relates to the energy density of the created medium whereas
the number of participants reflects the collision geometry. The centrality
integrated J/$\psi$ $R_{\rm{AA}}$ is $R^{0\%-80\%}_{\rm{AA}}=0.545\pm
0.032\rm{(stat.)}\pm 0.083\rm{(syst.)}$, indicating a clear J/$\psi$
suppression.

Figure 2: (Color online) Inclusive J/$\psi$ $R_{\rm{AA}}$ as a function of the
mid-rapidity charged-particle density (top) and the number of participating
nucleons (bottom) measured in Pb-Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=2.76$ TeV compared to PHENIX results in Au-Au
collisions at $\sqrt{s_{\mathrm{NN}}}=200$ GeV at mid-rapidity and forward
rapidity [4, 5, 20]. The ALICE data points are placed at the ${\rm
d}N_{\rm{ch}}^{\rm{w}}/{\rm d}\eta|_{\eta=0}$ and $\langle
N_{\rm{part}}^{\rm{w}}\rangle$ values defined in Table 1.

The contribution from beauty hadron feed-down to the inclusive J/$\psi$ yield
in our $y$ and $p_{\rm{t}}$ domain was measured by the LHCb collaboration to
be about 10% in pp collisions at $\sqrt{s}=7$ TeV [21]. Therefore, the
difference between the prompt J/$\psi$ $R_{\rm{AA}}$ and our inclusive
measurement is expected not to exceed 11% if $N_{\rm{coll}}$ scaling of beauty
production is assumed and shadowing effects are neglected. All $R_{\rm{AA}}$
results are presented assuming unpolarized J/$\psi$ production in pp and Pb-Pb
collisions. The comparison with the PHENIX measurements 222 The PHENIX mid-
rapidity J/$\psi$ $R_{\rm{AA}}$ was measured in centrality classes wider than
the ones in which the mid-rapidity charged-particle density is given [20].
Therefore a linear interpolation was done to extract the mid-rapidity charged-
particle density in the three most peripheral classes. at
$\sqrt{s_{\mathrm{NN}}}=200$ GeV at forward rapidity $1.2<|y|<2.2$ [5, 20]
shows that our inclusive J/$\psi$ $R_{\rm{AA}}$ is almost a factor of three
larger for d$N_{\rm{ch}}/$d$\eta|_{\eta=0}\gtrsim 600$ ($N_{\rm{part}}\gtrsim
180$). In addition, our results do not exhibit a significant centrality
dependence.

The rapidity dependence of the J/$\psi$ $R_{\rm{AA}}$ is presented in Fig. 3
for two $p_{\rm{t}}$ domains, $p_{\rm{t}}\geq$ 0 and $p_{\rm{t}}\geq 3\ {\rm
GeV}/c$. The J/$\psi$ reference cross sections in pp collisions 333We report
here $\sigma_{\rm{J/}\psi}^{\rm{pp}}(p_{\rm{t}}\geq 3\rm{GeV}/c,\;2.5<y\leq
3.25)=0.34\pm 0.03\rm{(stat.)}\pm 0.03\rm{(syst.)}\pm 0.02\rm{(lumi.)}\;\mu b$
and $\sigma_{\rm{J/}\psi}^{\rm{pp}}(p_{\rm{t}}\geq
3\rm{GeV}/c,\;3.25<y<4)=0.50\pm 0.04\rm{(stat.)}\pm 0.04\rm{(syst.)}\pm
0.02\rm{(lumi.)}\;\mu b$ that can not directly be extracted from [12]. and the
$R_{\rm{AA}}$ total systematic uncertainties, indicated as open boxes in the
figure, were evaluated in the same kinematic range.

Figure 3: (Color online) Centrality integrated inclusive J/$\psi$
$R_{\rm{AA}}$ measured in Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$
TeV as a function of rapidity for two $p_{\rm{t}}$ ranges. The open boxes
contain the total systematic uncertainties except the ones on the integrated
luminosity in the pp reference and on the $T_{\rm{AA}}$, i.e. 5.2% (8.3%) for
the ALICE (CMS [11]) data. The two models [22, 23] predict the $R_{\rm{AA}}$
due only to shadowing effects for nDSg (shaded areas) and EPS09 (lines) nPDF
respectively.

Our results are shown together with a measurement from CMS [11] of the
inclusive J/$\psi$ $R_{\rm{AA}}$ in the rapidity range $1.6<|y|<2.4$ with
$p_{\rm{t}}\geq 3\ {\rm GeV}/c$. No significant rapidity dependence can be
seen in the J/$\psi$ $R_{\rm{AA}}$ for $p_{\rm{t}}\geq 0$. For $p_{\rm{t}}\geq
3\ {\rm GeV}/c$, a decrease of $R_{\rm{AA}}$ is observed with increasing
rapidity reaching a value of $0.289\pm 0.061\rm{(stat.)}\pm 0.078\rm{(syst.)}$
for $3.25<y<4$. At LHC energies, J/$\psi$ nuclear absorption is likely to be
negligible and the modification of the gluon distribution function is
dominated by shadowing effects [24]. An estimate of shadowing effects is shown
in Fig. 3 within the Color Singlet Model at Leading Order [22] and the Color
Evaporation Model at Next to Leading Order [23]. The shadowing is respectively
calculated with the nDSg and the EPS09 parametrizations [23] of the nuclear
Parton Distribution Function (nPDF). For nDSg (EPS09) the upper and lower
limits correspond to the uncertainty in the factorization scale (uncertainty
of the nPDF). The effect of shadowing shows no dependence with rapidity and
its overall amount is reduced by the addition of a transverse momentum cut. At
most, shadowing effects are expected to lower the $R_{\rm{AA}}$ from 1 to 0.7.
Recent Color Glass Condensate (CGC) calculations for LHC energies may indicate
a larger initial state suppression ($R_{\rm{AA}}\approx 0.5$) [25]. However,
any J/$\psi$ suppression due to initial state effects, CGC or shadowing, will
be stronger at lower $p_{\rm{t}}$ contrary to the data behavior.

Figure 4: (Color online) Inclusive J/$\psi$ $R_{\rm{AA}}$ measured in Pb-Pb
collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV compared to the predictions by
Statistical Hadronization Model [26], Transport Model I [27] and II [28], see
text for details. The ALICE data points are placed at the $\langle
N_{\rm{part}}^{\rm{w}}\rangle$ values defined in Table 1.

