# Is the background evolution of $\Lambda$CDM model consistent with
observations?

Yang Liu  Department of Physics and Synergistic Innovation Center for Quantum
Effects and Applications, Hunan Normal University, Changsha, Hunan 410081,
China  Bao Wang  Department of Physics and Synergistic Innovation Center for
Quantum Effects and Applications, Hunan Normal University, Changsha, Hunan
410081, China  Purple Mountain Observatory, Chinese Academy of Sciences,
Nanjing 210023, China  School of Astronomy and Space Sciences, University of
Science and Technology of China, Hefei 230026, China  Hongwei Yu  Department
of Physics and Synergistic Innovation Center for Quantum Effects and
Applications, Hunan Normal University, Changsha, Hunan 410081, China
Institute of Interdisciplinary Studies, Hunan Normal University, Changsha,
Hunan 410081, China  Puxun Wu  Department of Physics and Synergistic
Innovation Center for Quantum Effects and Applications, Hunan Normal
University, Changsha, Hunan 410081, China  Institute of Interdisciplinary
Studies, Hunan Normal University, Changsha, Hunan 410081, China
<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

We establish a new and cosmological-model-independent method to explore the
cosmic background dynamics in this work. Utilizing the latest Pantheon+ type
Ia supernova sample and the Hubble parameter measurements, we obtain the
values of the Hubble parameter and the deceleration parameter at five
different redshift points ranging from 0.2 to 0.6, and find that they can
deviate from the predictions of the $\Lambda$CDM model at more than $2\sigma$.
We further probe the equation of state of dark energy and obtain that a
slightly oscillating equation of state of dark energy around the $-1$ line is
favored.

##  1 Introduction

The cosmological constant $\Lambda$ plus cold dark matter ($\Lambda$CDM) is
the simplest and most favored cosmological model to describe the cosmic
evolution. The $\Lambda$CDM model, although fits observational data very well,
still faces some challenges. Among them, the Hubble constant ($H_{0}$) tension
is the most notable one and it has been considered as the most serious crisis
in modern cosmology (Riess, 2020; Perivolaropoulos & Skara, 2022). The $H_{0}$
tension refers to the discrepancy (more than 5$\sigma$) between the
measurements of $H_{0}$ using the near type Ia supernova (SN Ia) calibrated by
Cepheids (Riess et al., 2022) and that from the high-redshift cosmic microwave
background (CMB) radiation observation within the framework of the
$\Lambda$CDM model (Planck Collaboration, 2020), and it indicates that the
assumed $\Lambda$CDM model used to determine the Hubble constant may be
inconsistent with our present Universe or there may be potentially unknown
systematic errors in the observational data. It is worth noting, however, that
any systematics, which could explain the $H_{0}$ tension, have not been found
(Efstathiou, 2014; Feeney et al., 2018; Riess et al., 2016; Cardona et al.,
2017; Zhang et al., 2017; Follin & Knox, 2018; Riess et al., 2018a, b). Thus,
it is necessary to investigate whether the $\Lambda$CDM model can correctly
describe our Universe.

Since the cosmological constant as dark energy has a constant equation of
state (EoS) parameter $w_{\mathrm{DE}}$ equal to $-1$, where $w_{\mathrm{DE}}$
is defined as
$w_{\mathrm{DE}}\equiv\frac{P_{\mathrm{DE}}}{\rho_{\mathrm{DE}}}$ with
$P_{\mathrm{DE}}$ and $\rho_{\mathrm{DE}}$ being the pressure and energy
density of dark energy, respectively. Generalizing the EoS of dark energy from
$-1$ to an arbitrary constant $w_{\mathrm{DE}}$ or a parametrized form as a
function of redshift $z$, e.g., the CPL parametrization (Chevallier &
Polarski, 2001; Linder, 2003), and constraining $w_{\mathrm{DE}}$ or the
coefficients in the parameterization from observational data, we can judge the
viability of the cosmological constant as dark energy by analyzing whether
$w_{\mathrm{DE}}=-1$ is allowed by the observations. Although the $\Lambda$CDM
model has been found to be supported by the observations, the result will be
unreliable if the EoS of dark energy is not a constant or the parametrized
form of EoS is inappropriate.

Reconstructing the cosmic background evolution directly from the observations
is a reliable method to understand the expanding history of our Universe. The
usual methods include the nonparametric Bayesian reconstruction (Zhao et al.,
2012, 2017) and the Gaussian process (Holsclaw et al., 2010; Seikel et al.,
2012; Shafieloo et al., 2012). Using the observational data, e.g., SN Ia, one
can reconstruct the Hubble parameter ($H(z)$) or luminosity distance
($d_{L}(z)$) with their derivatives, and then compare them with the
predictions from the $\Lambda$CDM model to determine whether the $\Lambda$CDM
model can correctly describe the cosmic evolution. However, since all
observational data are used together to reconstruct the cosmic evolution, the
low (high) redshift data will affect the reconstructed result of the high
(low) redshift regions.

In this work, we establish a new method to obtain the cosmic background
dynamics in different redshift regions from observational data. Our method
does not assume the EoS of dark energy and any cosmological model. Using the
Pantheon+ SN Ia and the Hubble parameter measurements, we obtain the values of
the Hubble parameter and the deceleration parameter at different redshifts,
and find that may be incompatible with the predictions of the $\Lambda$CDM
model at more than $2\sigma$.

##  2 Method

For a homogeneous and isotropic Universe described by the Friedmann-Lemaître-
Robertson-Walker metric, the Hubble parameter $H$, which gives the cosmic
expanding velocity, is defined as

$\displaystyle H$ $\displaystyle\equiv$
$\displaystyle\frac{1}{a}\frac{da}{dt}\,,$ (1)

where $a$ is the cosmic scale factor and $t$ the cosmic time. In the
$\Lambda$CDM model, the Hubble parameter has the form:
$H(z)=H_{0}\sqrt{\Omega_{\mathrm{m0}}(1+z)^{3}+(1-\Omega_{\mathrm{m0}})}$ with
$\Omega_{\mathrm{m0}}$ being the present dimensionless matter density
parameter. Using the Hubble parameter, one can obtain the luminosity distance
$d_{L}(z)$:

$\displaystyle d_{L}(z)$ $\displaystyle=$
$\displaystyle(1+z)\int_{0}^{z}\frac{1}{H(z)}\,dz\,.$ (2)

Comparing the theoretical value and the observational one of the luminosity
distance can yield constraints on the cosmological parameters, i.e.
$\Omega_{\mathrm{m0}}$, after choosing a concrete cosmological model. To
cosmological-model-independently understand the cosmic dynamics, we perform
the Taylor expansion of the Hubble parameter and the luminosity distance at a
given redshift $z_{i}$ and then obtain:

$\displaystyle
H(z)=H_{i}\bigg{(}1+(z-z_{i})\frac{1+q_{i}}{1+z_{i}}\bigg{)}+\mathcal{O}\left((z-z_{i})^{2}\right)\,,$
(3)

and

$\displaystyle d_{L}(z)$ $\displaystyle=$ $\displaystyle
d_{L,i}+(z-z_{i})\left(\frac{1+z_{i}}{H_{i}}+\frac{d_{L,i}}{1+z_{i}}\right)$
(4)
$\displaystyle+(z-z_{i})^{2}\left(\frac{1}{H_{i}}-\frac{1+q_{i}}{2H_{i}}\right)+\mathcal{O}\left((z-z_{i})^{3}\right)\,,$

where $H_{i}=H(z_{i})$, $d_{L,i}=d_{L}(z_{i})$, and $q_{i}=q(z_{i})$ with
$q\equiv-\frac{1}{aH^{2}}\frac{d^{2}a}{dt^{2}}$ being the cosmic deceleration
parameter. Clearly, $d_{L,i}$, $H_{i}$ and $q_{i}$ are constants. If we can
determine their values from the observational data, the cosmic dynamics will
be known. Since the convergence region of the Taylor series of the luminosity
distance and the Hubble parameter is the near region around $z=z_{i}$, we only
consider the observational data in the redshift region $|z-z_{i}|\leq\Delta z$
to constrain $d_{L,i}$, $H_{i}$ and $q_{i}$, where $\Delta z$ represents the
convergence radius. When $z_{i}=0$, our method reduces to the usual
cosmographic one, which has been widely used to study the cosmic expanding
history (Visser, 2005; Luongo, 2011; Aviles et al., 2012; Dunsby & Luongo,
2016; Capozziello et al., 2019, 2020).

Once the constraints on $H_{i}$ and $q_{i}$ at a given redshift are obtained,
we can calculate the EoS parameter of dark energy $w_{\mathrm{DE},i}$ at that
redshift

$\displaystyle
w_{\mathrm{DE},i}=\frac{H_{i}^{2}(1-2q_{i})}{3\left[H_{0}^{2}\Omega_{\mathrm{m0}}(1+z_{i})^{3}-H_{i}^{2}\right]}$
(5)

after assuming that the energy component of the Universe consists of
pressureless matter and dark energy and the Universe is spatially flat.

##  3 Samples and Results

The latest Pantheon+ SN Ia sample (Scolnic et al., 2022) will be used firstly
to constrain $H_{i}$ and $q_{i}$. We choose $\Delta z=0.2$, which is small
enough to avoid the convergence problem in the Taylor series, and consider
five redshift points ($z_{i}$) in redshift from 0.2 to 0.6 with an increment
of 0.1. The number of SN Ia data in each redshift region is summarized in
Table 1. Due to that the nearby SN Ia sample is strongly impacted by their
peculiar velocities (Brout et al., 2022), we exclude those data whose redshift
are less than 0.01 in our analysis. The redshift points at $z>0.6$ are not
considered since the data number in the $(z-\Delta z,z+\Delta z]$ range are
less than two hundred, which will not give tight constraints on the
cosmological parameters.

Table 1:  Number of data in each redshift range

$z_{i}$ | 0.2 | 0.3 | 0.4 | 0.5 | 0.6
---|---|---|---|---|---
Redshift range | $0.01<z\leq 0.4$ | $0.1<z\leq 0.5$ | $0.2<z\leq 0.6$ | $0.3<z\leq 0.7$ | $0.4<z\leq 0.8$
$N_{\mathrm{SN}}$ | 1282 | 750 | 624 | 419 | 278
$N_{H(z)}$ | 12 | 16 | 12 | 11 | 10
$N_{\mathrm{total}}$ | 1294 | 766 | 636 | 430 | 288

Note. — Number of data in each redshift range. The $N_{\mathrm{SN}}$,
$N_{H(z)}$, and $N_{\mathrm{total}}$ represent the number of SN Ia data,
$H(z)$ data, and the total data in each redshift range, respectively. The SN
Ia data with redshift less than 0.01 are excluded here.

To estimate the best-fit values of the cosmological parameters and their
uncertainties from SN Ia, we utilize the minimizing $\chi^{2}$ method:

$\displaystyle\chi^{2}_{\mathrm{SN}}=[\bm{\hat{m}}_{\mathrm{obs}}(z)-m_{\mathrm{th}}(z)]^{\dagger}C^{-1}[\bm{\hat{m}}_{\mathrm{obs}}(z)-m_{\mathrm{th}}(z)].$
(6)

Here the subscript ‘obs’ and ‘th’ refer to the observed and theoretical
values, respectively, $C$ is the covariance matrix, which is a submatrix of
the full SN Ia sample since only data within the range $(z_{i}-0.2,z_{i}+0.2]$
are used, and $\bm{\hat{m}}_{\mathrm{obs}}$ is a 1D array consisting of the SN
Ia apparent magnitudes. The theoretical value of the apparent magnitude can be
derived from the luminosity distance $d_{L}(z)$ and the absolute magnitude
$M$:

$\displaystyle m_{\mathrm{th}}(z)=M+25+5\log\left(d_{L}(z)\right).$ (7)

Since the Hubble parameter $H$ is highly correlated with the absolute
magnitude $M$, we need to fix $M$, which is set to satisfy a Gaussian prior:
$-19.253\pm 0.027~{}\mathrm{mag}$ (Riess et al., 2022), when only the SN Ia
data are used.

In Figure 1, we show the constraints on $H_{i}$ (Figure 1(a)) and $q_{i}$
(Figure 1(b)). The solid lines represent the evolutionary curves of $H(z)$ and
$q(z)$ in the $\Lambda$CDM model with $H_{0}=73.2~{}\mathrm{km/s/Mpc}$ and
$\Omega_{\mathrm{m0}}=0.33$, which are obtained from the SN Ia sample with
$M=-19.253\pm 0.027~{}\mathrm{mag}$. To show the difference between $H_{i}$
and $q_{i}$, and the predictions in the $\Lambda$CDM model clearly, we also
plot $\Delta H=H_{i}-H_{\mathrm{\Lambda CDM}}$ and $\Delta
q=q_{i}-q_{\mathrm{\Lambda CDM}}$. The corresponding numerical results are
summarized in Table 2. It is easy to see that the values of $H_{i}$ at
$z_{i}=0.2$, $0.3$ and $0.5$ are consistent with the $\Lambda$CDM model. But
they deviate from the $\Lambda$CDM model when $z_{i}=0.4$ and $0.6$, and the
deviation can reach about 1.4$\sigma$. For the deceleration parameter, the
values at $z_{i}=0.2,~{}0.4,~{}\mbox{and}~{}0.5$ are different from the
prediction of the $\Lambda$CDM model, the largest deviation, which occurs at
$z_{i}=0.2$, is about $2.8\sigma$. Furthermore, we find that at $z_{i}=0.4$
the SN Ia data support a decelerating expansion at more than $1\sigma$. Using
Eq. (5), we can derive the EoS parameter of dark energy at different redshifts
($w_{\mathrm{DE},i}$) by considering the constraints on $H_{i}$ and $q_{i}$.
Setting $H_{0}$ and $\Omega_{\mathrm{m0}}$ to be $73.2\pm
0.94~{}\mathrm{km/s/Mpc}$ and $0.33\pm 0.018$, respectively, we obtain five
values of $w_{\mathrm{DE}}$, which are shown in Figure 2. We find that
$w_{\mathrm{DE}}$ shows a slightly oscillating behavior around the $-1$ line.
The values of $w_{\mathrm{DE}}$ at $z_{i}=0.2,~{}0.4,~{}\mbox{and}~{}0.5$
exhibit discrepancy from $-1$, and the maximum statistical deviation is about
$2.1\sigma$, which occurs at $z_{i}=0.2$.

