# Meta-Learning for Robust Child-Adult Classification from Speech

###### Abstract

Computational modeling of naturalistic conversations in clinical applications
has seen growing interest in the past decade. An important use-case involves
child-adult interactions within the autism diagnosis and intervention domain.
In this paper, we address a specific sub-problem of speaker diarization,
namely child-adult speaker classification in such dyadic conversations with
specified roles. Training a speaker classification system robust to speaker
and channel conditions is challenging due to inherent variability in the
speech within children and the adult interlocutors. In this work, we propose
the use of meta-learning, in particular prototypical networks which optimize a
metric space across multiple tasks. By modeling every child-adult pair in the
training set as a separate task during meta-training, we learn a
representation with improved generalizability compared to conventional
supervised learning. We demonstrate improvements over state-of-the-art speaker
embeddings (x-vectors) under two evaluation settings: weakly supervised
classification (upto 14.53% relative improvement in F1-scores) and clustering
(upto relative 9.66% improvement in cluster purity). Our results show that
protonets can potentially extract robust speaker embeddings for child-adult
classification from speech.

Index Terms—  Autism Spectrum Disorder, Child Speech, Prototypical Networks,
Speaker Classification

##  1 INTRODUCTION

Automated child speech understanding using machines is an inherently more
difficult problem than that of adult speech. A variety of factors have been
identified and addressed in recent years, both from a signal processing
viewpoint (such as large within- and across-age and gender variability due to
a developing vocal tract [1], errors in semantic structure of spoken language
[2]), and limited data availability which has necessitated data augmentation
and transfer learning techniques [3].

An additional layer of complexity arises when addressing clinical and mental
health applications involving children, where the condition may give rise to
speech and language abnormalities. One such domain is autism spectrum disorder
(ASD). ASD refers to a complex group of neuro-developmental disorders that are
commonly characterized by social and communication idiosyncrasies, and whose
reported prevalence in US children has been steadily rising (1 in 59 children
as of 2014 [4]). Child-adult interactions have been used in the ASD domain
primarily for diagnosis (ADOS [5]) and measuring intervention response (BOSCC
[6]). Automated computational processing of the participants’ audio [7] and
language streams [8] has provided objective descriptions that characterize the
session progress and understanding the relation with symptom severity.

However, behavioral feature extraction in above studies has necessitated
manual annotation for speaker labels, which can be expensive and time-
consuming to obtain especially for large corpora. Automatic speaker label
extraction involves a combination of speech activity detection (speech/non-
speech classification) and speaker classification (categorization of speech
regions into child and adult). In this work, we assume that oracle speech
activity detection is available and focus on building a robust child-adult
classification model.

Interest in child-adult speaker classification in spontaneous conversations
has increased recently. Some of the early works used traditional feature
representations such as MFCC, PLP and i-vectors, and clustering techniques
such as Bayesian information criterion, information bottleneck and
agglomerative hierarchical clustering [9, 10, 11, 12, 13]. In [14], speech
from children and adults was found to be sufficiently different in the
embedding space to justify speaker classification. A recent work using DNN
embeddings (x-vectors) explored augmentation of child speech for PLDA training
[15]. The authors also observed that splitting the adult speech into gender-
specific portions while training the PLDA returned improvements in diarization
performance. However, similar to most of the above works, the authors do not
make any distinctions within the child speech.

Training a conventional child-adult classifier from speech has at least two
major issues: 1) Large within-class variability especially for child from age,
gender, clinical symptom severity; and 2) Lack of sufficient amounts of
balanced training data needed to tackle the above issue. We propose to address
the above issues using meta-learning, also known as learning-to-learn [16].
Meta-learning consists of two optimizations: the conventional learner which
learns within a task; and a meta-learner which learns across tasks. This is in
contrast to conventional supervised learning, which operates within a single
task for training and testing, and learns across samples. Meta-learning is
inspired by the human learning process for rapid generalization to new tasks,
for instance children who have never seen a new animal before can learn to
identify them using only a handful of images. As a consequence, meta-learning
has demonstrated success in low-resource applications [17, 16] in computer
vision in recent years.

In this work, we model each session in the training set as a separate task.
Hence, each task consists of two classes: child and adult from the particular
session. During training, classes are not shared across tasks, i.e., child in
one session is a separate class from child in another session. By optimizing
the network to discriminate between child-adult speaker pairs across all
training tasks (sessions), we mitigate the influence of within-class
variabilities. Further, we remove the need for large amounts of training data
by randomly sampling training and testing subsets (referred to as supports and
queries respectively in meta-learning [17]) within each batch. We evaluate our
proposed method under two settings: 1) Weak supervision - a handful of labeled
examples are available from the test session, and 2) Unsupervised - automated
clustering. The latter is similar to conventional speaker clustering in
diarization systems. We show that the learnt representations outperform
baselines in both settings.

