# Neural sequence labeling for Vietnamese
POS Tagging and NER

Anh-Duong Nguyen  Hanoi Univ of Science and Technology
Hanoi, Vietnam
<EMAIL_ADDRESS>Kiem-Hieu Nguyen  Hanoi Univ of Science and
Technology
Hanoi, Vietnam
<EMAIL_ADDRESS>Van-Vi Ngo  VCCorp
Hanoi, Vietnam
<EMAIL_ADDRESS>
###### Abstract

This paper presents a neural architecture for Vietnamese sequence labeling
tasks including part-of-speech (POS) tagging and named entity recognition
(NER). We applied the model described in [8] that is a combination of
bidirectional Long-Short Term Memory and Conditional Random Fields, which rely
on two sources of information about words: character-based word
representations learned from the supervised corpus and pre-trained word
embeddings learned from other unannotated corpora. Experiments on benchmark
datasets show that this work achieves state-of-the-art performances on both
tasks - 93.52% accuracy for POS tagging and 94.88% F1 for NER. Our sourcecode
is available at here.

###### Index Terms:

sequence labeling , part-of-speech tagging, named-entity recognition,
character-level knowledge, syntactic information

##  I Introduction

Linguistic sequence tagging is a well studied yet challenging problem in
natural language processing. Most traditional high performance sequence
tagging systems apply supervised learning techniques such as Hidden Markov
Models, Maximum entropy Markov models, and Conditional Random Fields (CRFs)
[23][19][12], which require large amounts of hand-crafted features and domain-
specific knowledge. For example, sequence taggers benefit from carefully
constructed word-shape features; external language-specific knowledge
resources such as gazetteers are also widely used for solving NER task.
However, such task-specific knowledge are inherently limited and can be costly
to develop, making these models difficult to adapt to new languages or new
domains.

Recently, deep learning has been extensively applied to sequence tagging in
many languages, and the focus has shifted from feature engineering to
designing and implementing effective neural network architectures [8] [13][5].

There are several work applying deep learning to sequence tagging in
Vietnamese [22][16][20]. However, they have not achieved accuracy that far
beyond that of classical machine learning methods. In this paper, we
demonstrate the success of applying a neural architecture for sequence
labeling to Vietnamese. The model requires no task-specific resources, hand-
engineered, or data pre-processing beyond pre-trained word embeddings on
unannotated corpora [8]. The model first uses bidirectional Long-Short Term
Memory units (Bidirectional LSTM) to learn character embeddings. Next,
character representation is concatenated with the pre-trained word embeddings
and then applying dropout [26] to encourage the model to learn to trust both
sources of evidence, then feed them into a bidirectional LSTM to capture
context information of each word. On top of bidirectional LSTM, sequential
CRFs are used to jointly decode labels for the whole sentence. Experiments on
benchmark datasets show that we obtain state-of-the-art results on both tasks
- 93.52% accuracy for POS tagging and 94.88% F1 for NER.

The main contributions of this paper are three-fold:

  * •

We demonstrate the effectiveness of leveraging character-level knowledge for
language representations.

  * •

We apply a neural sequence labeling system for Vietnamese that outperforms
traditionally machine learning methods and other deep learning models.

  * •

We release all code to the research community.

##  II Related Work

As mentioned earlier, we can basically categorize main approaches to sequence
tagging into feature-based machine learning models and deep learning models.

The first approach includes traditional models that rely heavily on hand-
crafted features and domain-specific knowledge. For Vietnamese, previously
published sequence labeling systems used traditional machine learning methods
such as CRFs [14] and MEMM [11], [14]. Recently, several participants at the
VLSP 2016 workshop for NER task use MEMM [10] and CRFs [9] to solve this
problem.

In deep learning approach, our work is closely related to NNVLP [22]. Being
motivated by CNN-LSTM-CRF architecture that achieves state-of-the-art
performance in many languages [13], NNVLP applied this architecture to
Vietnamese. In our work, instead of CNNs, we use LSTM to represent character
embeddings as in [8].

##  III Backgrounds on LSTM and CRFs

###  III-A Recurrent Neural Networks

Recurrent Neural Networks (RNNs) are a family of artificial neural network for
processing sequential data [24]. They take a sequence of vectors
$\boldsymbol{x}$ as input and return another sequence $\boldsymbol{h}$
representing some information about the sequence at every step in the input.
An RNN introduces the connection the previous hidden state and current hidden
state. At time step $t$, the value in the hidden layers and output layers
$\boldsymbol{o}$ are computed as follows:

$\displaystyle\boldsymbol{h}_{t}=f(\boldsymbol{Ux}_{t}+\boldsymbol{Wh}_{(t-1)})$
(1) $\displaystyle\boldsymbol{o}_{t}=\boldsymbol{g}(\boldsymbol{Vs}_{t}),$ (2)

where $\boldsymbol{U},\boldsymbol{W}$ and $\boldsymbol{V}$ are the parameters
computed in training time. $f$ usually is a nonlinear function such as tanh or
ReLU, and $g$ is a softmax function.

RNNs maintain a memory based on history information which enables the model
can, in theory, predict the current output conditioned on long distance
features. In practice they fail to do, and tend to be biased towards their
most recent inputs, due to the gradient vanishing/exploding problems [1] [18].

###  III-B LSTMs

LSTMs [4] are variants of RNNs which have been designed to deal with these
gradient vanishing problems by replacing the RNN’s hidden layers by purpose-
built memory cells, and have been shown to effectively capture long-range
dependencies. An LSTM unit is composed of several gates which control the
proportions of information to forget and to pass on to the next time. Thus
they can be better at finding and exploiting long range dependencies in the
data. Formally, the memory cell is updated at time $t$ as follow:

$\displaystyle\boldsymbol{f}_{t}=\sigma(\boldsymbol{W}_{f}\boldsymbol{h}_{t-1}+\boldsymbol{U}_{f}\boldsymbol{x}_{t}+\boldsymbol{b}_{f})$
(3)
$\displaystyle\boldsymbol{i}_{t}=\sigma(\boldsymbol{W}_{i}\boldsymbol{h}_{t-1}+\boldsymbol{U}_{i}\boldsymbol{x}_{t}+\boldsymbol{b}_{i})$
(4)
$\displaystyle\boldsymbol{\tilde{c}_{t}}=\text{tanh}(\boldsymbol{W}_{c}\boldsymbol{h}_{t-1}+\boldsymbol{U}_{c}\boldsymbol{x}_{t}+\boldsymbol{b}_{c})$
(5)
$\displaystyle\boldsymbol{c}_{t}=\boldsymbol{f}_{t}\odot\boldsymbol{c}_{t-1}+\boldsymbol{i}_{t}\odot\boldsymbol{\tilde{c}_{t}}$
(6)
$\displaystyle\boldsymbol{o}_{t}=\sigma(\boldsymbol{W}_{o}\boldsymbol{h}_{t-1}+\boldsymbol{U}_{o}\boldsymbol{x}_{t}+\boldsymbol{b}_{o})$
(7)
$\displaystyle\boldsymbol{h}_{t}=\boldsymbol{o}_{t}\odot\text{tanh}(\boldsymbol{c}_{t}),$
(8)

where $\sigma$ is the logistic sigmoid function and $\odot$ is the element-
wise product. $\boldsymbol{x}_{t}$ is the input vector at time $t$, and
$\boldsymbol{h}_{t}$ is the hidden state vector capturing the useful
information at current time (and all the previous time steps).
$\boldsymbol{f}$, $\boldsymbol{i}$, $\boldsymbol{o}$ and $\boldsymbol{c}$ are
the forget gate, input gate, output gate and cell vectors respectively, with
$\boldsymbol{U}_{f}$, $\boldsymbol{U}_{i}$, $\boldsymbol{U}_{o}$,
$\boldsymbol{U}_{c}$ are weight matrices of these gates for input
$\boldsymbol{x}_{t}$ and $\boldsymbol{W}_{f}$, $\boldsymbol{W}_{i}$,
$\boldsymbol{W}_{o}$, $\boldsymbol{W}_{c}$ are the weight matrices for hidden
state $\boldsymbol{h}_{t}$.

###  III-C Bidirectional LSTM

An LSTM takes information in a sequence only from past. However, in many
sequence tagging tasks, retrieving information from both past (left) and
future (right) contexts is beneficial. A straightforward way to do this is
using a bidirectional LSTM network (figure 1) as proposed in [2]. generates a
representation of the right context that can be achieved by using a second
LSTM reading the same sequence in reverse. Then the final output is obtained
by concatenating its left and right context representations.

Figure 1: Bidirectional LSTM

###  III-D Bidirectional LSTM-CRFs

For many sequence labeling tasks, a very simple but surprisingly effective
method is to consider the correlations between labels in neighborhoods and
jointly decode the best chain of labels for a given input sequence. For
example, in NER task with BIO2 annotation [25], B-LOC is certainly followed by
I-LOC, and I-PER cannot follow B-ORG. Therefore, instead of decoding each
label independently, we decode them jointly using a linear-chain first order
CRF [7]. CRFs is a family of discriminative probabilistic framework, which
directly model conditional probabilities of a tag sequence given a word
sequence. Formally, the score of the input sentence
$\boldsymbol{X}=(\boldsymbol{x}_{1},\boldsymbol{x}_{2},\dots,\boldsymbol{x}_{n})$,
where $\boldsymbol{x}_{i}$ is the vector of the $i^{\textit{th}}$ word,
associated with the sequence of tag $\boldsymbol{y}=(y_{1},y_{2},\dots,y_{n})$
is defined to be

$s(\boldsymbol{X,y})=\sum_{i=0}^{n}A_{y_{i},y_{i+1}}+\sum_{i=1}^{n}P_{y_{i},i},$

where $A_{i,j}$ denotes the score of a transition from the tag $i$ to the tag
$j$, $y_{0}$ and $y_{n+1}$ are the start and end tags of a sentence. $P_{y,i}$
represents the score of the tag $y$ of the $i_{th}$ word in a sentence
outputted by the bidirectional LSTM network.

Then, the probability of the tag sequence is given with the following form

$p(\boldsymbol{y}|\boldsymbol{X})=\frac{\exp{(s(\boldsymbol{X},\boldsymbol{y}}))}{\sum_{\boldsymbol{y}^{\prime}\in\boldsymbol{Y_{X}}}\exp({s(\boldsymbol{X},\boldsymbol{y}^{\prime}))}}$

where $\boldsymbol{Y}_{\boldsymbol{X}}$ is the set of all possible tag
sequences for a sentence $\boldsymbol{X}$. For CRF training, the parameters
can be estimated by maximizing the log-probability of the correct tag sequence
$\log({p(\boldsymbol{y|\boldsymbol{X}}))}$, and the output sequence
$\boldsymbol{y}^{*}$ is obtained by maximizing the score

$\boldsymbol{y}^{*}=\operatorname*{argmax}_{\boldsymbol{y}^{\prime}\in\boldsymbol{Y_{\boldsymbol{X}}}}s(\boldsymbol{X},\boldsymbol{y}^{\prime})$

The decoding stage in CRFs (i.e. linear first-order CRFs in our work) can be
efficiently solved by Viterbi algorithm.