Figure 1:  The constraints on $H_{i}$ and $q_{i}$ at different redshift points
by using the SN Ia dataset. The solid lines represent the predictions of the
$\Lambda$CDM model with $H_{0}=73.2~{}\mathrm{km/s/Mpc}$ and
$\Omega_{\mathrm{m0}}=0.33$. The symbol $\Delta$ denotes the differences
between the results of $H_{i}$ and $q_{i}$, and the predictions of the
$\Lambda$CDM model.  Figure 2:  The values of $w_{\mathrm{DE},i}$ derived from
Eq. (5) with $H_{0}=73.2\pm 0.94~{}\mathrm{km/s/Mpc}$ and
$\Omega_{\mathrm{m0}}=0.33\pm 0.018$ by using $H_{i}$ and $q_{i}$ constrained
from the SN Ia data.

A prior fixed $M$ may introduce some unknown bias in the results. To avoid
this issue, we add the Hubble parameter measurements (Simon et al., 2005;
Stern et al., 2010; Moresco et al., 2012; Cong et al., 2014; Moresco, 2015;
Moresco et al., 2016; Ratsimbazafy et al., 2017; Borghi et al., 2022) into our
analysis. Thus, $M$ can be treated as a free parameter. The number of $H(z)$
data in different redshift ranges is listed in Table 1. The results from SN
Ia+$H(z)$ are shown in Table 3 and Figure 3. While Figure 3(a) and 3(b),
respectively, represent $H_{i}$, $q_{i}$ and the predicted $H(z)$ and $q(z)$
from the $\Lambda$CDM model with $H_{0}=67.5~{}\mathrm{km/s/Mpc}$ and
$\Omega_{\mathrm{m0}}=0.33$, which are determined from the
$\mathrm{SN~{}Ia}+H(z)$ data. Figure 3(a) indicates that the values of $H_{i}$
are consistent with the $\Lambda$CDM model at 1$\sigma$ CL, which is different
from the results from the SN Ia data only. While, the values of $q_{i}$ at
$z_{i}=0.2$, $0.4$ and $0.5$ deviate from the prediction of the $\Lambda$CDM
model and the largest deviation is about $2.8\sigma$. At $z_{i}=0.4$, SN
Ia+$H(z)$ favor a decelerating expansion since $q_{i}>0$ is supported at more
than $1\sigma$. These results are almost the same as what are obtained from
the SN Ia data only. Figure 4 shows the values of $M_{i}$, from which, we find
that $M_{i}$ decreases almost linearly with the increase of redshift. To
illustrate clearly this trend, we use a simple linear function:
$M(z)=M_{0}+\alpha z$ to fit the evolution of $M_{i}$ between $z=0.2$ and
$0.6$, and obtain $M_{0}=-19.26\pm 0.12~{}\mathrm{mag}$ and $\alpha=-0.65\pm
0.33~{}\mathrm{mag}$. Apparently, $M_{0}$ is well consistent with that
obtained from the Cepheid host ($-19.253\pm 0.027~{}\mathrm{mag}$) (Riess et
al., 2022). The slope $\alpha$ deviates from zero at about $2\sigma$, which
indicates the observations seem to favor a non-constant absolute magnitude of
SN Ia.

Figure 5 shows the values of $w_{\mathrm{DE},i}$ after setting $H_{0}=67.5\pm
1.7~{}\mathrm{km/s/Mpc}$ and $\Omega_{\mathrm{m0}}=0.33\pm 0.017$. One can see
that $w_{\mathrm{DE},i}$ oscillates slightly around the $-1$ line and the
maximum deviation from $-1$ of $w_{\mathrm{DE},i}$ occurs at $z_{i}=0.4$ and
is at about $1.6\sigma$, which is similar to the results from the SN Ia data
only.

Figure 3:  The constraints on $H_{i}$ and $q_{i}$ by using the
$\mathrm{SN~{}Ia}+H(z)$ data. The solid lines are the predictions of the
$\Lambda$CDM model with $H_{0}=67.5~{}\mathrm{km/s/Mpc}$ and
$\Omega_{\mathrm{m0}}=0.33$. The symbol $\Delta$ denotes the differences
between the results of $H_{i}$ and $q_{i}$, and the predictions of the
$\Lambda$CDM model.  Figure 4:  The constraints on $M_{i}$ by using the
$\mathrm{SN~{}Ia}+H(z)$ data. The solid line represents the linear fitting
with the shadow region being the $1\sigma$ CL.  Figure 5: The values of
$w_{\mathrm{DE},i}$ derived from Eq. (5) with $H_{0}=67.5\pm
1.7~{}\mathrm{km/s/Mpc}$ and $\Omega_{\mathrm{m0}}=0.33\pm 0.017$ by using
$H_{i}$ and $q_{i}$ constrained from the SN Ia+$H(z)$ data.  Table 2:
Constraints on parameters from SN Ia dataset

$z_{i}$ | $H_{i}$ | $q_{i}$ | $w_{\mathrm{DE},i}$
---|---|---|---
$0.2$ |  $81.58\pm 1.13$ |  $-0.48\pm 0.06$ |  $-1.21\pm 0.10$
$0.3$ |  $86.66\pm 1.41$ |  $-0.30\pm 0.16$ |  $-1.11\pm 0.23$
$0.4$ |  $95.43\pm 2.03$ |  $0.33\pm 0.28$ |  $-0.24\pm 0.39$
$0.5$ |  $100.54\pm 2.95$ |  $-0.70\pm 0.47$ |  $-1.95\pm 0.80$
$0.6$ |  $109.78\pm 4.41$ |  $-0.41\pm 0.82$ |  $-1.53\pm 1.39$
$z_{i}$ |  $\Delta H_{i}$ |  $\Delta q_{i}$ |  $\Delta w_{\mathrm{DE},i}$
$0.2$ |  $0.06\pm 1.60$ |  $-0.17\pm 0.06$ |  $-0.21\pm 0.10$
$0.3$ |  $0.20\pm 1.91$ |  $-0.08\pm 0.16$ |  $-0.11\pm 0.23$
$0.4$ |  $3.55\pm 2.52$ |  $0.47\pm 0.28$ |  $0.76\pm 0.39$
$0.5$ |  $2.77\pm 3.42$ |  $-0.63\pm 0.47$ |  $-0.95\pm 0.80$
$0.6$ |  $5.70\pm 4.83$ |  $-0.42\pm 0.82$ |  $-0.53\pm 1.39$

Note. — The marginalized mean value and the 1$\sigma$ uncertainty of
parameters from the SN Ia data. The $M$ is set to be $-19.253\pm
0.027~{}\mathrm{mag}$. $\Delta$ denotes the difference between the constraint
results and the $\Lambda$CDM model with $H_{0}=73.2\pm
0.94~{}\mathrm{km/s/Mpc}$ and $\Omega_{\mathrm{m0}}=0.33\pm 0.018$.

Table 3:  Constraints on parameters from $\mathrm{SN}+H(z)$ dataset

$z_{i}$ | $H_{i}$ | $q_{i}$ | $w_{\mathrm{DE},i}$ | $M$
---|---|---|---|---
$0.2$ |  $76.64\pm 2.38$ |  $-0.48\pm 0.06$ |  $-1.17\pm 0.11$ |  $-19.39\pm 0.07$
$0.3$ |  $80.09\pm 2.42$ |  $-0.32\pm 0.15$ |  $-1.13\pm 0.23$ |  $-19.42\pm 0.07$
$0.4$ |  $82.92\pm 3.88$ |  $0.32\pm 0.26$ |  $-0.31\pm 0.44$ |  $-19.56\pm 0.11$
$0.5$ |  $87.59\pm 3.75$ |  $-0.57\pm 0.36$ |  $-2.10\pm 0.84$ |  $-19.56\pm 0.10$
$0.6$ |  $91.83\pm 4.07$ |  $-0.20\pm 0.42$ |  $-1.73\pm 1.18$ |  $-19.65\pm 0.11$
$z_{i}$ |  $\Delta H_{i}$ |  $\Delta q_{i}$ |  $\Delta w_{\mathrm{DE},i}$ |  …
$0.2$ |  $1.47\pm 3.07$ |  $-0.17\pm 0.06$ |  $-0.17\pm 0.11$ |  …
$0.3$ |  $0.36\pm 3.20$ |  $-0.10\pm 0.15$ |  $-0.13\pm 0.23$ |  …
$0.4$ |  $-1.81\pm 4.49$ |  $0.45\pm 0.26$ |  $0.69\pm 0.44$ |  …
$0.5$ |  $-2.56\pm 4.50$ |  $-0.51\pm 0.36$ |  $-1.10\pm 0.84$ |  …
$0.6$ |  $-4.15\pm 4.90$ |  $-0.20\pm 0.42$ |  $-0.73\pm 1.18$ |  …

Note. — The marginalized mean value and the 1$\sigma$ uncertainty of
parameters from $\mathrm{SN}+H(z)$ data. $\Delta$ denotes the difference
between the constraint results and the $\Lambda$CDM model with $H_{0}=67.5\pm
1.7~{}\mathrm{km/s/Mpc}$ and $\Omega_{\mathrm{m0}}=0.33\pm 0.017$.

##  4 Conclusions

To determine whether the cosmic evolution is consistent with the predictions
of the $\Lambda$CDM model, we establish a new and cosmological-model-
independent method to explore the cosmic dynamics from observational data.
Using the Pantheon+ SN Ia data, we obtain the values of $H$ and $q$ at five
different redshift points. We find that the deviation from the prediction of
the $\Lambda$CDM model is apparent and the largest deviation reaches
$2.8\sigma$. Further considering the Hubble parameter measurements, we
discover that the values of $q_{i}$ can deviate from the predictions of the
$\Lambda$CDM model at about $2.8\sigma$ although $H_{i}$ become consistent
with the $\Lambda$CDM model, and a linearly decreasing absolute magnitude of
SN Ia with the increase of redshift is favored. Furthermore, a slightly
oscillating EoS of dark energy around $-1$ is found. We think that this
property of dark energy may alleviate the $H_{0}$ tension, and this issue is
under current investigation.

This work was supported in part by the NSFC under Grant Nos. 12275080 and
12075084.

## References

  * Aviles et al. (2012) Aviles, A., Gruber, C., Luongo, O., & Quevedo, H. 2012, Phys. Rev. D, 86, 123516
  * Brout et al. (2022) Brout, D., Scolnic, D., Popovic, B., et al. 2022, ApJ, 938, 110
  * Borghi et al. (2022) Borghi, N., Moresco, M., & Cimatti, A. 2022, ApJ, 928, L4
  * Capozziello et al. (2019) Capozziello, S., D’Agostino, R., & Luongo, O. 2019, IJMPD, 28, 1930016
  * Capozziello et al. (2020) Capozziello, S., D’Agostino, R., & Luongo, O. 2020, MNRAS, 494, 2576
  * Cardona et al. (2017) Cardona, W., Kunz, M., & Pettorino, V. 2017, J. Cosmology Astropart. Phys, 03, 056
  * Chevallier & Polarski (2001) Chevallier, M., & Polarski, D. 2001, IJMPD, 10, 213
  * Cong et al. (2014) Cong, Z., Han, Z., Shuo, Y., et al. 2014, RAA, 14, 1221
  * Dunsby & Luongo (2016) Dunsby, P. K. S., & Luongo, O. 2016, IJGMM, 13, 1630002
  * Efstathiou (2014) Efstathiou, G. 2014, MNRAS, 400, 1138
  * Feeney et al. (2018) Feeney, S. M., Mortlock, D. J., & Dalmasso, N. 2018, MNRAS, 476, 3861
  * Follin & Knox (2018) Follin, B., & Knox, L. 2018, MNRAS, 477, 4534
  * Holsclaw et al. (2010) Holsclaw, T., Alam, U., Sansó, B., et al. 2010, Phys. Rev. Lett., 105, 241302
  * Linder (2003) Linder, E. V. 2003, Phys. Rev. Lett., 90, 091301
  * Luongo (2011) Luongo, O. 2011, Mod. Phys. Lett. A, 26, 1459
  * Moresco et al. (2012) Moresco, M., Cimatti, A., Jimenez, R., et al. 2012, J. Cosmology Astropart. Phys, 08, 006
  * Moresco (2015) Moresco, M. 2015, MNRAS Lett., 450, L16
  * Moresco et al. (2016) Moresco, M., Pozzetti, L., Cimatti, A., et al. 2016, J. Cosmology Astropart. Phys, 05, 014
  * Perivolaropoulos & Skara (2022) Perivolaropoulos, L., & Skara, F. 2022, NewAR, 95, 101659
  * Planck Collaboration (2020) Planck Collaboration. 2020, A&A, 641, A6
  * Ratsimbazafy et al. (2017) Ratsimbazafy, A. L., Loubser, S. I., Crawford, S. M., et al. 2017, MNRAS, 467, 3239
  * Riess et al. (2016) Riess, A. G., Macri, L. M., Hoffmann, S. L., et al. 2016, ApJ, 826, 56
  * Riess et al. (2018a) Riess, A. G., Casertano, S., Yuan, W., et al. 2018a, ApJ, 855, 136
  * Riess et al. (2018b) Riess, A. G., Casertano, S., Yuan, W., et al. 2018, ApJ, 861, 126
  * Riess (2020) Riess, A. G. 2020, NatRP, 2, 10
  * Riess et al. (2022) Riess, A. G., Yuan, W., Macri, L. M., et al. 2022, ApJ, 934, L7
  * Scolnic et al. (2022) Scolnic, D., Brout, D., Carr, A., et al. 2022, ApJ, 938, 113
  * Seikel et al. (2012) Seikel, M., Clarkson, C., & Smith, M. 2012, J. Cosmology Astropart. Phys, 06, 036
  * Shafieloo et al. (2012) Shafieloo, A., Kim, A. G., Linder, E. V. 2012, Phys. Rev. D, 85, 123530
  * Simon et al. (2005) Simon, J., Verde, L., & Jimenez, R. 2005, Phys. Rev. D, 71, 123001
  * Stern et al. (2010) Stern, D., Jimenez, R., Verde, L., Kamionkowski, M., & Stanford, S. A. 2010, J. Cosmology Astropart. Phys, 02, 008
  * Visser (2005) Visser, M. 2005, Gen. Relativ. Gravit., 37, 1541
  * Zhang et al. (2017) Zhang, B. R., Childress, M. J., Davis, T. M., et al. 2017, MNRAS, 471, 2254
  * Zhao et al. (2012) Zhao, G. B., Crittenden, R. G., Pogosian, L., & Zhang, X. 2012, Phys. Rev. Lett., 109, 171301
  * Zhao et al. (2017) Zhao, G. B., Raveri, M., Pogosian, L., et al. 2017, Nat. Astron., 1, 627


