# Geometric Fusion via Joint Delay Embeddings
††thanks: Both authors were partially supported by the Air Force Office of
Scientific Research under grant AFOSR FA9550-18-1-0266. We are grateful to
Erik Blasch for technical guidance, and to Kenneth Ball, John Harer, Jay
Hineman, Tessa Johnson, Gary Koplik, and Lihan Yao for helpful discussions.

1st Elchanan Solomon  Department of Mathematics,
Duke University
Durham, USA
<EMAIL_ADDRESS>2nd Paul Bendich  Department of Mathematics,
Duke University
Geometric Data Analytics
Durham, USA
<EMAIL_ADDRESS>
###### Abstract

We introduce geometric and topological methods to develop a new framework for
fusing multi-sensor time series. This framework consists of two steps: (1) a
joint delay embedding, which reconstructs a high-dimensional state space in
which our sensors correspond to observation functions, and (2) a simple
orthogonalization scheme, which accounts for tangencies between such
observation functions, and produces a more diversified geometry on the
embedding space. We conclude with some synthetic and real-world experiments
demonstrating that our framework outperforms traditional metric fusion
methods.

###### Index Terms:

fusion, time series, delay embeddings, computational geometry, applied
topology

##  I Introduction

Data fusion [blasch2012] is the task of synthesizing measurements made by
different sensors and sensing modalities, and is broadly divided into two
paradigms: downstream fusion, in which the synthesis happens after each sensor
has arrived at a classification or regression decision, and upstream fusion
[UpstreamDataFusion], where the synthesis happens on the level either of the
raw measurements or features extracted from the raw measurements. We are
interested in the task of upstream fusion, in particular for time series.

To motivate our particular approach to time series fusion, consider the
following real-world example. A hurricane passes over Durham Country, NC, and
the local weather station receives temperature, precipitation, wind strength,
humidity, and barometric time series. Intuitively, we understand that a model
of the full dynamics of the hurricane system is the ideal fusion of these
related measurements. By analogy, given any collection of time series, our
goal is to reconstruct a dynamical system in a higher-dimensional state space
for which our time series come from observation functions, measuring
statistics about the state of the system as it evolves.

In addition to its easy interpretability, this dynamical systems approach can
call upon a rich, mathematical literature, in particular the study of delay
embeddings. Delay embeddings provide a method for reconstructing higher-
dimensional dynamics from the time series of a single observation function. We
define _joint delay embeddings_ as a natural extension of this technique to
multiple time series, and propose it as a solution to this upstream fusion
task.

One challenge in building our state space is that its geometry is dependent on
the correlations between our observation functions. Returning to our hurricane
example, elementary physics tells us that the pressure and temperature of a
gas increase proportionally to one another. If we do not take this into
account, we will record an increase in temperature as being distinct from an
increase in pressure, inflating the dimensionality of the state space, and
introducing a bias into the geometry, wherein it appears the system is growing
at twice the rate it actually is. To address this lack of independence between
observation functions, we define a one-parameter family of operators, which we
call _Gram-Schmidt tensors_ , which take as input a set of vectors in
Euclidean space, partially orthogonalize them, and sum their norms.

Finally, we demonstrate that a combination of Joint Delay Embeddings with
Gram-Schmidt tensors produces superior results to other geometric fusion
algorithms for some synthetic and real-world data sets.

###  I-A Outline

The rest of this paper proceeds as follows. Delay embeddings and their
relation to the _topology_ of state space, as well as our novel concept of
_joint_ delay embedding, are discussed in Section II. Then Section III
introduces the problem of reconstructing the _geometry_ of state space and
proposes our solution. The concept of metric fusion, with two particular
manifestations from the literature, appears in Section IV. Finally, we show
the benefits of our approach via experiments with synthetic data in Section V,
and real data in Section VI.

##  II Delay Embeddings and Takens’ Theorem

We now review the concept of a delay embedding and outline Takens’
foundational embedding theorem. Given a metric space $\mathcal{O}$, consider a
continuous time series $x(t):\mathbb{R}\to\mathcal{O}$. For the sake of
concreteness, the reader can take $\mathcal{O}$ to be $\mathbb{R}$, but the
generality of our construction allows for higher dimensional Euclidean spaces,
function spaces, and even metric spaces of shapes. Concrete examples include
acoustic time series, moving vehicles, multi-sensor EEG scans, videos, graphs
with time-dependent edge weights, etc. Given a delay parameter $\tau$ and a
dimension parameter $d$, one can construct a time series $X_{\tau,d}(t)$ in
$\mathcal{O}^{d}$ called the _delay embedding_ or _sliding window embedding_ ,
defined as follows:

$X_{\tau,d}(t)=(x(t),x(t+\tau),x(t+2\tau),\cdots,x(t+(d-1)\tau))$

The name _delay embedding_ corresponds to the fact that $X_{\tau,d}(t)$
records the value of the time series at time $t$, as well as at $d$ delayed,
future times. Interest in delay embeddings is motivated by the following,
theoretical result of Takens:

######  Theorem II.1 ([takens1981detecting]).

Let $M$ be an $n$-dimensional manifold, and $f:M\to M$ a generic smooth
diffeomorphism. Let $\alpha:M\to\mathbb{R}$ be a smooth and suitably generic
observation function, and consider the $k$-dimensional embedding
$\phi:M\to\mathbb{R}^{k}$ given by
$\phi_{k}(x)=(\alpha(x),\alpha(f(x)),\cdots,\alpha(f^{k-1}(x)))$. Then, if
$k\geq 2n+1$, $\phi_{k}$ is an embedding of $M$ into $\mathbb{R}^{k}$.

To interpret this in the setting of data analysis, we may think of $M$ as the
state space of a complex, hidden system, and $f:M\to M$ as a discrete
evolution map, describing how the state evolves from one moment in time to the
next. The observation function $\alpha$ maps a state $p\in M$ to a single,
real-valued statistic $\alpha(p)$, such as the temperature of a solution, the
bearing of a ship, or the intensity of a sound wave (living in the state
spaces of a chemical reaction, naval trajectory, and musical performance,
respectively). If we fix an initial point $p_{0}\in M$, we obtain a discrete
time series $x(n):\mathbb{N}\to\mathbb{R}$:

$x(n)=\alpha(\overbracket{f\circ f\circ\cdots\circ f}^{\mbox{n
times}}(p_{0})).$

Because the observation function $\alpha$ only outputs a single, real value,
it will often fail to be injective, i.e. there will be distinct states $p,q\in
M$ with $\alpha(p)=\alpha(q)$. In order to distinguish such states, we can
consider the value of $\alpha$ at their successor states, $f(p)$ and $f(q)$.
By replacing the scalar value $\alpha(p)$ with the vector
$(\alpha(p),\alpha(f(p)))$, we remove some of the failures of injectivity, at
the cost of obtaining a time-series in $\mathbb{R}^{2}$. However, it may still
be the case that there exist distinct states $p,q\in M$ with
$(\alpha(p),\alpha(f(p)))=(\alpha(q),\alpha(f(q)))$, so we can go further and
consider $f(f(p)),f(f(f(p)))$, and so on. Takens’ theorem assures us that we
need to consider at most $2\operatorname{dim}(M)+1$ future time steps to
completely resolve any lack of injectivity, and so obtain a topologically
accurate reconstruction of $M$ in $\mathbb{R}^{2\operatorname{dim}(M)+1}$. The
utility of such a reconstruction is that it provides an interpretable and
structured summary of the data that reveals features that are otherwise either
invisible or the output of unwieldy, black-box trained models. Turning this
perspective around, if we start with a time series
$x(t):\mathbb{R}\to\mathbb{R}$ which we believe comes from an observation
function on a higher-dimensional state space, the delay embedding will build a
representation of an orbit in that state space. This construction naturally
generalizes to time series in any metric space, as outlined above. We point
the reader to a rich literature (e.g, [perea2015sliding], [Swipe], and
[tralie2016high]) about using sliding window embeddings to study the topology
of data.

###  II-A Joint Delay Embeddings

Consider next a set of time series $x_{1}(t),\cdots,x_{m}(t)$, each valued in
a distinct metric space $\mathcal{O}_{1},\cdots,\mathcal{O}_{m}$, as arises in
the setting of multisensor fusion. For example, a recording of a person using
microphones and cameras of various resolutions will be valued in distinct
discretizations of audio or pixel space, respectively. We can construct a
delay embedding $X_{i}(t)$ for each time series separately, but this only sees
the dynamics from the perspective of a single observation function. Instead,
we propose a _joint delay embedding_ :

######  Definition II.2 (Joint Delay Embedding).

Let $x_{1}(t),\cdots,x_{m}(t)$ be a finite collection of time series. Given a
delay parameter $\tau$ and dimension parameter $d$, the joint delay embedding
(JDE) of our time series is a time series of $m\times d$ matrices111This is a
slight abuse of terminology, as the entries of these matrices need not be
numbers, but are elements in a variety of metric spaces. $\mathbf{X}(t)$ with
elements $\mathbf{X}(t)_{ij}=x_{i}(t+(j-1)\tau)$.

In principle, the joint delay embedding $\mathbf{X}(t)$ requires a smaller
dimension parameter $d$ than any of the individual delay embeddings
$X_{1}(t),\cdots,X_{n}(t)$, due to the larger number of observation functions
used. Moreover, and more importantly, the resulting embedding fuses the
information of these time series in an interpretable and non-trivial way.

Before moving on, we point out two features of our definition of joint delay
embeddings: 1) The definition of a joint delay embedding can be modified to
allow for time-warping phenomena between time series. All that is required is
to replace the fixed delay parameter $\tau$ with a variable parameter keyed to
local time-warping effects. For the sake of improving readability, we ignore
this subtlety, with the understanding that the following analysis is
substantially identical in the more general setting. 2) A time series in
$\mathbb{R}^{k}$ can be split into $k$ time series in $\mathbb{R}$. For the
moment, this makes no difference to the resulting joint delay embedding.
However, it does have a subtle effect on the geometric constructions of the
next section. Put concisely, we do not consider tangencies between one-
dimensional time series once they are packaged together into a single
$\mathbb{R}^{k}$ time series. Thus, even if all the component time series are
identical, we consider them to contain orthogonal information.

##  III Geometry of Delay Embeddings

Takens’ theorem asserts that the delay time-series $\phi$ is an embedding, and
hence preserves the _topological_ structure of the manifold $M$. However, it
tells us nothing about how the geometry of the embedding relates to the
geometry of the state manifold. An accurate representation of the true,
underlying geometry is important for distinguishing noise from signal, as well
as for the effective application of most machine learning models, which are
sensitive to the scale and magnitude of the input vectors. Returning to our
recording example, we do not want to produce a state manifold that is
dominated by the speech of whichever person is the focus of the majority of
the audio or video sensors. In general, determining the geometry of $M$ from
one, or many, observation functions is not a well-posed problem, especially
when we do not have any constraints on the distortion of those functions.
However, there are some heuristics we can adopt that help narrow down the
solution space. The hypothesis we propose here is that it is very unlikely, in
the absence of highly symmetric data, for two independent observation
functions to produce delay embeddings with similar geometries. Thus, if we
observe such similarities, we can rescale our state manifold accordingly,
avoiding the distortion associated with recording the same feature multiple
times. Let us now make this precise.

Given a finite collection of time series $x_{1}(t),\cdots,x_{m}(t)$, consider
the joint delay embedding with parameters $d$ and $\tau$. For a pair of times
$t_{1}$ and $t_{2}$, we can form vectors $w_{i}$ in $\mathbb{R}^{d}$ as
follows:

$w_{i}=(d_{\mathcal{O}_{i}}(x_{i}(t_{1}),x_{i}(t_{2})),d_{\mathcal{O}_{i}}(x_{i}(t_{1}+\tau),x_{i}(t_{2}+\tau)),$
$\cdots d_{\mathcal{O}_{i}}(x_{i}(t_{1}+(d-1)\tau),x_{i}(t_{2}+(d-1)\tau)))$

That is, $w_{i}$ is the difference between the delay embedding vectors
$X_{i,\tau,d}(t_{1})$ and $X_{i,\tau,d}(t_{2})$. If we were to assume all our
observation functions were independent, we would define the distance between
the joint delay embedding vectors $\mathbf{X}(t_{1})$ and $\mathbf{X}(t_{2})$
to be $\sqrt{\|w_{1}\|^{2}+\cdots+\|w_{m}\|^{2}}$. However, if our observation
functions are not independent, this would give undue weight to repeated
observations, and minimize the impact of unique ones. To modify this distance
in a way that takes into account the angles between the vectors
$w_{1},\cdots,w_{m}$, we introduce the following tensor:

######  Definition III.1 (Gram-Schmidt Tensor).

Let $V=\\{w_{1},\cdots,w_{m}\\}$ be a collection of vectors, and
$\lambda\in[0,1]$ an orthogonality parameter. We define $N_{\lambda}(V)$ to be
the real value produced by the following algorithm.