##  IV Bidirectional LSTM-CRFs with character embeddings for sequence labeling

###  IV-A Bidirectional LSTM-CRFs with character embeddings for POS Tagging

Character-based model of word. Recently, character-level knowledge has been
leveraged and empirically verified to be helpful in sequence labeling tasks.
[8] has shown that LSTM is an effective approach to extract morphological
information (instead of hand-engineering prefix and suffix information about
words) from characters of words. Firstly, we randomly initialize an embedding
for every character. The character embeddings corresponding to characters in a
word are given to a forward and a backward LSTM. For each word, the character-
level word embedding is the concatenation of two last hidden states from
forward and backward layers of the Bidirectional LSTM as described in Figure
2. Then, this character-based word representation is concatenated with the
pre-trained word embedding to obtain the word representation.

Figure 2: The character embeddings of the word  “Hà_Nội”  are given to a
bidirectional LSTMs for extracting character-level word features. Character-
level representation of one word is the concatenation of its forward and
backward representations

Pre-trained word embeddings. In this work, we use available word embedding set
provided by [22], that trained from 7.3GB of 2 million articles collected
through a Vietnamese news portal by word2vec toolkit. For words that do not
have an embedding, a vector called unknown (UNK) embedding is used instead.
The UNK embedding is created by random vectors sampled uniformly from the
range $[-\sqrt{\frac{3}{dim}},+\sqrt{\frac{3}{dim}}]$ where dim is the
dimension of word embeddings [3]. Here the number of dimensions for word
embedding is 300. Dropout layers are applied on both the input and output
vectors of Bidirectional LSTM to prevent the models from depending on one
representation or the other too strongly. Experimental results have shown the
significant effectiveness of the use of dropout in training. Finally, the
output vectors of Bidirectional LSTM are fed to a CRF layer to jointly decode
the best label sequence. Figure 3 presents the architecture of this approach.

Figure 3: Bidirectional LSTM-CRFs architecture for POS tagging.

###  IV-B Bidirectional LSTM-CRFs with character embeddings for NER.

For NER task, we apply the same system as in the POS tagging task.
Furthermore, we utilizes other information such as POS tags or chunk tags that
are available in the dataset to provide additional syntactic information. To
do this, we encode every POS (and chunk) tag as a one-hot vector whose length
is equal to the number of POS tags (and chunk tags). For example:

  * •

N: $1000...000$

  * •

V: $0100...000$

  * •

R: $0000...010$

Then, the concatenation of these one-hot vectors and word representation are
fed into Bidirectional LSTM as described in Figure 4.

Figure 4: Bidirectional LSTM-CRFs architecture for NER

##  V Experiments

###  V-A Datasets

We use the following benchmark datasets in our experiments: VietTreebank (VTB)
[17] for POS tagging, and VLSP shared task 2016 corpus for NER task. While the
NER dataset has been originally released for evaluation, the POS tagging data
set are not previously divided. Therefore, we use cross-validation to evaluate
POS tagging. Table I provides some statistics about these corpus. The dataset
provided by VLSP 2016 organizers consist of four columns of word, POS, chunk
and NER tag respectively.

Table I: Dataset statistics Dataset | Task | #sent | #word
---|---|---|---
VTB | POS tagging | 10,383 | 221,464
VLSP 2016 - train | NER | 14,861 | 325,686
VLSP 2016 - dev | NER | 2,000 | 43,706
VLSP 2016 - test | NER | 2,831 | 66,097

###  V-B Hyper-parameters

Table II summarizes the chosen hyper-parameters for all experiments.

Table II: The model Hyper-parameters Hyper-parameter | Value
---|---
character dimension | 100
word dimension | 300
hidden size char | 100
hidden size word | 150
update function | Adam
learning rate | 0.0035
learning decay rate | 0.005
dropout rate | 0.35
batch size | 8

Hyper-parameters were tuned on the development set of NER. On the hand, we
used hyper-parameters tuned for NER to learn POS tagging.

We set the character embedding dimension at 100, the word embedding dimension
at 300, the dimension of hidden states of the char-level LSTMs at 100 and the
dimension of hidden states of the word-level LSTMs at 150. We optimize
parameters using Adaptive Moment Estimation (Adam) optimizer [6] with mini-
batch size 8. We choose an initial learning rate of $\eta_{0}=0.003$, and the
learning rate is updated on each epoch of training as
$\eta_{t}=\eta_{0}/(1+\alpha t)$, with decay rate $\alpha=0.05$ and $t$ is the
number of epoch completed [13]. Inputs for POS tagging task are gold word
segmentation, and for NER task are gold word segmentation, POS tags, and
chunks. As mention before, dropout method is applied on both the input and
output vectors of the second Bidirectional LSTM to prevent overfitting. We fix
the dropout rate to $0.35$. We use early stopping based on performance on
development sets in which the convergence is reached after around $25$ epochs.

###  V-C Experimental Results

For POS tagging, we compare our work with the following supervised taggers:

  * •

NNVLP [22] is a deep learning method based on Bidirectional LSTM-CRFs
architecture with character embeddings from CNNs.

  * •

RDRPOSTagger [16] learns tagging rules from annotation using Ripple-Down Rules
framework.

  * •

VNTagger [11] learns a Maximum Entropy model using handcraft features.

For NER, we compare our work with the following supervised methods:

  * •

Feature-rich CRFs [15]: As the name mentions, this system learn CRFs model
with a rich set of features including surrounding n-grams and word shape
features.

  * •

NNVLP [22]: This model is identical to the model for POS tagging except the
inclusion of POS tags and chunk embeddings.

We conduct experiments and compare the performance of our system and several
published systems on POS tagging and NER task. In experiments, we use micro-
averaged F1 score, the official evaluation metric in CoNLL 2003 [27] as the
evaluation measure for NER task. The results on these task are plotted in
Table III and Table IV respectively. These tables compares the Vietnamese POS
tagging and NER results of our system with results reported in prior work,
using the same experimental setup. In particular, our system achieves an
accuracy of 93.52% for POS tagging task and a F1 score of 94.88% for NER task,
which significantly outperform previous state-of-the-art work on Vietnamese.
Experimental results showed significant improvement on both tasks, especially
for NER, gained by leveraging character-level knowledge of words. We also
observed that NER task benefits from syntactic features including POS and
chunk information, which aligns with the results in [21].

Table III: POS tagging performance on VTB Method | Accuracy | Evaluation Method
---|---|---
NNVLP [22] | 91.92 |
RDRPOStagger [16] | 92.59 | 5-fold cross-validation
BiLSTM-CRFs w.o char | 91.74 |
BiLSTM-CRFs | 92.98 |
VNTagger [11] | 93.40 |
BiLSTM-CRFs w.o char | 92.22 | 10-fold cross-validation
BiLSTM-CRFs | 93.52 |
Table IV: NER performance on VLSP 2016 dataset Method | P | R | F1 | F1
---|---|---|---|---
|  |  |  | (w.o char)
Feature-rich CRFs [15] | 93.87 | 93.99 | 93.93 | -
NNVLP [22] | 92.76 | 93.07 | 92.91 | -
BiLSTM-CRFs | 90.97 | 87.52 | 89.21 | 76.43
BiLSTM-CRFs + POS | 90.90 | 90.39 | 90.64 | 86.06
BiLSTM-CRFs + Chunk | 95.24 | 92.16 | 93.67 | 87.13
BiLSTM-CRFs + POS + Chunk | 95.44 | 94.33 | 94.88 | 91.36

As our model significantly outperforms NNVLP which applies the same
Bidirectional LSTM-CRFs framework and the same pre-trained word embedding set,
we take a closer look at their model. Firstly, their neural networks have
different hyper-parameter values. Secondly, their CNNs use only one window
size of three subsequent characters. Therefore, it could possibly be that our
hyper-parameters were better tuned on development set; or their CNNs-based
character embeddings should be further improved, for instance by combining
several window sizes; or LSTMs, which capture long-range dependencies and
cross-syllable dependencies, are better for character embeddings of Vietnamese
words. In the future, we are going to investigate more on this.

##  VI Conclusions

In this work, we have applied a deep neural network model for Vietnamese
sequence tagging, which obtains state-of-the-art performance. Experiments on
benchmark data sets for Vietnamese sequence labeling tasks showed the
effectiveness of training character-based model of word by bidirectional LSTM
in language representation serving sequence labeling tasks, that outperform
models using CNN despite requiring less cost for building. We have also shown
that inserting syntactic features into the representation of a word improves
accuracy significantly, especially information about chunk.

## Acknowledgment

This work is supported by VCCorp. We would like to thank the NNVLP [22] team
for publishing the pre-trained word embedding set that we used during training
and evaluating stage of our model.

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EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

CERN-EP-2021-024 LHCb-PAPER-2020-048

Measurement of the prompt-production cross-section ratio
$\sigma(\chi_{c2})/\sigma(\chi_{c1})$ in $p\mkern 1.0mu\mathrm{Pb}$ collisions
at $\sqrt{s_{NN}}$ = 8.16 TeV

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

This article reports the first measurement of prompt $\chi_{c1}$ and
$\chi_{c2}$ charmonium production in nuclear collisions at Large Hadron
Collider energies. The cross-section ratio
$\sigma({\chi_{{c}2}})/\sigma({\chi_{{c}1}})$ is measured in $p$Pb collisions
at $\sqrt{s_{\scriptscriptstyle\text{NN}}}$ = 8.16 TeV, collected with the
LHCb experiment. The $\chi_{{c}1,2}$ states are reconstructed via their decay
to a ${{J\mskip-3.0mu/\mskip-2.0mu\psi}}$ meson, subsequently decaying into a
pair of oppositely charged muons, and a photon, which is reconstructed in the
calorimeter or via its conversion in the detector material. The cross-section
ratio is consistent with unity in the two considered rapidity regions.
Comparison with a corresponding cross-section ratio previously measured by the
LHCb collaboration in $pp$ collisions suggests that $\chi_{c1}$ and
$\chi_{c2}$ states are similarly affected by nuclear effects occurring in
$p$Pb collisions.

Published in Phys. Rev. C 103 (2021) 064905

© 2024 CERN for the benefit of the LHCb collaboration. CC BY 4.0 licence.