2017 305 28 November

$\text{Z}^{0}$-boson production in Pb-Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV

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

The production of $\text{Z}^{0}$ bosons at large rapidities in Pb-Pb
collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV is reported. $\text{Z}^{0}$
candidates are reconstructed in the dimuon decay channel
($\text{Z}^{0}\rightarrow\mu^{+}\,\mu^{-}$), based on muons selected with
pseudo-rapidity $-4.0<\eta<-2.5$ and $p_{\textrm{T}}>20$ GeV/$c$. The
invariant yield and the nuclear modification factor, $R_{\text{AA}}$, are
presented as a function of rapidity and collision centrality. The value of
$R_{\text{AA}}$ for the 0–20% central Pb-Pb collisions is $0.67\pm
0.11\,\mbox{(stat.)}\,\pm 0.03\,\mbox{(syst.)}\,\pm 0.06\,\mbox{(corr.
syst.)}$, exhibiting a deviation of $2.6\sigma$ from unity. The results are
well-described by calculations that include nuclear modifications of the
parton distribution functions, while the predictions using vacuum PDFs deviate
from data by $2.3\sigma$ in the 0–90% centrality class and by $3\sigma$ in the
0–20% central collisions.

##  1 Introduction

$\text{Z}^{0}$ bosons are weakly interacting probes formed early in the
evolution of hadronic collisions ($t_{f}\sim 1/M\ll 0.01$ fm/$c$), with a
typical decay time $t_{d}\sim 0.1$ fm/$c$. Their leptonic decays are of
particular interest in heavy-ion collisions, since leptons do not interact
strongly and their in-medium energy loss by bremsstrahlung is negligible [1].
$\text{Z}^{0}$-boson production rates in hadronic collisions are well-
understood, and their measurement via leptonic decays therefore serves as a
valuable medium-blind reference for hard processes in heavy-ion collisions [2,
3].

$\text{Z}^{0}$-boson properties have been extensively studied at LEP (CERN),
SLC (SLAC), Tevatron (FNAL) and LHC (CERN) in $e^{+}e^{-}$,
p$\overline{\mbox{p}}$ and pp collisions [4, 5, 6, 7, 8, 9, 10, 11, 12, 13,
14, 15]. $\text{Z}^{0}$-boson production in hadronic collisions is well-
described by perturbative Quantum Chromodynamics (pQCD) calculations at next-
to-next-to-leading order (NNLO) [16, 17], and their comparison with data
provides constraints on Parton Distribution Functions (PDFs) [18, 19]. In
heavy-ion collisions, $\text{Z}^{0}$-boson production can be affected by
initial-state effects. As a result of the different balance of the number of u
and d valence quarks in protons and in lead nuclei (isospin), the yield of
$\text{Z}^{0}$ bosons in Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV
is expected to increase relative to that in pp collisions by $5-8\%$ at large
rapidities, and decrease by $3\%$ at central rapidities [20]. Modifications of
the PDFs in nuclei (nPDFs) [21, 22, 23, 24, 25, 26, 27] introduce a rapidity-
dependent change in yield, with a decrease in yield relative to that in pp
collisions of $8-15\%$ at large rapidities, corresponding to the Bjorken-$x$
ranges $x_{1}\gtrsim 10^{-1}$ and $x_{2}\lesssim 10^{-3}$, and an increase by
$3\%$ at central rapidity, corresponding to $x_{1,2}\sim 10^{-2}$ [20, 21].
The yield could also depend upon effects such as multiple scattering and
medium-induced bremsstrahlung of the initial partons in large nuclei [28].

The ATLAS, ALICE, CMS and LHCb collaborations have reported measurements of
$\text{W}^{\pm}$\- and $\text{Z}^{0}$-boson production in p-Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV [29, 30, 31, 32, 33], with complementary
rapidity coverage. These measurements are well-described by next-to-leading
order (NLO) pQCD calculations [20] and by NNLO calculations using the Fully
Exclusive W and Z Production code (FEWZ) [34], utilising both nPDFs [32] and
vacuum PDFs. The forward-backward asymmetry of $\text{W}^{\pm}$-boson
production suggests the presence of nuclear modification of PDFs [31]. This
sensitivity to nuclear effects indicates the need to include these data in the
future nPDF fits.

In Pb-Pb collisions, $\text{W}^{\pm}$\- and $\text{Z}^{0}$-boson measurements
at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV have been carried out at central rapidity
by the ATLAS and CMS collaborations [35, 36, 37, 38]. Preliminary
$\text{Z}^{0}$-boson measurements in Pb-Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV at central rapidity have also been reported
recently by ATLAS [39]. The $\text{W}^{\pm}$\- and $\text{Z}^{0}$-boson
nuclear modification factor, $R_{\text{AA}}$, defined as the ratio of the
yields in Pb-Pb collisions and the cross-section in pp collisions normalised
by the nuclear overlap function $\langle T_{\rm AA}\rangle$, which represents
the effective overlap area of the two interacting nuclei [40], is measured to
be consistent with unity within uncertainties, with no centrality dependence
[37, 38, 39].

Measurements at high collision energy and large rapidities are sensitive to
low Bjorken-$x$ processes, and are therefore important to further constrain
the initial-state effects on electroweak boson production and to establish a
reference for medium-sensitive observables.

This paper presents the first measurement of $\text{Z}^{0}$-boson production
in Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV at large rapidities.
Opposite-sign muon pairs from $\text{Z}^{0}$-boson decays with
$2.5<y<4.0$111In the ALICE reference frame the muon spectrometer covers a
negative $\eta$ range and, consequently, a negative $y$ range. However, since
the Pb-Pb system is symmetric in rapidity, a positive $y$ notation is used to
present the results. are measured with the ALICE detector. The yield of
$\mu^{+}\,\mu^{-}$ pairs includes contributions from virtual-photon processes
and from their interference effects. This measurement probes the nPDFs of
large-$x$ valence quarks ($x_{1}\gtrsim 10^{-1}$) and low-$x$ sea quarks
($x_{2}\lesssim 10^{-3}$) at $Q^{2}\sim M_{\rm Z}^{2}$. The invariant yields
and $R_{\text{AA}}$ are reported as a function of rapidity and collision
centrality. The results are compared to model calculations including nPDFs.
These measurements complement the measurements in p-Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV at large rapidities [32, 33], providing
increased precision and new information on rapidity and centrality dependence.
The combination of these results with future $\text{W}^{\pm}$ measurements in
a similar kinematic interval will provide constraints on the flavor dependence
of nPDFs, in particular the strange quark contribution [21].

This letter is organised as follows: the experimental setup and data sample
are described in Sect. 2; the analysis procedure is presented in Sect. 3; the
results are presented in Sect. 4; and a summary is given in Sect. 5.

##  2 Experimental setup and dataset

The ALICE detector is described in detail in Ref. [41]. $\text{Z}^{0}$ bosons
are reconstructed via their muonic decay with the ALICE muon spectrometer,
which provides muon trigger, tracking and identification in the pseudo-
rapidity range $-4.0<\eta<-2.5$. The muon spectrometer, as seen from the
interaction point, consists of a front absorber of 10 interaction lengths
($\lambda_{\rm int}$) thickness, which reduces the contamination of hadrons
and muons from the decay of light particles; five tracking stations; an iron
absorber with thickness 7.2 $\lambda_{\rm int}$; and two trigger stations.
Each tracking station is composed of two planes of multi-wire proportional
chambers with cathode-plane readout, while each trigger station consists of
two planes of resistive plate chambers. The third tracking station is located
inside the gap of a dipole magnet, which provides a 3 T$\cdot$m magnetic field
integral. The muon spectrometer is completed by a beam shield surrounding the
beam pipe that protects the apparatus from secondary particles produced in the
interaction of large-$\eta$ primary particles with the pipe itself.

The interaction vertex is reconstructed using the two cylindrical layers of
the Silicon Pixel Detector, located at a radial distance of 3.9 and 7.6 cm
from the beam axis and covering $|\eta|<2$ and $|\eta|<1.4$, respectively. The
V0 detector, consisting of two arrays of scintillator counters covering
$2.8<\eta<5.1$ and $-3.7<\eta<-1.8$, is used for triggering and evaluation of
collision centrality. Finally, the Zero Degree Calorimeter, placed at 112.5 m
from the interaction point along the beam line, is used to reject
electromagnetic interactions [42].

The dataset used in this analysis consists of Pb-Pb events at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV selected with a dimuon trigger that requires
the coincidence of a minimum-bias (MB) trigger and a pair of tracks with
opposite sign in the muon spectrometer, each with $p_{\textrm{T}}\gtrsim 1$
GeV/$c$. The MB trigger is defined by the coincidence of the signals from both
arrays of the V0. The MB trigger is fully efficient for events within the
0–90% centrality interval, which are used in this analysis. The muon trigger
efficiency has a plateau of about 98% for muons with $p_{\textrm{T}}>5$
GeV/$c$. The resulting efficiency for pairs of opposite-sign muons, with muon
$p_{\textrm{T}}>20$ GeV/$c$ and $-4.0<\eta<-2.5$, is 95%. After all event
selection cuts, the dataset corresponds to an integrated luminosity of about
225 $\text{$\mu$b}^{-1}$.

##  3 Analysis procedure

The procedure for $\text{Z}^{0}$-boson signal extraction in this analysis is
the same as that used in the analysis of p-Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV [32]. Tracks are reconstructed in the muon
spectrometer using the algorithm described in Ref. [43]. Tracks are selected
for analysis if they have pseudorapidity $-4.0<\eta<-2.5$ and polar angle
$170^{\circ}<\theta_{\rm abs}<178^{\circ}$, measured at the end of the front
absorber. This selection rejects particles that cross the high-density region
of the front absorber and undergo significant multiple scattering. Tracks
reconstructed in the tracking stations are identified as muons if they match a
track segment in the trigger stations, placed downstream the iron wall. The
contamination from background tracks that do not point to the interaction
vertex is reduced by utilising the product of the momentum and the distance of
closest approach to the interaction vertex. This cut removes 88% of all tracks
for events in the 0–90% centrality interval, while retaining all signal
candidates with negligible residual background contribution.

Only muons with $p_{\textrm{T}}>20~{}\mbox{GeV/}c$ are used in this analysis.
This selection reduces the contribution of muons from the decay of charm,
beauty and low-mass resonances (see below). $\text{Z}^{0}$-boson candidates
are formed by combining pairs of opposite-sign muons. The candidates are
further selected by requiring that their rapidity, calculated using the
measured invariant mass, is in the interval $2.5<y<4.0$. Figure 1 presents the
$\mu^{+}\,\mu^{-}$ invariant mass distribution in the centrality intervals
0–90% in Figure 1, 0–20% in Figure 1, and 20–90% in Figure 1.

Figure 1:  Invariant mass distribution of $\mu^{+}\,\mu^{-}$ pairs for Pb-Pb
collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV, reconstructed using muons
with $-4.0<\eta<-2.5$ and $p_{\textrm{T}}>20$ GeV/$c$ (black points). The
panels present the distribution in different centrality intervals. The error
bars are of statistical origin only. The invariant mass distribution of like-
sign muon pairs is also shown (red open points). Only one like-sign candidate
is found in the 20–90% centrality interval. The solid blue line drawn in
Figure 1 represents the distribution from a POWHEG simulation for Pb-Pb
collisions without nuclear modification of PDFs (see text for details).

The distribution for the 0–90% centrality interval is compared with the result
of a Monte Carlo (MC) simulation obtained using the POWHEG [44] event
generator paired with PYTHIA 6.4.25 [45] for the parton shower. The
propagation of the particles through the detector is simulated with the GEANT3
code [46]. The isospin of the Pb-nucleus is accounted for by a weighted
average of neutron and proton interactions, but no modification of the nucleon
PDF was applied to account for nuclear effects. The simulations account for
variations in the detector response with time and in-situ alignment effects. A
data-driven description of the muon momentum resolution is also implemented
(see Ref. [32] for details). The shape of the $\mu^{+}\,\mu^{-}$ invariant
mass distribution, which is mainly affected by the momentum resolution, is
similar in data and MC.