  1. 1.

Initialize the algorithm with all vectors unmarked.

  2. 2.

Let $w^{*}$ be the unmarked vector with largest $\ell^{2}$ norm. Mark $w^{*}$.

  3. 3.

For all vectors $w\neq w^{*}$, replace $w$ with $w-\lambda\frac{\langle
w,w^{*}\rangle}{\langle w^{*},w^{*}\rangle}w^{*}$.

  4. 4.

If there are remaining unmarked vectors, return to step (2). Otherwise,
proceed to the next step.

  5. 5.

Return $\sqrt{\|w_{1}\|^{2}+\cdots+\|w_{m}\|^{2}}$.

When $\lambda=1$, the above algorithm reduces the collection $V$ to a set of
orthogonal vectors, as in the Gram-Schmidt algorithm. However, when
$\lambda<1$, we enforce orthogonality less strictly, and the resulting value
$N_{\lambda}(V)$ is larger than $N_{1}(V)$. We can also consider the role of
$\tau$ and $d$ in $N_{\lambda}(V)$: as the delay vector grows, we have more
data with which to determine orthogonality, affecting the result of our above
algorithm, and as the size of the delay parameter $\tau$ grows, the comparison
of our observation functions becomes more global.

##  IV SNF and JDL

Before considering the results of Joint Delay Embeddings on a synthetic data
set, we review two well-known techniques in metric fusion, against which the
performance of JDE will be evaluated. The first technique is Similarity
Network Fusion (SNF, [wang2014similarity]). As the name suggests, SNF is
designed for fusing similarities, rather than distances, so necessitates a
pre-processing step of turning distance matrices into similarity matrices. The
second technique is Joint Distance Learning (JDL), a modification of Joint
Manifold Learning in the context of discrete metric spaces.

###  IV-A The SNF Algorithm

The following pipeline and equations follow the treatment of SNF as outlined
by Tralie, Bendich, and Harer in [tralie2019multi]. The input to the SNF
algorithm is a collection of distance matrices. We first transform our
distance matrices into similarity matrices as follows. If $D=(D_{ij})$ is one
such matrix, we set:

$W_{ij}=\exp\left(-\frac{D_{ij}^{2}}{\Sigma_{ij}}\right),$

where $\Sigma_{ij}$ is a parameter that measures the average distances from
$x_{i}=x(t_{i})$ and $x_{j}=x(t_{j})$ to nearby points. If this is small, the
exponential decays faster, and hence only the closest points have large
similarity. If it is large, the exponential decays more slowly, and further
away points still have significant similarity. The formula for $\Sigma_{ij}$
is as follows, and depends on two constants: $\kappa\in[0,1]$ and
$\beta\in\mathbb{R}_{>0}$:

$\Sigma_{ij}^{\kappa}=\frac{\beta}{3}\left(\frac{1}{\kappa N}\left(\sum_{k\in
N^{\kappa}(i)}D_{ik}\right)+\frac{1}{\kappa N}\left(\sum_{k\in
N^{\kappa}(j)}D_{jk}\right)+D_{ij}\right).$

The set $N^{\kappa}(i)$ is obtained by ordering the points
$\\{x_{1},\cdots,x_{N}\\}$ in order of decreasing distance from $x_{i}$ and
taking the first $\kappa$ percent of these points. Thus $N^{\kappa}(i)$
consists of the first $\kappa N$ nearest neighbors of $x_{i}$. The next step
is to build two normalizations of $W_{ij}$. The first normalization is:

$P_{ij}=\begin{cases}\frac{W_{ij}}{2\sum_{k\neq i}W_{ik}}&j\neq i\\\
1/2&j=i\end{cases}.$

This has the effect of normalizing the rows of $W_{ij}$, so that they sum to
$1$. The second normalization is similar, but is only supported on pairs of
nearest neighbors. Let $N^{i}$ denote $N^{\kappa}(i)\setminus\\{x_{i}\\}$. We
define:

$S_{ij}=\begin{cases}\frac{W_{ij}}{2\sum_{k\in N_{i}}W_{ik}}&j\in N_{i}\\\
1/2&j=i\\\ 0&\mbox{otherwise}.\end{cases}$

Now, suppose we have distance matrices $D^{1},\cdots,D^{m}$, and thus
similarity matrices $W^{1},\cdots,W^{m}$ and normalizations
$P^{1},\cdots,P^{m}$ and $S^{1},\cdots,S^{m}$. The SNF algorithm consists of
iteratively updating the $P$ matrices in order of ascending index. That is,
for $l$ ranging from $1$ to $m$, we define:

$P^{l}=S^{l}\times\frac{\sum_{k\neq l}P^{k}}{m-1}\times(S^{l})^{T}.$

Updating all the $P$ matrices constitutes one step of the SNF algorithm. We
can repeat this process a number of times, cycling through the $P$ matrices.
Finally, we average the outputs to produce:

$\bar{P}=\frac{1}{m}\sum_{l=1}^{m}P^{l}.$

The matrix $\bar{P}$ is the output of the SNF algorithm, and can be thought of
as a fusion of the original $P$ matrices.

###  IV-B Joint Distance Learning

Joint Manifold Learning (JML), introduced by Davenport et. al. in
[davenport2010high] and developed further by Shen et al. in [ShenJML2018], is
a technique for fusing a family of $K$-dimensional manifolds
$\\{M_{1},\cdots,M_{J}\\}$ homeomorphic to a fixed, model manifold $M$ via
homeomorphisms $\psi_{i}:M_{i}\to M$. One considers the product manifold
$\mathbf{M}=M_{1}\times\cdots\times M_{J}$, and then restricts to the joint
manifold: $M^{*}\subset\mathbf{M}$:
$M^{*}=\\{(\psi_{1}(p),\cdots,\psi_{J}(p))\mid p\in M\\}$. The output of JML
is the intrinsic, geodesic distance on the joint manifold $M^{*}$. Although
JML is useful in a variety of contexts, it is poorly suited to fusing metrics
on time series. This is because the geodesic metric on a curve is blind to its
embedding in space, and so a non self-intersecting curve wrapping around a
torus or sphere inherits the same geometry as a straight line. Thus, the
limitation of JML is not the manifold assumption, which can be relaxed, but
the use of the geodesic metric. To that end, we propose the following,
extrinsic adaption of JML.

######  Definition IV.1 (Joint Distance Learning).

Let $d_{1},\cdots,d_{n}$ be a finite collection of metrics on a common set
$X$. The joint distance learning (JDL) fusion of these metrics is defined as:

$\hat{d}^{2}(x_{1},x_{2})=d_{1}^{2}(x_{1},x_{2})+\cdots+d_{n}^{2}(x_{1},x_{2})$

The common approach taken in JML and JDL is to view the set of geometries
observed as orthogonal slices of a single geometry embedded in high-
dimensional space. We can therefore view JDL as a special case of JDE, with
$d$ and $\lambda$ both being equal to $0$.

##  V Synthetic Experiments

In this section, we consider three experiments in multi-sensor fusion, and
compare the results of JDE, SNF and JDL. For all experiments, we work with the
same synthetic data set, for which we have access to a ground-truth distance
matrix. Our set $X$ of data points consists of $N=100$ points evenly spaced
along the parameterized space curve:

$x(t)=(R+r\cos(ax+x_{0}))\cos(bx+y_{0})$
$y(t)=(R+r\cos(ax+x_{0}))\sin(bx+y_{0})$ $z(t)=r\sin(ax+x_{0}),$

where $(x_{0},y_{0})=(0,0)$, $(R,r)=(5,2)$, and $(a,b)=(1,2)$. This is a curve
on a torus with outer radius $R=5$ and inner radius $r=2$. The curve starts at
the point $(0,0)$ and loops once around the meridian and twice around the
longitude of the torus; see Figure V.1 for a visualization of this curve. We
can compute a distance matrix whose entries are the pairwise Euclidean
distance between points on this curve, as well as the associated similarity
matrix, see Figure V.1.

Figure V.1: The $(1,2)$ torus curve and its associated Euclidean distance
matrix and similarity matrix $(\beta=0.5,\kappa=0.1$).

Our experiments are the following: (1) We uniformly pick three random vectors
$v_{1},v_{2},v_{3}$ on the sphere, and define time series via the coordinate
functions $\alpha_{i}(x)=\langle x,v_{i}\rangle$, (2) We uniformly pick three
random points $p_{1},p_{2},p_{3}$ in the box $[-2.5,2.5]^{3}$, and define time
series via the coordinate functions $\alpha_{i}(x)=\|x-p_{i}\|$, (3) We take
four sensors, two given by random projections, and two given by distances to
random basepoints. Our goal, for every experiment, is to produce a fused
distance matrix that most closely resembles the ground truth.

###  V-A Experiment (1)

We compare the results of JDL, SNF, and four variants of JDE, with $d$ equal
to $10$ or $20$, and $\lambda$ equal to $0$ and $1$. See Figure V.2. We
observe that JDL and SNF do a poor job of reconstructing the correct distance
or similarity matrix. For JDE with $d=10$, the reconstruction of the distance
matrix is much improved, especially when the orthogonality parameter $\lambda$
is set to $1$. Finally, when $d=20$, JDE does well at both values of
$\lambda$, with $\lambda=1$ only providing a slightly better result.

Figure V.2: Top Left: JDL. Top Right: SNF $(\beta=0.5,\kappa=0.1$). Center
Left: JDE $(d=10,\lambda=0)$. Center Right: JDE $(d=10,\lambda=1)$. Bottom
Left: JDE $(d=20,\lambda=0)$. Bottom Right: JDE $(d=20,\lambda=1)$.

###  V-B Experiment (2)

As in the prior experiment, the performance of JDL and SNF is quite poor.
However, the results of JDE now demonstrate the significant impact of the
orthogonality parameter $\lambda$, as the $\lambda=1$ fusion far outperforms
the $\lambda=0$ fusion in both $d=10$ and $d=20$. See Figure V.3.

Figure V.3: Top Left: JDL. Top Right: SNF $(\beta=0.5,\kappa=0.1$). Center
Left: JDE $(d=10,\lambda=0)$. Center Right: JDE $(d=10,\lambda=1)$. Bottom
Left: JDE $(d=20,\lambda=0)$. Bottom Right: JDE $(d=20,\lambda=1)$.

###  V-C Experiment (3)

Finally, in the third experiment, we again see that JDL and SNF produce
distorted fusions, and that JDE with $\lambda=1$ gives the best results. See
Figure V.4.

Figure V.4: Top Left: JDL. Top Right: SNF $(\beta=0.5,\kappa=0.1$). Center
Left: JDE $(d=10,\lambda=0)$. Center Right: JDE $(d=10,\lambda=1)$. Bottom
Left: JDE $(d=10,\lambda=0)$. Bottom Right: JDE $(d=10,\lambda=1)$.

##  VI MotionSense Data Set

The MotionSense Data Set, coming from the work of Malekzadeh et. al. in
[malekzadeh2019mobile], consists of smartphone accelerometer and gyroscope
measurements recorded for 24 individuals performing 6 activities in 15 trials
in the same environment and conditions: going downstairs, going upstairs,
walking, jogging, sitting, and standing. There are 12 modalities measured by
the smartphones: attitude.roll, attitude.pitch, attitude.yaw, gravity.x,
gravity.y, gravity.z, rotationRate.x, rotationRate.y, rotationRate.z,
userAcceleration.x, userAcceleration.y, userAcceleration.z. Our goal is to
apply time series fusion as a means of doing unsupervised learning, by
identifying meaningful geometric structure in the state space of human motion.
As JDE and JDL give distance matrices as output, we compare them in two ways:

  1. 1.

Using Multi-Dimensional Scaling (MDS), a method for embedding a discrete
metric space in low-dimensional Euclidean space that approximately preserves
its geometry.

  2. 2.

Using persistence diagrams [Edelsbrunner2000], a method from topological data
analysis that extracts salient, structural features, such as clusters and
cycles, from discrete shapes. Note that these features are extracted directly
from the high-dimensional embeddings, rather from than the low-dimensional
approximations provided by MDS.

As we consider the results for different fusion methods, we ask ourselves the
same question: “is there any meaningful structure or pattern observable using
this method that cannot be detected using the the other methods?” Due to the
relative complexity of our analysis, we focus on a single participant (the
first one), considering the first $200$ time steps for four tasks: going
downstairs (“downstairs 1”), going upstairs (“upstairs 12”), walking (“walking
8”), and jogging (“jogging 9”). See Figure VI.1 for plots of the raw time
series, in which the complexity of our fusion task is readily apparent.