##  1 Introduction

Collisions of protons with nuclei offer opportunities to study the production
and interaction of heavy quarks inside the nucleus. Charm-quark production in
hadron collisions is sensitive to the gluon content of colliding hadrons, and
can be used to probe modifications of the parton distributions inside the
nucleus [1]. While traversing the nucleus, heavy quarks are also subject to
energy loss that can lead to the suppression of bound states [2]. Once the
heavy-quark pair exits the nucleus, late-stage interactions with co-moving
hadrons can disrupt fully formed quarkonium states [3]. Measurements in
proton-nucleus collisions also give an experimental baseline for the
interpretation of quarkonium suppression in nucleus-nucleus collisions, where
color screening in a deconfined quark-gluon plasma is expected to be a
dominant effect [4]. Studies of quarkonium suppression in $p$Pb collisions
revealed that the excited states, such as the charmonium $\psi{(2S)}$ state or
the bottomonium $\mathchar 28935\relax{(2S)}$ and $\mathchar
28935\relax{(3S)}$ states, show a different suppression pattern compared to
the ${J\mskip-3.0mu/\mskip-2.0mu\psi}$ and $\mathchar 28935\relax(1{\rm S})$
states (see [5, 6, 7, 8, 9, 10, 11] and references therein). Such a difference
cannot be explained by processes taking place during the initial stages of the
collision, i.e. acting on the quark–antiquark pair. Instead, the processes
must occur after the hadronization of the heavy-quark pair into a final state,
e.g. through dissociation due to interactions with the co-moving matter
created at the collision point [12, 13]. Currently, the
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}$ and $\psi{(2S)}$ mesons are the only
charmonium states which have been measured in collisions of protons with
nuclei at the Large Hadron Collider (LHC).

The $\chi_{{c}J}$ states, with $J=0,1,2$ denoting the total angular momentum,
comprise a triplet of orbitally excited 1P charmonia. They are typically
studied in collider experiments via their radiative decay
${\chi_{{c}J}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}\gamma$, with a
subsequent decay
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}\\!\rightarrow\ell^{+}\ell^{-}$, where
$\ell$ denotes electron or muon. A selection of recent measurements in $pp$
and $p{\overline{p}}$ collisions can be found in Refs. [14, 15, 16, 17, 18].

The binding energies of $\chi_{{c}J}$ states are significantly smaller than
that of the ${J\mskip-3.0mu/\mskip-2.0mu\psi}$ state and greater than the
binding energy of $\psi{(2S)}$ state [19]. The small difference in the binding
energies of $\chi_{{c}1}$ and $\chi_{{c}2}$ charmonia makes the ratio of their
production cross-sections, $\sigma({\chi_{{c}2}})/\sigma({\chi_{{c}1}})$, a
useful tool to study their sensitivity to final-state nuclear effects, which
are expected to be similar for both states. The ${\chi_{{c}J}}$ states also
form an important feed-down contribution to
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}$ production, so measurements of nuclear
effects on ${\chi_{{c}J}}$ states can clarify interpretation of the
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}$ data. Moreover, various efficiency
factors and sources of uncertainty cancel out in the ratio, allowing for a
more precise measurement. In nuclear collisions, the $\chi_{{c}J}$ states have
been measured by the HERA-B [20] and PHENIX collaborations [21]. To date, no
measurement has been reported at the LHC energies.

Here we present the first measurement of the cross-section ratio of promptly
produced ${\chi_{{c}2}}$ and ${\chi_{{c}1}}$ states,
$\sigma({\chi_{{c}2}})/\sigma({\chi_{{c}1}})$, in nuclear collisions at the
LHC. The measurement is performed using data collected by the LHCb
collaboration in $p$Pb collisions, at the center-of-mass energy per nucleon
pair $\sqrt{s_{\scriptscriptstyle\text{NN}}}$ = 8.16 TeV, in 2016.

##  2 Experimental apparatus

The LHCb detector [22, 23] 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 consists of a high-precision
silicon-strip vertex locator (VELO) surrounding the interaction region, a set
of four planar tracking stations coupled to a dipole magnet with a 4 Tm
bending power, a pair of ring-imaging Cherenkov detectors to discriminate
between different types of charged hadrons, followed by calorimetric and muon
systems that are of particular importance in this measurement. The
calorimetric system allows for identification of electrons and photons and
consists of a scintillating pad detector (SPD), a pre-shower system (PS), an
electromagnetic (ECAL) calorimeter, and a hadronic (HCAL) calorimeter. The SPD
and PS are designed to discriminate between signals from photons and
electrons, while ECAL and HCAL provide the energy measurement and identify
electromagnetic radiation and neutral hadrons. Muons are identified by a
system composed of alternating layers of iron and multiwire proportional
chambers.

The $p$Pb data were collected with the LHCb experiment in two distinct beam
configurations. In the forward configuration, the particles produced in the
direction of the proton beam are measured in a center-of-mass rapidity region
$1.5<y^{*}<4.0$, while in the backward configuration, particles produced in
the lead-beam direction are measured at center-of-mass rapidity
$-5.0<y^{*}<-2.5$. The forward (backward) data sample corresponds to an
integrated luminosity of about $14\,\upmu\text{b}^{-1}$
($21\,\upmu\text{b}^{-1}$).

##  3 Data selection

The analyzed events are selected by a set of triggers designed to record
collisions containing the decay
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}\\!\rightarrow{\mu^{+}\mu^{-}}$. The
${J\mskip-3.0mu/\mskip-2.0mu\psi}$ candidates are reconstructed from a pair of
oppositely charged muons with momentum component transverse to the beam,
$p_{\mathrm{T}}$, larger than $700\mbox{ $\text{\,Me\kern-1.00006ptV\\!/}c$}$,
originating from a common vertex and an invariant mass within $\pm
42~{}\text{\,Me\kern-1.00006ptV\\!/}c^{2}$ of the known
${J\mskip-3.0mu/\mskip-2.0mu\psi}$ mass [24] (corresponding to three times the
dimuon mass resolution). The ${J\mskip-3.0mu/\mskip-2.0mu\psi}$ candidates are
combined with a photon candidate to form a $\chi_{{c}1,2}$ candidate. Photons
used in this analysis are classified in two mutually exclusive types: those
that converted in the detector material upstream of the dipole magnet and of
which the electron and positron tracks were reconstructed in the tracking
system (converted photons), or those reconstructed through their energy
deposits in the calorimetric system (calorimetric photons). The calorimetric
photon sample is about an order of magnitude larger than the converted photon
sample but has worse mass resolution. Converted photons are reconstructed from
a pair of oppositely charged electron candidates and are required to have a
transverse momentum $p_{\mathrm{T}}$ $>600$ $\text{\,Me\kern-1.00006ptV\\!/}c$
and a good-quality conversion vertex $\gamma\\!\rightarrow{e^{+}e^{-}}$.
Calorimetric photons are identified using the ratio of their energy deposited
in the hadronic and electromagnetic calorimeters and a pair of likelihood-
based classifiers that discriminate photons from electrons and hadrons [25,
26]. Calorimetric photons accepted for analysis are required to have
$p_{\mathrm{T}}$ $>1$ $\text{\,Ge\kern-1.00006ptV\\!/}c$. The two measurements
discussed here are independent given the different reconstruction between the
converted and the calorimetric photons. The selected $\mu^{+}\mu^{-}\gamma$
combinations, which comprise the $\chi_{{c}1,2}$ candidates, are required to
be reconstructed within the pseudorapidity window $2<\eta<4.5$ and in the
transverse momentum range of $3<p_{\mathrm{T}}<15$
$\text{\,Ge\kern-1.00006ptV\\!/}c$ for the converted and $5<p_{\mathrm{T}}<15$
$\text{\,Ge\kern-1.00006ptV\\!/}c$ for the calorimetric candidates. In order
to select the $\chi_{{c}1,2}$ candidates produced promptly at the primary-
collision vertex and to suppress nonprompt production from $b$-hadron decays
occurring away from the primary vertex, an upper limit is imposed on the
pseudo-decay time of the candidates, defined as

$t_{z}=\frac{\left(z_{\rm decay}-z_{\rm PV}\right)\times
M_{{\chi_{{c}1}}}}{p_{z}},$ (1)

where $z_{\rm decay}-z_{\rm PV}$ is the difference between the positions of
the reconstructed vertex of the $\chi_{{c}1,2}$ candidate and the primary
proton-nucleus collision vertex along the beam axis, $p_{z}$ is the
longitudinal component of the $\chi_{{c}1,2}$ candidate momentum and
$M_{{\chi_{{c}1}}}$ is the known mass of the $\chi_{{c}1}$ meson [24]. The
pseudo-decay time is limited to $t_{z}<0.1\text{ ps}$. The $\chi_{{c}1}$ and
$\chi_{{c}2}$ candidates originating from decays of short-lived resonances,
such as $\psi{(2S)}$ produced at the interaction point, are also considered in
the analysis.

The effects of the detector acceptance as well as of the reconstruction and
selection efficiencies are investigated with simulated events. The
$\chi_{{c}1,2}$ signal is generated in Pythia [27] with an LHCb specific
configuration [28]. The $\chi_{{c}1}$ and $\chi_{{c}2}$ states are generated
assuming unpolarized production. The underlying minimum bias forward and
backward $p$Pb collisions are generated using the Epos event generator
configured for the LHC [29]. Unstable particles are decayed via EvtGen [30].
The ${{J\mskip-3.0mu/\mskip-2.0mu\psi}}\\!\rightarrow{\mu^{+}\mu^{-}}$ decays
are corrected for final-state electromagnetic radiation using Photos [31]. The
response of the detector to the interactions of the generated particles is
implemented using the Geant4 toolkit [32, *Agostinelli:2002hh]; for a detailed
description see Ref. [34].

##  4 Data analysis

This paper aims at measuring the ratio of the cross sections for prompt
$\chi_{{c}1}$ and $\chi_{{c}2}$ production. The cross-section ratio is defined
as

$\frac{\sigma({\chi_{{c}2}})}{\sigma({\chi_{{c}1}})}=\frac{N_{{\chi_{{c}2}}}}{N_{{\chi_{{c}1}}}}\frac{\varepsilon_{{\chi_{{c}1}}}}{\varepsilon_{{\chi_{{c}2}}}}\frac{\mathcal{B}({\chi_{{c}1}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}\gamma)}{\mathcal{B}({\chi_{{c}2}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}\gamma)}.$
(2)

Here, $N_{{\chi_{{c}2}}}$ and $N_{{\chi_{{c}1}}}$ represent the signal yields
of the $\chi_{c2}$ and $\chi_{c1}$ states, respectively, and
$\varepsilon_{{\chi_{{c}2}}}$ and $\varepsilon_{{\chi_{{c}1}}}$ denote the
efficiencies to reconstruct and select the corresponding state. The branching
fractions for the $\chi_{{c}1,2}$ decays are
$\mathcal{B}({\chi_{{c}1}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}\gamma)=\left(34.3\pm
1.0\right)\%$ and
$\mathcal{B}({\chi_{{c}2}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}\gamma)=\left(19.0\pm
0.5\right)\%$ [24].