Various background sources contribute to the $\mu^{+}\,\mu^{-}$ invariant mass
distribution. Contamination from the decay of t$\overline{\mbox{t}}$
($\mbox{t}\overline{\mbox{t}}\longrightarrow\mu^{+}\,\mu^{-}\,X$) and $\tau$
($\text{Z}^{0}\longrightarrow\tau\tau\longrightarrow\mu^{+}\,\mu^{-}\,X$)
pairs is estimated with POWHEG simulations [44, 10, 47] and found to be
smaller than 0.5% of the signal yield, which is considered as a systematic
uncertainty. The contribution of opposite-sign muon pairs from the decay of
c$\overline{\mbox{c}}$
($\mbox{c}\overline{\mbox{c}}\longrightarrow\mu^{+}\,\mu^{-}\,X$) and
b$\overline{\mbox{b}}$
($\mbox{b}\overline{\mbox{b}}\longrightarrow\mu^{+}\,\mu^{-}\,X$) pairs was
studied in p-Pb collisions [32] and found to be smaller than that of
t$\overline{\mbox{t}}$ and $\tau$ pairs. In Pb-Pb collisions, the presence of
high-$p_{\textrm{T}}$ muons from the decay of heavy-flavour pairs is expected
to be further reduced due to the in-medium energy loss of heavy quarks. This
contribution was therefore neglected. Finally, the combinatorial contribution
from the random pairing of muons in the event is evaluated via like-sign muon
pairs ($\mu^{\pm}\,\mu^{\pm}$). This combinatorial contribution is found to be
small (one candidate in the 20–90% centrality interval) and is subtracted from
the signal estimate.

The number of $\text{Z}^{0}$ candidates is estimated using the procedure
described in Ref. [32], by counting the entries in the $\mu^{+}\,\mu^{-}$
invariant mass interval $60<M_{\mu\mu}<120$ GeV/$c^{2}$ after subtracting the
contribution from like-sign pairs for each centrality and rapidity interval. A
total of 64 candidates is found in the 0–90% centrality bin, of which 37 are
in the 0–20% bin and 27 in the 20–90% bin. As a function of rapidity, 33
candidates are in the interval $2.5<y<3.0$, and 31 are in the interval
$3.0<y<4.0$. The raw yields are corrected for the detector acceptance and for
reconstruction and selection efficiency ($A\cdot\epsilon$). The value of
$A\cdot\epsilon$ is 75% for events in the 0–90% centrality interval, estimated
using the POWHEG [44] simulations described previously. The dependence of the
efficiency on the detector occupancy was evaluated by embedding the generated
$\text{Z}^{0}$ signal in real MB Pb-Pb data. The $A\cdot\epsilon$ term is
constant as a function of centrality from peripheral to semi-central events
and decreases in the most central collisions. The value of $A\cdot\epsilon$ is
78% in the 20-90% centrality interval and 74% in the 0-20% interval, with
centrality-independent systematic uncertainty of 5%, as discussed below.

To evaluate the invariant yields (${\rm d}N/{\rm d}y$), the raw dimuon-
triggered mass distribution must be normalised by the factor
$F_{\mu\text{-trig/MB}}^{i}$, which is the inverse of the probability to
observe a dimuon pair in a MB event for the centrality class $i$. The value of
$F_{\mu\text{-trig/MB}}^{i}$ is calculated in two different ways, by applying
the dimuon selection criterion to MB events, and by the relative counting rate
of the two triggers [48]. The variation in $F_{\mu\text{-trig/MB}}^{i}$
determined by these two methods is 0.5% and contributes to the systematic
uncertainty.

The nuclear modification factor $R_{\text{AA}}$ requires the determination of
the collision centrality, which is typically quantified by the average number
of nucleons participating in the interaction for a given centrality bin,
$N_{\text{part}}$. However, the rate of hard processes is known to scale with
the average number of nucleon-nucleon collisions $N_{\text{coll}}$. The
average centrality for hard processes is therefore presented as the average
number of participant nucleons weighted by the number of collisions $\langle
N_{\text{part}}\rangle_{N_{\text{coll}}}$. Table 1 shows the estimates of the
average nuclear overlap function $\langle T_{\rm AA}\rangle$, the number of
participating nucleons $\langle N_{\text{part}}\rangle$ and the number of
binary nucleon-nucleon collisions $\langle N_{\text{coll}}\rangle$, which are
obtained via a Glauber model fit of the signal amplitude in the two arrays of
the V0 detector [49, 50]. The resulting $\langle
N_{\text{part}}\rangle_{N_{\text{coll}}}$ is also shown. The classification of
the events in given centrality intervals has an associated uncertainty of 1.5
– 2.3% (centrality dependent), that was estimated by comparing the number of
candidates selected by varying the centrality ranges by $\pm 0.5\%$, to
account for the centrality resolution [49, 50].

Centrality |  $\langle T_{\rm AA}\rangle$ ( $\text{mb}^{-1}$) | $\langle N_{\text{part}}\rangle$ | $\langle N_{\text{coll}}\rangle$ | $\langle N_{\text{part}}\rangle_{N_{\text{coll}}}$
---|---|---|---|---
0–90% | $\hphantom{0}6.2\hphantom{0}\pm 0.2\hphantom{0}$ | $126\pm 2$ | $\hphantom{0}435\pm\hphantom{0}41$ | $263\pm 3$
0–20% | $18.8\hphantom{0}\pm 0.6\hphantom{0}$ | $311\pm 3$ | $1318\pm 130$ | $322\pm 3$
20–90% | $\hphantom{0}2.61\pm 0.09$ | $\hphantom{0}73\pm 1$ | $\hphantom{0}183\pm\hphantom{0}15$ | $141\pm 2$
Table 1:  Values of the average nuclear overlap function, $\langle T_{\rm
AA}\rangle$, the number of participating nucleons, $\langle
N_{\text{part}}\rangle$, and the number of binary nucleon-nucleon collisions,
$\langle N_{\text{coll}}\rangle$, for each centrality interval. The average
number of participants as weighted by the average number of collisions,
$\langle N_{\text{part}}\rangle_{N_{\text{coll}}}$, is also reported.

The sources of systematic uncertainties in the yields and $R_{\text{AA}}$ are
summarised in Table 2. The systematic uncertainty in the tracking efficiency
is 3%, obtained from the comparison of the efficiency estimated in data and MC
by exploiting the redundancy of the tracking chamber information [51]. The
systematic uncertainty of the dimuon trigger efficiency is $1.5\%$, evaluated
by propagating the uncertainty of the efficiency of the detection elements,
which is estimated from data using the redundancy of the trigger chamber
information. In addition, the choice of the $\chi^{2}$ cut used to match the
tracker and trigger tracks introduces 1% uncertainty, obtained from the
difference between data and simulation when applying different $\chi^{2}$
cuts. The uncertainties in the track resolution and alignment are estimated by
comparing the $A\cdot\epsilon$ values obtained with two different simulations.
In the full simulation, the alignment is measured using the MILLIPEDE [52]
package and the residual misalignment is taken into account. In the fast
simulation, the tracker response is based on a parameterisation of the
measured resolution of the clusters associated with a track [32]. The
resulting systematic uncertainty is 3.5%.

The total systematic uncertainty in the yield and $R_{\text{AA}}$ are
determined by summing in quadrature the uncertainty from each source, listed
in Table 2. All uncertainties except those due to $\langle T_{\rm AA}\rangle$
and the centrality bin boundaries are independent of collision centrality.
Correlations in centrality or rapidity of the uncertainties of different
sources are indicated in Table 2. The relative systematic uncertainty in the
proton-proton reference $\sigma_{\rm pp}$, which affects the $R_{\text{AA}}$,
corresponds to 4.5% and is estimated by varying the factorization and
renormalisation scales and accounting for the uncertainties in the PDFs [20].

Source | Relative systematic uncertainty
---|---
Background contamination |  $<1.0\%$ 0000
Tracking efficiency | 3.0% ($\star$)
Trigger efficiency | 1.5% ($\star$)
Tracker/trigger matching | 1.0% ($\star$)
Alignment | 3.5% ($\star$)
$F_{\mu\text{-trig/MB}}$ | 0.5% ($\star\,\diamond$)
$\sigma_{\rm pp}$ | 4.5% ($\star$)
$\langle T_{\rm AA}\rangle$ | 3.2 – 3.5% ($\diamond$)
Centrality limits | 1.5 – 2.3% ($\diamond$)
Table 2:  Relative systematic uncertainties in the yields and $R_{\text{AA}}$.
The ranges quoted for $\langle T_{\rm AA}\rangle$ and the centrality limits,
represent the uncertainty variation with centrality. The centrality-dependent
correlated uncertainties are marked by the symbol ($\star$), while the
uncertainty sources that are correlated as a function of rapidity are
indicated by ($\diamond$).

##  4 Results

The invariant yield of $\mu^{+}\,\mu^{-}$ from $\text{Z}^{0}$ bosons in
$2.5<y<4.0$, divided by $\langle T_{\rm AA}\rangle$, is $6.11\pm
0.76\,{\rm(stat.)}\,\pm 0.38\,{\rm(syst.)}$ pb for the 0–90% centrality
interval. The comparison with theoretical calculations at NLO is shown in
Figure 2. The CT14 [53] prediction utilises free proton and neutron PDFs, with
relative weights to account for the isospin of the Pb nucleus. The uncertainty
on the model include the uncertainty on the NLO calculations and of the
measurements considered in the PDF fit. The measured invariant yield deviates
from the lower limit of this prediction by $2.3\sigma$. For the description of
nuclear PDFs, two different approaches were considered. The standard approach
evaluates the nPDF as the free PDF multiplied by a parameterisation of nuclear
modifications. The calculations obtained with the EPS09 [54] and the more
recent EPPS16 [22] parameterisations are shown. In the other approach, the
nPDFs are obtained by fitting the nuclear data in a similar way as done for
free proton data, but using a parameterisation that depends on the atomic mass
of the nucleus. The results obtained with the nCTEQ15 nuclear PDFs [55, 21]
are also presented. The nPDF sets are characterised by their different
approximations and by different input data included in the calculations (see
Ref. [22] and references therein for details). Only the most recent EPPS16
parameterisation includes LHC jet, $\text{W}^{\pm}$ and $\text{Z}^{0}$ data,
although the $\text{W}^{\pm}$ and $\text{Z}^{0}$ data provide only weak
constraints on nPDFs at the current perturbative order of the calculation
(NLO) [56, 21]. In general, the nPDFs have larger uncertainties compared to
the free proton PDFs, since they are less constrained from data. CT14+EPS09
and CT14+EPPS16 estimates combine CT14 and EPS09 or EPPS16 uncertainties,
whereas nCTEQ15 does a global study of the proton and nuclear measurement
uncertainties included in the fit. EPPS16 allows much more freedom for the
flavour dependence of nPDFs than other current analyses, which results in
larger uncertainties. All pQCD calculations shown in Figure 2 that use nPDFs
describe the measurement well.

Figure 2:  Invariant yield of $\mu^{+}\,\mu^{-}$ from $\text{Z}^{0}$
production in $2.5<y<4.0$ divided by the average nuclear overlap function in
the 0–90% centrality class, considering muons with $-4.0<\eta<-2.5$ and
$p_{\textrm{T}}>20$ GeV/$c$. The horizontal solid line represents the
statistical uncertainty of the measurement while the yellow filled band shows
the systematic uncertainty. The result is compared to theoretical calculations
with and without nuclear modification of the PDFs [53, 54, 22, 55, 21]. All
model calculations incorporate PDFs or nPDFs determined by considering the
isospin of the Pb-nucleus.

The rapidity dependence of the $\text{Z}^{0}$-boson invariant yields divided
by $\langle T_{\rm AA}\rangle$ is shown in Figure 3. The results are compared
to pQCD calculations using the CT14 [53] PDF set both with (green filled box)
and without (blue hatched box) the EPPS16 [22] parameterisation of the nPDFs.
In both cases, the Pb-isospin effect is modeled by combining the proton and
neutron PDFs or nPDFs. EPPS16 decreases the yields but does not have a strong
influence on the rapidity dependence of the calculation. The calculations that
utilise vacuum PDFs overestimate data in the two rapidity intervals, whereas
those that utilise nPDFs are in good agreement with data.

Figure 3:  Invariant yield of $\mu^{+}\,\mu^{-}$ from $\text{Z}^{0}$ in
$2.5<y<4.0$ divided by $\langle T_{\rm AA}\rangle$ (a) and nuclear
modification factor (b) as a function of rapidity for Pb-Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV, considering muons with $-4.0<\eta<-2.5$ and
$p_{\textrm{T}}>20$ GeV/$c$. The vertical error bars are statistical only. The
horizontal error bars display the measurement bin width, while the boxes
represent the systematic uncertainties. The filled black box in panel (b),
located at $R_{\text{AA}}=1$, shows the normalisation uncertainty. The results
are compared to theoretical calculations with and without nuclear modification
of the PDFs. The filled blue boxes show the calculation using the CT14 PDF,
while the green stippled boxes show the calculation using CT14 PDF with EPPS16
nPDF [53, 22]. All model calculations incorporate PDFs or nPDFs that account
for the isospin of the Pb nucleus.

In this analysis, the ratio $R_{\text{AA}}$ utilises a theoretically
calculated reference cross section for pp collisions [20], which is
$\sigma_{pp}=11.92\,\pm 0.43$ pb. The value of $R_{\text{AA}}$ for the 0–90%
centrality class is determined to be $0.77\pm 0.10\,{\rm(stat.)}\,\pm
0.06\,{\rm(syst.)}$, deviating by $2.1\sigma$ from unity. The pQCD calculation
using CT14 [53] and considering only the isospin effects, finds
$R_{\text{AA}}^{\rm CT14}=1.052\pm 0.038$. The modification of the PDFs in
nuclei results in a net reduction of the yields, and consequently in
$R_{\text{AA}}$ values lower than unity, with $R_{\text{AA}}^{\rm
CT14+EPPS16}=0.845\pm 0.068$, in agreement with data. The rapidity dependence
of $R_{\text{AA}}$ is presented in Figure 3. The values are smaller than
unity, with a slight rapidity dependence. The data are well-described by
calculations including nPDFs (green filled boxes), while the calculations
including only isospin effects (blue hatched boxes) tend to overestimate the
measured values.