###  VI-A Downstairs

See Figure VI.2. We see that the MDS plot of the JDL fusion is noisy, with
little apparent structure. Similarly, the persistence diagram of the JDL
fusion does not present interesting higher-dimensional features. By contrast,
the JDE fusion MDS shows a time series that loops around before wrapping
around a sphere, and the corresponding persistence diagrams contain
1-dimensional (orange) persistence points, corresponding to the loops, and a
2-dimensional (green) persistence point, corresponding to the sphere. The
advantage of the $\lambda=1$ fusion over the $\lambda=0$ fusion, as seen in
the MDS plots, is that the geometry of the sphere is more accurate. The
authors speculate that the emergence of this sphere is related to the nature
of the smartphone measurements, as pitch, yaw, and rotation are tied to
spherical geometry.

###  VI-B Upstairs

See Figure VI.3. As before, the MDS plot of the JDL fusion is noisy, with
little apparent structure. Similarly, the persistence diagram of the JDL
fusion does not present interesting higher-dimensional features. The JDE
fusion with $\lambda=0$ exhibits an interesting quasi-periodic structure, with
a single one-dimensional persistent point far from the diagonal, and one more
a middling distance away. The JDE fusion with $\lambda=1$ shows one more one-
dimensional persistence point far from the diagonal, as well as a two-
dimensional persistence point near the diagonal that may be noise, or may
correspond to a torus, a hypothesis matched by the associated MDS plot.

###  VI-C Walking

See Figure VI.4. The MDS plot of the JDL fusion is noisy, and the persistence
diagram captures a single one-dimensional cycle far from the diagonal. The JDE
fusions produce more structured MDS plots and reveal more one-dimensional
persistence points, especially for $\lambda=1$.

###  VI-D Jogging

See Figure VI.5. As in the walking trial, MDS plot of the JDL fusion is noisy,
and the persistence diagram captures a single one-dimensional cycle far from
the diagonal. The JDE fusions produce more structured MDS plots and reveal
more one-dimensional persistence points, especially for $\lambda=1$.

Figure VI.1: Smartphone measurement time series. Top Left: Downstairs. Top
Right: Upstairs. Bottom Left: Walking. Bottom Right: Jogging.

Figure VI.2: Downstairs. Top Left: MDS Embedding of JDL fusion. Top Right:
Persistence Diagram of JDL fusion. Middle Left: MDS Embedding of JDE
$(d=20,\lambda=0)$. Middle Right: Persistence Diagram of JDE
$(d=20,\lambda=0)$. Bottom Left: MDS Embedding of JDE $(d=20,\lambda=1)$.
Bottom Right: Persistence Diagram of JDE $(d=20,\lambda=1)$.

Figure VI.3: Upstairs. Top Left: MDS Embedding of JDL fusion. Top Right:
Persistence Diagram of JDL fusion. Middle Left: MDS Embedding of JDE
$(d=20,\lambda=0)$. Middle Right: Persistence Diagram of JDE
$(d=20,\lambda=0)$. Bottom Left: MDS Embedding of JDE $(d=20,\lambda=1)$.
Bottom Right: Persistence Diagram of JDE $(d=20,\lambda=1)$.

Figure VI.4: Walking. Top Left: MDS Embedding of JDL fusion. Top Right:
Persistence Diagram of JDL fusion. Middle Left: MDS Embedding of JDE
$(d=20,\lambda=0)$. Middle Right: Persistence Diagram of JDE
$(d=20,\lambda=0)$. Bottom Left: MDS Embedding of JDE $(d=20,\lambda=1)$.
Bottom Right: Persistence Diagram of JDE $(d=20,\lambda=1)$.

Figure VI.5: Jogging. Top Left: MDS Embedding of JDL fusion. Top Right:
Persistence Diagram of JDL fusion. Middle Left: MDS Embedding of JDE
$(d=20,\lambda=0)$. Middle Right: Persistence Diagram of JDE
$(d=20,\lambda=0)$. Bottom Left: MDS Embedding of JDE $(d=20,\lambda=1)$.
Bottom Right: Persistence Diagram of JDE $(d=20,\lambda=1)$.

Altogether, we see that JDE fusion produces more structured and interpretable
results as compared to JDL, and that this is further enhanced via our
orthogonalization scheme. A more thorough geometric and topological analysis
of the MotionSense data set is beyond the scope of this article, however, and
will be the subject of future work.

##  VII Conclusion

Our central thesis in this article was that the ideal fusion of a family of
time series is a reconstruction of their unified state space. We argued that a
joint delay embedding successfully accomplishes this fusion, but may not
produce the most accurate or informative geometry. To that end, we introduced
Gram-Schmidt tensors as a way of correcting for local tangencies between
sensors. Our synthetic and real-world experiments demonstrated that a
combination of joint delay embeddings with Gram-Schmidt tensors can outperform
other metric fusion methods in the literature.

With regards to future research, there are theoretical and applied directions
of interest. In the former area, we would like to provide precise guaranties
on the accuracy of our geometric reconstructions as depends on the distortion
of the individual observation functions. In the applied arena, the
investigation of the MotionSense data set seems promising, as does the
analysis of EEG data, which also fits neatly into our framework.

## References


EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2016-011 LHCb-PAPER-2015-058 29 January 2016

Study of ${\psi{(2S)}}$ production and cold nuclear matter effects in
$p\mathrm{Pb}$ collisions at $\sqrt{s_{\mbox{\small{\it
NN}}}}=5\mathrm{\,Te\kern-2.07413ptV}$

The LHCb collaboration†††Authors are listed at the end of this paper.

The production of ${\psi{(2S)}}$ mesons is studied in dimuon final states
using proton-lead collision data collected by the LHCb detector. The data
sample corresponds to an integrated luminosity of $1.6\mbox{\,nb}^{-1}$. The
nucleon-nucleon centre-of-mass energy of the proton-lead collisions is
$\sqrt{s_{\mbox{\tiny{\it NN}}}}=5\mathrm{\,Te\kern-1.00006ptV}$. The
measurement is performed using $\psi{(2S)}$ mesons with transverse momentum
less than $14{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and rapidity $y$ in the
ranges $1.5<y<4.0$ and $-5.0<y<-2.5$ in the nucleon-nucleon centre-of-mass
system. The forward-backward production ratio and the nuclear modification
factor are determined for ${\psi{(2S)}}$ mesons. Using the production cross-
section results of $\psi{(2S)}$ and ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ mesons from $b$-hadron decays, the ${{b}{\overline{b}}}$ cross-section
in $p\mathrm{Pb}$ collisions at $\sqrt{s_{\mbox{\tiny{\it
NN}}}}=5\mathrm{\,Te\kern-1.00006ptV}$ is obtained.

Submitted to JHEP

© CERN on behalf of the LHCb collaboration, licence CC-BY-4.0.

##  1 Introduction

The quark-gluon plasma (QGP) is a state of matter with asymptotically free
partons, which is expected to exist at extremely high temperature and density.
It is predicted that heavy quarkonium production will be significantly
suppressed in ultrarelativistic heavy-ion collisions if a QGP is created [1].
This suppression is regarded as one of the most important signatures for the
formation of the QGP. Heavy quarkonium production can also be suppressed in
proton-nucleus ($p\mathrm{A}$) collisions, where hot nuclear matter, i.e. QGP,
is not expected to be created and only cold nuclear matter (CNM) effects
exist. Such CNM effects include: initial-state nuclear effects on the parton
densities (shadowing); coherent energy loss consisting of initial-state parton
energy loss and final-state energy loss; and final-state absorption by
nucleons, which is expected to be negligible at LHC energies [2, 3, 4, 5, 6,
7, 8, 9]. The study of $p\mathrm{A}$ collisions is important to disentangle
the effects of QGP from those of CNM, and to provide essential input to the
understanding of nucleus-nucleus collisions.

Nuclear effects are usually characterized by the nuclear modification factor,
defined as the production cross-section of a given particle per nucleon in
$p\mathrm{A}$ collisions divided by that in proton-proton ($pp$) collisions,

$R_{p\mathrm{A}}(y,\mbox{$p_{\mathrm{T}}$},\sqrt{s_{\mbox{\tiny{\it
NN}}}})\equiv\frac{1}{A}\frac{\mathrm{d}^{2}\sigma_{p\mathrm{A}}(y,\mbox{$p_{\mathrm{T}}$},\sqrt{s_{\mbox{\tiny{\it
NN}}}})/\mathrm{d}y\mathrm{d}\mbox{$p_{\mathrm{T}}$}}{\mathrm{d}^{2}\sigma_{pp}(y,\mbox{$p_{\mathrm{T}}$},\sqrt{s_{\mbox{\tiny{\it
NN}}}})/\mathrm{d}y\mathrm{d}\mbox{$p_{\mathrm{T}}$}},$ (1)

where $A$ is the atomic mass number of the nucleus, $y$ ($p_{\mathrm{T}}$) is
the rapidity (transverse momentum) of the produced particle, and
$\sqrt{s_{\mbox{\tiny{\it NN}}}}$ is the centre-of-mass energy of the proton-
nucleon system. Throughout this paper, $y$ always indicates the rapidity in
the nucleon-nucleon centre-of-mass system.

The suppression of quarkonium and light hadrons at large rapidity has been
observed in $p\mathrm{A}$ collisions [10, 11, 12, 13] and in deuteron-gold
collisions [14, 15, 16, 17, 18]. The proton-lead ($p\mathrm{Pb}$) collisions
recorded at the LHC in 2013 enable the study of CNM effects at the
$\mathrm{\,Te\kern-1.00006ptV}$ scale. With these $p\mathrm{Pb}$ data, the
production cross-sections of prompt ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ mesons, ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mesons from
$b$-hadron decays, and $\mathchar 28935\relax$ mesons were measured, and the
CNM effects were studied by determining the nuclear modification factor
$R_{p\mathrm{Pb}}$ and the forward-backward production ratio
$R_{\mbox{\tiny{FB}}}$ [19, 20]. Working in the nucleon-nucleon rest frame,
the “forward” and “backward” directions are defined with respect to the
direction of the proton beam. The ratio $R_{\mbox{\tiny{FB}}}$ is defined as

$R_{\mbox{\tiny{FB}}}(y,\mbox{$p_{\mathrm{T}}$},\sqrt{s_{\mbox{\tiny{\it
NN}}}})\equiv\frac{\sigma_{p\mathrm{Pb}}(+|y|,\mbox{$p_{\mathrm{T}}$},\sqrt{s_{\mbox{\tiny{\it
NN}}}})}{\sigma_{p\mathrm{Pb}}(-|y|,\mbox{$p_{\mathrm{T}}$},\sqrt{s_{\mbox{\tiny{\it
NN}}}})}.$ (2)

The advantage of measuring this ratio is that it does not rely on knowledge of
the production cross-section in $pp$ collisions. Furthermore, part of the
experimental systematic uncertainties and theoretical scale uncertainties
cancel in the ratio.

Previous measurements in fixed-target $p\mathrm{A}$ collisions by E866 [10],
NA50 [11] and HERA-B [12] showed that the production cross-sections for both
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\psi{(2S)}$ mesons are
suppressed in $p\mathrm{A}$ collisions compared with those in $pp$ collisions.
These measurements also showed stronger suppression at central rapidity for
$\psi{(2S)}$ mesons than for ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
mesons, while at forward rapidity the suppressions were compatible within
large uncertainties. The PHENIX experiment made similar observations in
$d\mathrm{Au}$ collisions at RHIC [18]. The ALICE experiment measured the
$\psi{(2S)}$ suppression in $p\mathrm{Pb}$ collisions at the LHC [21]. Nuclear
shadowing and energy loss predict equal suppression of
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\psi{(2S)}$ mesons, and so
cannot explain the observations. One explanation is that the charmonium states
produced at central rapidity spend more time in the medium than those at
forward rapidities; therefore the loosely bound $\psi{(2S)}$ mesons are more
easily suppressed than ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mesons
at central rapidity [22, 23, 24]. In this picture it is expected that the
charmonium states will spend a much shorter time in the CNM at LHC energies
than at lower energies, leading to similar suppression for $\psi{(2S)}$ and
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mesons even at central
rapidity.

The excellent reconstruction resolution of the LHCb detector for primary and
secondary vertices [25] provides the ability to separate prompt ${\psi{(2S)}}$
mesons, which are produced directly from $pp$ collisions, from those
originating from $b$-hadron decays (called “${\psi{(2S)}}$ from $b$” in the
following). In this analysis, the production cross-sections of prompt
$\psi{(2S)}$ mesons and $\psi{(2S)}$ from $b$ are measured in $p\mathrm{Pb}$
collisions at $\sqrt{s_{\mbox{\tiny{\it
NN}}}}=5\mathrm{\,Te\kern-1.00006ptV}$. The nuclear modification factor
$R_{p\mathrm{Pb}}$ and the forward-backward production ratio
$R_{\mbox{\tiny{FB}}}$ are determined in the range $2.5<|y|<4.0$. Using the
production cross-sections of $\psi{(2S)}$ from $b$ and
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ from $b$, the
${b}{\overline{b}}$ production cross-section in $p\mathrm{Pb}$ collisions is
obtained.