In Fig. 4, our measurement is compared with theoretical models that include a
J/$\psi$ regeneration component from deconfined charm quarks in the medium.
The Statistical Hadronization Model [6, 26] assumes deconfinement and a
thermal equilibration of the bulk of the c$\bar{\rm{c}}$ pairs. Then
charmonium production occurs only at phase boundary by statistical
hadronization of charm quarks. The prediction is given for two values of ${\rm
d}\sigma_{\rm{c}\bar{\rm{c}}}/{\rm d}y$ in absence of a measurement for Pb-Pb
collisions. The two transport model results [27, 28] presented in the same
figure differ mostly in the rate equation controlling the J/$\psi$
dissociation and regeneration. Both are shown as a band which connects the
results obtained with (lower limit) and without (higher limit) shadowing. The
width of the band can be interpreted as the uncertainty of the prediction. In
both transport models, the amount of regenerated J/$\psi$ in the most central
collisions contributes to about 50% of the production yield, the rest being
from initial production.

In summary, we have presented the first measurement of inclusive J/$\psi$
nuclear modification factor down to $p_{\rm{t}}=0$ at forward rapidity in Pb-
Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV. The J/$\psi$ $R_{\rm{AA}}$
is larger than the one measured at the SPS and at RHIC for most central
collisions and does not exhibit a significant centrality dependence.
Statistical hadronization and transport models which respectively feature a
full and a partial J/$\psi$ production from charm quarks in the QGP phase can
describe the data. Towards a definitive conclusion about the role of J/$\psi$
production from deconfined charm quarks in a partonic phase, the amount of
shadowing needs to be measured precisely in pPb collisions. In this context,
the measurement of open charm and J/$\psi$ elliptic flow will also help to
determine the degree of thermalization for charm quarks.

## References

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##  1 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 acknowledges the following funding agencies for their
support in building and running the ALICE detector:
Calouste Gulbenkian Foundation from Lisbon 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 BMBF and the Helmholtz Association;
General Secretariat for Research and Technology, Ministry of Development,
Greece;
Hungarian 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) of Italy;
MEXT Grant-in-Aid for Specially Promoted Research, Japan;
Joint Institute for Nuclear Research, Dubna;
National Research Foundation of Korea (NRF);
CONACYT, DGAPA, México, ALFA-EC and the HELEN Program (High-Energy physics
Latin-American–European Network);
Stichting voor Fundamenteel Onderzoek der Materie (FOM) and the Nederlandse
Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands;
Research Council of Norway (NFR);
Polish Ministry of Science and Higher Education;
National Authority for Scientific Research - NASR (Autoritatea Naţională
pentru Cercetare Ştiinţifică - ANCS);
Federal Agency of Science of the Ministry of Education and Science of Russian
Federation, International Science and Technology Center, Russian Academy of
Sciences, Russian Federal Agency of Atomic Energy, Russian Federal Agency for
Science and Innovations and CERN-INTAS;
Ministry of Education of Slovakia;
Department of Science and Technology, South Africa;
CIEMAT, EELA, Ministerio de Educación y Ciencia of Spain, Xunta de Galicia
(Consellería de Educación), 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.