$\text{Z}^{0}$-boson production is studied as a function of the collision
centrality, expressed in terms of $\langle
N_{\text{part}}\rangle_{N_{\text{coll}}}$ as shown in Figure 4. The value of
$R_{\text{AA}}$ is compatible with unity in peripheral collisions, with
$R_{\text{AA}}$ (20–90%) = $0.96\pm 0.19\,\mbox{(stat.)}\,\pm
0.04\,\mbox{(syst.)}\,\pm 0.06\,\mbox{(corr. syst.)}$, while it is $2.6\sigma$
smaller than unity in the central collisions, with $R_{\text{AA}}$ (0–20%) =
$0.67\pm 0.11\,\mbox{(stat.)}\,\pm 0.03\,\mbox{(syst.)}\,\pm
0.04\,\mbox{(corr. syst.)}$. The value for 0-20% central collisions deviates
from the predictions using vacuum PDFs ($R_{\text{AA}}^{\rm CT14}$) by
$3\sigma$. The data are compared to calculations including a centrality-
dependent nuclear modification of the PDFs [57], which describe the data
within uncertainties.

(a)

Figure 4:  Invariant yield of $\mu^{+}\,\mu^{-}$ from $\text{Z}^{0}$ in
$2.5<y<4.0$ divided by $\langle T_{\rm AA}\rangle$ (a) and nuclear
modification factor (b) as a function of centrality (represented by $\langle
N_{\text{part}}\rangle_{N_{\text{coll}}}$) for Pb-Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV, considering muons with $-4.0<\eta<-2.5$ and
$p_{\textrm{T}}>20$ GeV/$c$. The vertical error bars are statistical only,
while the boxes represent the systematic uncertainties. The filled black box
in panel (b), located at $R_{\text{AA}}=1$, shows the normalisation
uncertainty. The results are compared to theoretical calculations with
centrality-dependent nPDFs that account for the isospin of the Pb nucleus [53,
54, 57].

##  5 Conclusion

We have reported the first measurement of $\text{Z}^{0}$-boson production at
forward rapidities in Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV.
The invariant yields divided by the average nuclear overlap function are
evaluated as a function of rapidity and average number of participant nucleons
weighted by the number of binary nucleon-nucleon collisions. The corresponding
values of the nuclear modification factor are estimated by dividing the
measured yields in Pb-Pb collisions by the expected cross-section in pp
collisions estimated with NLO pQCD calculations. The value of $R_{\text{AA}}$
is compatible with unity in the 20–90% centrality class (within large
statistical uncertainty), whereas it is smaller than unity by 2.6 times the
quadratic sum of the statistical and systematic uncertainties in the 0–20%
most central collisions. The results are well-described by the calculations
that include modifications of the PDFs in nuclei. In contrast, the
calculations with vacuum PDFs overestimate the centrality-integrated
$R_{\text{AA}}$ by $2.3\sigma$ and $R_{\text{AA}}$ in the 0–20% most central
collisions by $3\sigma$.

## Acknowledgements

The ALICE Collaboration would like to thank H. Paukkunen for providing the
pQCD calculations with EPS09 and EPPS16, and F. Lyonnet and A. Kusina for
providing the pQCD calculations with nCTEQ15.

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: A. I.
Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation
(ANSL), State Committee of Science and World Federation of Scientists (WFS),
Armenia; Austrian Academy of Sciences and Nationalstiftung für Forschung,
Technologie und Entwicklung, Austria; Ministry of Communications and High
Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional
de Desenvolvimento Científico e Tecnológico (CNPq), Universidade Federal do
Rio Grande do Sul (UFRGS), Financiadora de Estudos e Projetos (Finep) and
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Brazil;
Ministry of Science & Technology of China (MSTC), National Natural Science
Foundation of China (NSFC) and Ministry of Education of China (MOEC) , China;
Ministry of Science, Education and Sport and Croatian Science Foundation,
Croatia; Ministry of Education, Youth and Sports of the Czech Republic, Czech
Republic; The Danish Council for Independent Research — Natural Sciences, the
Carlsberg Foundation and Danish National Research Foundation (DNRF), Denmark;
Helsinki Institute of Physics (HIP), Finland; Commissariat à l’Energie
Atomique (CEA) and Institut National de Physique Nucléaire et de Physique des
Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS),
France; Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie
(BMBF) and GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany;
General Secretariat for Research and Technology, Ministry of Education,
Research and Religions, Greece; National Research, Development and Innovation
Office, Hungary; Department of Atomic Energy Government of India (DAE),
Department of Science and Technology, Government of India (DST), University
Grants Commission, Government of India (UGC) and Council of Scientific and
Industrial Research (CSIR), India; Indonesian Institute of Science, Indonesia;
Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche Enrico
Fermi and Istituto Nazionale di Fisica Nucleare (INFN), Italy; Institute for
Innovative Science and Technology , Nagasaki Institute of Applied Science
(IIST), Japan Society for the Promotion of Science (JSPS) KAKENHI and Japanese
Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan;
Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de
Cooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección
General de Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse
Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research
Council of Norway, Norway; Commission on Science and Technology for
Sustainable Development in the South (COMSATS), Pakistan; Pontificia
Universidad Católica del Perú, Peru; Ministry of Science and Higher Education
and National Science Centre, Poland; Korea Institute of Science and Technology
Information and National Research Foundation of Korea (NRF), Republic of
Korea; Ministry of Education and Scientific Research, Institute of Atomic
Physics and Romanian National Agency for Science, Technology and Innovation,
Romania; Joint Institute for Nuclear Research (JINR), Ministry of Education
and Science of the Russian Federation and National Research Centre Kurchatov
Institute, Russia; Ministry of Education, Science, Research and Sport of the
Slovak Republic, Slovakia; National Research Foundation of South Africa, South
Africa; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN),
Cubaenergía, Cuba and Centro de Investigaciones Energéticas, Medioambientales
y Tecnológicas (CIEMAT), Spain; Swedish Research Council (VR) and Knut & Alice
Wallenberg Foundation (KAW), Sweden; European Organization for Nuclear
Research, Switzerland; National Science and Technology Development Agency
(NSDTA), Suranaree University of Technology (SUT) and Office of the Higher
Education Commission under NRU project of Thailand, Thailand; Turkish Atomic
Energy Agency (TAEK), Turkey; National Academy of Sciences of Ukraine,
Ukraine; Science and Technology Facilities Council (STFC), United Kingdom;
National Science Foundation of the United States of America (NSF) and United
States Department of Energy, Office of Nuclear Physics (DOE NP), United States
of America.