The $\chi_{{c}1}$ and $\chi_{{c}2}$ signal yields are determined by performing
a binned maximum-likelihood fit to the spectra of the difference between the
invariant mass of the ${\mu^{+}\mu^{-}}\gamma$ candidate and that of the
$\mu^{+}\mu^{-}$ pair, $\Delta M\equiv
M({\mu^{+}\mu^{-}}\gamma)-M({\mu^{+}\mu^{-}})$. The fit function comprises a
Gaussian shape for the $\chi_{{c}1}$ and $\chi_{{c}2}$ resonances and a
background component described with a second-order Chebyshev polynomial. In
the fit, the difference between the values of the $\chi_{c1}$ and $\chi_{c2}$
masses is set to the known mass difference [24]. The widths of the $\chi_{c1}$
and $\chi_{c2}$ peaks are set to be equal, following expectations from
simulation, and left as a free parameter. The $\chi_{c0}$ peak is also
included in the fit, however no significant $\chi_{c0}$ yield is observed. The
fit to the spectra of converted candidates is performed in the range
$200<\Delta M<800\ (850)$ MeV/$c^{2}$ at forward (backward) rapidity. For the
calorimetric candidates, the invariant-mass difference spectrum is fitted
between $250<\Delta M<650$ MeV/$c^{2}$ in the two rapidity intervals. The
mass-difference spectra of the converted and calorimetric samples are shown,
together with the fit components, in Figs. 1 and 2, respectively. In the
converted samples, the yield ratio $N_{{\chi_{{c}2}}}/N_{{\chi_{{c}1}}}$ is
determined to be $0.51\pm 0.23$ at forward and $0.56\pm 0.26$ at backward
rapidity, where the uncertainties are statistical. In the calorimetric
samples, these ratios are found to be $0.63\pm 0.08$ at forward and $0.67\pm
0.10$ at backward rapidity. Individual yields as well as their corresponding
significance are listed in Table 1.

Figure 1:  Mass-difference spectra of converted $\chi_{{c}1,2}$ candidates in
forward (left) and backward (right) configuration data. The data are
superimposed with a fit (solid blue line) comprising $\chi_{{c}1}$ and
$\chi_{{c}2}$ signals and combinatorial background (dashed black line).

Figure 2:  Mass-difference spectra of calorimetric $\chi_{{c}1,2}$ candidates
in forward (left) and backward (right) data. The data are superimposed with a
fit result (solid blue line) comprising ${\chi_{{c}1}}$ and ${\chi_{{c}2}}$
signals and combinatorial background (dashed black line).

Since the kinematics of ${\chi_{{c}1}}$ and ${\chi_{{c}2}}$ decays are nearly
identical, various detector effects such as tracking and particle-
identification efficiencies cancel out in the ratio, so that the efficiency
ratio in Eq. (2) can be expressed as
$\displaystyle{\frac{\varepsilon_{{\chi_{{c}1}}}}{\varepsilon_{{\chi_{{c}2}}}}=\frac{\varepsilon^{\rm
acc}_{{\chi_{{c}1}}}}{\varepsilon^{\rm
acc}_{{\chi_{{c}2}}}}\frac{\varepsilon^{\rm
reco}_{{\chi_{{c}1}}}}{\varepsilon^{\rm reco}_{{\chi_{{c}2}}}}}$. The factor
$\varepsilon^{\rm acc}$ expresses the geometrical acceptance of the decay
products to fall within the LHCb acceptance, while the factor
$\varepsilon^{\rm reco}$ represents the efficiency of selection and
reconstruction of the signal candidates. These correction factors are computed
from dedicated simulated events.

Table 1:  Yields of $\chi_{{c}1}$ and $\chi_{{c}2}$ signals with statistical uncertainties and corresponding significance (given in standard deviations).  Data sample | $N_{{\chi_{{c}1}}}$ | Significance | $N_{{\chi_{{c}2}}}$ | Significance
---|---|---|---|---
Converted photons | $1.5<y^{*}<4.0$ | $41\pm 9$ | $6.0$ | $21\pm 8$ | $3.1$
$-5.0<y^{*}<-2.5$ | $38\pm 9$ | $4.4$ | $21\pm 8$ | $3.0$
Calorimetric photons | $1.5<y^{*}<4.0$ | $1151\pm 69$ | $15.7$ | $721\pm 76$ | $9.8$
$-5.0<y^{*}<-2.5$ | $1004\pm 73$ | $13.3$ | $676\pm 82$ | $8.5$

##  5 Systematic uncertainties

The systematic uncertainties on the cross-section ratios are determined as
follows. A systematic uncertainty on the signal extraction is determined by
varying the models used in the mass-difference fits. Several different signal
and background models are tested. The signal shapes are varied between
Gaussian functions and Voigtian functions (a convolution of a Breit-Wigner and
a Gaussian function), and the background shape is varied between second- and
third-order Chebyshev polynomials. The natural widths of the $\chi_{{c}1}$ and
$\chi_{{c}2}$ states are narrow compared to the resolution, the Breit-Wigner
widths are therefore fixed to the known values [24]. The fit range is varied
between $100\ (150)<\Delta M<900~{}\text{\,Me\kern-1.00006ptV\\!/}c^{2}$ and
$200<\Delta M<800\ (850)~{}\text{\,Me\kern-1.00006ptV\\!/}c^{2}$ for the
converted candidates at forward (backward) rapidity. For the calorimetric
candidates, the fit range is varied between $250<\Delta
M<650~{}\text{\,Me\kern-1.00006ptV\\!/}c^{2}$ and $300<\Delta
M<600~{}\text{\,Me\kern-1.00006ptV\\!/}c^{2}$ in the two rapidity intervals.
The various choices of signal shape, background parametrization, and range
give a total of eight fits to each of the mass-difference spectra in each
rapidity interval. In all cases, the $\chi_{c0}$ peak is also included in the
fit; however, no significant $\chi_{c0}$ yield is observed. The systematic
uncertainty on the yield ratios due to the fitting procedure is assigned as
the standard deviation between the values returned by the eight individual
fits. For the converted sample, this systematic uncertainty amounts to $4.9\%$
($3.2\%$) at forward (backward) rapidity. For the calorimetric sample it is
$2.6\%$ ($6.8\%$) at forward (backward) rapidity. The residual background from
the nonprompt $\chi_{c1,2}$ production is verified as negligible and shown to
cancel out in the ratio, hence no related uncertainty is assigned. The
systematic uncertainty on the acceptance and efficiency corrections includes
contributions from the limited size of the simulated samples used to compute
the $\varepsilon^{\rm acc}$ and $\varepsilon^{\rm reco}$ factors, and the
uncertainty due to the discrepancy of the $\chi_{c1,2}$ and photon properties
between data and simulation. The latter is estimated using simulated samples,
weighted to reproduce the kinematic distributions of $\chi_{c1,2}$ and photons
in background-subtracted data, and obtained using the sPlot technique, with
$\Delta M$ as the discriminating variable [35]. The weights are extracted by
comparing the transverse momentum and rapidity dependent ratios of the
simulated counts $N_{{\chi_{{c}1}}}/N_{{\chi_{{c}2}}}$ with those in data. The
simulated ${\chi_{{c}1}}$ samples are then weighted event-by-event and the
uncertainty is assessed as the difference between the efficiency ratios
computed from simulated samples prior to and after weighting. In the case of
calorimetric photons, an additional weighting process is required in order to
recover kinematic distributions of final-state photons observed in the data as
well, in a similar event-by-event process as the weights obtained from
$\chi_{c1,2}$ kinematic distributions. The effect of the photon-identification
selection and the reproducibility of relevant variables in simulation are also
taken into account. For the converted $\chi_{c1,2}$ sample, the total
systematic uncertainty on the acceptance and efficiency equals $9.6\%$ at
forward and $14.9\%$ at backward rapidity, while for the calorimetric sample
the uncertainty is $8.1\%$ at forward rapidity and $12.4\%$ at backward
rapidity. The ratio of the branching fractions of the
${\chi_{{c}1,2}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}\gamma$ decays
contributes with an uncertainty of $3.9\%$. A summary of contributions to the
statistical and systematic uncertainties of each analyzed sample is given in
Table 2.

Table 2:  Statistical and systematic uncertainties on the cross-section ratio, $\sigma({\chi_{{c}2}})/\sigma({\chi_{{c}1}})$. The total systematic uncertainty is also quoted. Analyzed sample | Source | $1.5<y^{*}<4.0$ | $-5.0<y^{*}<-2.5$
---|---|---|---
Converted photons | Signal extraction | $4.9\%$ | $3.2\%$
Limited simulation sample size | $5.6\%$ | $6.5\%$
Efficiency correction | $7.7\%$ | $13.4\%$
Branching fraction ratio | $3.9\%$ | $3.9\%$
Total systematic uncertainty | $11.4\%$ | $15.7\%$
Statistical uncertainty | $45.2\%$ | $47.0\%$
Calorimetric photons | Signal extraction | $2.6\%$ | $6.8\%$
Limited simulation sample size | $2.5\%$ | $2.8\%$
Efficiency correction | $7.7\%$ | $12.1\%$
Branching fraction ratio | $3.9\%$ | $3.9\%$
Total systematic uncertainty | $9.3\%$ | $14.7\%$
Statistical uncertainty | $12.2\%$ | $14.2\%$

##  6 Results

The prompt-production cross-section ratio
$\sigma({\chi_{{c}2}})/\sigma({\chi_{{c}1}})$ in $p$Pb collisions at the
center-of-mass energy per nucleon pair
$\sqrt{s_{\scriptscriptstyle\text{NN}}}$ = 8.16 TeV is shown for the two
rapidity regions in Fig. 3. The ratio measured from converted photons amounts
to

$\displaystyle\frac{\sigma({\chi_{{c}2}})}{\sigma({\chi_{{c}1}})}$
$\displaystyle=0.92\pm 0.42\mbox{ (stat.) }\pm 0.11\mbox{ (syst.) }$
$\displaystyle\mbox{ for }1.5<y^{*}<4.0,$
$\displaystyle\frac{\sigma({\chi_{{c}2}})}{\sigma({\chi_{{c}1}})}$
$\displaystyle=0.98\pm 0.46\mbox{ (stat.) }\pm 0.15\mbox{ (syst.) }$
$\displaystyle\mbox{ for }-5.0<y^{*}<-2.5.$

The ratio measured from calorimetric photons is found to be

$\displaystyle\frac{\sigma({\chi_{{c}2}})}{\sigma({\chi_{{c}1}})}$
$\displaystyle=1.11\pm 0.14\mbox{ (stat.) }\pm 0.10\mbox{ (syst.) }$
$\displaystyle\mbox{ for }1.5<y^{*}<4.0,$
$\displaystyle\frac{\sigma({\chi_{{c}2}})}{\sigma({\chi_{{c}1}})}$
$\displaystyle=1.14\pm 0.16\mbox{ (stat.) }\pm 0.17\mbox{ (syst.) }$
$\displaystyle\mbox{ for }-5.0<y^{*}<-2.5.$

The cross-section ratios for both converted and calorimetric samples are
consistent with unity in both rapidity regions. The significantly larger yield
of the calorimetric sample allows more precise conclusions on the observed
trend to be drawn.