##  Appendix A The ALICE Collaboration

B. Abelevorg1234&J. Adamorg1274&D. Adamováorg1283&A.M. Adareorg1260&M.M.
Aggarwalorg1157&G. Aglieri Rinellaorg1192&A.G. Agocsorg1143&A.
Agostinelliorg1132&S. Aguilar Salazarorg1247&Z. Ahammedorg1225&A. Ahmad
Masoodiorg1106&N. Ahmadorg1106&S.U. Ahnorg1160,org1215&A. Akindinovorg1250&D.
Aleksandrovorg1252&B. Alessandroorg1313&R. Alfaro Molinaorg1247&A.
Aliciorg1133,org1335&A. Alkinorg1220&E. Almaráz Aviñaorg1247&J. Almeorg1122&T.
Altorg1184&V. Altiniorg1114&S. Altinpinarorg1121&I. Altsybeevorg1306&C.
Andreiorg1140&A. Andronicorg1176&V. Anguelovorg1200&J. Anielskiorg1256&C.
Ansonorg1162&T. Antičićorg1334&F. Antinoriorg1271&P. Antonioliorg1133&L.
Aphecetcheorg1258&H. Appelshäuserorg1185&N. Arbororg1194&S. Arcelliorg1132&A.
Arendorg1185&N. Armestoorg1294&R. Arnaldiorg1313&T. Aronssonorg1260&I.C.
Arseneorg1176&M. Arslandokorg1185&A. Asryanorg1306&A. Augustinusorg1192&R.
Averbeckorg1176&T.C. Awesorg1264&J. Äystöorg1212&M.D. Azmiorg1106&M.
Bachorg1184&A. Badalàorg1155&Y.W. Baekorg1160,org1215&R. Bailhacheorg1185&R.
Balaorg1313&R. Baldini Ferroliorg1335&A. Baldisseriorg1288&A. Balditorg1160&F.
Baltasar Dos Santos Pedrosaorg1192&J. Bánorg1230&R.C. Baralorg1127&R.
Barberaorg1154&F. Barileorg1114&G.G. Barnaföldiorg1143&L.S. Barnbyorg1130&V.
Barretorg1160&J. Bartkeorg1168&M. Basileorg1132&N. Bastidorg1160&B.
Bathenorg1256&G. Batigneorg1258&B. Batyunyaorg1182&C. Baumannorg1185&I.G.
Beardenorg1165&H. Beckorg1185&I. Belikovorg1308&F. Belliniorg1132&R.
Bellwiedorg1205&E. Belmont-Morenoorg1247&G. Bencediorg1143&S. Beoleorg1312&I.
Berceanuorg1140&A. Bercuciorg1140&Y. Berdnikovorg1189&D. Berenyiorg1143&C.
Bergmannorg1256&D. Berzanoorg1313&L. Betevorg1192&A. Bhasinorg1209&A.K.
Bhatiorg1157&N. Bianchiorg1187&L. Bianchiorg1312&C. Bianchinorg1270&J.
Bielčíkorg1274&J. Bielčíkováorg1283&A. Bilandzicorg1109&S.
Bjelogrlicorg1320&F. Blancoorg1205&F. Blancoorg1242&D. Blauorg1252&C.
Blumeorg1185&M. Boccioliorg1192&N. Bockorg1162&A. Bogdanovorg1251&H.
Bøggildorg1165&M. Bogolyubskyorg1277&L. Boldizsárorg1143&M. Bombaraorg1229&J.
Bookorg1185&H. Borelorg1288&A. Borissovorg1179&S. Boseorg1224&F.
Bossúorg1312&M. Botjeorg1109&S. Böttgerorg27399&B. Boyerorg1266&P. Braun-
Munzingerorg1176&M. Bregantorg1258&T. Breitnerorg27399&T.A. Browningorg1325&M.
Brozorg1136&R. Brunorg1192&E. Brunaorg1312,org1313&G.E. Brunoorg1114&D.
Budnikovorg1298&H. Bueschingorg1185&S. Bufalinoorg1312,org1313&K.
Bugaievorg1220&O. Buschorg1200&Z. Butheleziorg1152&D. Caballero
Ordunaorg1260&D. Caffarriorg1270&X. Caiorg1329&H. Cainesorg1260&E. Calvo
Villarorg1338&P. Cameriniorg1315&V. Canoa Romanorg1244,org1279&G. Cara
Romeoorg1133&F. Carenaorg1192&W. Carenaorg1192&N. Carlin Filhoorg1296&F.
Carminatiorg1192&C.A. Carrillo Montoyaorg1192&A. Casanova Díazorg1187&J.
Castillo Castellanosorg1288&J.F. Castillo Hernandezorg1176&E.A.R.
Casulaorg1145&V. Catanescuorg1140&C. Cavicchioliorg1192&J. Cepilaorg1274&P.
Cerelloorg1313&B. Changorg1212,org1301&S. Chapelandorg1192&J.L.
Charvetorg1288&S. Chattopadhyayorg1224&S. Chattopadhyayorg1225&M.
Cherneyorg1170&C. Cheshkovorg1192,org1239&B. Cheynisorg1239&E.
Chiavassaorg1313&V. Chibante Barrosoorg1192&D.D. Chinellatoorg1149&P.
Chochulaorg1192&M. Chojnackiorg1320&P. Christakoglouorg1109,org1320&C.H.
Christensenorg1165&P. Christiansenorg1237&T. Chujoorg1318&S.U. Chungorg1281&C.
Cicaloorg1146&L. Cifarelliorg1132,org1192&F. Cindoloorg1133&J.
Cleymansorg1152&F. Coccettiorg1335&F. Colamariaorg1114&D. Colellaorg1114&G.
Conesa Balbastreorg1194&Z. Conesa del Valleorg1192&P. Constantinorg1200&G.
Continorg1315&J.G. Contrerasorg1244&T.M. Cormierorg1179&Y. Corrales
Moralesorg1312&P. Corteseorg1103&I. Cortés Maldonadoorg1279&M.R.
Cosentinoorg1125,org1149&F. Costaorg1192&M.E. Cotalloorg1242&E.
Crescioorg1244&P. Crochetorg1160&E. Cruz Alanizorg1247&E. Cuautleorg1246&L.
Cunqueiroorg1187&A. Daineseorg1270,org1271&H.H. Dalsgaardorg1165&A.
Danuorg1139&I. Dasorg1224,org1266&K. Dasorg1224&D. Dasorg1224&S.
Dashorg1254,org1313&A. Dashorg1149&S. Deorg1225&A. De Azevedo
Moregulaorg1187&G.O.V. de Barrosorg1296&A. De Caroorg1290,org1335&G. de
Cataldoorg1115&J. de Cuvelandorg1184&A. De Falcoorg1145&D. De
Gruttolaorg1290&H. Delagrangeorg1258&E. Del Castillo Sanchezorg1192&A.
Delofforg1322&V. Demanovorg1298&N. De Marcoorg1313&E. Dénesorg1143&S. De
Pasqualeorg1290&A. Deppmanorg1296&G. D Erasmoorg1114&R. de Rooijorg1320&D. Di
Bariorg1114&T. Dietelorg1256&C. Di Giglioorg1114&S. Di Libertoorg1286&A. Di
Mauroorg1192&P. Di Nezzaorg1187&R. Diviàorg1192&Ø. Djuvslandorg1121&A.
Dobrinorg1179,org1237&T. Dobrowolskiorg1322&I. Domínguezorg1246&B.
Dönigusorg1176&O. Dordicorg1268&O. Drigaorg1258&A.K. Dubeyorg1225&L.
Ducrouxorg1239&P. Dupieuxorg1160&A.K. Dutta Majumdarorg1224&M.R. Dutta