## References

  * [1] S. Peigne and A. Peshier, “Collisional Energy Loss of a Fast Muon in a Hot QED Plasma,” Phys. Rev. D77 (2008) 014015, arXiv:0710.1266 [hep-ph].
  * [2] V. Kartvelishvili, R. Kvatadze, and R. Shanidze, “On Z and Z + jet production in heavy ion collisions,” Phys. Lett. B356 (1995) 589–594, arXiv:hep-ph/9505418 [hep-ph].
  * [3] Z. Conesa del Valle, “Vector bosons in heavy-ion collisions at the LHC,” Eur. Phys. J. C61 (2009) 729–733, arXiv:0903.1432 [hep-ex].
  * [4] UA1 Collaboration, C. Albajar et al., “Intermediate Vector Boson Cross-Sections at the CERN Super Proton Synchrotron Collider and the Number of Neutrino Types,” Phys. Lett. B198 (1987) 271.
  * [5] UA2 Collaboration, J. Alitti et al., “A Measurement of the $W$ and $Z$ production cross-sections and a determination of $\Gamma_{W}$ at the CERN $\bar{p}p$ collider,” Phys. Lett. B276 (1992) 365–374.
  * [6] CDF Collaboration, F. Abe et al., “Measurement of $\sigma\cdot B(W\to e\nu)$ and $\sigma\cdot B(Z^{0}\to e^{+}e^{-})$ in $p\bar{p}$ collisions at $\sqrt{s}=1.8$ TeV,” Phys. Rev. Lett. 76 (1996) 3070–3075, arXiv:hep-ex/9509010 [hep-ex].
  * [7] D0 Collaboration, B. Abbott et al., “Extraction of the width of the $W$ boson from measurements of $\sigma(p\bar{p}\to W+X)\times B(W\to e\nu)$ and $\sigma(p\bar{p}\to Z+X)\times B(Z\to ee)$ and their ratio,” Phys. Rev. D61 (2000) 072001, arXiv:hep-ex/9906025 [hep-ex].
  * [8] CDF Collaboration, A. Abulencia et al., “Measurements of inclusive W and Z cross sections in $p\overline{p}$ collisions at $\sqrt{s}$ = 1.96 TeV,” J. Phys. G34 (2007) 2457–2544, arXiv:hep-ex/0508029 [hep-ex].
  * [9] ATLAS Collaboration, G. Aad et al., “Measurement of the $W\to\ell\nu$ and $Z/\gamma^{*}\to\ell\ell$ production cross sections in proton-proton collisions at $\sqrt{s}=7$ TeV with the ATLAS detector,” JHEP 12 (2010) 060, arXiv:1010.2130 [hep-ex].
  * [10] ATLAS Collaboration, G. Aad et al., “Measurement of the inclusive $W^{\pm}$ and $Z/\gamma^{*}$ cross sections in the electron and muon decay channels in $pp$ collisions at $\sqrt{s}=7$ TeV with the ATLAS detector,” Phys. Rev. D85 (2012) 072004, arXiv:1109.5141 [hep-ex].
  * [11] ATLAS Collaboration, G. Aad et al., “Measurement of $W^{\pm}$ and $Z$-boson production cross sections in $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector,” Phys. Lett. B759 (2016) 601–621, arXiv:1603.09222 [hep-ex].
  * [12] CMS Collaboration, S. Chatrchyan et al., “Measurement of the Inclusive $W$ and $Z$ Production Cross Sections in $pp$ Collisions at $\sqrt{s}=7$ TeV,” JHEP 10 (2011) 132, arXiv:1107.4789 [hep-ex].
  * [13] CMS Collaboration, S. Chatrchyan et al., “Measurement of inclusive W and Z boson production cross sections in pp collisions at $\sqrt{s}$ = 8 TeV,” Phys. Rev. Lett. 112 (2014) 191802, arXiv:1402.0923 [hep-ex].
  * [14] LHCb Collaboration, R. Aaij et al., “Measurement of the forward $Z$ boson production cross-section in $pp$ collisions at $\sqrt{s}=7$ TeV,” JHEP 08 (2015) 039, arXiv:1505.07024 [hep-ex].
  * [15] LHCb Collaboration, R. Aaij et al., “Measurement of forward W and Z boson production in $pp$ collisions at $\sqrt{s}=8$ TeV,” JHEP 01 (2016) 155, arXiv:1511.08039 [hep-ex].
  * [16] A. D. Martin, R. G. Roberts, W. J. Stirling, and R. S. Thorne, “Parton distributions and the LHC: $W$ and $Z$ production,” Eur. Phys. J. C14 (2000) 133–145, arXiv:hep-ph/9907231 [hep-ph].
  * [17] U. Baur, S. Keller, and D. Wackeroth, “Electroweak radiative corrections to $W$ boson production in hadronic collisions,” Phys. Rev. D59 (1999) 013002, arXiv:hep-ph/9807417 [hep-ph].
  * [18] J. Rojo et al., “The PDF4LHC report on PDFs and LHC data: Results from Run I and preparation for Run II,” J. Phys. G42 (2015) 103103, arXiv:1507.00556 [hep-ph].
  * [19] J. Butterworth et al., “PDF4LHC recommendations for LHC Run II,” J. Phys. G43 (2016) 023001, arXiv:1510.03865 [hep-ph].
  * [20] H. Paukkunen and C. A. Salgado, “Constraints for the nuclear parton distributions from Z and W production at the LHC,” JHEP 1103 (2011) 071, arXiv:1010.5392 [hep-ph].
  * [21] A. Kusina, F. Lyonnet, D. B. Clark, E. Godat, T. Jezo, K. Kovarik, F. I. Olness, I. Schienbein, and J. Y. Yu, “Vector boson production in proton-lead and lead-lead collisions at the LHC and its impact on nCTEQ15 PDFs,” arXiv:1610.02925 [nucl-th].
  * [22] K. J. Eskola, P. Paakkinen, H. Paukkunen, and C. A. Salgado, “EPPS16: Nuclear parton distributions with LHC data,” Eur. Phys. J. C77 (2017) 163, arXiv:1612.05741 [hep-ph].
  * [23] D. de Florian and R. Sassot, “Nuclear parton distributions at next-to-leading order,” Phys. Rev. D69 (2004) 074028, arXiv:hep-ph/0311227 [hep-ph].
  * [24] M. Hirai, S. Kumano, and T. H. Nagai, “Determination of nuclear parton distribution functions and their uncertainties in next-to-leading order,” Phys. Rev. C76 (2007) 065207, arXiv:0709.3038 [hep-ph].
  * [25] S. Atashbar Tehrani, “Nuclear parton densities and their uncertainties at the next-to-leading order,” Phys. Rev. C86 (2012) 064301.
  * [26] H. Khanpour and S. Atashbar Tehrani, “Global Analysis of Nuclear Parton Distribution Functions and Their Uncertainties at Next-to-Next-to-Leading Order,” Phys. Rev. D93 (2016) 014026, arXiv:1601.00939 [hep-ph].
  * [27] R. Vogt, “Shadowing effects on vector boson production,” Phys. Rev. C64 (2001) 044901, arXiv:hep-ph/0011242 [hep-ph].
  * [28] R. B. Neufeld, I. Vitev, and B.-W. Zhang, “A possible determination of the quark radiation length in cold nuclear matter,” Phys. Lett. B704 (2011) 590–595, arXiv:1010.3708 [hep-ph].
  * [29] ATLAS Collaboration, G. Aad et al., “$Z$ boson production in $p+$Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV measured with the ATLAS detector,” Phys. Rev. C92 (2015) 044915, arXiv:1507.06232 [hep-ex].
  * [30] CMS Collaboration, V. Khachatryan et al., “Study of Z boson production in pPb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV,” Phys. Lett. B759 (2016) 36–57, arXiv:1512.06461 [hep-ex].
  * [31] CMS Collaboration, V. Khachatryan et al., “Study of W boson production in pPb collisions at $\sqrt{s_{\mathrm{NN}}}=$ 5.02 TeV,” Phys. Lett. B750 (2015) 565–586, arXiv:1503.05825 [nucl-ex].
  * [32] ALICE Collaboration, J. Adam et al., “W and Z boson production in p-Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV,” JHEP 02 (2017) 077, arXiv:1611.03002 [nucl-ex].
  * [33] LHCb Collaboration, R. Aaij et al., “Observation of $Z$ production in proton-lead collisions at LHCb,” JHEP 1409 (2014) 030, arXiv:1406.2885 [hep-ex].
  * [34] R. Gavin, Y. Li, F. Petriello, and S. Quackenbush, “FEWZ 2.0: A code for hadronic Z production at Next-to-Next-to-Leading order,” Comput. Phys. Commun. 182 (2011) 2388–2403, arXiv:1011.3540 [hep-ph].
  * [35] ATLAS Collaboration, G. Aad et al., “Measurement of the production and lepton charge asymmetry of $W$ bosons in Pb+Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV with the ATLAS detector,” Eur.Phys.J. C75 (2015) 23, arXiv:1408.4674 [hep-ex].
  * [36] ATLAS Collaboration, G. Aad et al., “Measurement of $Z$ boson Production in Pb+Pb Collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV with the ATLAS Detector,” Phys.Rev.Lett. 110 (2013) 022301, arXiv:1210.6486 [hep-ex].
  * [37] CMS Collaboration, S. Chatrchyan et al., “Study of Z production in PbPb and pp collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV in the dimuon and dielectron decay channels,” JHEP 1503 (2015) 022, arXiv:1410.4825 [nucl-ex].
  * [38] CMS Collaboration, S. Chatrchyan et al., “Study of $W$ boson production in PbPb and $pp$ collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV,” Phys.Lett. B715 (2012) 66–87, arXiv:1205.6334 [nucl-ex].
  * [39] ATLAS Collaboration, “$Z$ boson production in Pb+Pb collisions at$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV with the ATLAS detector at the LHC,” ATLAS-CONF-2017-010 (2017) .
  * [40] M. L. Miller, K. Reygers, S. J. Sanders, and P. Steinberg, “Glauber modeling in high energy nuclear collisions,” Ann. Rev. Nucl. Part. Sci. 57 (2007) 205–243, arXiv:nucl-ex/0701025 [nucl-ex].
  * [41] ALICE Collaboration, K. Aamodt et al., “The ALICE experiment at the CERN LHC,” JINST 3 (2008) S08002.
  * [42] ALICE Collaboration, B. Abelev et al., “Measurement of the Cross Section for Electromagnetic Dissociation with Neutron Emission in Pb-Pb Collisions at $\sqrt{s_{NN}}$ = 2.76 TeV,” Phys. Rev. Lett. 109 (2012) 252302, arXiv:1203.2436 [nucl-ex].
  * [43] ALICE Collaboration, K. Aamodt et al., “Rapidity and transverse momentum dependence of inclusive J$/\psi$ production in $pp$ collisions at $\sqrt{s}=7$ TeV,” Phys. Lett. B704 (2011) 442–455, arXiv:1105.0380 [hep-ex]. [Erratum: Phys. Lett.B718,692(2012)].
  * [44] S. Alioli, P. Nason, C. Oleari, and E. Re, “NLO vector-boson production matched with shower in POWHEG,” JHEP 07 (2008) 060, arXiv:0805.4802 [hep-ph].
  * [45] T. Sjostrand, S. Mrenna, and P. Z. Skands, “PYTHIA 6.4 Physics and Manual,” JHEP 05 (2006) 026, arXiv:hep-ph/0603175 [hep-ph].
  * [46] R. Brun, F. Carminati, and S. Giani, “GEANT Detector Description and Simulation Tool,” CERN-W-5013 (1994) .
  * [47] CMS Collaboration, S. Chatrchyan et al., “Measurement of the Rapidity and Transverse Momentum Distributions of $Z$ Bosons in $pp$ Collisions at $\sqrt{s}=7$ TeV,” Phys. Rev. D85 (2012) 032002, arXiv:1110.4973 [hep-ex].
  * [48] ALICE Collaboration, J. Adam et al., “J/$\psi$ suppression at forward rapidity in Pb-Pb collisions at $\sqrt{s_{{\rm NN}}}=5.02$ TeV,” Phys. Lett. B766 (2017) 212–224, arXiv:1606.08197 [nucl-ex].
  * [49] ALICE Collaboration, J. Adam et al., “Centrality dependence of particle production in p-Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV,” Phys.Rev. C91 (2015) 064905, arXiv:1412.6828 [nucl-ex].
  * [50] ALICE Collaboration, J. Adam et al., “Centrality dependence of the charged-particle multiplicity density at midrapidity in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV,” Phys. Rev. Lett. 116 (2016) 222302, arXiv:1512.06104 [nucl-ex].
  * [51] ALICE Collaboration, B. B. Abelev et al., “Performance of the ALICE Experiment at the CERN LHC,” Int. J. Mod. Phys. A29 (2014) 1430044, arXiv:1402.4476 [nucl-ex].
  * [52] V. Blobel and C. Kleinwort, “A New method for the high precision alignment of track detectors,” in Advanced statistical techniques in particle physics. Proceedings, Conference, Durham, UK, March 18-22, 2002, pp. URL–STR(9).  2002\.  arXiv:hep-ex/0208021 [hep-ex].  http://www.ippp.dur.ac.uk/Workshops/02/statistics/proceedings//blobel1.pdf.
  * [53] S. Dulat, T.-J. Hou, J. Gao, M. Guzzi, J. Huston, P. Nadolsky, J. Pumplin, C. Schmidt, D. Stump, and C. P. Yuan, “New parton distribution functions from a global analysis of quantum chromodynamics,” Phys. Rev. D93 (2016) 033006, arXiv:1506.07443 [hep-ph].
  * [54] K. J. Eskola, H. Paukkunen, and C. A. Salgado, “EPS09: A New Generation of NLO and LO Nuclear Parton Distribution Functions,” JHEP 04 (2009) 065, arXiv:0902.4154 [hep-ph].
  * [55] K. Kovarik et al., “nCTEQ15 - Global analysis of nuclear parton distributions with uncertainties in the CTEQ framework,” Phys. Rev. D93 (2016) 085037, arXiv:1509.00792 [hep-ph].
  * [56] N. Armesto, H. Paukkunen, J. M. Penín, C. A. Salgado, and P. Zurita, “An analysis of the impact of LHC Run I proton–lead data on nuclear parton densities,” Eur. Phys. J. C76 (2016) 218, arXiv:1512.01528 [hep-ph].
  * [57] I. Helenius, K. J. Eskola, H. Honkanen, and C. A. Salgado, “Impact-Parameter Dependent Nuclear Parton Distribution Functions: EPS09s and EKS98s and Their Applications in Nuclear Hard Processes,” JHEP 07 (2012) 073, arXiv:1205.5359 [hep-ph].