##  2 METHODS

###  2.1 Meta learning using prototypical networks

Meta-learning methods were introduced to address the problem of few-shot
learning [16], where only a handful of labeled examples are available in new
tasks not seen by the trained model. Deep metric-learning methods were
developed within the meta-learning paradigm to specifically address
generalization in the few-shot scenario. We choose prototypical networks
(protonets) [17] which presume a simple learning bias when compared to other
metric-learning methods, and have demonstrated state-of-the-art performance in
image classification [16] and natural language processing tasks such as
sequence classification [18]. Protonets learn a non-linear transformation into
an embedding space where each class is represented using a single sample,
specifically the centroid of examples from that class. During inference, a
test sample is assigned to the nearest centroid.

Our application of protonets for speaker classification is motivated by the
fact that participants in a test session represent unseen classes, i.e.,
speakers in an audio recording to be diarized are typically assumed unknown.
However, the target roles namely child and adult are shared across train and
test sessions. Hence, by treating child-adult speaker classification in each
train session as an independent task, we hypothesize that protonets learn the
common discriminating characteristics between child and adult classes
irrespective of local variabilities which might influence the task
performance.

As a metric-learning method, protonets share similarities with triplet
networks [19] and siamese networks [20] for learning speaker embeddings. Other
than a recently proposed work which used protonet loss function for speaker ID
and verification [14], to the best of our knowledge this work is one of the
early applications of protonets for speaker clustering. Following, we
illustrate the protonet training process using a single batch, then extend it
to multiple training sessions.

####  2.1.1 Batch training

Consider a set of labeled training examples from $C$ classes
$(\mathbf{X_{tr}},Y_{tr})$ =
$\\{(\mathbf{x_{1}},y_{1}),...(\mathbf{x_{N}},y_{N})\\}$ where each sample
$\mathbf{x_{i}}$ is a vector in $D$-dimensional space and
$y_{i}\in\\{1,2,..,C\\}$. Protonets learn a non-linear mapping
$f_{\theta}:\mathbb{R}^{D}\rightarrow\mathbb{R}^{M}$ where the prototype of
each class is computed as follows:

$\mathbf{p}_{c}=\frac{1}{|S_{c}|}\sum_{(x_{i},y_{i})\epsilon
S_{c}}f_{\theta}(\mathbf{x_{i}})$ (1)

$S_{c}$ represents the set of train samples belonging to class $c$. For every
test sample $(x,y)$, the posterior probability given class $c$ is as follows:

$p_{\theta}(y=c|x)=\frac{\exp\left(-d_{\varphi}\left(f_{\theta}(\mathbf{x}),\mathbf{p}_{c}\right)\right)}{\sum_{c^{\prime}\in
C}\exp\left(-d_{\varphi}\left(f_{\theta}(\mathbf{x}),\mathbf{p}_{c^{\prime}}\right)\right)}$
(2)

$d_{\varphi}$ denotes distance metric. While the choice of $d_{\varphi}$ can
be arbitrary, it was shown in [17] that using Euclidean distance is equivalent
to modeling the supports using Gaussian mixture density functions, and
empirically performed better than other functions. Thus, we use Euclidean
distance in this work. Learning proceeds by minimizing the negative log
probability for the true class using gradient descent.

$L(y,\mathbf{x})=-\sum_{c=1}^{C}y_{c}\log(p_{\theta}(y=c\mid\mathbf{x}))$ (3)

Pseudo-code for training a batch is provided in Algorithm 1.

Algorithm 1 Single batch of protonet training

$\mathcal{U}$(S,N) denotes uniform sampling of $N$ elements from $S$ without
replacement
Input: $D=\bigcup_{c=1}^{C}D_{c}$, where $D_{c}=\\{(x_{i},y_{i})\;;y_{i}=c\\}$
Output: $L$ (Batch training loss)

1:for $c$ in $\\{1,...,C\\}$ do

2: $S_{c}=\mathcal{U}(D_{c},k)$ $\triangleright$ Supports

3: $Q_{c}=\mathcal{U}(D_{c}\setminus S_{c},B-k)$ $\triangleright$ Queries

4: $p_{c}=\frac{1}{k}\sum_{(x_{i},y_{i})\in S_{c}}f_{\theta}(x_{i})$
$\triangleright$ Prototypes

5:$L\leftarrow 0$

6:for $c$ in $\\{1,...,C\\}$ do

7: for $(x,y)$ in $Q_{c}$ do

8: $L\leftarrow L+\frac{1}{C\times(B-k)}[-\log(p_{\theta}(y=c|x)]$

####  2.1.2 Extension to multiple sessions

Consider $S$ sessions in the training corpus, with $N_{c,s}$ number of samples
belonging to class $c$ in session $s$. We iterate through each session $s$,
and randomly sample $k$ examples each from child and adult without
replacement. These samples (supports) are used to construct the prototypes
using Equation (1). From the remaining $N_{c,s}-k$ samples, $B-k$ samples are
chosen without replacement from each class, where $B$ denotes the training
batch size. These samples (queries) are used to update the weights in a single
back-propagation step according to Equation (3). Although a significant
fraction of samples are not seen during a single epoch (1 epoch $\equiv$ $S$
batches), random sampling of supports and queries over multiple epochs improve
the generalizability of protonets.