The cross-section ratio obtained in $p$Pb data is compared with the
corresponding ratio measured in $pp$ collisions at $\sqrt{s}$ = 7 TeV by the
LHCb collaboration [16]. The two measurements are consistent within two
standard deviations. While the ratio in the $pp$ data was measured at a lower
center-of-mass energy than that of $p$Pb collisions, results show that the
relative cross-section of different charmonium states is independent of energy
at the LHC energy scale [36]. Thus, the only aspect to consider in a direct
comparison between the shown $p$Pb and $pp$ data is the rapidity range, where
the $p$Pb results are shifted by $-0.5$ in rapidity. Bearing that in mind, we
can express the relative suppression of $\chi_{c2}$ and $\chi_{c1}$ states via
the ratio of their nuclear modification factors

$\mathcal{R}\equiv\frac{\sigma({\chi_{{c}2}})/\sigma({\chi_{{c}1}})\scalebox{1.5}{$|$}_{p{\rm
Pb}}}{\sigma({\chi_{{c}2}})/\sigma({\chi_{{c}1}})\scalebox{1.5}{$|$}_{pp}}.$
(3)

Using the more precise calorimetric $p$Pb results, the ratio of nuclear-
modification factors amounts to $\mathcal{R}=1.41\pm 0.21\mbox{ (stat.) }\pm
0.18\mbox{ (syst.)}$ at forward and $\mathcal{R}=1.44\pm 0.24\mbox{ (stat.)
}\pm 0.25\mbox{ (syst.)}$ at backward rapidity, showing no significant change
relative to the $pp$ ratio in either rapidity region. The measured cross-
section ratio and ratio of nuclear-modification factors suggest that the
nuclear effects have the same impact on both ${\chi_{{c}1}}$ and
${\chi_{{c}2}}$ states within uncertainties, independent of rapidity.

Figure 3:  Cross-section ratio, $\sigma({\chi_{{c}2}})/\sigma({\chi_{{c}1}})$
as a function of center-of-mass rapidity $y^{*}$, for the ${\chi_{{c}2}}$ and
${\chi_{{c}1}}$ promptly produced in $p$Pb collisions measured using converted
photons (red circles) and calorimetric photons (blue squares). The error bars
correspond to the total uncertainties. Blue points and vertical uncertainties
are shifted horizontally to improve visibility. The $p$Pb data are compared
with results of the converted sample in $pp$ collisions at $\sqrt{s}$ = 7 TeV
[16] (yellow triangles).

##  7 Summary

In summary, we present the first measurement of $\chi_{c1,2}$ charmonium
production in nuclear collisions at the LHC. The cross-section ratio
$\sigma({\chi_{{c}2}})/\sigma({\chi_{{c}1}})$ is consistent with unity for
both forward and backward rapidity regions. Moreover, comparison with the
ratio measured in $pp$ collisions hints at a suppression pattern between the
two states, which is comparable within uncertainties. This suggests that the
final-state nuclear effects impact the ${\chi_{{c}1}}$ and ${\chi_{{c}2}}$
states similarly within the achieved precision.

## 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); MOST
and NSFC (China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN
(Italy); NWO (Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MSHE
(Russia); MICINN (Spain); SNSF and SER (Switzerland); NASU (Ukraine); STFC
(United Kingdom); DOE NP and NSF (USA). We acknowledge the computing resources
that are provided by CERN, IN2P3 (France), KIT and DESY (Germany), INFN
(Italy), SURF (Netherlands), PIC (Spain), GridPP (United Kingdom), RRCKI and
Yandex LLC (Russia), CSCS (Switzerland), IFIN-HH (Romania), CBPF (Brazil), PL-
GRID (Poland) and NERSC (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 ARC and ARDC (Australia); AvH Foundation
(Germany); EPLANET, Marie Skłodowska-Curie Actions and ERC (European Union);
A*MIDEX, ANR, Labex P2IO and OCEVU, and Région Auvergne-Rhône-Alpes (France);
Key Research Program of Frontier Sciences of CAS, CAS PIFI, CAS CCEPP,
Fundamental Research Funds for the Central Universities, and Sci. & Tech.
Program of Guangzhou (China); RFBR, RSF and Yandex LLC (Russia); GVA, XuntaGal
and GENCAT (Spain); the Leverhulme Trust, the Royal Society and UKRI (United
Kingdom).