Majumdarorg1225&D. Eliaorg1115&D. Emschermannorg1256&H. Engelorg27399&H.A.
Erdalorg1122&B. Espagnonorg1266&M. Estienneorg1258&S. Esumiorg1318&D.
Evansorg1130&G. Eyyubovaorg1268&D. Fabrisorg1270,org1271&J. Faivreorg1194&D.
Falchieriorg1132&A. Fantoniorg1187&M. Faselorg1176&R. Fearickorg1152&A.
Fedunovorg1182&D. Fehlkerorg1121&L. Feldkamporg1256&D. Feleaorg1139&G.
Feofilovorg1306&A. Fernández Téllezorg1279&R. Ferrettiorg1103&A.
Ferrettiorg1312&J. Figielorg1168&M.A.S. Figueredoorg1296&S.
Filchaginorg1298&D. Finogeevorg1249&F.M. Fiondaorg1114&E.M. Fioreorg1114&M.
Florisorg1192&S. Foertschorg1152&P. Fokaorg1176&S. Fokinorg1252&E.
Fragiacomoorg1316&M. Fragkiadakisorg1112&U. Frankenfeldorg1176&U.
Fuchsorg1192&C. Furgetorg1194&M. Fusco Girardorg1290&J.J. Gaardhøjeorg1165&M.
Gagliardiorg1312&A. Gagoorg1338&M. Gallioorg1312&D.R. Gangadharanorg1162&P.
Ganotiorg1264&C. Garabatosorg1176&E. Garcia-Solisorg17347&I.
Garishviliorg1234&J. Gerhardorg1184&M. Germainorg1258&C. Geunaorg1288&A.
Gheataorg1192&M. Gheataorg1192&B. Ghidiniorg1114&P. Ghoshorg1225&P.
Gianottiorg1187&M.R. Girardorg1323&P. Giubellinoorg1192&E. Gladysz-
Dziadusorg1168&P. Glässelorg1200&R. Gomezorg1173&E.G. Ferreiroorg1294&L.H.
González-Truebaorg1247&P. González-Zamoraorg1242&S. Gorbunovorg1184&A.
Goswamiorg1207&S. Gotovacorg1304&V. Grabskiorg1247&L.K. Graczykowskiorg1323&R.
Grajcarekorg1200&A. Grelliorg1320&A. Grigorasorg1192&C. Grigorasorg1192&V.
Grigorievorg1251&A. Grigoryanorg1332&S. Grigoryanorg1182&B. Grinyovorg1220&N.
Grionorg1316&P. Grosorg1237&J.F. Grosse-Oetringhausorg1192&J.-Y.
Grossiordorg1239&R. Grossoorg1192&F. Guberorg1249&R. Guernaneorg1194&C. Guerra
Gutierrezorg1338&B. Guerzoniorg1132&M. Guilbaudorg1239&K.
Gulbrandsenorg1165&T. Gunjiorg1310&A. Guptaorg1209&R. Guptaorg1209&H.
Gutbrodorg1176&Ø. Haalandorg1121&C. Hadjidakisorg1266&M. Haiducorg1139&H.
Hamagakiorg1310&G. Hamarorg1143&B.H. Hanorg1300&L.D. Hanrattyorg1130&A.
Hansenorg1165&Z. Harmanovaorg1229&J.W. Harrisorg1260&M. Hartigorg1185&D.
Haseganorg1139&D. Hatzifotiadouorg1133&A. Hayrapetyanorg1192,org1332&S.T.
Heckelorg1185&M. Heideorg1256&H. Helstruporg1122&A. Herghelegiuorg1140&G.
Herrera Corralorg1244&N. Herrmannorg1200&K.F. Hetlandorg1122&B.
Hicksorg1260&P.T. Hilleorg1260&B. Hippolyteorg1308&T. Horaguchiorg1318&Y.
Horiorg1310&P. Hristovorg1192&I. Hřivnáčováorg1266&M. Huangorg1121&S.
Huberorg1176&T.J. Humanicorg1162&D.S. Hwangorg1300&R. Ichouorg1160&R.
Ilkaevorg1298&I. Ilkivorg1322&M. Inabaorg1318&E. Incaniorg1145&G.M.
Innocentiorg1312&P.G. Innocentiorg1192&M. Ippolitovorg1252&M. Irfanorg1106&C.
Ivanorg1176&M. Ivanovorg1176&A. Ivanovorg1306&V. Ivanovorg1189&O.
Ivanytskyiorg1220&A. Jachołkowskiorg1192&P. M. Jacobsorg1125&L.
Jancurováorg1182&H.J. Jangorg20954&S. Jangalorg1308&M.A. Janikorg1323&R.
Janikorg1136&P.H.S.Y. Jayarathnaorg1205&S. Jenaorg1254&R.T. Jimenez
Bustamanteorg1246&L. Jirdenorg1192&P.G. Jonesorg1130&H. Jungorg1215&W.
Jungorg1215&A. Juskoorg1130&A.B. Kaidalovorg1250&V. Kakoyanorg1332&S.
Kalcherorg1184&P. Kaliňákorg1230&M. Kaliskyorg1256&T. Kalliokoskiorg1212&A.
Kalweitorg1177&K. Kanakiorg1121&J.H. Kangorg1301&V. Kaplinorg1251&A. Karasu
Uysalorg1192,org15649&O. Karavichevorg1249&T. Karavichevaorg1249&E.
Karpechevorg1249&A. Kazantsevorg1252&U. Kebschullorg27399&R.
Keidelorg1327&S.A. Khanorg1225&M.M. Khanorg1106&P. Khanorg1224&A.
Khanzadeevorg1189&Y. Kharlovorg1277&B. Kilengorg1122&M. Kimorg1301&T.
Kimorg1301&S. Kimorg1300&D.J. Kimorg1212&J.H. Kimorg1300&J.S. Kimorg1215&S.H.
Kimorg1215&D.W. Kimorg1215&B. Kimorg1301&S. Kirschorg1184,org1192&I.
Kiselorg1184&S. Kiselevorg1250&A. Kisielorg1192,org1323&J.L. Klayorg1292&J.
Kleinorg1200&C. Klein-Bösingorg1256&M. Kliemantorg1185&A. Klugeorg1192&M.L.
Knichelorg1176&A.G. Knospeorg17361&K. Kochorg1200&M.K. Köhlerorg1176&A.
Kolojvariorg1306&V. Kondratievorg1306&N. Kondratyevaorg1251&A.
Konevskikhorg1249&A. Korneevorg1298&C. Kottachchi Kankanamge Donorg1179&R.
Kourorg1130&M. Kowalskiorg1168&S. Koxorg1194&G. Koyithatta
Meethaleveeduorg1254&J. Kralorg1212&I. Králikorg1230&F. Kramerorg1185&I.
Krausorg1176&T. Krawutschkeorg1200,org1227&M. Krelinaorg1274&M.
Kretzorg1184&M. Krivdaorg1130,org1230&F. Krizekorg1212&M. Krusorg1274&E.
Kryshenorg1189&M. Krzewickiorg1109,org1176&Y. Kucheriaevorg1252&C.
Kuhnorg1308&P.G. Kuijerorg1109&P. Kurashviliorg1322&A.B. Kurepinorg1249&A.
Kurepinorg1249&A. Kuryakinorg1298&V. Kushpilorg1283&S. Kushpilorg1283&H.
Kvaernoorg1268&M.J. Kweonorg1200&Y. Kwonorg1301&P. Ladrón de Guevaraorg1246&I.
Lakomovorg1266,org1306&R. Langoyorg1121&C. Laraorg27399&A. Lardeuxorg1258&P.
La Roccaorg1154&C. Lazzeroniorg1130&R. Leaorg1315&Y. Le Bornecorg1266&K.S.
Leeorg1215&S.C. Leeorg1215&F. Lefèvreorg1258&J. Lehnertorg1185&L.
Leistamorg1192&M. Lenhardtorg1258&V. Lentiorg1115&H. Leónorg1247&I. León