###  2.2 Siamese networks

For unsupervised evaluation (clustering), we compare protonets with siamese
networks [21], which learn a metric space to maximize pairwise similarity
between same-class pairs and minimize similarity between different-class
pairs. Specifically, we implement the variant used in speaker diarization
[22], where the training label for each input pair represents the probability
of belonging to the same speaker. The network jointly learns both the
embedding space and distance metric for computing similarity. In our work, we
randomly select same-speaker (child-child, adult-adult) and different speaker
(child-adult) x-vector pairs to provide input to the model.

Fig. 1 illustrates the differences between siamese networks and protonets
during training.

Table 1: Statistics of child-adult corpora used in this work.

Corpus |  Duration(min) |  Child Age(yrs) | # Utts
---|---|---|---
(mean $\pm$ std.) | (mean $\pm$ std.) | Child | Adult
ASD | 17.76 $\pm$ 11.99 | 9.02 $\pm$ 3.10 | 11045 | 20313
ASD-Infants | 10.35 $\pm$ 0.51 | 1.87 $\pm$ 0.78 | 1371 | 4120
|  |  |  |

##  3 EXPERIMENTS

###  3.1 Dataset

We select two types of child-adult interactions from the ASD domain: the gold-
standard Autism Diagnostic Observation Schedule (ADOS [5]) which is used for
diagnostic purposes and a recently proposed treatment outcome measure, Brief
Observation of Social Communication Change (BOSCC [6]) for verbal children who
fluently used complex sentences. The ADOS Module 3 typically lasts between 45
and 60 minutes and includes over 10 semi-structured tasks. The ADOS produces a
diagnostic algorithm score which can be used to classify children between ASD
vs. non-ASD groups. On the other hand, BOSCC is a treatment outcome measure
used to track changes in social-communication skills over the course of
treatment in individuals with ASD, and is applicable in different collection
settings (clinics, homes, research labs). A BOSCC session lasts typically for
12 minutes and consists of 4 segments (two 4-minute-play segments with toys
and two 2-minute-conversation segments). We used a combination of ADOS (n=3)
and BOSCC (n=24) sessions which were administered by clinicians and manually
labeled by trained annotators for speaking times and transcripts. We refer to
this corpus as ASD. The sessions in ASD cover sources of variability in child
age, collection centers (4) and amount of available speech per child (Table
1).

To check generalization performance, we train our models on ASD and evaluate
on a different child-adult corpus within the autism diagnosis and intervention
domain. The ASD-Infants corpus (Table 1) consists of BOSCC (n=12) sessions
with minimally verbal toddlers and preschoolers with limited language
(nonverbal, single words or phrase speech). As opposed to ASD, these sessions
are administered by a caregiver, and represent a more naturalistic data
collection setup aimed at early behavioral assessments with a familiar adult.
The age differences between children in both corpora provides a significant
domain mismatch.

###  3.2 Features and Model Architecture

We use x-vectors from the CALLHOME recipe111https://kaldi-asr.org/models/m6 as
pre-trained audio embeddings in this work, which have demonstrated state-of-
the-art performance in speaker diarization [23] and recognition systems [24].
X-vectors are fixed-length embeddings extracted from variable length
utterances using a time-delay neural network followed by a statistics pooling
layer. In all our experiments, 128 dimensional x-vectors are input to a feed-
forward neural network with 3 hidden layers (128, 64 and 32 units per layer).
Embeddings from the third hidden layer (32-dimensional) are treated as speaker
representations. Rectified linear unit (ReLU) non-linearity is used in between
the layers. Batch-normalization and dropout ($p$ = 0.2) are used for
regularization. Adam optimizer ($lr$ = $3\mathrm{e}{-4}$, $\beta_{1}$ = 0.9,
$\beta_{2}$ = 0.999) is used for weight updates. A batch size of 128 samples
is employed. Since ASD corpus contains only 27 sessions, we use nine-fold
cross validation to estimate test performance. At each fold, 18 sessions are
used for model training. The best model is chosen using validation loss
computed with 6 sessions. The remaining 3 sessions are treated as evaluation
data. No two folds share the data from same speaker.

Fig. 1: Training in protonets (left) vs siamese networks (right) in the
embedding space. Colored backgrounds represent class decision regions.
Distances from the query sample (non-filled) to prototypes from each class
(filled with black) are used to estimate loss training loss using Equations
(2) and (3). siamese networks are trained to maximize similarity between same-
speaker pairs (dashed line) and minimize similarity between different-speaker
pairs (solid line). Illustration adopted from [17, 14].

###  3.3 Evaluation

####  3.3.1 Weak Supervision

We evaluate our models in a few-shot setting similar to the original
formulation of protonets [17] which is equivalent to sparsely labeled segments
from the test session. In practice, such labels can be made available from the
session through random selection or active learning [25]. We train a baseline
model using the architecture from Section 3.2 and a softmax layer to minimize
cross-entropy loss between child and adult classes. This model is directly
used to estimate class posteriors on the testing data. We refer to this model
as Base. We use a second baseline where the labeled samples from test sessions
in each fold are made available during the training process, i.e., updating
protonet weights using back-propagation (Base-backprop).