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LHCb collaboration

R. Aaij32, C. Abellán Beteta50, T. Ackernley60, B. Adeva46, M. Adinolfi54, H.
Afsharnia9, C.A. Aidala85, S. Aiola25, Z. Ajaltouni9, S. Akar65, J.
Albrecht15, F. Alessio48, M. Alexander59, A. Alfonso Albero45, Z. Aliouche62,
G. Alkhazov38, P. Alvarez Cartelle55, S. Amato2, Y. Amhis11, L. An48, L.
Anderlini22, A. Andreianov38, M. Andreotti21, F. Archilli17, A. Artamonov44,
M. Artuso68, K. Arzymatov42, E. Aslanides10, M. Atzeni50, B. Audurier12, S.
Bachmann17, M. Bachmayer49, J.J. Back56, S. Baker61, P. Baladron Rodriguez46,
V. Balagura12, W. Baldini21,48, J. Baptista Leite1, R.J. Barlow62, S.
Barsuk11, W. Barter61, M. Bartolini24, F. Baryshnikov82, J.M. Basels14, G.
Bassi29, B. Batsukh68, A. Battig15, A. Bay49, M. Becker15, F. Bedeschi29, I.
Bediaga1, A. Beiter68, V. Belavin42, S. Belin27, V. Bellee49, K. Belous44, I.
Belov40, I. Belyaev41, G. Bencivenni23, E. Ben-Haim13, A. Berezhnoy40, R.
Bernet50, D. Berninghoff17, H.C. Bernstein68, C. Bertella48, A. Bertolin28, C.
Betancourt50, F. Betti20,d, Ia. Bezshyiko50, S. Bhasin54, J. Bhom35, L.
Bian73, M.S. Bieker15, S. Bifani53, P. Billoir13, M. Birch61, F.C.R. Bishop55,
A. Bitadze62, A. Bizzeti22,k, M. Bjørn63, M.P. Blago48, T. Blake56, F.
Blanc49, S. Blusk68, D. Bobulska59, J.A. Boelhauve15, O. Boente Garcia46, T.
Boettcher64, A. Boldyrev81, A. Bondar43, N. Bondar38,48, S. Borghi62, M.
Borisyak42, M. Borsato17, J.T. Borsuk35, S.A. Bouchiba49, T.J.V. Bowcock60, A.
Boyer48, C. Bozzi21, M.J. Bradley61, S. Braun66, A. Brea Rodriguez46, M.
Brodski48, J. Brodzicka35, A. Brossa Gonzalo56, D. Brundu27, A. Buonaura50, C.
Burr48, A. Bursche27, A. Butkevich39, J.S. Butter32, J. Buytaert48, W.
Byczynski48, S. Cadeddu27, H. Cai73, R. Calabrese21,f, L. Calefice15,13, L.
Calero Diaz23, S. Cali23, R. Calladine53, M. Calvi26,j, M. Calvo Gomez84, P.
Camargo Magalhaes54, A. Camboni45,84, P. Campana23, A.F. Campoverde Quezada6,
S. Capelli26,j, L. Capriotti20,d, A. Carbone20,d, G. Carboni31, R.
Cardinale24,h, A. Cardini27, I. Carli4, P. Carniti26,j, L. Carus14, K.
Carvalho Akiba32, A. Casais Vidal46, G. Casse60, M. Cattaneo48, G.
Cavallero48, S. Celani49, J. Cerasoli10, A.J. Chadwick60, M.G. Chapman54, M.
Charles13, Ph. Charpentier48, G. Chatzikonstantinidis53, C.A. Chavez
Barajas60, M. Chefdeville8, C. Chen3, S. Chen27, A. Chernov35, V. Chobanova46,
S. Cholak49, M. Chrzaszcz35, A. Chubykin38, V. Chulikov38, P. Ciambrone23,
M.F. Cicala56, X. Cid Vidal46, G. Ciezarek48, P.E.L. Clarke58, M. Clemencic48,
H.V. Cliff55, J. Closier48, J.L. Cobbledick62, V. Coco48, J.A.B. Coelho11, J.
Cogan10, E. Cogneras9, L. Cojocariu37, P. Collins48, T. Colombo48, L.
Congedo19,c, A. Contu27, N. Cooke53, G. Coombs59, G. Corti48, C.M. Costa
Sobral56, B. Couturier48, D.C. Craik64, J. Crkovská67, M. Cruz Torres1, R.
Currie58, C.L. Da Silva67, E. Dall’Occo15, J. Dalseno46, C. D’Ambrosio48, A.
Danilina41, P. d’Argent48, A. Davis62, O. De Aguiar Francisco62, K. De
Bruyn78, S. De Capua62, M. De Cian49, J.M. De Miranda1, L. De Paula2, M. De
Serio19,c, D. De Simone50, P. De Simone23, J.A. de Vries79, C.T. Dean67, D.
Decamp8, L. Del Buono13, B. Delaney55, H.-P. Dembinski15, A. Dendek34, V.
Denysenko50, D. Derkach81, O. Deschamps9, F. Desse11, F. Dettori27,e, B.
Dey73, P. Di Nezza23, S. Didenko82, L. Dieste Maronas46, H. Dijkstra48, V.
Dobishuk52, A.M. Donohoe18, F. Dordei27, A.C. dos Reis1, L. Douglas59, A.
Dovbnya51, A.G. Downes8, K. Dreimanis60, M.W. Dudek35, L. Dufour48, V. Duk77,
P. Durante48, J.M. Durham67, D. Dutta62, M. Dziewiecki17, A. Dziurda35, A.
Dzyuba38, S. Easo57, U. Egede69, V. Egorychev41, S. Eidelman43,v, S.
Eisenhardt58, S. Ek-In49, L. Eklund59,w, S. Ely68, A. Ene37, E. Epple67, S.
Escher14, J. Eschle50, S. Esen32, T. Evans48, A. Falabella20, J. Fan3, Y.
Fan6, B. Fang73, S. Farry60, D. Fazzini26,j, P. Fedin41, M. Féo48, P.
Fernandez Declara48, A. Fernandez Prieto46, J.M. Fernandez-tenllado Arribas45,
F. Ferrari20,d, L. Ferreira Lopes49, F. Ferreira Rodrigues2, S. Ferreres
Sole32, M. Ferrillo50, M. Ferro-Luzzi48, S. Filippov39, R.A. Fini19, M.
Fiorini21,f, M. Firlej34, K.M. Fischer63, C. Fitzpatrick62, T. Fiutowski34, F.
Fleuret12, M. Fontana13, F. Fontanelli24,h, R. Forty48, V. Franco Lima60, M.
Franco Sevilla66, M. Frank48, E. Franzoso21, G. Frau17, C. Frei48, D.A.
Friday59, J. Fu25, Q. Fuehring15, W. Funk48, E. Gabriel32, T. Gaintseva42, A.
Gallas Torreira46, D. Galli20,d, S. Gambetta58,48, Y. Gan3, M. Gandelman2, P.
Gandini25, Y. Gao5, M. Garau27, L.M. Garcia Martin56, P. Garcia Moreno45, J.
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C. Gaspar48, R.E. Geertsema32, D. Gerick17, L.L. Gerken15, E. Gersabeck62, M.
Gersabeck62, T. Gershon56, D. Gerstel10, Ph. Ghez8, V. Gibson55, H.K.
Giemza36, M. Giovannetti23,p, A. Gioventù46, P. Gironella Gironell45, L.
Giubega37, C. Giugliano21,f,48, K. Gizdov58, E.L. Gkougkousis48, V.V.
Gligorov13, C. Göbel70, E. Golobardes84, D. Golubkov41, A. Golutvin61,82, A.
Gomes1,a, S. Gomez Fernandez45, F. Goncalves Abrantes63, M. Goncerz35, G.
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Grabowski17, R. Graciani Diaz45, T. Grammatico13, L.A. Granado Cardoso48, E.
Graugés45, E. Graverini49, G. Graziani22, A. Grecu37, L.M. Greeven32, P.
Griffith21,f, L. Grillo62, S. Gromov82, B.R. Gruberg Cazon63, C. Gu3, M.
Guarise21, P. A. Günther17, E. Gushchin39, A. Guth14, Y. Guz44,48, T. Gys48,
T. Hadavizadeh69, G. Haefeli49, C. Haen48, J. Haimberger48, T. Halewood-
leagas60, P.M. Hamilton66, Q. Han7, X. Han17, T.H. Hancock63, S. Hansmann-
Menzemer17, N. Harnew63, T. Harrison60, C. Hasse48, M. Hatch48, J. He6,b, M.
Hecker61, K. Heijhoff32, K. Heinicke15, A.M. Hennequin48, K. Hennessy60, L.
Henry25,47, J. Heuel14, A. Hicheur2, D. Hill49, M. Hilton62, S.E. Hollitt15,
J. Hu17, J. Hu72, W. Hu7, W. Huang6, X. Huang73, W. Hulsbergen32, R.J.
Hunter56, M. Hushchyn81, D. Hutchcroft60, D. Hynds32, P. Ibis15, M. Idzik34,
D. Ilin38, P. Ilten65, A. Inglessi38, A. Ishteev82, K. Ivshin38, R.
Jacobsson48, S. Jakobsen48, E. Jans32, B.K. Jashal47, A. Jawahery66, V.
Jevtic15, M. Jezabek35, F. Jiang3, M. John63, D. Johnson48, C.R. Jones55, T.P.
Jones56, B. Jost48, N. Jurik48, S. Kandybei51, Y. Kang3, M. Karacson48, M.
Karpov81, N. Kazeev81, F. Keizer55,48, M. Kenzie56, T. Ketel33, B. Khanji15,
A. Kharisova83, S. Kholodenko44, K.E. Kim68, T. Kirn14, V.S. Kirsebom49, O.
Kitouni64, S. Klaver32, K. Klimaszewski36, S. Koliiev52, A. Kondybayeva82, A.
Konoplyannikov41, P. Kopciewicz34, R. Kopecna17, P. Koppenburg32, M.
Korolev40, I. Kostiuk32,52, O. Kot52, S. Kotriakhova38,30, P. Kravchenko38, L.
Kravchuk39, R.D. Krawczyk48, M. Kreps56, F. Kress61, S. Kretzschmar14, P.
Krokovny43,v, W. Krupa34, W. Krzemien36, W. Kucewicz35,t, M. Kucharczyk35, V.
Kudryavtsev43,v, H.S. Kuindersma32, G.J. Kunde67, T. Kvaratskheliya41, D.
Lacarrere48, G. Lafferty62, A. Lai27, A. Lampis27, D. Lancierini50, J.J.
Lane62, R. Lane54, G. Lanfranchi23, C. Langenbruch14, J. Langer15, O.
Lantwin50,82, T. Latham56, F. Lazzari29,q, R. Le Gac10, S.H. Lee85, R.
Lefèvre9, A. Leflat40, S. Legotin82, O. Leroy10, T. Lesiak35, B.
Leverington17, H. Li72, L. Li63, P. Li17, Y. Li4, Y. Li4, Z. Li68, X. Liang68,
T. Lin61, R. Lindner48, V. Lisovskyi15, R. Litvinov27, G. Liu72, H. Liu6, S.
Liu4, X. Liu3, A. Loi27, J. Lomba Castro46, I. Longstaff59, J.H. Lopes2, G.H.
Lovell55, Y. Lu4, D. Lucchesi28,l, S. Luchuk39, M. Lucio Martinez32, V.
Lukashenko32, Y. Luo3, A. Lupato62, E. Luppi21,f, O. Lupton56, A. Lusiani29,m,
X. Lyu6, L. Ma4, R. Ma6, S. Maccolini20,d, F. Machefert11, F. Maciuc37, V.
Macko49, P. Mackowiak15, S. Maddrell-Mander54, O. Madejczyk34, L.R. Madhan
Mohan54, O. Maev38, A. Maevskiy81, D. Maisuzenko38, M.W. Majewski34, J.J.
Malczewski35, S. Malde63, B. Malecki48, A. Malinin80, T. Maltsev43,v, H.
Malygina17, G. Manca27,e, G. Mancinelli10, R. Manera Escalero45, D.
Manuzzi20,d, D. Marangotto25,i, J. Maratas9,s, J.F. Marchand8, U. Marconi20,
S. Mariani22,g,48, C. Marin Benito11, M. Marinangeli49, P. Marino49,m, J.
Marks17, P.J. Marshall60, G. Martellotti30, L. Martinazzoli48,j, M.
Martinelli26,j, D. Martinez Santos46, F. Martinez Vidal47, A. Massafferri1, M.
Materok14, R. Matev48, A. Mathad50, Z. Mathe48, V. Matiunin41, C. Matteuzzi26,
K.R. Mattioli85, A. Mauri32, E. Maurice12, J. Mauricio45, M. Mazurek36, M.
McCann61, L. Mcconnell18, T.H. Mcgrath62, A. McNab62, R. McNulty18, J.V.
Mead60, B. Meadows65, C. Meaux10, G. Meier15, N. Meinert76, D. Melnychuk36, S.
Meloni26,j, M. Merk32,79, A. Merli25, L. Meyer Garcia2, M. Mikhasenko48, D.A.
Milanes74, E. Millard56, M. Milovanovic48, M.-N. Minard8, L. Minzoni21,f, S.E.
Mitchell58, B. Mitreska62, D.S. Mitzel48, A. Mödden 15, R.A. Mohammed63, R.D.
Moise61, T. Mombächer15, I.A. Monroy74, S. Monteil9, M. Morandin28, G.
Morello23, M.J. Morello29,m, J. Moron34, A.B. Morris75, A.G. Morris56, R.
Mountain68, H. Mu3, F. Muheim58,48, M. Mukherjee7, M. Mulder48, D. Müller48,
K. Müller50, C.H. Murphy63, D. Murray62, P. Muzzetto27,48, P. Naik54, T.
Nakada49, R. Nandakumar57, T. Nanut49, I. Nasteva2, M. Needham58, I. Neri21,
N. Neri25,i, S. Neubert75, N. Neufeld48, R. Newcombe61, T.D. Nguyen49, C.
Nguyen-Mau49,x, E.M. Niel11, S. Nieswand14, N. Nikitin40, N.S. Nolte48, C.
Nunez85, A. Oblakowska-Mucha34, V. Obraztsov44, D.P. O’Hanlon54, R.
Oldeman27,e, M.E. Olivares68, C.J.G. Onderwater78, A. Ossowska35, J.M. Otalora
Goicochea2, T. Ovsiannikova41, P. Owen50, A. Oyanguren47, B. Pagare56, P.R.
Pais48, T. Pajero29,m,48, A. Palano19, M. Palutan23, Y. Pan62, G. Panshin83,
A. Papanestis57, M. Pappagallo19,c, L.L. Pappalardo21,f, C. Pappenheimer65, W.
Parker66, C. Parkes62, C.J. Parkinson46, B. Passalacqua21, G. Passaleva22, A.
Pastore19, M. Patel61, C. Patrignani20,d, C.J. Pawley79, A. Pearce48, A.
Pellegrino32, M. Pepe Altarelli48, S. Perazzini20, D. Pereima41, P. Perret9,
K. Petridis54, A. Petrolini24,h, A. Petrov80, S. Petrucci58, M. Petruzzo25,
T.T.H. Pham68, A. Philippov42, L. Pica29,n, M. Piccini77, B. Pietrzyk8, G.
Pietrzyk49, M. Pili63, D. Pinci30, F. Pisani48, A. Piucci17, Resmi P.K10, V.
Placinta37, J. Plews53, M. Plo Casasus46, F. Polci13, M. Poli Lener23, M.
Poliakova68, A. Poluektov10, N. Polukhina82,u, I. Polyakov68, E. Polycarpo2,
G.J. Pomery54, S. Ponce48, D. Popov6,48, S. Popov42, S. Poslavskii44, K.
Prasanth35, L. Promberger48, C. Prouve46, V. Pugatch52, H. Pullen63, G.
Punzi29,n, W. Qian6, J. Qin6, R. Quagliani13, B. Quintana8, N.V. Raab18, R.I.
Rabadan Trejo10, B. Rachwal34, J.H. Rademacker54, M. Rama29, M. Ramos
Pernas56, M.S. Rangel2, F. Ratnikov42,81, G. Raven33, M. Reboud8, F. Redi49,
F. Reiss13, C. Remon Alepuz47, Z. Ren3, V. Renaudin63, R. Ribatti29, S.
Ricciardi57, K. Rinnert60, P. Robbe11, A. Robert13, G. Robertson58, A.B.
Rodrigues49, E. Rodrigues60, J.A. Rodriguez Lopez74, A. Rollings63, P.
Roloff48, V. Romanovskiy44, M. Romero Lamas46, A. Romero Vidal46, J.D. Roth85,
M. Rotondo23, M.S. Rudolph68, T. Ruf48, J. Ruiz Vidal47, A. Ryzhikov81, J.
Ryzka34, J.J. Saborido Silva46, N. Sagidova38, N. Sahoo56, B. Saitta27,e, D.
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Rios46, M. Santimaria23, E. Santovetti31,p, D. Saranin82, G. Sarpis59, M.
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H. Sazak9, L.G. Scantlebury Smead63, S. Schael14, M. Schellenberg15, M.
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J.G. Smeaton55, A. Smetkina41, E. Smith14, M. Smith61, A. Snoch32, M.
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O. Steinkamp50,82, S. Stemmle17, O. Stenyakin44, H. Stevens15, S. Stone68,
M.E. Stramaglia49, M. Straticiuc37, D. Strekalina82, F. Suljik63, J. Sun27, L.
Sun73, Y. Sun66, P. Svihra62, P.N. Swallow53, K. Swientek34, A. Szabelski36,
T. Szumlak34, M. Szymanski48, S. Taneja62, F. Teubert48, E. Thomas48, K.A.
Thomson60, M.J. Tilley61, V. Tisserand9, S. T’Jampens8, M. Tobin4, S. Tolk48,
L. Tomassetti21,f, D. Torres Machado1, D.Y. Tou13, M. Traill59, M.T. Tran49,
E. Trifonova82, C. Trippl49, G. Tuci29,n, A. Tully49, N. Tuning32,48, A.
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Wilson57, W. Wislicki36, M. Witek35, L. Witola17, G. Wormser11, S.A. Wotton55,
H. Wu68, K. Wyllie48, Z. Xiang6, D. Xiao7, Y. Xie7, A. Xu5, J. Xu6, L. Xu3, M.
Xu7, Q. Xu6, Z. Xu5, Z. Xu6, D. Yang3, S. Yang6, Y. Yang6, Z. Yang3, Z.
Yang66, Y. Yao68, L.E. Yeomans60, H. Yin7, J. Yu71, X. Yuan68, O.
Yushchenko44, E. Zaffaroni49, K.A. Zarebski53, M. Zavertyaev16,u, M. Zdybal35,
O. Zenaiev48, M. Zeng3, D. Zhang7, L. Zhang3, S. Zhang5, Y. Zhang5, Y.
Zhang63, A. Zhelezov17, Y. Zheng6, X. Zhou6, Y. Zhou6, X. Zhu3, V.
Zhukov14,40, J.B. Zonneveld58, S. Zucchelli20,d, D. Zuliani28, G. Zunica62.