Monzónorg1173&H. León Vargasorg1185&P. Lévaiorg1143&J. Lienorg1121&R.
Lietavaorg1130&S. Lindalorg1268&V. Lindenstruthorg1184&C.
Lippmannorg1176,org1192&M.A. Lisaorg1162&L. Liuorg1121&P.I. Loenneorg1121&V.R.
Logginsorg1179&V. Loginovorg1251&S. Lohnorg1192&D. Lohnerorg1200&C.
Loizidesorg1125&K.K. Looorg1212&X. Lopezorg1160&E. López Torresorg1197&G.
Løvhøidenorg1268&X.-G. Luorg1200&P. Luettigorg1185&M. Lunardonorg1270&J.
Luoorg1329&G. Luparelloorg1320&L. Luquinorg1258&C. Luzziorg1192&K.
Maorg1329&R. Maorg1260&D.M. Madagodahettige-Donorg1205&A. Maevskayaorg1249&M.
Magerorg1177,org1192&D.P. Mahapatraorg1127&A. Maireorg1308&M. Malaevorg1189&I.
Maldonado Cervantesorg1246&L. Malininaorg1182,M.V.Lomonosov Moscow State
University, D.V.Skobeltsyn Institute of Nuclear Physics, Moscow, Russia&D.
Mal’Kevichorg1250&P. Malzacherorg1176&A. Mamonovorg1298&L. Manceauorg1313&L.
Mangotraorg1209&V. Mankoorg1252&F. Mansoorg1160&V. Manzariorg1115&Y.
Maoorg1194,org1329&M. Marchisoneorg1160,org1312&J. Marešorg1275&G.V.
Margagliottiorg1315,org1316&A. Margottiorg1133&A. Marínorg1176&C.A. Marin
Tobonorg1192&C. Markertorg17361&I. Martashviliorg1222&P.
Martinengoorg1192&M.I. Martínezorg1279&A. Martínez Davalosorg1247&G. Martínez
Garcíaorg1258&Y. Martynovorg1220&A. Masorg1258&S. Masciocchiorg1176&M.
Maseraorg1312&A. Masoniorg1146&L. Massacrierorg1239,org1258&M.
Mastromarcoorg1115&A. Mastroserioorg1114,org1192&Z.L. Matthewsorg1130&A.
Matyjaorg1168,org1258&D. Mayaniorg1246&C. Mayerorg1168&J. Mazerorg1222&M.A.
Mazzoniorg1286&F. Meddiorg1285&A. Menchaca-Rochaorg1247&J. Mercado
Pérezorg1200&M. Meresorg1136&Y. Miakeorg1318&L. Milanoorg1312&J.
Milosevicorg1268,Institute of Nuclear Sciences, Belgrade, Serbia&A.
Mischkeorg1320&A.N. Mishraorg1207&D. Miśkowiecorg1176,org1192&C.
Mituorg1139&J. Mlynarzorg1179&B. Mohantyorg1225&A.K. Mohantyorg1192&L.
Molnarorg1192&L. Montaño Zetinaorg1244&M. Montenoorg1313&E. Montesorg1242&T.
Moonorg1301&M. Morandoorg1270&D.A. Moreira De Godoyorg1296&S.
Morettoorg1270&A. Morschorg1192&V. Mucciforaorg1187&E. Mudnicorg1304&S.
Muhuriorg1225&H. Müllerorg1192&M.G. Munhozorg1296&L. Musaorg1192&A.
Mussoorg1313&B.K. Nandiorg1254&R. Naniaorg1133&E. Nappiorg1115&C.
Nattrassorg1222&N.P. Naumovorg1298&S. Navinorg1130&T.K. Nayakorg1225&S.
Nazarenkoorg1298&G. Nazarovorg1298&A. Nedosekinorg1250&M. Nicassioorg1114&B.S.
Nielsenorg1165&T. Niidaorg1318&S. Nikolaevorg1252&V. Nikolicorg1334&S.
Nikulinorg1252&V. Nikulinorg1189&B.S. Nilsenorg1170&M.S. Nilssonorg1268&F.
Noferiniorg1133,org1335&P. Nomokonovorg1182&G. Noorenorg1320&N.
Novitzkyorg1212&A. Nyaninorg1252&A. Nyathaorg1254&C. Nygaardorg1165&J.
Nystrandorg1121&A. Ochirovorg1306&H. Oeschlerorg1177,org1192&S.K. Ohorg1215&S.
Ohorg1260&J. Oleniaczorg1323&C. Oppedisanoorg1313&A. Ortiz
Velasquezorg1237,org1246&G. Ortonaorg1312&A. Oskarssonorg1237&P.
Ostrowskiorg1323&J. Otwinowskiorg1176&K. Oyamaorg1200&K. Ozawaorg1310&Y.
Pachmayerorg1200&M. Pachrorg1274&F. Padillaorg1312&P. Paganoorg1290&G.
Paićorg1246&F. Painkeorg1184&C. Pajaresorg1294&S.K. Palorg1225&S.
Palorg1288&A. Palahaorg1130&A. Palmeriorg1155&V. Papikyanorg1332&G.S.
Pappalardoorg1155&W.J. Parkorg1176&A. Passfeldorg1256&B. Pastirčákorg1230&D.I.
Patalakhaorg1277&V. Paticchioorg1115&A. Pavlinovorg1179&T. Pawlakorg1323&T.
Peitzmannorg1320&E. Pereira De Oliveira Filhoorg1296&D. Peresunkoorg1252&C.E.
Pérez Laraorg1109&E. Perez Lezamaorg1246&D. Periniorg1192&D. Perrinoorg1114&W.
Perytorg1323&A. Pesciorg1133&V. Peskovorg1192,org1246&Y. Pestovorg1262&V.
Petráčekorg1274&M. Petranorg1274&M. Petrisorg1140&P. Petrovorg1130&M.
Petroviciorg1140&C. Pettaorg1154&S. Pianoorg1316&A. Piccottiorg1313&M.
Piknaorg1136&P. Pillotorg1258&O. Pinazzaorg1192&L. Pinskyorg1205&N.
Pitzorg1185&F. Piuzorg1192&D.B. Piyarathnaorg1205&M. Płoskońorg1125&J.
Plutaorg1323&T. Pocheptsovorg1182,org1268&S. Pochybovaorg1143&P.L.M. Podesta-
Lermaorg1173&M.G. Poghosyanorg1192,org1312&K. Polákorg1275&B.
Polichtchoukorg1277&A. Poporg1140&S. Porteboeuf-Houssaisorg1160&V.
Pospíšilorg1274&B. Potukuchiorg1209&S.K. Prasadorg1179&R.
Preghenellaorg1133,org1335&F. Prinoorg1313&C.A. Pruneauorg1179&I.
Pshenichnovorg1249&S. Puchaginorg1298&G. Pudduorg1145&J. Pujol
Teixidoorg27399&A. Pulvirentiorg1154,org1192&V. Puninorg1298&M.
Putišorg1229&J. Putschkeorg1179,org1260&E. Quercighorg1192&H.
Qvigstadorg1268&A. Rachevskiorg1316&A. Rademakersorg1192&S.
Radomskiorg1200&T.S. Räihäorg1212&J. Rakorg1212&A. Rakotozafindrabeorg1288&L.
Ramelloorg1103&A. Ramírez Reyesorg1244&S. Raniwalaorg1207&R.
Raniwalaorg1207&S.S. Räsänenorg1212&B.T. Rascanuorg1185&D. Ratheeorg1157&K.F.
Readorg1222&J.S. Realorg1194&K. Redlichorg1322,org23333&P. Reicheltorg1185&M.
Reicherorg1320&R. Renfordtorg1185&A.R. Reolonorg1187&A. Reshetinorg1249&F.
Rettigorg1184&J.-P. Revolorg1192&K. Reygersorg1200&L. Riccatiorg1313&R.A.