##  2 Detector and datasets

The LHCb detector [25, 26] is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, designed for the study of particles
containing $b$ or $c$ quarks. The detector includes a high-precision tracking
system consisting of a silicon-strip vertex detector surrounding the
$p\mathrm{Pb}$ interaction region, a large-area silicon-strip detector located
upstream of a dipole magnet with a bending power of about $4{\mathrm{\,Tm}}$,
and three stations of silicon-strip detectors and straw drift tubes placed
downstream of the magnet. The tracking system provides a measurement of
momentum, $p$, of charged particles with a relative uncertainty that varies
from 0.5% at low momentum to 1.0% at
200${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The minimum distance of a track to
a primary vertex, the impact parameter, is measured with a resolution of
$(15+29/\mbox{$p_{\mathrm{T}}$}){\,\upmu\mathrm{m}}$, where $p_{\mathrm{T}}$
is the component of the momentum transverse to the beam, in
${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. Different types of charged hadrons are
distinguished using information from two ring-imaging Cherenkov detectors.
Photons, electrons and hadrons are identified by a calorimeter system
consisting of scintillating-pad and preshower detectors, an electromagnetic
calorimeter and a hadronic calorimeter. Muons are identified by a system
composed of alternating layers of iron and multiwire proportional chambers.
The online event selection is performed by a trigger, which consists of a
hardware stage, based on information from the calorimeter and muon systems,
followed by a software stage, which applies a full event reconstruction.

With the proton beam travelling in the direction from the vertex detector to
the muon system and the lead beam circulating in the opposite direction, the
LHCb spectrometer covers forward rapidities. With reversed beam directions
backward rapidities are accessible. The data sample used in this analysis is
collected from the $p\mathrm{Pb}$ collisions in early 2013, corresponding to
an integrated luminosity of $1.1\mbox{\,nb}^{-1}$ ($0.5\mbox{\,nb}^{-1}$) for
forward (backward) collisions. The instantaneous luminosity was around
$5\times 10^{27}~{}\mathrm{\,cm}^{-2}\mathrm{{\,s}}^{-1}$, five orders of
magnitude below the nominal LHCb luminosity for $pp$ collisions. Therefore,
the data were taken using a hardware trigger which simply rejected empty
events. The software trigger for this analysis required one well-reconstructed
track with hits in the muon system and $p_{\mathrm{T}}$ greater than
$600{\mathrm{\,Me\kern-1.00006ptV\\!/}c}$.

Simulated samples based on $pp$ collisions at $8\mathrm{\,Te\kern-1.00006ptV}$
are used to determine the acceptance and reconstruction efficiencies. The
simulation samples are reweighted so that the track multiplicity distribution
reproduces the experimental data of $p\mathrm{Pb}$ collisions at
$5\mathrm{\,Te\kern-1.00006ptV}$. In the simulation, $pp$ collisions are
generated using Pythia [27] with a specific LHCb configuration [28]. Decays of
hadronic particles are described by EvtGen [29], in which final-state
radiation is generated using Photos [30]. The interaction of the generated
particles with the detector, and its response, are implemented using the
Geant4 toolkit [31, *Agostinelli:2002hh] as described in Ref. [33].

##  3 Event selection and cross-section determination

The measurement of ${\psi{(2S)}}$ production is based on the method described
in Refs. [34, 35, 19]. The ${\psi{(2S)}}$ candidates are reconstructed using
dimuon final states from events with at least one primary vertex. The tracks
should be of good quality, have opposite sign charges and be identified as
muons with high $p_{\mathrm{T}}$. The two muon tracks are required to
originate from a common vertex with good vertex fit quality, and the
reconstructed $\psi{(2S)}$ mass should be in the range $\pm
145{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ around the known $\psi{(2S)}$
mass [36].

Due to the small size of the data sample, only one-dimensional differential
cross-sections are measured. The differential production cross-section of
${\psi{(2S)}}$ mesons in a given kinematic bin is defined as

$\frac{\mathrm{d}\sigma}{\mathrm{d}{}X}=\frac{N}{\mathcal{L}\times{\mathcal{B}}\times\Delta{}X},$
(3)

where $X$ denotes $p_{\mathrm{T}}$ or $y$, $N$ is the efficiency-corrected
number of ${\psi{(2S)}}$ signal candidates reconstructed with the dimuon final
state in the given bin of $X$, $\Delta{}X$ is the bin width, $\mathcal{L}$ is
the integrated luminosity, and ${\mathcal{B}}$ is the branching fraction of
the ${\psi{(2S)}}\rightarrow{\mu^{+}\mu^{-}}$ decay,
${\mathcal{B}}({\psi{(2S)}}\rightarrow{\mu^{+}\mu^{-}})=(7.9\pm 0.9)\times
10^{-3}$ [36]. Assuming lepton universality in electromagnetic decays, this
branching fraction is replaced by that of the
${\psi{(2S)}}\rightarrow{e^{+}e^{-}}$, which has a much smaller uncertainty,
${\mathcal{B}}({\psi{(2S)}}\rightarrow{e^{+}e^{-}})=(7.89\pm 0.17)\times
10^{-3}$ [36].

The integrated luminosity of the data sample used in this analysis was
determined using a van der Meer scan, and calibrated separately for the
$p\mathrm{Pb}$ forward and backward samples [37]. The kinematic region of the
measurement is
$\mbox{$p_{\mathrm{T}}$}<14{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and
$1.5<y<4.0$ ($-5.0<y<-2.5$) for the forward (backward) sample. For the single
differential cross-section measurements, the transverse momentum range
$\mbox{$p_{\mathrm{T}}$}<14~{}{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ is divided
into five bins with edges at
$(0,~{}2,~{}3,~{}5,~{}7,~{}14){\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The
rapidity range is divided into five bins of width $\Delta y=0.5$.

##  4 Signal extraction and efficiencies

The numbers of prompt ${\psi{(2S)}}$ and $\psi{(2S)}$ from $b$ in each
kinematic bin are determined from an extended unbinned maximum likelihood fit
performed simultaneously to the distributions of the dimuon invariant mass
$M_{\mu\mu}$ and the pseudo proper decay time $t_{z}$ [34], defined as

$t_{z}=\frac{(z_{\psi}-z_{\mathrm{PV}})\times{}M_{\psi}}{p_{z}},$ (4)

where $z_{\psi}$ is the position of the $\psi{(2S)}$ decay vertex along the
beam axis, $z_{\mathrm{PV}}$ that of the primary vertex refitted after
removing the two muon tracks from the $\psi{(2S)}$ candidate, $p_{z}$ the $z$
component of the measured $\psi{(2S)}$ momentum, and $M_{\psi}$ the known
$\psi{(2S)}$ mass [36].

The invariant mass distribution of the signal in each bin is modelled by a
Crystal Ball (CB) function [38], where the tail parameters are fixed to the
values found in simulation and the other parameters are allowed to vary. For
differential cross-section measurements, the sample size in each bin is very
small. Therefore, in order to stabilise the fit, the mass resolution of the CB
function is fixed to the value obtained from the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ sample, scaled by the ratio of
the $\psi{(2S)}$ mass to the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
mass. The invariant mass distribution of the combinatorial background is
described by an exponential function with variable slope parameter. The signal
distribution of $t_{z}$ can be described [39] by a $\delta$-function at
$t_{z}=0$ for prompt $\psi{(2S)}$ and an exponential function for the
component of $\psi{(2S)}$ from $b$, both convolved with a Gaussian resolution
function. The width of the resolution function and the slope of the
exponential function are free in the fit. The background distribution of
$t_{z}$ in each kinematic bin is modelled with an empirical function
determined from sidebands of the invariant mass distribution.

Figure 1 shows projections of the fit to $M_{\mu\mu}$ and $t_{z}$ for the full
$p\mathrm{Pb}$ forward and backward samples. The combinatorial background in
the backward region is higher than that in the forward region, because the
track multiplicity in the backward region is larger. The mass resolution is
$13{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ for both the forward and backward
samples. The total estimated signal yield for prompt $\psi{(2S)}$ mesons in
the forward (backward) sample is $285\pm 34$ ($81\pm 23$), and that for
$\psi{(2S)}$ from $b$ in the forward (backward) sample is $108\pm 16$ ($21\pm
8$), where the uncertainties are statistical only.

Figure 1: Projections of the fit results to (top) the dimuon invariant mass
$M_{\mu\mu}$ and (bottom) the pseudo proper decay time $t_{z}$ in (left)
$p\mathrm{Pb}$ forward and (right) backward data. In all plots the total
fitted function is shown by the (black) solid line, the combinatorial
background component is shown as the (green) hatched area, the prompt signal
component by the (blue) shaded area, and the $b$-component by the (red) light
solid line.

The efficiency-corrected signal yield $N$ is obtained from the sum of
$w_{i}/{\varepsilon}_{i}$ over all candidates in the given bin. The weight
$w_{i}$ is obtained with the sPlot technique using $M_{\mu\mu}$ and $t_{z}$ as
discriminating variables [40]. The total efficiency ${\varepsilon}_{i}$, which
depends on $p_{\mathrm{T}}$ and $y$, includes the geometrical acceptance, the
reconstruction efficiency, the muon identification efficiency, and the trigger
efficiency. The acceptance and reconstruction efficiencies are determined from
simulation, assuming that the produced $\psi{(2S)}$ mesons are unpolarised.
The efficiency of the muon identification and the trigger efficiency are
obtained from data using a tag-and-probe method as described below.

##  5 Systematic uncertainties

Several sources of systematic uncertainties affecting the production cross-
section measurements are discussed in the following and summarised in Table 1.

The uncertainty on the muon track reconstruction efficiency is studied with a
data-driven tag-and-probe method, using a
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ sample in which one muon track
is fully reconstructed while the other one is reconstructed using only
specific sub-detectors [41]. Taking into account the difference of the track
multiplicity distribution between data and simulation, the total uncertainty
is found to be $1.5\%$.

The uncertainty due to the muon identification efficiency is assigned to be
$1.3\%$ for both the forward and backward samples as obtained in the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ analysis in $p\mathrm{Pb}$
collisions [19]. It is estimated using ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ candidates reconstructed with one muon identified by the muon system
and the other identified by selecting a track depositing the energy of a
minimum-ionising particle in the calorimeters.

Table 1: Summary of the relative systematic uncertainties on cross-section
measurements (%).

Source | Forward | Backward
---|---|---
| prompt | from $b$ | inclusive | prompt | from $b$ | inclusive
Correlated between bins |  |  |  |  |  |
Track reconstruction | 1.5 | 1.5 | 1.5 | 1.5 | 1.5 | 1.5
Muon identification | 1.3 | 1.3 | 1.3 | 1.3 | 1.3 | 1.3
Trigger | 1.9 | 1.9 | 1.9 | 1.9 | 1.9 | 1.9
Luminosity | 1.9 | 1.9 | 1.9 | 2.1 | 2.1 | 2.1
Branching fraction | 2.2 | 2.2 | 2.2 | 2.2 | 2.2 | 2.2
Track quality and radiative tail | 1.5 | 1.5 | 1.5 | 1.5 | 1.5 | 1.5
Mass fit | $3.8-6.9$ | $0.3-3.9$ | $3.2-8.2$ | $9.2-10$ | $16-20$ | $3.0-5.4$
Uncorrelated between bins |  |  |  |  |  |
Multiplicity reweighting | 0.7 | 0.7 | 0.7 | 1.7 | 1.7 | 1.7
Simulation kinematics | $0.6-10$ | $0.4-10$ | $0.2-9.8$ | 1.4 | 2.4 | $0.7-23$
$t_{z}$ fit | $1.6-12$ | $0.3-92$ | $0.1-18$ | $1.4-7.8$ | $8.5-29$ | $0.1-17$

The trigger efficiency is determined from data using a sample unbiased with
respect to the trigger decision. The corresponding uncertainty of $1.9\%$ is
taken as the systematic uncertainty due to the trigger efficiency.

To estimate the uncertainty due to reweighting the track multiplicity in
simulation, the efficiency is calculated without reweighting. The difference
between cross-sections calculated with these two efficiencies is considered as
the systematic uncertainty, which is less than $0.7\%$ in the forward sample,
and about $1.7\%$ in the backward sample.

The possible difference of the $p_{\mathrm{T}}$ and $y$ spectra inside each
kinematic bin between data and simulation can introduce a systematic
uncertainty. To estimate the size of this effect the acceptance and
reconstruction efficiencies have been checked by doubling the number of bins
in $p_{\mathrm{T}}$ or in $y$. The difference from the nominal binning scheme
is taken as systematic uncertainty, which is $0.2\%-10\%$ ($0.7\%-23\%$) in
the forward (backward) sample. For the backward sample the separation into
prompt $\psi{(2S)}$ and $\psi{(2S)}$ from $b$ was not done in bins of
$p_{\mathrm{T}}$ and $y$ due to the limited sample size.