For protonets, we train two variants: P20 and P30 with 20 and 30 supports per
class during training. A larger number of supports translates into more
samples for reliable prototype computation, however it results in fewer
queries for back-propagation. During evaluation, 5 samples from each class in
the test session are randomly chosen as training data. These samples are used
to compute prototypes for child and adult followed by minimum-distance based
assignment for the remaining samples in that session. In order to estimate a
robust performance measure for Base-backprop, P20 and P30, we repeat each
evaluation 200 times by selecting a different set of 5 samples and compute the
mean macro (unweighted) F1-score over the corpus.

####  3.3.2 Unsupervised: Clustering

Clustering x-vectors using AHC and PLDA scores (trained with supervision) is
an integral part of recent diarization systems [23]. This method forms our
first baseline. We note that the training data for PLDA transformation
represents significant domain mismatch with our corpora. We use k-means and
spectral clustering (using cosine-distance based affinity matrix) as
unsupervised clustering methods for comparing x-vectors, siamese embeddings
and protonet embeddings. In the siamese network, the distance measure between
a segment pair is learnt between outputs from the third hidden layer
(32-dimensional). For protonets, we use the models trained for weak
supervision and extract embeddings at the prototype space (32-dimensional) for
clustering. We use purity as the clustering metric, which describes to what
extent samples from a cluster belong to the same speaker.

Table 2: Child-adult classification results using macro-F1 (%) Method | ASD | ASD-Infants
---|---|---
Base | 82.67 | 53.67
Base-backprop | 78.64 | 56.29
P20 | 86.66 | 61.30
P30 | 86.10 | 61.47

##  4 Results

###  4.1 Classification

Weakly-supervised classification results are presented in Table 2. In general,
both variants of protonet outperform the baselines significantly in their
respective corpora (ASD: $p$ <0.05, ASD-Infants: $p$<0.01). However, all
models degrade in performance on the ASD-Infants corpus as compared to ASD. As
mentioned before, the data from younger children presents a large domain
mismatch between training and evaluation data and we suspect this as the
primary reason for lower performance. Surprisingly in ASD, updating network
weights using samples from test session (Base-backprop) reduces classification
performance. We suspect that the network overfits on the labeled samples.
However in the case of ASD-Infants, the labeled samples from the test session
provide useful information about the speakers resulting in modest improvement
over a weaker Base. While protonets provide the best F1-scores in both
corpora, the performance in ASD-Infants leaves room for improvement. We do not
observe any significant difference between P20 and P30, suggesting that the
performance is robust to the number of supports and queries during training.

Table 3: Speaker clustering results using purity (%) Method | ASD | ASD-Infants
---|---|---
K-Means | SC | K-Means | SC
x-vectors | 77.05 | 75.22 | 77.98 | 75.97
siamese | 78.22 | 79.18 | 78.30 | 76.86
P20 | 81.39 | 80.70 | 85.51 | 85.55
P30 | 79.80 | 80.24 | 83.57 | 83.26

###  4.2 Clustering

Clustering x-vectors using AHC and PLDA scores results in a purity of 63.45%
in ASD, which is significantly lower than both K-means and Spectral Clustering
(SC) for all the models in Table 3. This suggests that the supervised PLDA
models may be susceptible to unknown speaker types. Unsupervised PLDA
adaptation using x-vectors’ mean and variance from ASD marginally improves the
performance to 64.32%, hence we do not include this method in the rest of our
comparisons. As opposed to classification, clustering performance does not
degrade in ASD-Infants, suggesting that discriminative information between
child and adult speakers within a session is preserved in all the embeddings
compared in Table 3. siamese networks present a modest improvement over
x-vectors, upto 5.26% relative improvement for spectral clustering in ASD.
However, protonets provide the best performance in both the corpora. In
particular, P20 results in slightly higher purity scores than P30 across
clustering methods and corpora. Hence, a larger number of queries within a
batch appears beneficial for speaker clustering in this work. We also note
that the best clustering performance (P20) is better in the out-of-domain
corpus. We believe that the younger ages of children in ASD-Infants over ASD
might benefit the clustering process.

Fig. 2: TSNE visualizations for protonet embeddings (left) and x-vectors
(right) for 3 test sessions in ASD corpora

###  4.3 TSNE Analysis

We provide a qualitative analysis using TSNE in Figure 2. We collect
embeddings from both child and adult from a single-fold (3 sessions) in ASD
and provide the TSNE visualizations for protonet embeddings and x-vectors.
Embeddings from child and adult class are represented using 3 shades of red
and blue respectively, one shade for each session. Although x-vectors cluster
compactly within each speaker in a session, embeddings across sessions from
the same class are spread apart. Protonets are able to cluster within classes
compactly, while preserving the discriminative information between classes. In
particular, embeddings belonging to child (which are expected to cover more
sources of variability) are as compact as embeddings from adult. This suggests
that protonets are able to learn across within-class variabilities for child-
adult classification from speech.