Ricciorg1232&T. Richertorg1237&M. Richterorg1268&P. Riedlerorg1192&W.
Rieglerorg1192&F. Riggiorg1154,org1155&M. Rodríguez Cahuantziorg1279&K.
Røedorg1121&D. Rohrorg1184&D. Röhrichorg1121&R. Romitaorg1176&F.
Ronchettiorg1187&P. Rosnetorg1160&S. Rosseggerorg1192&A. Rossiorg1270&F.
Roukoutakisorg1112&C. Royorg1308&P. Royorg1224&A.J. Rubio Monteroorg1242&R.
Ruiorg1315&E. Ryabinkinorg1252&A. Rybickiorg1168&S. Sadovskyorg1277&K.
Šafaříkorg1192&R. Sahooorg36378&P.K. Sahuorg1127&J. Sainiorg1225&H.
Sakaguchiorg1203&S. Sakaiorg1125&D. Sakataorg1318&C.A. Salgadoorg1294&J.
Salzwedelorg1162&S. Sambyalorg1209&V. Samsonovorg1189&X. Sanchez
Castroorg1246,org1308&L. Šándororg1230&A. Sandovalorg1247&S. Sanoorg1310&M.
Sanoorg1318&R. Santoorg1256&R. Santoroorg1115,org1192&J. Sarkamoorg1212&E.
Scapparoneorg1133&F. Scarlassaraorg1270&R.P. Scharenbergorg1325&C.
Schiauaorg1140&R. Schickerorg1200&C. Schmidtorg1176&H.R.
Schmidtorg1176,org21360&S. Schreinerorg1192&S. Schuchmannorg1185&J.
Schukraftorg1192&Y. Schutzorg1192,org1258&K. Schwarzorg1176&K.
Schwedaorg1176,org1200&G. Scioliorg1132&E. Scomparinorg1313&P.A.
Scottorg1130&R. Scottorg1222&G. Segatoorg1270&I. Selyuzhenkovorg1176&S.
Senyukovorg1103,org1308&J. Seoorg1281&S. Serciorg1145&E.
Serradillaorg1242,org1247&A. Sevcencoorg1139&I. Sguraorg1115&A.
Shabetaiorg1258&G. Shabratovaorg1182&R. Shahoyanorg1192&N. Sharmaorg1157&S.
Sharmaorg1209&K. Shigakiorg1203&M. Shimomuraorg1318&K. Shtejerorg1197&Y.
Sibiriakorg1252&M. Sicilianoorg1312&E. Sickingorg1192&S. Siddhantaorg1146&T.
Siemiarczukorg1322&D. Silvermyrorg1264&G. Simonettiorg1114,org1192&R.
Singarajuorg1225&R. Singhorg1209&S. Singhaorg1225&B.C. Sinhaorg1225&T.
Sinhaorg1224&B. Sitarorg1136&M. Sittaorg1103&T.B. Skaaliorg1268&K.
Skjerdalorg1121&R. Smakalorg1274&N. Smirnovorg1260&R.J.M. Snellingsorg1320&C.
Søgaardorg1165&R. Soltzorg1234&H. Sonorg1300&J. Songorg1281&M. Songorg1301&C.
Soosorg1192&F. Soramelorg1270&I. Sputowskaorg1168&M. Spyropoulou-
Stassinakiorg1112&B.K. Srivastavaorg1325&J. Stachelorg1200&I. Stanorg1139&I.
Stanorg1139&G. Stefanekorg1322&G. Stefaniniorg1192&T. Steinbeckorg1184&M.
Steinpreisorg1162&E. Stenlundorg1237&G. Steynorg1152&D. Stoccoorg1258&M.
Stolpovskiyorg1277&K. Strabykinorg1298&P. Strmenorg1136&A.A.P.
Suaideorg1296&M.A. Subieta Vásquezorg1312&T. Sugitateorg1203&C.
Suireorg1266&M. Sukhorukovorg1298&R. Sultanovorg1250&M. Šumberaorg1283&T.
Susaorg1334&A. Szanto de Toledoorg1296&I. Szarkaorg1136&A. Szostakorg1121&C.
Tagridisorg1112&J. Takahashiorg1149&J.D. Tapia Takakiorg1266&A.
Tauroorg1192&G. Tejeda Muñozorg1279&A. Telescaorg1192&C. Terrevoliorg1114&J.
Thäderorg1176&D. Thomasorg1320&R. Tieulentorg1239&A.R. Timminsorg1205&D.
Tlustyorg1274&A. Toiaorg1184,org1192&H. Toriiorg1203,org1310&L.
Toscanoorg1313&F. Toselloorg1313&D. Truesdaleorg1162&W.H. Trzaskaorg1212&T.
Tsujiorg1310&A. Tumkinorg1298&R. Turrisiorg1271&T.S. Tveterorg1268&J.
Uleryorg1185&K. Ullalandorg1121&J. Ulrichorg1199,org27399&A. Urasorg1239&J.
Urbánorg1229&G.M. Urciuoliorg1286&G.L. Usaiorg1145&M. Vajzerorg1274,org1283&M.
Valaorg1182,org1230&L. Valencia Palomoorg1266&S. Valleroorg1200&N. van der
Kolkorg1109&P. Vande Vyvreorg1192&M. van Leeuwenorg1320&L. Vannucciorg1232&A.
Vargasorg1279&R. Varmaorg1254&M. Vasileiouorg1112&A. Vasilievorg1252&V.
Vecherninorg1306&M. Veldhoenorg1320&M. Venaruzzoorg1315&E. Vercellinorg1312&S.
Vergaraorg1279&D.C. Vernekohlorg1256&R. Vernetorg14939&M. Verweijorg1320&L.
Vickovicorg1304&G. Viestiorg1270&O. Vikhlyantsevorg1298&Z. Vilakaziorg1152&O.
Villalobos Baillieorg1130&A. Vinogradovorg1252&L. Vinogradovorg1306&Y.
Vinogradovorg1298&T. Virgiliorg1290&Y.P. Viyogiorg1225&A. Vodopyanovorg1182&K.
Voloshinorg1250&S. Voloshinorg1179&G. Volpeorg1114,org1192&B. von
Hallerorg1192&D. Vranicorg1176&G. Øvrebekkorg1121&J. Vrlákováorg1229&B.
Vulpescuorg1160&A. Vyushinorg1298&B. Wagnerorg1121&V. Wagnerorg1274&R.
Wanorg1308,org1329&D. Wangorg1329&M. Wangorg1329&Y. Wangorg1200&Y.
Wangorg1329&K. Watanabeorg1318&J.P. Wesselsorg1192,org1256&U.
Westerhofforg1256&J. Wiechulaorg21360&J. Wikneorg1268&M. Wildeorg1256&G.
Wilkorg1322&A. Wilkorg1256&M.C.S. Williamsorg1133&B. Windelbandorg1200&L.
Xaplanteris Karampatsosorg17361&H. Yangorg1288&S. Yangorg1121&S.
Yasnopolskiyorg1252&J. Yiorg1281&Z. Yinorg1329&H. Yokoyamaorg1318&I.-K.
Yooorg1281&J. Yoonorg1301&W. Yuorg1185&X. Yuanorg1329&I. Yushmanovorg1252&C.
Zachorg1274&C. Zampolliorg1133,org1192&S. Zaporozhetsorg1182&A.
Zarochentsevorg1306&P. Závadaorg1275&N. Zaviyalovorg1298&H.
Zbroszczykorg1323&P. Zelnicekorg27399&I.S. Zguraorg1139&M. Zhalovorg1189&X.
Zhangorg1160,org1329&Y. Zhouorg1320&D. Zhouorg1329&F. Zhouorg1329&X.
Zhuorg1329&A. Zichichiorg1132,org1335&A. Zimmermannorg1200&G.
Zinovjevorg1220&Y. Zoccaratoorg1239&M. Zynovyevorg1220