The luminosity is determined with an uncertainty of $1.9\%$ ($2.1\%$) for the
$p\mathrm{Pb}$ forward (backward) sample [37]. The uncertainty on the
${\psi{(2S)}}\rightarrow{\mu^{+}\mu^{-}}$ branching fraction is $2.2\%$. The
combined uncertainty related to the track quality, the vertex finding and the
radiative tail is estimated to be $1.5\%$.

The uncertainty due to modelling the invariant mass distribution is estimated
by using the signal shape from simulation convolved with a Gaussian function,
or by replacing the exponential function by a second-order polynomial. The
maximum differences from the nominal results are taken as the systematic
uncertainties due to the mass fit. To estimate the corresponding systematic
uncertainty on the differential production cross-section due to the fixed mass
resolution, the mass resolution is shifted by one standard deviation. It is
found that this uncertainty is negligible. The uncertainty due to modelling
the $t_{z}$ distribution is estimated by fitting the signal sample extracted
from the sPlot technique using the invariant mass alone as the discriminating
variable.

##  6 Results

###  6.1 Cross-sections

The differential cross-sections of prompt $\psi{(2S)}$, $\psi{(2S)}$ from $b$
and inclusive $\psi{(2S)}$ in the $p\mathrm{Pb}$ forward region as functions
of $p_{\mathrm{T}}$ and $y$ are shown in Fig. 2. The differential cross-
sections of inclusive $\psi{(2S)}$ in the $p\mathrm{Pb}$ backward region as
functions of $p_{\mathrm{T}}$ and $y$ are shown in Fig. 3. As stated in Sect.
5, for the differential production cross-section in the backward data sample,
no attempt is made to separate prompt $\psi{(2S)}$ and $\psi{(2S)}$ from $b$
due to the small statistics. However, these two components are separated for
the integrated production cross-sections. All these cross-sections decrease
with increasing $|y|$.

The integrated production cross-sections for prompt $\psi{(2S)}$, $\psi{(2S)}$
from $b$, and their sum representing inclusive $\psi{(2S)}$, are given in
Table 2. To determine the forward-backward production ratio
$R_{\mbox{\tiny{FB}}}$, the integrated production cross-sections in the common
rapidity region, $2.5<|y|<4.0$, are also given in the table.

Figure 2:  Differential cross-section of $\psi{(2S)}$ meson production as a
function of (left) $p_{\mathrm{T}}$ and (right) $y$ in $p\mathrm{Pb}$ forward
collisions. The (black) dots represent inclusive $\psi{(2S)}$, the (blue)
triangles indicate prompt $\psi{(2S)}$, and the (red) squares show
$\psi{(2S)}$ from $b$. The error bars indicate the total uncertainties.

Figure 3:  Differential cross-section of $\psi{(2S)}$ meson production as a
function of (left) $p_{\mathrm{T}}$ and (right) $y$ in $p\mathrm{Pb}$ backward
collisions. The error bars indicate the total uncertainties.  Table 2:
Integrated production cross-sections for prompt $\psi{(2S)}$, $\psi{(2S)}$
from $b$, and inclusive $\psi{(2S)}$ in the forward region and the backward
region. The $p_{\mathrm{T}}$ range is
$\mbox{$p_{\mathrm{T}}$}<14{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The first
uncertainty is statistical and the second is systematic.

| prompt [${\mathrm{\upmu b}}$ ] | from $b$ [${\mathrm{\upmu b}}$ ] | inclusive [${\mathrm{\upmu b}}$ ]
---|---|---|---
Forward ($+1.5<y<+4.0$) | $138\pm 17\pm\kern 5.0pt8$ | $53.7\pm 7.9\pm 3.6$ | $192\pm 19\pm 10$
Backward ($-5.0<y<-2.5$) | $\kern 5.0pt93\pm 25\pm 10$ | $20.2\pm 8.0\pm 4.3$ | $113\pm 26\pm 11$
Forward ($+2.5<y<+4.0$) | $\kern 5.0pt65\pm 10\pm\kern 5.0pt6$ | $21.4\pm 4.5\pm 1.1$ | $\kern 5.0pt86\pm 11\pm\kern 5.0pt7$
Backward ($-4.0<y<-2.5$) | $\kern 5.0pt76\pm 23\pm 10$ | $13.8\pm 6.9\pm 5.7$ | $\kern 5.0pt90\pm 24\pm 12$

The production cross-sections, $\sigma({{b}{\overline{b}}})$, of the
${b}{\overline{b}}$ pair can be obtained from

$\sigma({{b}{\overline{b}}})=\sigma({\psi{(2S)}}\mbox{ from
}b)/2f_{b\rightarrow{\psi{(2S)}}}=\sigma({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\mbox{ from }b)/2f_{b\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}},$ (5)

where $f_{b\rightarrow{\psi{(2S)}}}$
($f_{b\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}}$) indicates
the production fraction of $b\rightarrow{\psi{(2S)}}X$
($b\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}X$). The world
average values are $f_{b\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}}=(1.16\pm 0.10)\times 10^{-2}$ and
$f_{b\rightarrow{\psi{(2S)}}}=(2.83\pm 0.29)\times 10^{-3}$ [36]. The
production cross-sections $\sigma({{b}{\overline{b}}})$ obtained from the
results of ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\psi{(2S)}$
from $b$ are shown in Table 3. The results of the ${{b}{\overline{b}}}$ cross-
sections obtained from $\psi{(2S)}$ from $b$ are consistent with those from
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ from $b$.

In the combination of the results the partial correlation between
$f_{b\rightarrow{\psi{(2S)}}}$ and
$f_{b\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}}$ is taken into
account. The systematic uncertainties due to the muon identification, the
tracking efficiency, and the track quality are considered to be fully
correlated. The systematic uncertainties due to the luminosities are partially
correlated. The averaged results are also shown in Table 3.

Table 3:  Production cross-sections $\sigma({{b}{\overline{b}}})$ of
${{b}{\overline{b}}}$ pairs in $p\mathrm{Pb}$ collisions obtained from the
production cross-sections of ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
and $\psi{(2S)}$ from $b$. The superscript $\psi$ denotes
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ or $\psi{(2S)}$. The first
uncertainties are statistical, the second are systematic, and the third are
due to the production branching fractions. The last row gives the averaged
results, with the first uncertainty uncorrelated and the second correlated.

|  $\sigma_{\rm Fwd}({{b}{\overline{b}}})$ [${\mathrm{mb}}$] |  $\sigma_{\rm Bwd}({{b}{\overline{b}}})$ [${\mathrm{mb}}$]
---|---|---
| ($\mbox{$p_{\mathrm{T}}$}^{\psi}<14{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, $1.5<y^{\psi}<4.0$) | ($\mbox{$p_{\mathrm{T}}$}^{\psi}<14{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, $-5.0<y^{\psi}<-2.5$)
$\psi{(2S)}$ | $9.49\pm 1.40\pm 0.64\pm 0.97$ | $3.57\pm 1.41\pm 0.76\pm 0.37$
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ | $7.16\pm 0.18\pm 0.40\pm 0.62$ | $5.09\pm 0.29\pm 0.53\pm 0.44$
Averaged | $7.43\pm 0.56(\rm uncorr)\pm 0.49(\rm corr)$ | $4.87\pm 0.62(\rm uncorr)\pm 0.32(\rm corr)$

###  6.2 Cold nuclear matter effects

Cold nuclear matter effects on $\psi{(2S)}$ mesons can be studied with the
production cross-sections obtained in the previous section. As defined in Eq.
2, the forward-backward production ratio, $R_{\mbox{\tiny{FB}}}$, can be
determined with the cross-sections in the common rapidity range
($2.5<|y|<4.0)$. The results are

$R_{\mbox{\tiny{FB}}}(\mbox{$p_{\mathrm{T}}$}<14{\mathrm{\,Ge\kern-1.00006ptV\\!/}c},2.5<|y|<4.0)=\begin{cases}0.93\pm
0.29\pm 0.08,\qquad\mathrm{inclusive},\\\ 0.86\pm 0.29\pm
0.10,\qquad\mathrm{prompt},\\\ 1.55\pm 0.84\pm
0.59,\qquad\mathrm{from}~{}b,\end{cases}$

where the first uncertainties are statistical and the second systematic. The
ratios $R_{\mbox{\tiny{FB}}}$ for inclusive $\psi{(2S)}$ production as
functions of $y$ and $p_{\mathrm{T}}$ are shown in Fig. 4. For comparison, the
plots also show the results for inclusive
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ production [19] and the
theoretical predictions for $\psi{(2S)}$ [4, 3, 5]. The uncertainties for the
theoretical predictions are obtained by taking into account minimum and
maximum nuclear shadowing effects, with many of them cancelling in the ratios.
Calculations in Ref. [3] are based on the Leading Order Colour Singlet Model
(LO CSM) [42, 43], taking into account the modification effects of the gluon
distribution function in nuclei with the parameterisation EPS09 [2] or nDSg
[44]. The next-to-leading order Colour Evaporation Model (NLO CEM) [45] is
used in Ref. [5], considering parton shadowing with the EPS09
parameterisation. Reference [4] provides theoretical predictions of a coherent
parton energy loss effect both in initial and final states, with or without
additional parton shadowing effects according to EPS09. The single free
parameter $q_{0}$ in this model is
$0.055~{}(0.075){\mathrm{\,Ge\kern-1.00006ptV}^{2}\\!/\mathrm{fm}}$ when
parton shadowing in the EPS09 parameterisation is (not) taken into account.
Within uncertainties the measurements agree with all these calculations.

Figure 4:  Forward-backward production ratios $R_{\mbox{\tiny{FB}}}$ as
functions of (left) $|y|$ and (right) $p_{\mathrm{T}}$ for inclusive
${\psi{(2S)}}$ mesons, together with inclusive
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ results [19] and the
theoretical predictions [4, 3, 5], only some of which are available for $|y|$.
The inner error bars (delimited by the horizontal lines) show the statistical
uncertainties; the outer ones show the statistical and systematic
uncertainties added in quadrature.

To obtain the nuclear modification factor $R_{p\mathrm{Pb}}$, the $\psi{(2S)}$
production cross-section in $pp$ collisions at
$5\mathrm{\,Te\kern-1.00006ptV}$ is needed, which is not yet available.
However, it is reasonable to assume that

$\frac{\sigma_{pp}^{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}}(5\mathrm{\,Te\kern-1.00006ptV})}{\sigma_{pp}^{{\psi{(2S)}}}(5\mathrm{\,Te\kern-1.00006ptV})}=\frac{\sigma_{pp}^{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}}(7\mathrm{\,Te\kern-1.00006ptV})}{\sigma_{pp}^{{\psi{(2S)}}}(7\mathrm{\,Te\kern-1.00006ptV})},$
(6)

where $\sigma_{pp}$ indicates the production cross-section of
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ or $\psi{(2S)}$ in $pp$
collisions. The systematic uncertainty due to this assumption is taken to be
negligible compared with the statistical uncertainties in this analysis. The
ratio $R$ of nuclear matter effects between $\psi{(2S)}$ and
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ can then be determined as

$R\equiv\frac{R_{p\mathrm{Pb}}^{{\psi{(2S)}}}}{R_{p\mathrm{Pb}}^{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}}}=\frac{\sigma_{p\mathrm{Pb}}^{{\psi{(2S)}}}(5\mathrm{\,Te\kern-1.00006ptV})}{\sigma_{p\mathrm{Pb}}^{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}}(5\mathrm{\,Te\kern-1.00006ptV})}\times\frac{\sigma_{pp}^{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}}(5\mathrm{\,Te\kern-1.00006ptV})}{\sigma_{pp}^{{\psi{(2S)}}}(5\mathrm{\,Te\kern-1.00006ptV})}=\frac{\sigma_{p\mathrm{Pb}}^{{\psi{(2S)}}}(5\mathrm{\,Te\kern-1.00006ptV})}{\sigma_{p\mathrm{Pb}}^{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}}(5\mathrm{\,Te\kern-1.00006ptV})}\times\frac{\sigma_{pp}^{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}}(7\mathrm{\,Te\kern-1.00006ptV})}{\sigma_{pp}^{{\psi{(2S)}}}(7\mathrm{\,Te\kern-1.00006ptV})},$
(7)

where $R_{p\mathrm{Pb}}^{{\psi{(2S)}}}$ and
$R_{p\mathrm{Pb}}^{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}}$ are the
nuclear modification factors for $\psi{(2S)}$ and
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$. The ratio $R$ indicates
whether there is relative suppression between $\psi{(2S)}$ and
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ production in the collisions.
If $R$ is less than unity, it suggests that the suppression of $\psi{(2S)}$
mesons due to nuclear matter effects in $p\mathrm{Pb}$ collisions is stronger
than that of ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mesons. Using
previous LHCb measurements [34, 46, 19], the values of $R$ for prompt
$\psi{(2S)}$, $\psi{(2S)}$ from $b$ and inclusive $\psi{(2S)}$ are calculated.
The results are shown in Fig. 5, together with those from ALICE [21] and
PHENIX [18]. The LHCb measurement is consistent with ALICE, which is in a
comparable kinematic range. All results suggest a stronger suppression for
prompt $\psi{(2S)}$ mesons than that for prompt
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mesons.