##  5 Conclusions

In this work, we used meta-learning to perform child-adult speaker
classification in spontaneous conversations. By modeling speaker
classification from different sessions as separate tasks, we train protonets
to learn speaker representations invariant to local variabilities. Using
weakly-supervised and unsupervised settings, we show that protonets outperform
x-vectors. Further, protonets outperform siamese networks for clustering when
trained on the same input representations (x-vectors). In the future, we would
like to train a generic speaker diarization system using protonets. Protonets
are a suitable choice for this problem, since an arbitrary number of speakers
can be accommodated in every training session, and speaker identities need not
be shared across sessions.

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EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2018-044 LHCb-PAPER-2018-003 June 10, 2018

Measurement of the inelastic $p$ $p$ cross-section at a centre-of-mass energy
of 13 TeV

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

The cross-section for inelastic proton-proton collisions at a centre-of-mass
energy of 13 TeV is measured with the LHCb detector. The fiducial cross-
section for inelastic interactions producing at least one prompt long-lived
charged particle with momentum $p>2$ ${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ in
the pseudorapidity range $2<\eta<5$ is determined to be $\sigma_{\rm
acc}=62.2\pm 0.2\pm 2.5\mathrm{\,mb}$. The first uncertainty is the intrinsic
systematic uncertainty of the measurement, the second is due to the
uncertainty on the integrated luminosity. The statistical uncertainty is
negligible. Extrapolation to full phase space yields the total inelastic
proton-proton cross-section $\sigma_{\rm inel}=75.4\pm 3.0\pm 4.5$ mb, where
the first uncertainty is experimental and the second due to the extrapolation.
An updated value of the inelastic cross-section at a centre-of-mass energy of
7 TeV is also reported.

Published in JHEP 06 (2018) 100

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

##  1 Introduction

The inelastic cross-section is a fundamental quantity in the phenomenology of
high-energy hadronic interactions that are studied at particle accelerators.
It is also important for astroparticle physics, e.g. in the description of
extensive air showers induced by cosmic rays hitting the atmosphere of the
Earth [1], or for the modelling of the transport of cosmic ray particles in
the interstellar medium [2, 3]. Since quantum chromodynamics cannot yet be
solved in the nonperturbative regime, it is currently not possible to
calculate the inelastic cross-section from first principles. Models based on
Regge phenomenology predict, within the limits of the Froissart-Martin bound
[4, 5], an increase with energy according to a power law [6]. Asymptotically
the Froissart-Martin bound grows proportional to $(\ln s)^{2}$, where $s$ is
the square of the centre-of-mass energy of the collision. Although originally
derived for the total cross-section, this bound has been shown to apply also
for the inelastic cross-section [7].

This paper presents a measurement of the inelastic proton-proton cross-section
at $\sqrt{s}=13$ TeV, which is the highest collision energy reached so far at
any particle accelerator. The measurement is performed with the LHCb detector
in the pseudorapidity range $2<\eta<5$. Other measurements of the inelastic
proton-proton cross-section at LHC energies have been reported by the ALICE
[8] (2.76 and 7 TeV), ATLAS [9, 10, 11, 12] (7, 8 and 13 TeV), CMS [13, 14] (7
and 13 TeV), LHCb [15] (7 TeV) and TOTEM [16, 17, 18, 19, 20, 21] (7, 8 and 13
TeV) collaborations, covering also central and very forward rapidities.

##  2 Detector and data samples

The LHCb detector [22, 23] is a single-arm forward spectrometer, 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 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 (PV), 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 for this measurement is based on unbiased triggers,
which randomly accept a small subset of all bunch crossings. The bulk of the
recorded data are from collisions between leading bunches in the bunch trains
of the LHC filling pattern [24], thus largely reducing background from
previous bunch crossings. Data were collected for both polarities of the LHCb
dipole magnet to test for magnetic-field dependent systematic effects. The
total data sample consists of 691 million events in 49 runs from 8 LHC fills,
recorded in 2015 between July 8 and August 13. A run corresponds to a data set
recorded under stable conditions and for a duration of up to one hour. Data
from a long fill are spread over several runs.

The integrated luminosity of this data set was determined in a separate study.
The standard way to determine the relative luminosity in LHCb is based on
continuous monitoring of the rate of interactions with at least two tracks
reconstructed in the vertex detector [25]. This is done online by applying the
empty-event counting method (see Sect. 3) to a dedicated set of randomly
sampled events that are partially reconstructed in the trigger. The integrated
luminosity is obtained by dividing the number of those interactions by their
”reference” cross-section. With independent data from a dedicated LHC fill at
$\sqrt{s}=13$ TeV, this reference cross-section was determined to be 63.4 mb
with an uncertainty of 3.9%, using the beam-gas imaging method as described in
Ref. [25]. For the unbiased data from leading bunch crossings the number of
partially reconstructed events for the luminosity measurement is much smaller
than the number of fully reconstructed events available for offline analysis.
Therefore, to obtain precise relative luminosity measurements that permit
sensitive studies of systematic effects, the empty-event counting method is
applied to the fully reconstructed events. The analysis is performed per
leading bunch crossing and in time intervals of $O(1{\rm s})$, thereby
minimising systematic uncertainties due to differences in the individual bunch
currents and variations of the instantaneous interaction rates. Differences
between the partial reconstruction in the trigger and the full reconstruction
result in a difference of about 1% in the visible interaction rates. The ratio
was measured with a statistical uncertainty of 0.2%. Accounting for this
difference and taking the absolute calibration from the beam gas imaging
method, a total integrated luminosity of 10.7 nb-1 is obtained for the full
data set, with an uncertainty of 4%, which is dominated by the 3.9%
uncertainty on the reference cross-section. Additional contributions are the
0.2% statistical uncertainty of the cross-calibration factor and a 0.8%
difference when requiring at least one reconstructed primary vertex instead of
two vertex-detector tracks.