## Affiliation notes

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

Institute of Nuclear Sciences, Belgrade, SerbiaAlso at: ”Vinča” Institute of
Nuclear Sciences, Belgrade, Serbia

## Collaboration Institutes

org1279Benemérita Universidad Autónoma de Puebla, Puebla, Mexico

org1220Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine

org1262Budker Institute for Nuclear Physics, Novosibirsk, Russia

org1292California Polytechnic State University, San Luis Obispo, California,
United States

org14939Centre de Calcul de l’IN2P3, Villeurbanne, France

org1197Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN),
Havana, Cuba

org1242Centro de Investigaciones Energéticas Medioambientales y Tecnológicas
(CIEMAT), Madrid, Spain

org1244Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico
City and Mérida, Mexico

org1335Centro Fermi – Centro Studi e Ricerche e Museo Storico della Fisica
“Enrico Fermi”, Rome, Italy

org17347Chicago State University, Chicago, United States

org1288Commissariat à l’Energie Atomique, IRFU, Saclay, France

org1294Departamento de Física de Partículas and IGFAE, Universidad de Santiago
de Compostela, Santiago de Compostela, Spain

org1106Department of Physics Aligarh Muslim University, Aligarh, India

org1121Department of Physics and Technology, University of Bergen, Bergen,
Norway

org1162Department of Physics, Ohio State University, Columbus, Ohio, United
States

org1300Department of Physics, Sejong University, Seoul, South Korea

org1268Department of Physics, University of Oslo, Oslo, Norway

org1145Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari,
Italy

org1270Dipartimento di Fisica dell’Università and Sezione INFN, Padova, Italy

org1315Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy

org1132Dipartimento di Fisica dell’Università and Sezione INFN, Bologna, Italy

org1285Dipartimento di Fisica dell’Università ‘La Sapienza’ and Sezione INFN,
Rome, Italy

org1154Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Catania, Italy

org1290Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo
Collegato INFN, Salerno, Italy

org1312Dipartimento di Fisica Sperimentale dell’Università and Sezione INFN,
Turin, Italy

org1103Dipartimento di Scienze e Tecnologie Avanzate dell’Università del
Piemonte Orientale and Gruppo Collegato INFN, Alessandria, Italy

org1114Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari,
Italy

org1237Division of Experimental High Energy Physics, University of Lund, Lund,
Sweden

org1192European Organization for Nuclear Research (CERN), Geneva, Switzerland

org1227Fachhochschule Köln, Köln, Germany

org1122Faculty of Engineering, Bergen University College, Bergen, Norway

org1136Faculty of Mathematics, Physics and Informatics, Comenius University,
Bratislava, Slovakia

org1274Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Prague, Czech Republic

org1229Faculty of Science, P.J. Šafárik University, Košice, Slovakia

org1184Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-
Universität Frankfurt, Frankfurt, Germany