The nuclear modification factor of $\psi{(2S)}$,
$R_{p\mathrm{Pb}}^{{\psi{(2S)}}}$, can be expressed in terms of
$R_{p\mathrm{Pb}}^{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}}$ and $R$

$R_{p\mathrm{Pb}}^{{\psi{(2S)}}}=R_{p\mathrm{Pb}}^{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}}\times{}R\,.$ (8)

The nuclear modification factor
$R_{p\mathrm{Pb}}^{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}}$ was
determined in a previous measurement [19]. The result for inclusive
$\psi{(2S)}$ is shown in Fig. 6. For comparison, the inclusive
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ result from previous
measurements [19] and the result from ALICE [21] are also shown in the plot.
The LHCb measurement is consistent with ALICE. The results for prompt
$\psi{(2S)}$ and $\psi{(2S)}$ from $b$ are shown in Fig. 7, suggesting that in
$p\mathrm{Pb}$ collisions the suppression of prompt $\psi{(2S)}$ mesons is
stronger than that of prompt ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
mesons. For $\psi{(2S)}$ from $b$, no conclusion can be made because of the
limited sample size. Figure 7 also shows several theoretical predictions [4,
3, 5, 47], where only those from Ref. [47] are available for $\psi{(2S)}$ from
$b$. For prompt $\psi{(2S)}$, stronger suppression is seen in the data than
expected by the theoretical calculations. Final-state effects, such as the
interaction of the ${c}{\overline{c}}$ pair with the dense medium created in
the collisions, could be involved [48].

Figure 5:  Ratio (left) between nuclear modification factors of $\psi{(2S)}$
and ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ as a function of $y$ for
prompt ${\psi{(2S)}}$ mesons and $\psi{(2S)}$ from $b$. The blue triangles
represent prompt $\psi{(2S)}$ and the red rectangles indicate $\psi{(2S)}$
from $b$. Ratio (right) between nuclear modification factors of $\psi{(2S)}$
and ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ as a function of $y$ for
inclusive ${\psi{(2S)}}$ mesons. The black dots show the LHCb result, the
hollow circles indicate the ALICE result, and the brown triangle is the PHENIX
result at $0.2\mathrm{\,Te\kern-1.00006ptV}$. The inner error bars (delimited
by the horizontal lines) show the statistical uncertainties; the outer ones
show the statistical and systematic uncertainties added in quadrature.  Figure
6:  Nuclear modification factor $R_{p\mathrm{Pb}}$ as a function of $y$ for
inclusive ${\psi{(2S)}}$ and ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
mesons. The black dots represent the $\psi{(2S)}$ result, the red squares
indicate the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ result, and the
blue hollow circles show the ALICE result for $\psi{(2S)}$. The inner error
bars (delimited by the horizontal lines) show the statistical uncertainties;
the outer ones show the statistical and systematic uncertainties added in
quadrature.

Figure 7:  Nuclear modification factor $R_{p\mathrm{Pb}}$ as a function of $y$
for (left) prompt ${\psi{(2S)}}$ and (right) $\psi{(2S)}$ from $b$, together
with the theoretical predictions from (yellow dashed line and brown band)
Refs. [3, 47], (blue band) Ref. [5], and (green solid and blue dash-dotted
lines) Ref. [4], where only those from Ref. [47] are available for
$\psi{(2S)}$ from $b$. The inner error bars (delimited by the horizontal
lines) show the statistical uncertainties; the outer ones show the statistical
and systematic uncertainties added in quadrature.

##  7 Conclusions

The production cross-sections of prompt ${\psi{(2S)}}$ mesons and those from
$b$-hadron decays are studied in $p\mathrm{Pb}$ collisions with the LHCb
detector. The nucleon-nucleon centre-of-mass energy in the collisions is
$\sqrt{s_{\mbox{\tiny{\it NN}}}}=5\mathrm{\,Te\kern-1.00006ptV}$. The
measurement is performed as a function of the transverse momentum and rapidity
of ${\psi{(2S)}}$ mesons in the region
$\mbox{$p_{\mathrm{T}}$}<14{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and
$1.5<y<4.0$ (forward) and $-5.0<y<-2.5$ (backward). The ${{b}{\overline{b}}}$
production cross-sections in $p\mathrm{Pb}$ collisions are extracted using the
results of $\psi{(2S)}$ from $b$ and ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ from $b$. The forward-backward production ratio $R_{\mbox{\tiny{FB}}}$
is determined separately for prompt $\psi{(2S)}$ mesons and those from
$b$-hadron decays. These results show agreement within uncertainties with
available theoretical predictions. The nuclear modification factor
$R_{p\mathrm{Pb}}$ is also determined separately for prompt $\psi{(2S)}$
mesons and $\psi{(2S)}$ from $b$. These results show that prompt $\psi{(2S)}$
mesons are significantly more suppressed than prompt
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mesons in the backward region;
the results are not well described by theoretical predictions based on
shadowing and energy loss mechanisms.

## Acknowledgements

We express our gratitude to our colleagues in the CERN accelerator departments
for the excellent performance of the LHC. We thank the technical and
administrative staff at the LHCb institutes. We acknowledge support from CERN
and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC
(China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN (Italy); FOM
and NWO (The Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MinES
and FANO (Russia); MinECo (Spain); SNSF and SER (Switzerland); NASU (Ukraine);
STFC (United Kingdom); NSF (USA). We acknowledge the computing resources that
are provided by CERN, IN2P3 (France), KIT and DESY (Germany), INFN (Italy),
SURF (The Netherlands), PIC (Spain), GridPP (United Kingdom), RRCKI and Yandex
LLC (Russia), CSCS (Switzerland), IFIN-HH (Romania), CBPF (Brazil), PL-GRID
(Poland) and OSC (USA). We are indebted to the communities behind the multiple
open source software packages on which we depend. Individual groups or members
have received support from AvH Foundation (Germany), EPLANET, Marie
Skłodowska-Curie Actions and ERC (European Union), Conseil Général de Haute-
Savoie, Labex ENIGMASS and OCEVU, Région Auvergne (France), RFBR and Yandex
LLC (Russia), GVA, XuntaGal and GENCAT (Spain), The Royal Society, Royal
Commission for the Exhibition of 1851 and the Leverhulme Trust (United
Kingdom).

## References

  * [1] T. Matsui and H. Satz, _$J/\psi$ suppression by quark-gluon plasma formation_, Phys. Lett. B178 (1986) 416
  * [2] 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
  * [3] E. G. Ferreiro, F. Fleuret, J. P. Lansberg, and A. Rakotozafindrabe, _Impact of the nuclear modification of the gluon densities on $J/\psi$ production in $p$Pb collisions at $\sqrt{s_{\mbox{\tiny{\it NN}}}}=5~{}\mathrm{TeV}$_, Phys. Rev. C88 (2013) 047901, arXiv:1305.4569
  * [4] F. Arleo and S. Peigné, _Heavy-quarkonium suppression in p-A collisions from parton energy loss in cold QCD matter_ , JHEP 03 (2013) 122, arXiv:1212.0434
  * [5] J. L. Albacete et al., _Predictions for $p+$Pb collisions at $\sqrt{s_{\mbox{\tiny{\it NN}}}}=5$ TeV_, Int. J. Mod. Phys. E22 (2013) 1330007, arXiv:1301.3395
  * [6] A. Adeluyi and T. Nguyen, _Coherent photoproduction of $\psi$ and $\Upsilon$ mesons in ultraperipheral pPb and PbPb collisions at the CERN Large Hadron Collider at $\sqrt{s_{\mbox{\tiny{\it NN}}}}=5~{}\mathrm{TeV}$ and $\sqrt{s_{\mbox{\tiny{\it NN}}}}=2.76~{}\mathrm{TeV}$_, Phys. Rev. C87 (2013) 027901, arXiv:1302.4288
  * [7] G. A. Chirilli, B.-W. Xiao, and F. Yuan, _Inclusive hadron productions in pA collisions_ , Phys. Rev. D86 (2012) 054005, arXiv:1203.6139
  * [8] G. A. Chirilli, _High-energy QCD factorization from DIS to pA collisions_ , Int. J. Mod. Phys. Conf. Ser. 20 (2012) 200, arXiv:1209.1614
  * [9] F. Arleo, R. Kolevatov, S. Peigné, and M. Rustamova, _Centrality and $p_{\perp}$ dependence of $J/\psi$ suppression in proton-nucleus collisions from parton energy loss_, JHEP 05 (2013) 155, arXiv:1304.0901
  * [10] FNAL E866/NuSea collaboration, M. J. Leitch et al., _Measurement of differences between $J/\psi$ and $\psi^{\prime}$ suppression in p-A collisions_, Phys. Rev. Lett. 84 (2000) 3256, arXiv:nucl-ex/9909007
  * [11] NA50 collaboration, B. Alessandro et al., _${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ and $\psi^{\prime}$ production and their normal nuclear absorption in proton-nucleus collisions at $400\mathrm{\,Ge\kern-1.00006ptV}$_, Eur. Phys. J. C48 (2006) 329, arXiv:nucl-ex/0612012
  * [12] HERA-B collaboration, I. Abt et al., _A Measurement of the $\psi^{\prime}$ to ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ production ratio in $920\mathrm{\,Ge\kern-1.00006ptV}$ proton-nucleus interactions_, Eur. Phys. J. C49 (2007) 545, arXiv:hep-ex/0607046
  * [13] HERA-B collaboration, I. Abt et al., _Kinematic distributions and nuclear effects of ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ production in $920\mathrm{\,Ge\kern-1.00006ptV}$ fixed-target proton-nucleus collisions_, Eur. Phys. J. C60 (2009) 525, arXiv:0812.0734
  * [14] BRAHMS collaboration, I. Arsene et al., _Evolution of the nuclear modification factors with rapidity and centrality in d + Au collisions at $\sqrt{s_{\mbox{\tiny{\it NN}}}}=200~{}\mathrm{GeV}$_, Phys. Rev. Lett. 93 (2004) 242303, arXiv:nucl-ex/0403005
  * [15] PHENIX collaboration, S. S. Adler et al., _Nuclear modification factors for hadrons at forward and backward rapidities in deuteron-gold collisions at $\sqrt{s_{\mbox{\tiny{\it NN}}}}=200~{}\mathrm{GeV}$_, Phys. Rev. Lett. 94 (2005) 082302, arXiv:nucl-ex/0411054
  * [16] PHENIX collaboration, A. Adare et al., _Cold nuclear matter effects on $J/\psi$ yields as a function of rapidity and nuclear geometry in d + Au collisions at $\sqrt{s_{\mbox{\tiny{\it NN}}}}=200~{}\mathrm{GeV}$_, Phys. Rev. Lett. 107 (2011) 142301, arXiv:1010.1246
  * [17] PHENIX collaboration, A. Adare et al., _$\Upsilon(1S+2S+3S)$ production in $d+$Au and $p+p$ collisions at $\sqrt{s_{\mbox{\tiny{\it NN}}}}=200\mathrm{\,Ge\kern-1.00006ptV}$ and cold-nuclear matter effects_, Phys. Rev. C87 (2013) 044909, arXiv:1211.4017
  * [18] PHENIX collaboration, A. Adare et al., _Nuclear modification of $\psi^{\prime}$, ${\chi_{c}}$, and ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ production in d+Au collisions at $\sqrt{s_{\mbox{\tiny{\it NN}}}}=200\mathrm{\,Ge\kern-1.00006ptV}$_, Phys. Rev. Lett. 111 (2013) 202301, arXiv:1305.5516
  * [19] LHCb collaboration, R. Aaij et al., _Study of ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ production and cold nuclear matter effects in $p$Pb collisions at $\sqrt{s_{\mbox{\tiny{NN}}}}=5$ TeV_, JHEP 02 (2014) 072, arXiv:1308.6729
  * [20] LHCb collaboration, R. Aaij et al., _Study of $\Upsilon$ production and cold nuclear effects in $p$Pb collisions at $\sqrt{s_{\text{\tiny{NN}}}}=5$ TeV_, JHEP 07 (2014) 094, arXiv:1405.5152
  * [21] ALICE collaboration, B. B. Abelev et al., _Suppression of ${\psi{(2S)}}$ production in p-Pb collisions at $\sqrt{s_{\mbox{\tiny{\it NN}}}}=5.02~{}T\kern-0.50003pteV$_, JHEP 12 (2014) 073, arXiv:1405.3796
  * [22] R. Vogt, _Are the ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ and ${\chi_{c}}$ $A$ dependencies the same?_, Nucl. Phys. A700 (2002) 539, arXiv:hep-ph/0107045
  * [23] B. Z. Kopeliovich and B. G. Zakharov, _Quantum effects and color transparency in charmonium photoproduction on nuclei_ , Phys. Rev. D44 (1991) 3466
  * [24] D. C. McGlinchey, A. D. Frawley, and R. Vogt, _Impact parameter dependence of the nuclear modification of $J/\psi$ production in $d+$Au collisions at $\sqrt{s_{\mbox{\tiny{\it NN}}}}=200$ GeV_, Phys. Rev. C87 (2013) 054910, arXiv:1208.2667
  * [25] LHCb collaboration, A. A. Alves Jr. et al., _The LHCb detector at the LHC_, JINST 3 (2008) S08005
  * [26] LHCb collaboration, R. Aaij et al., _LHCb detector performance_ , Int. J. Mod. Phys. A30 (2015) 1530022, arXiv:1412.6352
  * [27] T. Sjöstrand, S. Mrenna, and P. Skands, _PYTHIA 6.4 physics and manual_ , JHEP 05 (2006) 026, arXiv:hep-ph/0603175
  * [28] I. Belyaev et al., _Handling of the generation of primary events in Gauss, the LHCb simulation framework_ , J. Phys. Conf. Ser. 331 (2011) 032047
  * [29] D. J. Lange, _The EvtGen particle decay simulation package_ , Nucl. Instrum. Meth. A462 (2001) 152
  * [30] P. Golonka and Z. Was, _PHOTOS Monte Carlo: A precision tool for QED corrections in $Z$ and $W$ decays_, Eur. Phys. J. C45 (2006) 97, arXiv:hep-ph/0506026
  * [31] Geant4 collaboration, J. Allison et al., _Geant4 developments and applications_ , IEEE Trans. Nucl. Sci. 53 (2006) 270
  * [32] Geant4 collaboration, S. Agostinelli et al., _Geant4: A simulation toolkit_ , Nucl. Instrum. Meth. A506 (2003) 250
  * [33] M. Clemencic et al., _The LHCb simulation application, Gauss: Design, evolution and experience_, J. Phys. Conf. Ser. 331 (2011) 032023
  * [34] LHCb collaboration, R. Aaij et al., _Measurement of $J/\psi$ production in $pp$ collisions at $\sqrt{s}=7$ TeV_, Eur. Phys. J. C71 (2011) 1645, arXiv:1103.0423
  * [35] LHCb collaboration, R. Aaij et al., _Production of $J/\psi$ and $\Upsilon$ mesons in $pp$ collisions at $\sqrt{s}=8$ TeV_, JHEP 06 (2013) 064, arXiv:1304.6977
  * [36] Particle Data Group, K. A. Olive et al., _Review of particle physics_ , Chin. Phys. C38 (2014) 090001, and 2015 update
  * [37] LHCb collaboration, R. Aaij et al., _Precision luminosity measurements at LHCb_ , JINST 9 (2014) P12005, arXiv:1410.0149
  * [38] T. Skwarnicki, A study of the radiative cascade transitions between the Upsilon-prime and Upsilon resonances, PhD thesis, Institute of Nuclear Physics, Krakow, 1986, DESY-F31-86-02
  * [39] W. Qian, _${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ production study at the LHCb experiment _, CERN-THESIS-2010-307
  * [40] M. Pivk and F. R. Le Diberder, _sPlot: A statistical tool to unfold data distributions_ , Nucl. Instrum. Meth. A555 (2005) 356, arXiv:physics/0402083
  * [41] LHCb collaboration, R. Aaij et al., _Measurement of the track reconstruction efficiency at LHCb_ , JINST 10 (2015) P02007, arXiv:1408.1251
  * [42] C.-H. Chang, _Hadronic production of ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ associated with a gluon_, Nucl. Phys. B172 (1980) 425
  * [43] R. Baier and R. Rückl, _Hadronic production of ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ and $\Upsilon$: Transverse momentum distributions_, Phys. Lett. B102 (1981) 364
  * [44] D. de Florian and R. Sassot, _Nuclear parton distributions at next-to-leading order_ , Phys. Rev. D69 (2004) 074028, arXiv:hep-ph/0311227
  * [45] M. Glück, J. F. Owens, and E. Reya, _Gluon contribution to hadronic ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ production_, Phys. Rev. D17 (1978) 2324
  * [46] LHCb collaboration, R. Aaij et al., _Measurement of $\psi(2S)$ meson production in $pp$ collisions at $\sqrt{s}=7$ TeV_, Eur. Phys. J. C72 (2012) 2100, arXiv:1204.1258
  * [47] Z. Conesa del Valle et al., _Open-beauty production in $p$-Pb collisions at $\sqrt{s_{\mbox{\tiny{\it NN}}}}=5~{}T\kern-0.50003pteV$: Effect of the gluon nuclear densities_, Nucl. Phys. A926 (2014) 236, arXiv:1402.1747
  * [48] E. G. Ferreiro, _Excited charmonium suppression in proton-nucleus collisions as a consequence of comovers_ , Phys. Lett. B749 (2015) 98, arXiv:1411.0549