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
4Institute Of High Energy Physics (IHEP), Beijing, China
5School of Physics State Key Laboratory of Nuclear Physics and Technology,
Peking University, Beijing, China
6University of Chinese Academy of Sciences, Beijing, China
7Institute of Particle Physics, Central China Normal University, Wuhan, Hubei,
China
8Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, IN2P3-LAPP, Annecy,
France
9Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France
10Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France
11Université Paris-Saclay, CNRS/IN2P3, IJCLab, Orsay, France
12Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, Institut
Polytechnique de Paris, Palaiseau, France
13LPNHE, Sorbonne Université, Paris Diderot Sorbonne Paris Cité, CNRS/IN2P3,
Paris, France
14I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
15Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
16Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
17Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
18School of Physics, University College Dublin, Dublin, Ireland
19INFN Sezione di Bari, Bari, Italy
20INFN Sezione di Bologna, Bologna, Italy
21INFN Sezione di Ferrara, Ferrara, Italy
22INFN Sezione di Firenze, Firenze, Italy
23INFN Laboratori Nazionali di Frascati, Frascati, Italy
24INFN Sezione di Genova, Genova, Italy
25INFN Sezione di Milano, Milano, Italy
26INFN Sezione di Milano-Bicocca, Milano, Italy
27INFN Sezione di Cagliari, Monserrato, Italy
28Universita degli Studi di Padova, Universita e INFN, Padova, Padova, Italy
29INFN Sezione di Pisa, Pisa, Italy
30INFN Sezione di Roma La Sapienza, Roma, Italy
31INFN Sezione di Roma Tor Vergata, Roma, Italy
32Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands
33Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, Netherlands
34AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
35Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
36National Center for Nuclear Research (NCBJ), Warsaw, Poland
37Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
38Petersburg Nuclear Physics Institute NRC Kurchatov Institute (PNPI NRC KI),
Gatchina, Russia
39Institute for Nuclear Research of the Russian Academy of Sciences (INR RAS),
Moscow, Russia
40Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
41Institute of Theoretical and Experimental Physics NRC Kurchatov Institute
(ITEP NRC KI), Moscow, Russia
42Yandex School of Data Analysis, Moscow, Russia
43Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia
44Institute for High Energy Physics NRC Kurchatov Institute (IHEP NRC KI),
Protvino, Russia, Protvino, Russia
45ICCUB, Universitat de Barcelona, Barcelona, Spain
46Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de
Santiago de Compostela, Santiago de Compostela, Spain
47Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia -
CSIC, Valencia, Spain
48European Organization for Nuclear Research (CERN), Geneva, Switzerland
49Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL),
Lausanne, Switzerland
50Physik-Institut, Universität Zürich, Zürich, Switzerland
51NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
52Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
53University of Birmingham, Birmingham, United Kingdom
54H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
55Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
56Department of Physics, University of Warwick, Coventry, United Kingdom
57STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
58School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
59School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
60Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
61Imperial College London, London, United Kingdom
62Department of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
63Department of Physics, University of Oxford, Oxford, United Kingdom
64Massachusetts Institute of Technology, Cambridge, MA, United States
65University of Cincinnati, Cincinnati, OH, United States
66University of Maryland, College Park, MD, United States
67Los Alamos National Laboratory (LANL), Los Alamos, United States
68Syracuse University, Syracuse, NY, United States
69School of Physics and Astronomy, Monash University, Melbourne, Australia,
associated to 56
70Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
71Physics and Micro Electronic College, Hunan University, Changsha City,
China, associated to 7
72Guangdong Provencial Key Laboratory of Nuclear Science, Institute of Quantum
Matter, South China Normal University, Guangzhou, China, associated to 3
73School of Physics and Technology, Wuhan University, Wuhan, China, associated
to 3
74Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 13
75Universität Bonn - Helmholtz-Institut für Strahlen und Kernphysik, Bonn,
Germany, associated to 17
76Institut für Physik, Universität Rostock, Rostock, Germany, associated to 17
77INFN Sezione di Perugia, Perugia, Italy, associated to 21
78Van Swinderen Institute, University of Groningen, Groningen, Netherlands,
associated to 32
79Universiteit Maastricht, Maastricht, Netherlands, associated to 32
80National Research Centre Kurchatov Institute, Moscow, Russia, associated to
41
81National Research University Higher School of Economics, Moscow, Russia,
associated to 42
82National University of Science and Technology “MISIS”, Moscow, Russia,
associated to 41
83National Research Tomsk Polytechnic University, Tomsk, Russia, associated to
41
84DS4DS, La Salle, Universitat Ramon Llull, Barcelona, Spain, associated to 45
85University of Michigan, Ann Arbor, United States, associated to 68

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bHangzhou Institute for Advanced Study, UCAS, Hangzhou, China
cUniversità di Bari, Bari, Italy
dUniversità di Bologna, Bologna, Italy
eUniversità di Cagliari, Cagliari, Italy
fUniversità di Ferrara, Ferrara, Italy
gUniversità di Firenze, Firenze, Italy
hUniversità di Genova, Genova, Italy
iUniversità degli Studi di Milano, Milano, Italy
jUniversità di Milano Bicocca, Milano, Italy
kUniversità di Modena e Reggio Emilia, Modena, Italy
lUniversità di Padova, Padova, Italy
mScuola Normale Superiore, Pisa, Italy
nUniversità di Pisa, Pisa, Italy
oUniversità della Basilicata, Potenza, Italy
pUniversità di Roma Tor Vergata, Roma, Italy
qUniversità di Siena, Siena, Italy
rUniversità di Urbino, Urbino, Italy
sMSU - Iligan Institute of Technology (MSU-IIT), Iligan, Philippines
tAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
uP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
vNovosibirsk State University, Novosibirsk, Russia
wDepartment of Physics and Astronomy, Uppsala University, Uppsala, Sweden
xHanoi University of Science, Hanoi, Vietnam


# Sensitivity to eV-scale Neutrinos of Experiments at a
Very Low Energy Neutrino Factory

J.H. Cobb  C.D. Tunnell  Corresponding author<EMAIL_ADDRESS>Subdepartment
of Particle Physics, University of Oxford, Denys Wilkinson Building, Keble
Road, Oxford, OX1 3RH, UK  A.D. Bross  Fermilab, P.O. Box 500, Batavia, IL
60510-0500, USA

###### Abstract

The results of LSND have yet to be confirmed at the $5\sigma$-level. An
experiment is proposed utilizing a 3 GeV muon storage ring that would allow
for both disappearance and appearance channels to be explored at short-
baselines. The appearance channel could provide well over $5\sigma$
confirmation or rejection of the LSND result. Other physics could also be
performed at such a facility such as the measurement of electron-neutrino
cross sections. The sensitivity of experiments at a Very Low Energy Neutrino
Factory (VLENF) to neutrinos at the eV-scale is presented.

Suggested keywords

###### pacs:

14.60.Pq, 14.60.St

††preprint: APS/123-QED

Despite the experimental success of the past decade in establishing that
neutrinos are massive and mix, whether they be produced in the Sun Aharmim
_et al._ (2008), reactors Ahn  _et al._ (2006), accelerators Adamson  _et al._
(2008), or the atmosphere Wendell  _et al._ (2010), there exist nevertheless
some anomalies. All oscillation experiments to date can be explained with
three neutrinos except LSND — and various experiments could be made to agree
with either. The LEP collider experiments lep (2006) showed that additional
light neutrinos cannot couple to the $Z$. The MiniBooNe experiment has been
unable to deny or confirm the LSND result since their data that uses the same
anti-neutrino beam polarity as LSND agrees with the background-only hypothesis
at 0.5% and agrees with short-baseline oscillations at 8.7% Aguilar-Arevalo
_et al._ (2010). An experiment with a sensitivity greater than $5\sigma$ is
needed in order to refute or confirm evidence of neutrinos at the eV-scale.

The LSND data suggests a new mass splitting Athanassopoulos  _et al._ (1998)
that is potentially observed elsewhere. Recently, a recalculation of reactor
fluxes resulted in the _reactor neutrino anomaly_ Mueller  _et al._ (2011);
Huber (2011) which, along with the _Gallium anomaly_ Acero  _et al._ (2008),
are possibly caused by sterile neutrinos. Global fits reconcile these
anomalies into a framework that introduces a sterile neutrino at the eV-scale,
_e.g._ , Giunti and Laveder (2011a); Kopp  _et al._ (2011). Additional
indications come from cosmology where WMAP favors more than three neutrinos
Komatsu  _et al._ (2011).

The Very Low Energy Neutrino Factory (VLENF) would utilize a muon storage ring
to study eV-scale oscillation physics and measure cross sections (including
$\nu_{e}$). Pions are collected from a target and injected into a storage ring
where they decay to muons. The storage ring is optimized for 2 GeV muons where
the energy is optimized for the needs of both oscillation and cross section
physics. The muons decay according to $\mu^{+}\to
e^{+}\bar{\nu}_{\mu}\nu_{e}$. Straight sections in the storage ring result in
neutrinos directed at a near- and far-detector.

The storage ring could be a fixed field alternating gradient (FFAG) lattice
for large momentum acceptance, which is important given the large momentum
spectrum after the target. The pricing and engineering of FFAGs are well-
understood because of experience building them c:f (2005). The design would
require only normal conducting magnets which simplifies construction,
commissioning, and operations. Design work for the injection into the storage
ring and the particle collection downstream of the target are underway.

The near detector will be placed at 20-50 meters from the end of the straight
and will measure neutrino-nucleon cross sections of interest to future long-
baseline experiments including the first precision measurement of $\nu_{e}$
cross sections. The far detector at 800 m would measure disappearance and
wrong-sign muon appearance channels. The detector would need to be magnetized
for the wrong-sign muon appearance channel. Numerous possibilities exist for
detector technologies that include liquid argon, MINOS inspired, and totally
active scintillating detectors. For the purposes of this study, a detector
inspired by MINOS but with thinner plates is assumed. The experiment will take
advantage of the “golden channel” of oscillation appearance
$\nu_{e}\to\nu_{\mu}$ where the resulting final state is a wrong-sign muon.