org1215Gangneung-Wonju National University, Gangneung, South Korea

org1212Helsinki Institute of Physics (HIP) and University of Jyväskylä,
Jyväskylä, Finland

org1203Hiroshima University, Hiroshima, Japan

org1329Hua-Zhong Normal University, Wuhan, China

org1254Indian Institute of Technology, Mumbai, India

org36378Indian Institute of Technology Indore (IIT), Indore, India

org1266Institut de Physique Nucléaire d’Orsay (IPNO), Université Paris-Sud,
CNRS-IN2P3, Orsay, France

org1277Institute for High Energy Physics, Protvino, Russia

org1249Institute for Nuclear Research, Academy of Sciences, Moscow, Russia

org1320Nikhef, National Institute for Subatomic Physics and Institute for
Subatomic Physics of Utrecht University, Utrecht, Netherlands

org1250Institute for Theoretical and Experimental Physics, Moscow, Russia

org1230Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovakia

org1127Institute of Physics, Bhubaneswar, India

org1275Institute of Physics, Academy of Sciences of the Czech Republic,
Prague, Czech Republic

org1139Institute of Space Sciences (ISS), Bucharest, Romania

org27399Institut für Informatik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

org1185Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

org1177Institut für Kernphysik, Technische Universität Darmstadt, Darmstadt,
Germany

org1256Institut für Kernphysik, Westfälische Wilhelms-Universität Münster,
Münster, Germany

org1246Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de
México, Mexico City, Mexico

org1247Instituto de Física, Universidad Nacional Autónoma de México, Mexico
City, Mexico

org23333Institut of Theoretical Physics, University of Wroclaw

org1308Institut Pluridisciplinaire Hubert Curien (IPHC), Université de
Strasbourg, CNRS-IN2P3, Strasbourg, France

org1182Joint Institute for Nuclear Research (JINR), Dubna, Russia

org1143KFKI Research Institute for Particle and Nuclear Physics, Hungarian
Academy of Sciences, Budapest, Hungary

org1199Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg,
Heidelberg, Germany

org20954Korea Institute of Science and Technology Information

org1160Laboratoire de Physique Corpusculaire (LPC), Clermont Université,
Université Blaise Pascal, CNRS–IN2P3, Clermont-Ferrand, France

org1194Laboratoire de Physique Subatomique et de Cosmologie (LPSC), Université
Joseph Fourier, CNRS-IN2P3, Institut Polytechnique de Grenoble, Grenoble,
France

org1187Laboratori Nazionali di Frascati, INFN, Frascati, Italy

org1232Laboratori Nazionali di Legnaro, INFN, Legnaro, Italy

org1125Lawrence Berkeley National Laboratory, Berkeley, California, United
States

org1234Lawrence Livermore National Laboratory, Livermore, California, United
States

org1251Moscow Engineering Physics Institute, Moscow, Russia

org1140National Institute for Physics and Nuclear Engineering, Bucharest,
Romania

org1165Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

org1109Nikhef, National Institute for Subatomic Physics, Amsterdam,
Netherlands

org1283Nuclear Physics Institute, Academy of Sciences of the Czech Republic,
Řež u Prahy, Czech Republic

org1264Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States

org1189Petersburg Nuclear Physics Institute, Gatchina, Russia

org1170Physics Department, Creighton University, Omaha, Nebraska, United
States

org1157Physics Department, Panjab University, Chandigarh, India

org1112Physics Department, University of Athens, Athens, Greece

org1152Physics Department, University of Cape Town, iThemba LABS, Cape Town,
South Africa

org1209Physics Department, University of Jammu, Jammu, India

org1207Physics Department, University of Rajasthan, Jaipur, India

org1200Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg,
Heidelberg, Germany

org1325Purdue University, West Lafayette, Indiana, United States

org1281Pusan National University, Pusan, South Korea

org1176Research Division and ExtreMe Matter Institute EMMI, GSI
Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany

org1334Rudjer Bošković Institute, Zagreb, Croatia

org1298Russian Federal Nuclear Center (VNIIEF), Sarov, Russia

org1252Russian Research Centre Kurchatov Institute, Moscow, Russia

org1224Saha Institute of Nuclear Physics, Kolkata, India

org1130School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom

org1338Sección Física, Departamento de Ciencias, Pontificia Universidad
Católica del Perú, Lima, Peru

org1316Sezione INFN, Trieste, Italy

org1271Sezione INFN, Padova, Italy

org1313Sezione INFN, Turin, Italy

org1286Sezione INFN, Rome, Italy

org1146Sezione INFN, Cagliari, Italy

org1133Sezione INFN, Bologna, Italy

org1115Sezione INFN, Bari, Italy

org1155Sezione INFN, Catania, Italy

org1322Soltan Institute for Nuclear Studies, Warsaw, Poland

org1258SUBATECH, Ecole des Mines de Nantes, Université de Nantes, CNRS-IN2P3,
Nantes, France

org1304Technical University of Split FESB, Split, Croatia

org1168The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy
of Sciences, Cracow, Poland

org17361The University of Texas at Austin, Physics Department, Austin, TX,
United States

org1173Universidad Autónoma de Sinaloa, Culiacán, Mexico

org1296Universidade de São Paulo (USP), São Paulo, Brazil

org1149Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

org1239Université de Lyon, Université Lyon 1, CNRS/IN2P3, IPN-Lyon,
Villeurbanne, France

org1205University of Houston, Houston, Texas, United States

org1222University of Tennessee, Knoxville, Tennessee, United States

org1310University of Tokyo, Tokyo, Japan

org1318University of Tsukuba, Tsukuba, Japan

org21360Eberhard Karls Universität Tübingen, Tübingen, Germany

org1225Variable Energy Cyclotron Centre, Kolkata, India

org1306V. Fock Institute for Physics, St. Petersburg State University, St.
Petersburg, Russia

org1323Warsaw University of Technology, Warsaw, Poland

org1179Wayne State University, Detroit, Michigan, United States

org1260Yale University, New Haven, Connecticut, United States

org1332Yerevan Physics Institute, Yerevan, Armenia

org15649Yildiz Technical University, Istanbul, Turkey

org1301Yonsei University, Seoul, South Korea

org1327Zentrum für Technologietransfer und Telekommunikation (ZTT),
Fachhochschule Worms, Worms, Germany