LHCb collaboration

R. Aaij39, C. Abellán Beteta41, B. Adeva38, M. Adinolfi47, A. Affolder53, Z.
Ajaltouni5, S. Akar6, J. Albrecht10, F. Alessio39, M. Alexander52, S. Ali42,
G. Alkhazov31, P. Alvarez Cartelle54, A.A. Alves Jr58, S. Amato2, S. Amerio23,
Y. Amhis7, L. An3,40, L. Anderlini18, G. Andreassi40, M. Andreotti17,g, J.E.
Andrews59, R.B. Appleby55, O. Aquines Gutierrez11, F. Archilli39, P.
d’Argent12, A. Artamonov36, M. Artuso60, E. Aslanides6, G. Auriemma26,n, M.
Baalouch5, S. Bachmann12, J.J. Back49, A. Badalov37, C. Baesso61, W.
Baldini17,39, R.J. Barlow55, C. Barschel39, S. Barsuk7, W. Barter39, V.
Batozskaya29, V. Battista40, A. Bay40, L. Beaucourt4, J. Beddow52, F.
Bedeschi24, I. Bediaga1, L.J. Bel42, V. Bellee40, N. Belloli21,k, I.
Belyaev32, E. Ben-Haim8, G. Bencivenni19, S. Benson39, J. Benton47, A.
Berezhnoy33, R. Bernet41, A. Bertolin23, F. Betti15, M.-O. Bettler39, M. van
Beuzekom42, S. Bifani46, P. Billoir8, T. Bird55, A. Birnkraut10, A.
Bizzeti18,i, T. Blake49, F. Blanc40, J. Blouw11, S. Blusk60, V. Bocci26, A.
Bondar35, N. Bondar31,39, W. Bonivento16, A. Borgheresi21,k, S. Borghi55, M.
Borisyak66, M. Borsato38, T.J.V. Bowcock53, E. Bowen41, C. Bozzi17,39, S.
Braun12, M. Britsch12, T. Britton60, J. Brodzicka55, N.H. Brook47, E.
Buchanan47, C. Burr55, A. Bursche2, J. Buytaert39, S. Cadeddu16, R.
Calabrese17,g, M. Calvi21,k, M. Calvo Gomez37,p, P. Campana19, D. Campora
Perez39, L. Capriotti55, A. Carbone15,e, G. Carboni25,l, R. Cardinale20,j, A.
Cardini16, P. Carniti21,k, L. Carson51, K. Carvalho Akiba2, G. Casse53, L.
Cassina21,k, L. Castillo Garcia40, M. Cattaneo39, Ch. Cauet10, G. Cavallero20,
R. Cenci24,t, M. Charles8, Ph. Charpentier39, M. Chefdeville4, S. Chen55,
S.-F. Cheung56, N. Chiapolini41, M. Chrzaszcz41,27, X. Cid Vidal39, G.
Ciezarek42, P.E.L. Clarke51, M. Clemencic39, H.V. Cliff48, J. Closier39, V.
Coco39, J. Cogan6, E. Cogneras5, V. Cogoni16,f, L. Cojocariu30, G.
Collazuol23,r, P. Collins39, A. Comerma-Montells12, A. Contu39, A. Cook47, M.
Coombes47, S. Coquereau8, G. Corti39, M. Corvo17,g, B. Couturier39, G.A.
Cowan51, D.C. Craik51, A. Crocombe49, M. Cruz Torres61, S. Cunliffe54, R.
Currie54, C. D’Ambrosio39, E. Dall’Occo42, J. Dalseno47, P.N.Y. David42, A.
Davis58, O. De Aguiar Francisco2, K. De Bruyn6, S. De Capua55, M. De Cian12,
J.M. De Miranda1, L. De Paula2, P. De Simone19, C.-T. Dean52, D. Decamp4, M.
Deckenhoff10, L. Del Buono8, N. Déléage4, M. Demmer10, D. Derkach66, O.
Deschamps5, F. Dettori39, B. Dey22, A. Di Canto39, F. Di Ruscio25, H.
Dijkstra39, S. Donleavy53, F. Dordei39, M. Dorigo40, A. Dosil Suárez38, A.
Dovbnya44, K. Dreimanis53, L. Dufour42, G. Dujany55, K. Dungs39, P. Durante39,
R. Dzhelyadin36, A. Dziurda27, A. Dzyuba31, S. Easo50,39, U. Egede54, V.
Egorychev32, S. Eidelman35, S. Eisenhardt51, U. Eitschberger10, R. Ekelhof10,
L. Eklund52, I. El Rifai5, Ch. Elsasser41, S. Ely60, S. Esen12, H.M. Evans48,
T. Evans56, A. Falabella15, C. Färber39, N. Farley46, S. Farry53, R. Fay53, D.
Fazzini21,k, D. Ferguson51, V. Fernandez Albor38, F. Ferrari15, F. Ferreira
Rodrigues1, M. Ferro-Luzzi39, S. Filippov34, M. Fiore17,39,g, M. Fiorini17,g,
M. Firlej28, C. Fitzpatrick40, T. Fiutowski28, F. Fleuret7,b, K. Fohl39, P.
Fol54, M. Fontana16, F. Fontanelli20,j, D. C. Forshaw60, R. Forty39, M.
Frank39, C. Frei39, M. Frosini18, J. Fu22, E. Furfaro25,l, A. Gallas
Torreira38, D. Galli15,e, S. Gallorini23, S. Gambetta51, M. Gandelman2, P.
Gandini56, Y. Gao3, J. García Pardiñas38, J. Garra Tico48, L. Garrido37, D.
Gascon37, C. Gaspar39, L. Gavardi10, G. Gazzoni5, D. Gerick12, E. Gersabeck12,
M. Gersabeck55, T. Gershon49, Ph. Ghez4, S. Gianì40, V. Gibson48, O.G.
Girard40, L. Giubega30, V.V. Gligorov39, C. Göbel61, D. Golubkov32, A.
Golutvin54,39, A. Gomes1,a, C. Gotti21,k, M. Grabalosa Gándara5, R. Graciani
Diaz37, L.A. Granado Cardoso39, E. Graugés37, E. Graverini41, G. Graziani18,
A. Grecu30, P. Griffith46, L. Grillo12, O. Grünberg64, B. Gui60, E.
Gushchin34, Yu. Guz36,39, T. Gys39, T. Hadavizadeh56, C. Hadjivasiliou60, G.
Haefeli40, C. Haen39, S.C. Haines48, S. Hall54, B. Hamilton59, X. Han12, S.
Hansmann-Menzemer12, N. Harnew56, S.T. Harnew47, J. Harrison55, J. He39, T.
Head40, V. Heijne42, A. Heister9, K. Hennessy53, P. Henrard5, L. Henry8, J.A.
Hernando Morata38, E. van Herwijnen39, M. Heß64, A. Hicheur2, D. Hill56, M.
Hoballah5, C. Hombach55, L. Hongming40, W. Hulsbergen42, T. Humair54, M.
Hushchyn66, N. Hussain56, D. Hutchcroft53, D. Hynds52, M. Idzik28, P. Ilten57,
R. Jacobsson39, A. Jaeger12, J. Jalocha56, E. Jans42, A. Jawahery59, M.
John56, D. Johnson39, C.R. Jones48, C. Joram39, B. Jost39, N. Jurik60, S.
Kandybei44, W. Kanso6, M. Karacson39, T.M. Karbach39,†, S. Karodia52, M.
Kecke12, M. Kelsey60, I.R. Kenyon46, M. Kenzie39, T. Ketel43, E. Khairullin66,
B. Khanji21,39,k, C. Khurewathanakul40, T. Kirn9, S. Klaver55, K.
Klimaszewski29, O. Kochebina7, M. Kolpin12, I. Komarov40, R.F. Koopman43, P.
Koppenburg42,39, M. Kozeiha5, L. Kravchuk34, K. Kreplin12, M. Kreps49, P.
Krokovny35, F. Kruse10, W. Krzemien29, W. Kucewicz27,o, M. Kucharczyk27, V.
Kudryavtsev35, A. K. Kuonen40, K. Kurek29, T. Kvaratskheliya32, D.
Lacarrere39, G. Lafferty55,39, A. Lai16, D. Lambert51, G. Lanfranchi19, C.
Langenbruch49, B. Langhans39, T. Latham49, C. Lazzeroni46, R. Le Gac6, J. van
Leerdam42, J.-P. Lees4, R. Lefèvre5, A. Leflat33,39, J. Lefrançois7, E. Lemos
Cid38, O. Leroy6, T. Lesiak27, B. Leverington12, Y. Li7, T. Likhomanenko66,65,
M. Liles53, R. Lindner39, C. Linn39, F. Lionetto41, B. Liu16, X. Liu3, D.
Loh49, I. Longstaff52, J.H. Lopes2, D. Lucchesi23,r, M. Lucio Martinez38, H.
Luo51, A. Lupato23, E. Luppi17,g, O. Lupton56, A. Lusiani24, F. Machefert7, F.
Maciuc30, O. Maev31, K. Maguire55, S. Malde56, A. Malinin65, G. Manca7, G.
Mancinelli6, P. Manning60, A. Mapelli39, J. Maratas5, J.F. Marchand4, U.
Marconi15, C. Marin Benito37, P. Marino24,39,t, J. Marks12, G. Martellotti26,
M. Martin6, M. Martinelli40, D. Martinez Santos38, F. Martinez Vidal67, D.
Martins Tostes2, L.M. Massacrier7, A. Massafferri1, R. Matev39, A. Mathad49,
Z. Mathe39, C. Matteuzzi21, A. Mauri41, B. Maurin40, A. Mazurov46, M.
McCann54, J. McCarthy46, A. McNab55, R. McNulty13, B. Meadows58, F. Meier10,
M. Meissner12, D. Melnychuk29, M. Merk42, A Merli22,u, E Michielin23, D.A.
Milanes63, M.-N. Minard4, D.S. Mitzel12, J. Molina Rodriguez61, I.A. Monroy63,
S. Monteil5, M. Morandin23, P. Morawski28, A. Mordà6, M.J. Morello24,t, J.
Moron28, A.B. Morris51, R. Mountain60, F. Muheim51, D. Müller55, J. Müller10,
K. Müller41, V. Müller10, M. Mussini15, B. Muster40, P. Naik47, T. Nakada40,
R. Nandakumar50, A. Nandi56, I. Nasteva2, M. Needham51, N. Neri22, S.
Neubert12, N. Neufeld39, M. Neuner12, A.D. Nguyen40, C. Nguyen-Mau40,q, V.
Niess5, S. Nieswand9, R. Niet10, N. Nikitin33, T. Nikodem12, A. Novoselov36,
D.P. O’Hanlon49, A. Oblakowska-Mucha28, V. Obraztsov36, S. Ogilvy52, O.
Okhrimenko45, R. Oldeman16,48,f, C.J.G. Onderwater68, B. Osorio Rodrigues1,
J.M. Otalora Goicochea2, A. Otto39, P. Owen54, A. Oyanguren67, A. Palano14,d,
F. Palombo22,u, M. Palutan19, J. Panman39, A. Papanestis50, M. Pappagallo52,
L.L. Pappalardo17,g, C. Pappenheimer58, W. Parker59, C. Parkes55, G.
Passaleva18, G.D. Patel53, M. Patel54, C. Patrignani20,j, A. Pearce55,50, A.
Pellegrino42, G. Penso26,m, M. Pepe Altarelli39, S. Perazzini15,e, P. Perret5,
L. Pescatore46, K. Petridis47, A. Petrolini20,j, M. Petruzzo22, E. Picatoste
Olloqui37, B. Pietrzyk4, M. Pikies27, D. Pinci26, A. Pistone20, A. Piucci12,
S. Playfer51, M. Plo Casasus38, T. Poikela39, F. Polci8, A. Poluektov49,35, I.
Polyakov32, E. Polycarpo2, A. Popov36, D. Popov11,39, B. Popovici30, C.
Potterat2, E. Price47, J.D. Price53, J. Prisciandaro38, A. Pritchard53, C.
Prouve47, V. Pugatch45, A. Puig Navarro40, G. Punzi24,s, W. Qian56, R.
Quagliani7,47, B. Rachwal27, J.H. Rademacker47, M. Rama24, M. Ramos Pernas38,