##  Appendix A The ALICE Collaboration

S. Acharyaorg137&D. Adamováorg94&J. Adolfssonorg33&M.M. Aggarwalorg99&G.
Aglieri Rinellaorg34&M. Agnelloorg30&N. Agrawalorg47&Z. Ahammedorg137&S.U.
Ahnorg78&S. Aiolaorg141&A. Akindinovorg63&M. Al-Turanyorg106&S.N.
Alamorg137&D.S.D. Albuquerqueorg122&D. Aleksandrovorg90&B. Alessandroorg57&R.
Alfaro Molinaorg73&Y. Aliorg15&A. Aliciorg11,org26,org52&A. Alkinorg3&J.
Almeorg21&T. Altorg69&L. Altenkamperorg21&I. Altsybeevorg136&C. Andreiorg87&D.
Andreouorg34&H.A. Andrewsorg110&A. Andronicorg106&M. Angelettiorg34&V.
Anguelovorg104&C. Ansonorg97&T. Antičićorg107&F. Antinoriorg55&P.
Antonioliorg52&N. Apadulaorg81&L. Aphecetcheorg114&H. Appelshäuserorg69&S.
Arcelliorg26&R. Arnaldiorg57&O.W. Arnoldorg105,org35&I.C. Arseneorg20&M.
Arslandokorg104&B. Audurierorg114&A. Augustinusorg34&R. Averbeckorg106&M.D.
Azmiorg16&A. Badalàorg54&Y.W. Baekorg77,org59&S. Bagnascoorg57&R.
Bailhacheorg69&R. Balaorg101&A. Baldisseriorg74&M. Ballorg44&R.C.
Baralorg66,org88&A.M. Barbanoorg25&R. Barberaorg27&F. Barileorg32&L.
Barioglioorg25&G.G. Barnaföldiorg140&L.S. Barnbyorg93&V. Barretorg131&P.
Bartaliniorg7&K. Barthorg34&E. Bartschorg69&N. Bastidorg131&S. Basuorg139&G.
Batigneorg114&B. Batyunyaorg76&P.C. Batzingorg20&J.L. Bazo Albaorg111&I.G.
Beardenorg91&H. Beckorg104&C. Beddaorg62&N.K. Beheraorg59&I. Belikovorg133&F.
Belliniorg34,org26&H. Bello Martinezorg2&R. Bellwiedorg124&L.G.E.
Beltranorg120&V. Belyaevorg82&G. Bencediorg140&S. Beoleorg25&A.
Bercuciorg87&Y. Berdnikovorg96&D. Berenyiorg140&R.A. Bertensorg127&D.
Berzanoorg57,org34&L. Betevorg34&P.P. Bhaduriorg137&A. Bhasinorg101&I.R.
Bhatorg101&B. Bhattacharjeeorg43&J. Bhomorg118&A. Bianchiorg25&L.
Bianchiorg124&N. Bianchiorg50&C. Bianchinorg139&J. Bielčíkorg38&J.
Bielčíkováorg94&A. Bilandzicorg35,org105&G. Biroorg140&R. Biswasorg4&S.
Biswasorg4&J.T. Blairorg119&D. Blauorg90&C. Blumeorg69&G. Bocaorg134&F.
Bockorg34&A. Bogdanovorg82&L. Boldizsárorg140&M. Bombaraorg39&G.
Bonomiorg135&M. Bonoraorg34&H. Borelorg74&A. Borissovorg18,org104&M.
Borriorg126&E. Bottaorg25&C. Bourjauorg91&L. Bratrudorg69&P. Braun-
Munzingerorg106&M. Bregantorg121&T.A. Brokerorg69&M. Brozorg38&E.J.
Bruckenorg45&E. Brunaorg57&G.E. Brunoorg34,org32&D. Budnikovorg108&H.
Bueschingorg69&S. Bufalinoorg30&P. Buhlerorg113&P. Buncicorg34&O.
Buschorg130&Z. Butheleziorg75&J.B. Buttorg15&J.T. Buxtonorg17&J.
Cabalaorg116&D. Caffarriorg34,org92&H. Cainesorg141&A. Calivaorg106,org62&E.
Calvo Villarorg111&R.S. Camachoorg2&P. Cameriniorg24&A.A. Caponorg113&F.
Carenaorg34&W. Carenaorg34&F. Carnesecchiorg11,org26&J. Castillo
Castellanosorg74&A.J. Castroorg127&E.A.R. Casulaorg53&C. Ceballos
Sanchezorg9&S. Chandraorg137&B. Changorg125&W. Changorg7&S. Chapelandorg34&M.
Chartierorg126&S. Chattopadhyayorg137&S. Chattopadhyayorg109&A.
Chauvinorg105,org35&C. Cheshkovorg132&B. Cheynisorg132&V. Chibante
Barrosoorg34&D.D. Chinellatoorg122&S. Choorg59&P. Chochulaorg34&M.
Chojnackiorg91&S. Choudhuryorg137&T. Chowdhuryorg131&P.
Christakoglouorg92&C.H. Christensenorg91&P. Christiansenorg33&T.
Chujoorg130&S.U. Chungorg18&C. Cicaloorg53&L. Cifarelliorg11,org26&F.
Cindoloorg52&J. Cleymansorg100&F. Colamariaorg51,org32&D.
Colellaorg64,org34,org51&A. Colluorg81&M. Colocciorg26&M. Concasorg57orgI&G.
Conesa Balbastreorg80&Z. Conesa del Valleorg60&J.G. Contrerasorg38&T.M.
Cormierorg95&Y. Corrales Moralesorg57&I. Cortés Maldonadoorg2&P.
Corteseorg31&M.R. Cosentinoorg123&F. Costaorg34&S. Costanzaorg134&J.
Crkovskáorg60&P. Crochetorg131&E. Cuautleorg71&L. Cunqueiroorg70,org95&T.
Dahmsorg105,org35&A. Daineseorg55&M.C. Danischorg104&A. Danuorg67&D.
Dasorg109&I. Dasorg109&S. Dasorg4&A. Dashorg88&S. Dashorg47&S. Deorg48&A. De
Caroorg29&G. de Cataldoorg51&C. de Contiorg121&J. de Cuvelandorg41&A. De
Falcoorg23&D. De Gruttolaorg29,org11&N. De Marcoorg57&S. De Pasqualeorg29&R.D.
De Souzaorg122&H.F. Degenhardtorg121&A. Deistingorg106,org104&A.
Delofforg86&C. Deplanoorg92&P. Dhankherorg47&D. Di Bariorg32&A. Di
Mauroorg34&P. Di Nezzaorg50&B. Di Ruzzaorg55&T. Dietelorg100&P.
Dillensegerorg69&Y. Dingorg7&R. Diviàorg34&Ø. Djuvslandorg21&A. Dobrinorg34&D.
Domenicis Gimenezorg121&B. Dönigusorg69&O. Dordicorg20&L.V.R.
Doremalenorg62&A.K. Dubeyorg137&A. Dublaorg106&L. Ducrouxorg132&S.
Dudiorg99&A.K. Duggalorg99&M. Dukhishyamorg88&P. Dupieuxorg131&R.J.
Ehlersorg141&D. Eliaorg51&E. Endressorg111&H. Engelorg68&E. Eppleorg141&B.
Erazmusorg114&F. Erhardtorg98&B. Espagnonorg60&G. Eulisseorg34&J. Eumorg18&D.
Evansorg110&S. Evdokimovorg112&L. Fabbiettiorg105,org35&J. Faivreorg80&A.
Fantoniorg50&M. Faselorg95&L. Feldkamporg70&A. Felicielloorg57&G.
Feofilovorg136&A. Fernández Téllezorg2&A. Ferrettiorg25&A.
Festantiorg28,org34&V.J.G. Feuillardorg74,org131&J. Figielorg118&M.A.S.
Figueredoorg121&S. Filchaginorg108&D. Finogeevorg61&F.M. Fiondaorg21,org23&M.
Florisorg34&S. Foertschorg75&P. Fokaorg106&S. Fokinorg90&E. Fragiacomoorg58&A.
Francesconorg34&A. Franciscoorg114&U. Frankenfeldorg106&G.G. Fronzeorg25&U.
Fuchsorg34&C. Furgetorg80&A. Fursorg61&M. Fusco Girardorg29&J.J.
Gaardhøjeorg91&M. Gagliardiorg25&A.M. Gagoorg111&K. Gajdosovaorg91&M.
Gallioorg25&C.D. Galvanorg120&P. Ganotiorg85&C. Garabatosorg106&E. Garcia-
Solisorg12&K. Gargorg27&C. Gargiuloorg34&P. Gasikorg105,org35&E.F.
Gaugerorg119&M.B. Gay Ducatiorg72&M. Germainorg114&J. Ghoshorg109&P.
Ghoshorg137&S.K. Ghoshorg4&P. Gianottiorg50&P. Giubellinoorg34,org106,org57&P.
Giubilatoorg28&E. Gladysz-Dziadusorg118&P. Glässelorg104&D.M. Goméz
Coralorg73&A. Gomez Ramirezorg68&A.S. Gonzalezorg34&P. González-Zamoraorg2&S.
Gorbunovorg41&L. Görlichorg118&S. Gotovacorg117&V. Grabskiorg73&L.K.
Graczykowskiorg138&K.L. Grahamorg110&L. Greinerorg81&A. Grelliorg62&C.
Grigorasorg34&V. Grigorievorg82&A. Grigoryanorg1&S. Grigoryanorg76&J.M.
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Guberorg61&R. Guernaneorg80&B. Guerzoniorg26&M. Guittiereorg114&K.
Gulbrandsenorg91&T. Gunjiorg129&A. Guptaorg101&R. Guptaorg101&I.B.
Guzmanorg2&R. Haakeorg34&C. Hadjidakisorg60&H. Hamagakiorg83&G.
Hamarorg140&J.C. Hamonorg133&M.R. Haqueorg62&J.W. Harrisorg141&A.
Hartonorg12&H. Hassanorg80&D. Hatzifotiadouorg52,org11&S. Hayashiorg129&S.T.
Heckelorg69&E. Hellbärorg69&H. Helstruporg36&A. Herghelegiuorg87&E.G.
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Hetlandorg36&H. Hillemannsorg34&C. Hillsorg126&B. Hippolyteorg133&B.
Hohlwegerorg105&D. Horakorg38&S. Hornungorg106&R. Hosokawaorg80,org130&P.
Hristovorg34&C. Hughesorg127&T.J. Humanicorg17&N. Hussainorg43&T.
Hussainorg16&D. Hutterorg41&D.S. Hwangorg19&J.P. Iddonorg126&S.A. Iga
Buitronorg71&R. Ilkaevorg108&M. Inabaorg130&M. Ippolitovorg82,org90&M.S.
Islamorg109&M. Ivanovorg106&V. Ivanovorg96&V. Izucheevorg112&B. Jacakorg81&N.
Jacazioorg26&P.M. Jacobsorg81&M.B. Jadhavorg47&S. Jadlovskaorg116&J.
Jadlovskyorg116&S. Jaelaniorg62&C. Jahnkeorg35&M.J. Jakubowskaorg138&M.A.
Janikorg138&P.H.S.Y. Jayarathnaorg124&C. Jenaorg88&M. Jercicorg98&R.T. Jimenez
Bustamanteorg106&P.G. Jonesorg110&A. Juskoorg110&P. Kalinakorg64&A.
Kalweitorg34&J.H. Kangorg142&V. Kaplinorg82&S. Karorg137&A. Karasu
Uysalorg79&O. Karavichevorg61&T. Karavichevaorg61&L. Karayanorg106,org104&P.
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Kimorg130&D. Kimorg142&D.J. Kimorg125&E.J. Kimorg14&H. Kimorg142&J.S.
Kimorg42&J. Kimorg104&M. Kimorg59&S. Kimorg19&T. Kimorg142&S. Kirschorg41&I.
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Kryshenorg96&M. Krzewickiorg41&A.M. Kuberaorg17&V. Kučeraorg94&C.
Kuhnorg133&P.G. Kuijerorg92&A. Kumarorg101&J. Kumarorg47&L. Kumarorg99&S.
Kumarorg47&S. Kunduorg88&P. Kurashviliorg86&A. Kurepinorg61&A.B.
Kurepinorg61&A. Kuryakinorg108&S. Kushpilorg94&M.J. Kweonorg59&Y.
Kwonorg142&S.L. La Pointeorg41&P. La Roccaorg27&C. Lagana Fernandesorg121&Y.S.
Laiorg81&I. Lakomovorg34&R. Langoyorg40&K. Lapidusorg141&C. Laraorg68&A.
Lardeuxorg20&A. Lattucaorg25&E. Laudiorg34&R. Lavickaorg38&R. Leaorg24&L.
Leardiniorg104&S. Leeorg142&F. Lehasorg92&S. Lehnerorg113&J.
Lehrbachorg41&R.C. Lemmonorg93&E. Leograndeorg62&I. León Monzónorg120&P.
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Limorg18&S. Lindalorg20&V. Lindenstruthorg41&S.W. Lindsayorg126&C.
Lippmannorg106&M.A. Lisaorg17&V. Litichevskyiorg45&A. Liuorg81&W.J.
Llopeorg139&D.F. Lodatoorg62&P.I. Loenneorg21&V. Loginovorg82&C.
Loizidesorg81,org95&P. Loncarorg117&X. Lopezorg131&E. López Torresorg9&A.
Loweorg140&P. Luettigorg69&J.R. Luhderorg70&M. Lunardonorg28&G.
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Marquardorg69&N.A. Martinorg106&P. Martinengoorg34&J.A.L. Martinezorg68&M.I.
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Masciocchiorg106&M. Maseraorg25&A. Masoniorg53&L. Massacrierorg60&E.
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Matuokaorg121&A. Matyjaorg127&C. Mayerorg118&J. Mazerorg127&M.
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Mhlangaorg100&Y. Miakeorg130&M.M. Mieskolainenorg45&D.L. Mihaylovorg105&K.
Mikhaylovorg63,org76&A. Mischkeorg62&A.N. Mishraorg48&D. Miśkowiecorg106&J.
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Mohantyorg88&M. Mohisin Khanorg16orgIII&D.A. Moreira De Godoyorg70&L.A.P.
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Mukherjeeorg4&J.D. Mulliganorg141&M.G. Munhozorg121&K. Münningorg44&M.I.A.
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Musinskyorg64&C.J. Myersorg124&J.W. Myrchaorg138&D. Nagorg4&B. Naikorg47&R.
Nairorg86&B.K. Nandiorg47&R. Naniaorg11,org52&E. Nappiorg51&A.
Narayanorg47&M.U. Naruorg15&H. Natal da Luzorg121&C. Nattrassorg127&S.R.
Navarroorg2&K. Nayakorg88&R. Nayakorg47&T.K. Nayakorg137&S.
Nazarenkoorg108&R.A. Negrao De Oliveiraorg69,org34&L. Nellenorg71&S.V.
Nesboorg36&G. Neskovicorg41&F. Ngorg124&M. Nicassioorg106&M. Niculescuorg67&J.
Niedzielaorg138,org34&B.S. Nielsenorg91&S. Nikolaevorg90&S. Nikulinorg90&V.
Nikulinorg96&A. Nobuhiroorg46&F. Noferiniorg11,org52&P. Nomokonovorg76&G.
Noorenorg62&J.C.C. Norisorg2&J. Normanorg126,org80&A. Nyaninorg90&J.
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Olahorg140&J. Oleniaczorg138&A.C. Oliveira Da Silvaorg121&M.H. Oliverorg141&J.
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Pachmayerorg104&V. Pacikorg91&D. Paganoorg135&G. Paićorg71&P. Palniorg7&J.
Panorg139&A.K. Pandeyorg47&S. Panebiancoorg74&V. Papikyanorg1&P.
Pareekorg48&J. Parkorg59&S. Parmarorg99&A. Passfeldorg70&S.P.
Pathakorg124&R.N. Patraorg137&B. Paulorg57&H. Peiorg7&T. Peitzmannorg62&X.
Pengorg7&L.G. Pereiraorg72&H. Pereira Da Costaorg74&D. Peresunkoorg82,org90&E.
Perez Lezamaorg69&V. Peskovorg69&Y. Pestovorg5&V. Petráčekorg38&M.
Petroviciorg87&C. Pettaorg27&R.P. Pezziorg72&S. Pianoorg58&M. Piknaorg37&P.
Pillotorg114&L.O.D.L. Pimentelorg91&O. Pinazzaorg52,org34&L. Pinskyorg124&D.B.
Piyarathnaorg124&M. Płoskońorg81&M. Planinicorg98&F. Pliquettorg69&J.
Plutaorg138&S. Pochybovaorg140&P.L.M. Podesta-Lermaorg120&M.G.
Poghosyanorg95&B. Polichtchoukorg112&N. Poljakorg98&W. Poonsawatorg115&A.
Poporg87&H. Poppenborgorg70&S. Porteboeuf-Houssaisorg131&V.
Pozdniakovorg76&S.K. Prasadorg4&R. Preghenellaorg52&F. Prinoorg57&C.A.
Pruneauorg139&I. Pshenichnovorg61&M. Puccioorg25&V. Puninorg108&J.
Putschkeorg139&S. Rahaorg4&S. Rajputorg101&J. Rakorg125&A.
Rakotozafindrabeorg74&L. Ramelloorg31&F. Ramiorg133&D.B. Ranaorg124&R.
Raniwalaorg102&S. Raniwalaorg102&S.S. Räsänenorg45&B.T. Rascanuorg69&D.
Ratheeorg99&V. Ratzaorg44&I. Ravasengaorg30&K.F. Readorg127,org95&K.
Redlichorg86orgIV&A. Rehmanorg21&P. Reicheltorg69&F. Reidtorg34&X. Renorg7&R.
Renfordtorg69&A. Reshetinorg61&K. Reygersorg104&V. Riabovorg96&T.
Richertorg62,org33&M. Richterorg20&P. Riedlerorg34&W. Rieglerorg34&F.
Riggiorg27&C. Risteaorg67&M. Rodríguez Cahuantziorg2&K. Røedorg20&R.
Rogalevorg112&E. Rogochayaorg76&D. Rohrorg34,org41&D. Röhrichorg21&P.S.
Rokitaorg138&F. Ronchettiorg50&E.D. Rosasorg71&K. Roslonorg138&P.
Rosnetorg131&A. Rossiorg55,org28&A. Rotondiorg134&F. Roukoutakisorg85&C.
Royorg133&P. Royorg109&O.V. Ruedaorg71&R. Ruiorg24&B. Rumyantsevorg76&A.
Rustamovorg89&E. Ryabinkinorg90&Y. Ryabovorg96&A. Rybickiorg118&S.
Saarinenorg45&S. Sadhuorg137&S. Sadovskyorg112&K. Šafaříkorg34&S.K.
Sahaorg137&B. Sahooorg47&P. Sahooorg48&R. Sahooorg48&S. Sahooorg66&P.K.
Sahuorg66&J. Sainiorg137&S. Sakaiorg130&M.A. Salehorg139&J. Salzwedelorg17&S.
Sambyalorg101&V. Samsonovorg96,org82&A. Sandovalorg73&A. Sarkarorg75&D.
Sarkarorg137&N. Sarkarorg137&P. Sarmaorg43&M.H.P. Sasorg62&E.
Scapparoneorg52&F. Scarlassaraorg28&B. Schaeferorg95&H.S. Scheidorg69&C.
Schiauaorg87&R. Schickerorg104&C. Schmidtorg106&H.R. Schmidtorg103&M.O.
Schmidtorg104&M. Schmidtorg103&N.V. Schmidtorg95,org69&J. Schukraftorg34&Y.
Schutzorg34,org133&K. Schwarzorg106&K. Schwedaorg106&G. Scioliorg26&E.
Scomparinorg57&M. Šefčíkorg39&J.E. Segerorg97&Y. Sekiguchiorg129&D.
Sekihataorg46&I. Selyuzhenkovorg106,org82&K. Senosiorg75&S. Senyukovorg133&E.
Serradillaorg73&P. Settorg47&A. Sevcencoorg67&A. Shabanovorg61&A.
Shabetaiorg114&R. Shahoyanorg34&W. Shaikhorg109&A. Shangaraevorg112&A.
Sharmaorg99&A. Sharmaorg101&M. Sharmaorg101&M. Sharmaorg101&N.
Sharmaorg99&A.I. Sheikhorg137&K. Shigakiorg46&M. Shimomuraorg84&S.
Shirinkinorg63&Q. Shouorg7&K. Shtejerorg9,org25&Y. Sibiriakorg90&S.
Siddhantaorg53&K.M. Sielewiczorg34&T. Siemiarczukorg86&S. Silaevaorg90&D.
Silvermyrorg33&G. Simatovicorg92,org98&G. Simonettiorg34&R. Singarajuorg137&R.
Singhorg88&V. Singhalorg137&T. Sinhaorg109&B. Sitarorg37&M. Sittaorg31&T.B.
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Snellmanorg125&J. Songorg18&F. Soramelorg28&S. Sorensenorg127&F.
Sozziorg106&I. Sputowskaorg118&J. Stachelorg104&I. Stanorg67&P.
Stankusorg95&E. Stenlundorg33&D. Stoccoorg114&M.M. Storetvedtorg36&P.
Strmenorg37&A.A.P. Suaideorg121&T. Sugitateorg46&C. Suireorg60&M.
Suleymanovorg15&M. Suljicorg24&R. Sultanovorg63&M. Šumberaorg94&S.
Sumowidagdoorg49&K. Suzukiorg113&S. Swainorg66&A. Szaboorg37&I. Szarkaorg37&U.
Tabassamorg15&J. Takahashiorg122&G.J. Tambaveorg21&N. Tanakaorg130&M.
Tarhiniorg114,org60&M. Tariqorg16&M.G. Tarzilaorg87&A. Tauroorg34&G. Tejeda
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Teyssierorg132&D. Thakurorg48&S. Thakurorg137&D. Thomasorg119&F.
Thoresenorg91&R. Tieulentorg132&A. Tikhonovorg61&A.R. Timminsorg124&A.
Toiaorg69&M. Toppiorg50&S.R. Torresorg120&S. Tripathyorg48&S. Trogoloorg25&G.
Trombettaorg32&L. Tropporg39&V. Trubnikovorg3&W.H. Trzaskaorg125&B.A.
Trzeciakorg62&T. Tsujiorg129&A. Tumkinorg108&R. Turrisiorg55&T.S.
Tveterorg20&K. Ullalandorg21&E.N. Umakaorg124&A. Urasorg132&G.L. Usaiorg23&A.
Utrobicicorg98&M. Valaorg116,org64&J. Van Der Maarelorg62&J.W. Van
Hoorneorg34&M. van Leeuwenorg62&T. Vanatorg94&P. Vande Vyvreorg34&D.
Vargaorg140&A. Vargasorg2&M. Vargyasorg125&R. Varmaorg47&M. Vasileiouorg85&A.
Vasilievorg90&A. Vauthierorg80&O. Vázquez Doceorg105,org35&V.
Vecherninorg136&A.M. Veenorg62&A. Velureorg21&E. Vercellinorg25&S. Vergara
Limónorg2&L. Vermuntorg62&R. Vernetorg8&R. Vértesiorg140&L. Vickovicorg117&J.
Viinikainenorg125&Z. Vilakaziorg128&O. Villalobos Baillieorg110&A. Villatoro
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Vislaviciusorg33&A. Vodopyanovorg76&M.A. Völklorg103&K. Voloshinorg63&S.A.
Voloshinorg139&G. Volpeorg32&B. von Hallerorg34&I. Vorobyevorg105,org35&D.
Voscekorg116&D. Vranicorg34,org106&J. Vrlákováorg39&B. Wagnerorg21&H.
Wangorg62&M. Wangorg7&Y. Watanabeorg129,org130&M. Weberorg113&S.G.
Weberorg106&A. Wegrzynekorg34&D.F. Weiserorg104&S.C. Wenzelorg34&J.P.
Wesselsorg70&U. Westerhofforg70&A.M. Whiteheadorg100&J. Wiechulaorg69&J.
Wikneorg20&G. Wilkorg86&J. Wilkinsonorg52&G.A. Willemsorg70,org34&M.C.S.
Williamsorg52&E. Willsherorg110&B. Windelbandorg104&W.E. Wittorg127&R.
Xuorg7&S. Yalcinorg79&K. Yamakawaorg46&P. Yangorg7&S. Yanoorg46&Z. Yinorg7&H.
Yokoyamaorg80,org130&I.-K. Yooorg18&J.H. Yoonorg59&E. Yunorg18&V.
Yurchenkoorg3&V. Zaccoloorg57&A. Zamanorg15&C. Zampolliorg34&H.J.C.
Zanoliorg121&N. Zardoshtiorg110&A. Zarochentsevorg136&P. Závadaorg65&N.
Zaviyalovorg108&H. Zbroszczykorg138&M. Zhalovorg96&H. Zhangorg7,org21&X.
Zhangorg7&Y. Zhangorg7&C. Zhangorg62&Z. Zhangorg131,org7&C. Zhaoorg20&N.
Zhigarevaorg63&D. Zhouorg7&Y. Zhouorg91&Z. Zhouorg21&H. Zhuorg21&J. Zhuorg7&Y.
Zhuorg7&A. Zichichiorg26,org11&M.B. Zimmermannorg34&G. Zinovjevorg3&J.
Zmeskalorg113&S. Zouorg7&