The probability $\nu_{e}\to\nu_{\mu}$ depends on the mixing matrix, $U$. Let
$R_{ij}$ be a rotation between the $i$th and $j$th mass eigenstates without CP
violation. For $N$ neutrinos, $R_{ij}$ has dimension $N\times N$. By
convention, the three neutrino mixing matrix is
$U_{\text{PMNS}}=R_{23}R_{13}R_{12}$. In the (3+1) model of neutrino
oscillations, extra rotations can be introduced such that the mixing matrix is
$U_{\text{(3+1)}}=R_{34}R_{24}R_{14}U_{\text{PMNS}}$. Given that $\Delta
m^{2}_{41}>>\Delta m^{2}_{31}$, $U_{\text{PMNS}}$ can be approximated by the
identity matrix (_ie._ the “short-baseline approximation”). It then follows
that $|U_{e4}|^{2}=\sin(\theta_{14})$ and $|U_{\mu
4}|^{2}=\sin(\theta_{24})\cos(\theta_{14})$.

The oscillation probabilities for appearance and disappearance, respectively,
are:

$\displaystyle\text{P}_{\nu_{e}\to\nu_{\mu}}=$ $\displaystyle
4|U_{e4}|^{2}|U_{\mu 4}|^{2}\sin^{2}\left(\frac{\Delta
m^{2}_{41}L}{4E}\right),$ (1)
$\displaystyle\text{P}_{\nu_{\alpha}\to\nu_{\alpha}}=$ $\displaystyle
1-\left[4|U_{\alpha 4}|^{2}(1-|U_{\alpha
4}|^{2})\right]\sin^{2}\left(\frac{\Delta m^{2}_{41}L}{4E}\right).$ (2)

Disappearance measurements will constrain $|U_{\mu 4}|^{2}$ and $|U_{e4}|^{2}$
while the appearance channel measures their product $|U_{e4}|^{2}|U_{\mu
4}|^{2}$. These parameters are over-constrained. Only the appearance channel
will be assumed since the physics sensitivity of disappearance measurements is
well-understood for short-baseline experiments. Without oscillations there
would be $\sim 10^{5}$ charge current (CC) events in the far detector. The
disappearance oscillation probability, if LSND is correct, would be on the
order of a few percent for this experiment; the statistical errors and
systematic errors are expected to be about half a percent from the presence of
a near detector and beam instrumentation.

The oscillation sensitivities have been computed using the GLoBES software
(version 3.1.10) Huber  _et al._ (2005, 2007). Since GLoBES, by default, only
allows for a $3\times 3$ mixing matrix, the SNU (version 1.1) add-on Kopp
(2008); Kopp  _et al._ (2008) is used to extend computations in GLoBES to
$4\times 4$ mixing matrices.

Unlike previous analyses, the far detector approximation of the source and
detector being treated as point-sources cannot be used since the size of the
detector and accelerator straight are comparable to the baseline. This study
computes the neutrino flux by integrating the phase space of the stored muons
using Monte Carlo (MC) integration. The beam occupies a 6D phase space ($x$,
$y$, $z$, $p_{x}$, $p_{y}$, $p_{z}$) and the detector has a $6\text{ m}\times
6\text{ m}$ cross section. A random point is chosen within the beam phase
space and within the detector volume. The transverse phase space is
represented by the Twiss parameters $\alpha=0$ and $\beta=25\text{ m}$ where
the $1\sigma$ Gaussian emittance is assumed to be $15\text{ mm}$. It follows
that the spread in, for example, $x$ is $\sigma_{x}=\sqrt{\beta\epsilon}$ and
the angular divergence in $x$ is $\sigma_{x^{\prime}}=\sqrt{\epsilon/\beta}$.
The longitudinal phase space ($z$ and $p_{z}$) is described by assuming a
uniform distribution in $z$ and $p_{z}=(2\pm 20\%)\text{ GeV}$. The code for
the analysis herein is available online Tunnell (2011) under the GPL license
gpl .

This analysis assumes $2\times 10^{17}$ decays of $\mu^{+}$ in each straight,
normalized to an exposure similar to MiniBooNe of $10^{21}$ protons on target
(POT). The far detector at 800 m consists of a kilotonne of fiducial target
mass. The background rejection for the wrong-sign muons is assumed to be
$10^{-4}$ for the $\bar{\nu}_{\mu}\to\bar{\nu}_{\mu}$ neutral current (NC)
events and $10^{-5}$ for the charge misidentification of
$\bar{\nu}_{\mu}\to\bar{\nu}_{\mu}$ CC events. The backgrounds from
$\nu_{e}\to\nu_{e}$ CC and NC are negligible. The $\nu_{e}\to\nu_{\mu}$ CC
events have a 90% detection efficiency. These efficiencies were extrapolated
from previous studies Laing (2010) and reconfirmation of these calculations
for energies below 2 GeV is still required.

Figure 1: The oscillation probability for the “golden channel”
$\nu_{e}\to\nu_{\mu}$ using the (3+1) oscillation parameters in TABLE 1. A
baseline of 800 meters is assumed. This numerical treatment of the binned
oscillation probability agrees with Eq. 1.

To initially gauge the sensitivity of this experimental setup, some
oscillation parameters must be assumed that include the LSND effect. The best-
fit data for (3+1) sterile neutrinos is used Giunti and Laveder (2011b) where
the MB $\bar{\nu}$ and LSND $\bar{\nu}$ data was fit (TABLE 1). Lower energy
neutrinos contain the most information about the mixing matrix (FIG. 1).

Table 1: Best-fit oscillation parameters for the (3+1) sterile neutrino scenario for MB $\bar{\nu}$ and LSND $\bar{\nu}$ data Giunti and Laveder (2011b). Parameter | Value
---|---
$\Delta m^{2}_{41}$ [$\text{eV}^{2}$] | 0.89
$|U_{e4}|^{2}$ | 0.025
$|U_{\mu 4}|^{2}$ | 0.023
Figure 2: The spectrum of signal and background events at the far-detector.
The number of wrong-sign muon appearance signal events is 27 which arises
through the “golden channel” oscillation probability $\nu_{e}\to\nu_{\mu}$.
Roughly 2 background events are in the signal box and correspond to both
$\bar{\nu}_{\mu}$ CC with charge misidentification and $\bar{\nu}_{\mu}$ NC
events where a short-lived pion has faked a wrong-sign muon. An exposure of
$10^{21}$ POT is assumed.

The best-fit values allow for an estimation of the event rates. The true
number of events without efficiencies is shown in TABLE 2. Applying the
assumed efficiencies of $10^{-5}$ and $10^{-4}$ for
$\bar{\nu}_{\mu}\to\bar{\nu}_{\mu}$ CC and $\bar{\nu}_{X}\to\bar{\nu}_{X}$ NC,
respectively, reveals the event spectrum (FIG. 2). After cuts, there are 27
signal events and 2 background events.

Table 2: A table of the raw event rates. The first row corresponds to the “golden channel” appearance signal. The other rows are potential backgrounds to the signal. The background that drives the analysis is $\bar{\nu}_{\mu}\to\bar{\nu}_{\mu}$. Channel | Interaction | Pre-cuts
---|---|---
$\nu_{e}\to\nu_{\mu}$ | CC | 30
$\bar{\nu}_{X}\to\bar{\nu}_{X}$ | NC | 16850
$\bar{\nu}_{\mu}\to\bar{\nu}_{\mu}$ | CC | 42545
$\nu_{e}\to\nu_{e}$ | CC | 78974
Figure 3: Optimization of the mean stored muon energy and far detector
baseline. Above muon energies of 1 GeV, appearance physics is not sensitive to
the muon energy. For a fixed neutrino energy, the boosted muon frame will
result in more events the more it is boosted. The optimal baseline is around
800 meters.

In practice the muon energy is fixed by the needs of the cross section
physics. However, given a fixed fiducial mass, the baseline and muon energy
can be optimized for short-baseline physics. The metric for comparison is the
$\chi^{2}$ between simulations for the (3+1) best-fit mentioned earlier and
the background-only hypothesis. The short-baseline oscillation physics reach
is comparable at energies above 2 GeV and the optimal baseline is around 800
meters (FIG. 3).

Having chosen a baseline and energy, it is possible to investigate the physics
reach of this facility if we appropriately define the desired $\chi^{2}$
value. The design requirement is to measure the LSND effect at “$5\sigma$” but
that can be ambiguously defined. Herein “$n\sigma$” is defined according to
the Gaussian probability of the respective deviation. Let $\text{CDF}_{X}$ be
the cumulative distribution function of some distribution $X$. If $G$ is a
Gaussian with $\mu=0$ and $\sigma=1$, then the $p$-value of a $5\sigma$ effect
is $1-\text{CDF}_{G}(5)\simeq 3\times 10^{-7}$. Similarly, if $\chi^{2}_{2}$
is the chi-squared distribution with two degrees of freedom, then the required
value of the $\chi^{2}$ to be an $n\sigma$ effect is
$\text{CDF}^{-1}_{\chi^{2}_{2}}(\text{CDF}_{G}(n))$.

Figure 4: Sensitivity to sterile parameters. The orange band corresponds to
the LSND $\bar{\nu}$ and MiniBooNe $\bar{\nu}$ sterile neutrino fit performed
by Giunti and Laveder Giunti and Laveder (2011a) where they assumed only one
extra massive neutrino. The contours are the sensitivities of an experiment at
a 3 GeV FFAG storage ring using parameters defined in the text. The entire 99%
confidence interval for the LSND $\bar{\nu}$ and MiniBooNe $\bar{\nu}$ results
would be confirmed or excluded at $7\sigma$.

The $\chi^{2}$ is computed using the pull-method, which allows for systematics
to be included. The signal and background normalization errors are assigned to
be 2% and 20%, respectively, and these systematic uncertainties are
marginalized over. Spectral information is also used. The sensitivity to new
physics is shown in FIG. 4. The 99% confidence interval of a fit in a (3+1)
scheme to the MiniBooNe $\bar{\nu}$ and LSND $\bar{\nu}$ data is shown and
excluded at $7\sigma$. This meets and exceeds the requested criterion for
future eV-scale experiments.

Some effects are ignored that could reduce the significance of the result. For
example, not included are backgrounds associated with cosmic muons. This could
be problematic since muons fill the storage ring which results in a large duty
factor. One solution, if it is an issue, would be to put RF cavities in the
storage ring to bunch the beam. This merits further study.

It has been demonstrated that a VLENF has sensitivity to eV-scale
oscillations. Further optimizations of the target horn, collection, injection,
and the dynamic aperture of the storage ring will increase the neutrino flux.
But previously unthought-of backgrounds may arise and detector charge
identification performance is difficult at 1 GeV and below. A design study
must be performed to ensure enough contingency in the sensitivity to guarantee
a firm confirmation or refutation of the LSND effect. Further study is
required.

_Thanks_ for guidance and useful discussions with Joachim Kopp, David Neuffer,
Kenneth Long, and Alain Blondel. Also thanks to Nick Ryder for a careful
reading.

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