Simulated events are used to study the detector response and effects of the
reconstruction chain. In the simulation, proton-proton collisions for both
magnet polarities are generated using Pythia 8 [26, 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 Analysis method

The primary measurement is a fiducial cross-section, defined as the cross-
section for proton-proton collisions with at least one prompt, long-lived
charged particle with momentum $p>2$ GeV/$c$ and pseudorapidity in the range
$2<\eta<5$. A particle is defined as “long-lived” if its lifetime is larger
than 30 ps, and it is prompt if it is produced directly in the primary
collision or if none of its ancestors is long-lived. At the LHCb experiment a
lifetime of 30 ps corresponds to a typical flight length of $O(100)$ mm.
According to this definition, for instance, ground-state hyperons are long-
lived, but not any particle containing charm or beauty quarks.

The experimental selection of prompt long-lived charged particles requires
well reconstructed charged tracks with momentum $p>2$ GeV/$c$ and $2<\eta<5$
that traverse the entire LHCb tracking system and have an estimated point of
origin located longitudinally (along the beam direction) within 200 mm and
transversally within 0.4 mm of the average PV position in the run. From a
parametrisation of the PV density by a three-dimensional Gaussian function,
the estimated point of origin is determined as that point on the particle
trajectory, parametrised by a straight line, where the PV density is highest.
With this selection all events can be used in the analysis, independently of
whether a PV was reconstructed. The above requirements select almost
exclusively inelastic interactions. From about 8.7 million elastic proton-
proton scattering processes in the simulation none is accepted.

The cross-section measurement exploits the fact that the recorded event sample
is unbiased, with the number of inelastic interactions per event drawn from a
Poisson distribution. The average number of interactions $\mu$ per event can
then be inferred from the fraction $p_{0}$ of empty events, $\mu=-\ln p_{0}$,
and for a given number $N_{\rm evt}$ of events the fiducial cross-section is
given by

${}\sigma_{\rm acc}=\frac{(\mu-\mu_{\rm bkg})N_{\rm evt}}{\mathcal{L}}\;,$ (1)

where $\mathcal{L}$ is the integrated luminosity of the event sample. The
number $\mu_{\rm bkg}$ of background interactions per event is estimated from
bunch crossings where only the bunch from one of the beams was populated. The
largest background levels are found for the first LHC fill used in the
analysis, with $\mu_{\rm bkg}/\mu$ around 1%. The cross-section measurement is
performed separately for all leading bunch crossings, and in time intervals of
$O(8{\rm s})$ to follow variations of the interaction rate during a run.

The determination of the empty-event probability $p_{0}$ takes into account
that, because of inefficiencies, events may be wrongly tagged as empty, and
that events which have no prompt long-lived charged particle inside the
fiducial region can be classified as non-empty because of misreconstructed
tracks. For the measurement presented here, the detector related effects are
accounted for by an approach that relates $p_{0}$ to the observed charged
track multiplicity distribution inside the fiducial region.

A good approximation for the low-multiplicity events that dominate the empty-
event counting is the assumption that on average the detector response is the
same for every true particle. In other words, the multiplicity distribution of
reconstructed tracks is assumed to be the same for every true particle. As
shown below, in this case $p_{0}$ can be determined from the observed
multiplicity distribution of long-lived prompt charged tracks in the detector
acceptance.

The relation between $p_{0}$ and experimentally accessible information can be
derived starting from the probability generating function (PGF) of the
observed multiplicity distribution $F_{q}(x)=\sum_{n}q_{n}x^{n}$, where the
probability $q_{n}$ to observe $n$ tracks is weighted by the $n$-th power of a
continuous variable $x$. It can be shown that the PGF of a convolution of two
discrete probability distributions is the product of the individual PGFs.
Introducing $G(x)$ as the PGF of the multiplicity distribution that is
reconstructed for a single true particle, the PGF for the case of $k$ true
particles is the PGF of the convolution of $k$ single particle distributions,
i.e. the $k$-th power $G^{k}(x)$. Weighting each true multiplicity $k$ with
its probability $p_{k}$, the relation between the PGF of the observed
multiplicity distribution $q_{n}$ and the true multiplicity distribution
$p_{k}$ is given by

${}F_{q}(x)=\sum_{n=0}^{\infty}q_{n}x^{n}=\sum_{k=0}^{\infty}p_{k}\,G^{k}(x)\;.$
(2)

The true empty-event probability $p_{0}$ can be inferred by setting $x=\alpha$
such that $G(\alpha)=0$, which yields

${}p_{0}=\sum_{n=0}^{\infty}q_{n}\alpha^{n}\;.$ (3)