## Affiliation notes

org*Deceased

orgIDipartimento DET del Politecnico di Torino, Turin, Italy

orgIIM.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute of
Nuclear, Physics, Moscow, Russia

orgIIIDepartment of Applied Physics, Aligarh Muslim University, Aligarh, India

orgIVInstitute of Theoretical Physics, University of Wroclaw, Poland

## 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, Lyon, France

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

org10Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City
and Mérida, Mexico

org11Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche
“Enrico Fermi’, Rome, Italy

org12Chicago State University, Chicago, Illinois, United States

org13China Institute of Atomic Energy, Beijing, China

org14Chonbuk National University, Jeonju, Republic of Korea

org15COMSATS Institute of Information Technology (CIIT), Islamabad, Pakistan

org16Department of Physics, Aligarh Muslim University, Aligarh, India

org17Department of Physics, Ohio State University, Columbus, Ohio, United
States

org18Department of Physics, Pusan National University, Pusan, Republic of
Korea

org19Department of Physics, Sejong University, Seoul, Republic of Korea

org20Department of Physics, University of Oslo, Oslo, Norway

org21Department of Physics and Technology, University of Bergen, Bergen,
Norway

org22Dipartimento di Fisica dell’Università ’La Sapienza’ and Sezione INFN,
Rome, Italy

org23Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy

org24Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy

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

org26Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Bologna, Italy

org27Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Catania, Italy

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

org29Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo
Collegato INFN, Salerno, Italy

org30Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy

org31Dipartimento di Scienze e Innovazione Tecnologica dell’Università del
Piemonte Orientale and INFN Sezione di Torino, Alessandria, Italy

org32Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari,
Italy

org33Division of Experimental High Energy Physics, University of Lund, Lund,
Sweden

org34European Organization for Nuclear Research (CERN), Geneva, Switzerland

org35Excellence Cluster Universe, Technische Universität München, Munich,
Germany

org36Faculty of Engineering, Bergen University College, Bergen, Norway

org37Faculty of Mathematics, Physics and Informatics, Comenius University,
Bratislava, Slovakia

org38Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Prague, Czech Republic

org39Faculty of Science, P.J. Šafárik University, Košice, Slovakia

org40Faculty of Technology, Buskerud and Vestfold University College,
Tonsberg, Norway

org41Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-
Universität Frankfurt, Frankfurt, Germany

org42Gangneung-Wonju National University, Gangneung, Republic of Korea

org43Gauhati University, Department of Physics, Guwahati, India

org44Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-
Wilhelms-Universität Bonn, Bonn, Germany

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, India

org49Indonesian Institute of Sciences, Jakarta, Indonesia

org50INFN, Laboratori Nazionali di Frascati, Frascati, Italy

org51INFN, Sezione di Bari, Bari, Italy

org52INFN, Sezione di Bologna, Bologna, Italy

org53INFN, Sezione di Cagliari, Cagliari, Italy

org54INFN, Sezione di Catania, Catania, Italy

org55INFN, Sezione di Padova, Padova, Italy

org56INFN, Sezione di Roma, Rome, Italy

org57INFN, Sezione di Torino, Turin, Italy

org58INFN, Sezione di Trieste, Trieste, Italy

org59Inha University, Incheon, Republic of Korea

org60Institut de Physique Nucléaire d’Orsay (IPNO), Université Paris-Sud,
CNRS-IN2P3, Orsay, France

org61Institute for Nuclear Research, Academy of Sciences, Moscow, Russia

org62Institute for Subatomic Physics of Utrecht University, Utrecht,
Netherlands

org63Institute for Theoretical and Experimental Physics, Moscow, Russia

org64Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovakia

org65Institute of Physics, Academy of Sciences of the Czech Republic, Prague,
Czech Republic

org66Institute of Physics, Bhubaneswar, India

org67Institute of Space Science (ISS), Bucharest, Romania

org68Institut für Informatik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

org69Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

org70Institut für Kernphysik, Westfälische Wilhelms-Universität Münster,
Münster, Germany

org71Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico

org72Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS),
Porto Alegre, Brazil

org73Instituto de Física, Universidad Nacional Autónoma de México, Mexico
City, Mexico

org74IRFU, CEA, Université Paris-Saclay, Saclay, France

org75iThemba LABS, National Research Foundation, Somerset West, South Africa

org76Joint Institute for Nuclear Research (JINR), Dubna, Russia

org77Konkuk University, Seoul, Republic of Korea

org78Korea Institute of Science and Technology Information, Daejeon, Republic
of Korea

org79KTO Karatay University, Konya, Turkey

org80Laboratoire de Physique Subatomique et de Cosmologie, Université
Grenoble-Alpes, CNRS-IN2P3, Grenoble, France

org81Lawrence Berkeley National Laboratory, Berkeley, California, United
States

org82Moscow Engineering Physics Institute, Moscow, Russia

org83Nagasaki Institute of Applied Science, Nagasaki, Japan

org84Nara Women’s University (NWU), Nara, Japan

org85National and Kapodistrian University of Athens, Physics Department,
Athens, Greece

org86National Centre for Nuclear Studies, Warsaw, Poland

org87National Institute for Physics and Nuclear Engineering, Bucharest,
Romania

org88National Institute of Science Education and Research, HBNI, Jatni, India

org89National Nuclear Research Center, Baku, Azerbaijan

org90National Research Centre Kurchatov Institute, Moscow, Russia

org91Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

org92Nikhef, Nationaal instituut voor subatomaire fysica, Amsterdam,
Netherlands

org93Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United
Kingdom

org94Nuclear Physics Institute, Academy of Sciences of the Czech Republic, Řež
u Prahy, Czech Republic

org95Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States

org96Petersburg Nuclear Physics Institute, Gatchina, Russia

org97Physics Department, Creighton University, Omaha, Nebraska, United States

org98Physics department, Faculty of science, University of Zagreb, Zagreb,
Croatia

org99Physics Department, Panjab University, Chandigarh, India

org100Physics Department, University of Cape Town, Cape Town, South Africa

org101Physics Department, University of Jammu, Jammu, India

org102Physics Department, University of Rajasthan, Jaipur, India

org103Physikalisches Institut, Eberhard Karls Universität Tübingen, Tübingen,
Germany

org104Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg,
Heidelberg, Germany

org105Physik Department, Technische Universität München, Munich, Germany

org106Research Division and ExtreMe Matter Institute EMMI, GSI
Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany

org107Rudjer Bošković Institute, Zagreb, Croatia

org108Russian Federal Nuclear Center (VNIIEF), Sarov, Russia

org109Saha Institute of Nuclear Physics, Kolkata, India

org110School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom

org111Sección Física, Departamento de Ciencias, Pontificia Universidad
Católica del Perú, Lima, Peru

org112SSC IHEP of NRC Kurchatov institute, Protvino, Russia

org113Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria

org114SUBATECH, IMT Atlantique, Université de Nantes, CNRS-IN2P3, Nantes,
France

org115Suranaree University of Technology, Nakhon Ratchasima, Thailand

org116Technical University of Košice, Košice, Slovakia

org117Technical University of Split FESB, Split, Croatia

org118The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy
of Sciences, Cracow, Poland

org119The University of Texas at Austin, Austin, Texas, United States

org120Universidad Autónoma de Sinaloa, Culiacán, Mexico

org121Universidade de São Paulo (USP), São Paulo, Brazil

org122Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

org123Universidade Federal do ABC, Santo Andre, Brazil

org124University of Houston, Houston, Texas, United States

org125University of Jyväskylä, Jyväskylä, Finland

org126University of Liverpool, Liverpool, United Kingdom

org127University of Tennessee, Knoxville, Tennessee, United States

org128University of the Witwatersrand, Johannesburg, South Africa

org129University of Tokyo, Tokyo, Japan

org130University of Tsukuba, Tsukuba, Japan

org131Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France

org132Université de Lyon, Université Lyon 1, CNRS/IN2P3, IPN-Lyon,
Villeurbanne, Lyon, France

org133Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg,
France, Strasbourg, France

org134Università degli Studi di Pavia, Pavia, Italy

org135Università di Brescia, Brescia, Italy

org136V. Fock Institute for Physics, St. Petersburg State University, St.
Petersburg, Russia

org137Variable Energy Cyclotron Centre, Kolkata, India

org138Warsaw University of Technology, Warsaw, Poland

org139Wayne State University, Detroit, Michigan, United States

org140Wigner Research Centre for Physics, Hungarian Academy of Sciences,
Budapest, Hungary

org141Yale University, New Haven, Connecticut, United States

org142Yonsei University, Seoul, Republic of Korea

org143Zentrum für Technologietransfer und Telekommunikation (ZTT),
Fachhochschule Worms, Worms, Germany