M.S. Rangel2, I. Raniuk44, G. Raven43, F. Redi54, S. Reichert55, A.C. dos
Reis1, V. Renaudin7, S. Ricciardi50, S. Richards47, M. Rihl39, K.
Rinnert53,39, V. Rives Molina37, P. Robbe7,39, A.B. Rodrigues1, E.
Rodrigues55, J.A. Rodriguez Lopez63, P. Rodriguez Perez55, A. Rogozhnikov66,
S. Roiser39, V. Romanovsky36, A. Romero Vidal38, J. W. Ronayne13, M.
Rotondo23, T. Ruf39, P. Ruiz Valls67, J.J. Saborido Silva38, N. Sagidova31, B.
Saitta16,f, V. Salustino Guimaraes2, C. Sanchez Mayordomo67, B. Sanmartin
Sedes38, R. Santacesaria26, C. Santamarina Rios38, M. Santimaria19, E.
Santovetti25,l, A. Sarti19,m, C. Satriano26,n, A. Satta25, D.M. Saunders47, D.
Savrina32,33, S. Schael9, M. Schiller39, H. Schindler39, M. Schlupp10, M.
Schmelling11, T. Schmelzer10, B. Schmidt39, O. Schneider40, A. Schopper39, M.
Schubiger40, M.-H. Schune7, R. Schwemmer39, B. Sciascia19, A. Sciubba26,m, A.
Semennikov32, A. Sergi46, N. Serra41, J. Serrano6, L. Sestini23, P. Seyfert21,
M. Shapkin36, I. Shapoval17,44,g, Y. Shcheglov31, T. Shears53, L. Shekhtman35,
V. Shevchenko65, A. Shires10, B.G. Siddi17, R. Silva Coutinho41, L. Silva de
Oliveira2, G. Simi23,s, M. Sirendi48, N. Skidmore47, T. Skwarnicki60, E.
Smith54, I.T. Smith51, J. Smith48, M. Smith55, H. Snoek42, M.D. Sokoloff58,39,
F.J.P. Soler52, F. Soomro40, D. Souza47, B. Souza De Paula2, B. Spaan10, P.
Spradlin52, S. Sridharan39, F. Stagni39, M. Stahl12, S. Stahl39, S.
Stefkova54, O. Steinkamp41, O. Stenyakin36, S. Stevenson56, S. Stoica30, S.
Stone60, B. Storaci41, S. Stracka24,t, M. Straticiuc30, U. Straumann41, L.
Sun58, W. Sutcliffe54, K. Swientek28, S. Swientek10, V. Syropoulos43, M.
Szczekowski29, T. Szumlak28, S. T’Jampens4, A. Tayduganov6, T. Tekampe10, G.
Tellarini17,g, F. Teubert39, C. Thomas56, E. Thomas39, J. van Tilburg42, V.
Tisserand4, M. Tobin40, J. Todd58, S. Tolk43, L. Tomassetti17,g, D. Tonelli39,
S. Topp-Joergensen56, E. Tournefier4, S. Tourneur40, K. Trabelsi40, M.
Traill52, M.T. Tran40, M. Tresch41, A. Trisovic39, A. Tsaregorodtsev6, P.
Tsopelas42, N. Tuning42,39, A. Ukleja29, A. Ustyuzhanin66,65, U. Uwer12, C.
Vacca16,39,f, V. Vagnoni15, G. Valenti15, A. Vallier7, R. Vazquez Gomez19, P.
Vazquez Regueiro38, C. Vázquez Sierra38, S. Vecchi17, M. van Veghel43, J.J.
Velthuis47, M. Veltri18,h, G. Veneziano40, M. Vesterinen12, B. Viaud7, D.
Vieira2, M. Vieites Diaz38, X. Vilasis-Cardona37,p, V. Volkov33, A.
Vollhardt41, D. Voong47, A. Vorobyev31, V. Vorobyev35, C. Voß64, J.A. de
Vries42, R. Waldi64, C. Wallace49, R. Wallace13, J. Walsh24, J. Wang60, D.R.
Ward48, N.K. Watson46, D. Websdale54, A. Weiden41, M. Whitehead39, J. Wicht49,
G. Wilkinson56,39, M. Wilkinson60, M. Williams39, M.P. Williams46, M.
Williams57, T. Williams46, F.F. Wilson50, J. Wimberley59, J. Wishahi10, W.
Wislicki29, M. Witek27, G. Wormser7, S.A. Wotton48, K. Wraight52, S. Wright48,
K. Wyllie39, Y. Xie62, Z. Xu40, Z. Yang3, H. Yin62, J. Yu62, X. Yuan35, O.
Yushchenko36, M. Zangoli15, M. Zavertyaev11,c, L. Zhang3, Y. Zhang3, A.
Zhelezov12, A. Zhokhov32, L. Zhong3, V. Zhukov9, S. Zucchelli15.

1Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil
2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3Center for High Energy Physics, Tsinghua University, Beijing, China
4LAPP, Université Savoie Mont-Blanc, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France
7LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot,
CNRS/IN2P3, Paris, France
9I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
10Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
11Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
12Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
13School of Physics, University College Dublin, Dublin, Ireland
14Sezione INFN di Bari, Bari, Italy
15Sezione INFN di Bologna, Bologna, Italy
16Sezione INFN di Cagliari, Cagliari, Italy
17Sezione INFN di Ferrara, Ferrara, Italy
18Sezione INFN di Firenze, Firenze, Italy
19Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
20Sezione INFN di Genova, Genova, Italy
21Sezione INFN di Milano Bicocca, Milano, Italy
22Sezione INFN di Milano, Milano, Italy
23Sezione INFN di Padova, Padova, Italy
24Sezione INFN di Pisa, Pisa, Italy
25Sezione INFN di Roma Tor Vergata, Roma, Italy
26Sezione INFN di Roma La Sapienza, Roma, Italy
27Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
28AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
29National Center for Nuclear Research (NCBJ), Warsaw, Poland
30Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
31Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
32Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
33Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
34Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN),
Moscow, Russia
35Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State
University, Novosibirsk, Russia
36Institute for High Energy Physics (IHEP), Protvino, Russia
37Universitat de Barcelona, Barcelona, Spain
38Universidad de Santiago de Compostela, Santiago de Compostela, Spain
39European Organization for Nuclear Research (CERN), Geneva, Switzerland
40Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
41Physik-Institut, Universität Zürich, Zürich, Switzerland
42Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
43Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
44NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
45Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
46University of Birmingham, Birmingham, United Kingdom
47H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
48Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
49Department of Physics, University of Warwick, Coventry, United Kingdom
50STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
51School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
52School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
53Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
54Imperial College London, London, United Kingdom
55School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
56Department of Physics, University of Oxford, Oxford, United Kingdom
57Massachusetts Institute of Technology, Cambridge, MA, United States
58University of Cincinnati, Cincinnati, OH, United States
59University of Maryland, College Park, MD, United States
60Syracuse University, Syracuse, NY, United States
61Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
62Institute of Particle Physics, Central China Normal University, Wuhan,
Hubei, China, associated to 3
63Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 8
64Institut für Physik, Universität Rostock, Rostock, Germany, associated to 12
65National Research Centre Kurchatov Institute, Moscow, Russia, associated to
32
66Yandex School of Data Analysis, Moscow, Russia, associated to 32
67Instituto de Fisica Corpuscular (IFIC), Universitat de Valencia-CSIC,
Valencia, Spain, associated to 37
68Van Swinderen Institute, University of Groningen, Groningen, The
Netherlands, associated to 42

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bLaboratoire Leprince-Ringuet, Palaiseau, France
cP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
dUniversità di Bari, Bari, Italy
eUniversità di Bologna, Bologna, Italy
fUniversità di Cagliari, Cagliari, Italy
gUniversità di Ferrara, Ferrara, Italy
hUniversità di Urbino, Urbino, Italy
iUniversità di Modena e Reggio Emilia, Modena, Italy
jUniversità di Genova, Genova, Italy
kUniversità di Milano Bicocca, Milano, Italy
lUniversità di Roma Tor Vergata, Roma, Italy
mUniversità di Roma La Sapienza, Roma, Italy
nUniversità della Basilicata, Potenza, Italy
oAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
pLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
qHanoi University of Science, Hanoi, Viet Nam
rUniversità di Padova, Padova, Italy
sUniversità di Pisa, Pisa, Italy
tScuola Normale Superiore, Pisa, Italy
uUniversità degli Studi di Milano, Milano, Italy
†Deceased