The parameter $\alpha$ is the only detector-related parameter of the analysis.
It is an unfolding parameter that relates $p_{0}$ to the observed charged
particle multiplicity distribution in the fiducial region. For an ideal
detector it would be zero. For a given experiment the value of $\alpha$
depends mainly on the average reconstruction efficiency. Assuming for example
a binomial detector response, where a particle is either reconstructed with
efficiency ${\varepsilon}$ or missed, one has
$G(x)=(1-{\varepsilon})+{\varepsilon}x$ and thus
$\alpha=({\varepsilon}-1)/{\varepsilon}$, which is always negative. When
taking $p_{0}$ and $q_{n}$ from fully simulated events and solving Eq. (3) for
$\alpha$, one obtains an effective parameter that also accounts for higher-
order effects due to background tracks and nonlinear detector response.

For proton-proton collisions at high centre-of-mass energies, where inelastic
interactions have high multiplicity final states, and for data with a small
average number of simultaneous interactions per bunch crossing, the cross-
section measurement has only very little sensitivity to the exact value of
$\alpha$. The measurements presented below are based on events with $\mu$ in
the range between 0.4 and 1.4 and values of $q_{0}$ that are at least an order
of magnitude larger than the values $q_{n}$ for $n>0$. With a typical value
$\alpha\approx-0.6$ the values of $p_{0}$ are on average only about 3% smaller
than their leading-order estimates $q_{0}$, which results in robust cross-
section measurements even in case of sizeable systematic uncertainties on
$\alpha$.

##  4 Measurement of the fiducial cross-section

The inelastic fiducial cross-section is determined separately for all runs
recorded with unbiased triggers and, within a run, all leading bunch
crossings. In total 243 independent measurements are done, with different
filling patterns of the LHC, different bunch currents and both magnet
polarities. For each measurement an initial estimate for the unfolding
parameter $\alpha$ is obtained from a simulation that has been weighted to
match the average reconstructed track multiplicity in data. This initial value
is then corrected to account for differences between data and simulation in
the average track reconstruction efficiency and the average fraction of
misreconstructed tracks. The efficiency correction uses an independent
calibration for the analysed data set, determined as described in Ref. [34].
The fraction of misreconstructed tracks is estimated from the fraction of
tracks rejected by the track selection criteria, with a constant of
proportionality taken from simulation. The observed differences between data
and simulation are propagated into $\alpha$ by means of a simplified model
that relates it to the average track reconstruction efficiency and the
fraction of misreconstructed tracks.

The individual cross-section measurements are combined in a weighted average,
assuming uncorrelated statistical and fully correlated systematic
uncertainties. The weight of each measurement is proportional to the
integrated luminosity of the corresponding data set, resulting in an overall
fiducial cross-section $\sigma_{\rm acc}=62.237\pm 0.002$ mb, where the
uncertainty is purely statistical. The contributions to the systematic
uncertainty are summarised in Table 1. The dominant contribution is the 4%
uncertainty on the integrated luminosity. The intrinsic uncertainty of the
analysis is driven by a 16% uncertainty on the unfolding parameter $\alpha$,
which propagates into a 0.25% systematic uncertainty on $\sigma_{\rm acc}$.
The largest contribution is due to the difference between either determining
$\alpha$ from all simulated events or only from events with particles inside
the fiducial region. The systematic uncertainties due to the efficiency
calibration and the differences in the fraction of misreconstructed tracks
between data and simulation, where the full size of the correction is assigned
as a systematic uncertainty, are slightly smaller.

Figure 1 shows a comparison of the overall fiducial cross-section with the
averages within the individual LHC fills. While within a fill all measurements
are found to be consistent within their statistical uncertainties, small but
significant differences are seen between fills. These differences are found to
be correlated with quantities not studied in the simulation, namely the
vertical position and extension of the luminous region and, to a lesser
extent, the background level seen in the data. The spread associated to those
variables corresponds to an additional systematic uncertainty of $0.05\%$.
Also given in Fig. 1 are the $\chi^{2}$-values of the individual averages,
calculated with only the statistical uncertainties. Inspection of the
$\chi^{2}$-values shows that, except for the last fill, the agreement between
the results within one fill is actually better than expected. This is due to
the fact that the luminosity calibration and the inelastic cross-section
measurement are correlated by the use of information recorded by the vertex
detector. The average for the last fill, which in comparison to the others has
an enlarged $\chi^{2}$ value, is dominated by two runs with more than 100
million events. This points to the existence of additional systematic effects
of about the size of the statistical uncertainty of this average, which in
view of the other uncertainties are negligible. Cross-checks from variations
of the track selection criteria show no indication of additional systematic
effects.

Figure 1: Overall fiducial cross-section (vertical line), compared to the averages of the individual results in different LHC fills. The error bars indicate the statistical uncertainties. The grey band indicates the systematic uncertainty on the overall average due to the unfolding parameter $\alpha$. The $\chi^{2}$-values for the averages inside a fill are calculated with only the statistical uncertainties and the number of degrees of freedom ($\rm ndf$) is one less than the number of individual results contributing to the average. Systematic uncertainties inferred from the observed spread between the fills are discussed in the text. Table 1: Summary of systematic uncertainties on the fiducial cross-section. For the contribution from the unfolding parameter $\alpha$ a breakdown into the individual components is given. Source | Relative uncertainty
---|---
Integrated luminosity | 4.00%
Unfolding parameter $\alpha$ | 0.25%
— Interactions not in acceptance |  0.18%
— Efficiency |  0.15%
— Misreconstructed tracks |  0.12%
Luminous region and background | 0.05%
Total | 4.01%

##  5 Extrapolation to full phase space

The extrapolation from the fiducial cross-section $\sigma_{\rm acc}$ to the
total inelastic cross-section $\sigma_{\rm inel}=F_{\rm T}\,\sigma_{\rm acc}$
follows the same approach as in Ref. [15]. The extrapolation factor $F_{\rm
T}$ is determined from generator-level simulations. Neglecting interference
effects between different contributions, it is assumed that the total
inelastic cross-section can be written as an incoherent sum of distinct
contributions

${}\sigma_{\rm inel}=\sum_{X}\sigma_{X}\quad\mbox{with}\quad X\in\\{\rm
ND,SDA,SDB,DD\\}\;.$ (4)

Here $\sigma_{\rm ND}$ is the non-diffractive cross-section, $\sigma_{\rm
SDA}$ and $\sigma_{\rm SDB}$ are the single diffractive contributions with the
diffractively excited system travelling towards (A) or away (B) from the
detector, which have the same cross-section but different contributions to the
visible cross-section, and $\sigma_{\rm DD}$ is the double diffractive cross-
section. State-of-the-art event generators are assumed to provide a realistic
parametrisation of the properties of the various contributions. This has been
studied with the 32 proton-proton tunes that come with Pythia 8.230 [35] and
which do not require external libraries. Table 2 gives mean values and
standard deviations of the fractions $f_{X}$ of the inelastic cross-section,
the fractions $v_{X}$ of interactions with at least one prompt long-lived
charged particle within the acceptance and, for those interactions, the
average multiplicities $n_{{\rm ch},X}$ of those particles inside the
acceptance.

Table 2: Properties of Pythia 8.230 proton-proton tunes. Mean values and standard deviations are given for the fractions $f_{X}$ of the inelastic cross-section, the fractions $v_{X}$ of interactions inside the acceptance and, for those interactions, the average numbers of long-lived prompt charged particles $n_{{\rm ch},X}$ inside the acceptance. | $f_{X}$ | $v_{X}$ | $n_{{\rm ch},X}$
---|---|---|---
| mean | s.d. | mean | s.d. | mean | s.d.
Non-diffractive (ND) | 0.720 | 0.012 | 0.9963 | 0.0005 | 17.94 | 1.45
Single diffractive (SDA) | 0.083 | 0.003 | 0.7154 | 0.0051 | 8.11 | 0.52
Single diffractive (SDB) | 0.083 | 0.003 | 0.3411 | 0.0077 | 7.83 | 0.44
Double diffractive (DD) | 0.114 | 0.006 | 0.6263 | 0.0049 | 6.15 | 0.31

Given the fractions $f_{X}$ of the total inelastic cross-section and the
fractions of visible interactions $v_{X}$, the extrapolation factor $F_{\rm
T}$ is

${}F_{\rm
T}=\frac{\sum_{X}\sigma_{X}}{\sum_{X}\sigma_{X}\,v_{X}}=\frac{1}{\sum_{X}f_{X}\,v_{X}}\;.$
(5)

Taking the standard deviations from Table 2 as model uncertainties would
likely underestimate the uncertainty of the extrapolation factor, since in
particular the cross-section fractions have a much smaller spread than the
uncertainties obtained in a measurement of the diffractive contributions to
the inelastic cross-section, $f_{\rm SD}=0.20^{+0.04}_{-0.07}$ and $f_{\rm
DD}=0.12^{+0.05}_{-0.04}$, performed by the ALICE collaboration at
$\sqrt{s}=7$ TeV [8].

To reduce the model dependence in the determination of $F_{\rm T}$, the cross-
section fractions are considered to be a priori unknown and only subject to
the constraint $\sum_{X}f_{X}=1$. The extrapolation factor is estimated from
sets $\\{f_{X}\\}$ that uniformly sample the subspace defined by this
constraint. For each set $\\{f_{X}\\}$ the extrapolation factor $F_{\rm T}$
and the average multiplicity $n_{\rm ch}=\sum_{X}f_{X}\,n_{{\rm ch},X}$ inside
the fiducial region are calculated using $v_{X}$ and $n_{{\rm ch},X}$ from
Table 2. The spread of the different tunes is propagated into the
extrapolation factor by drawing $v_{X}$ and $n_{{\rm ch},X}$ from Gaussian
distributions with mean values and standard deviations as given in the table.
An additional experimental constraint is imposed by assigning a Gaussian
weight $w=\exp(-(n_{\rm ch}-N)^{2}/2\sigma^{2}_{N})$ to $\\{f_{X}\\}$ and
$F_{\rm T}$, where $N=13.9\pm 0.9$ is the average multiplicity per interaction
of prompt long-lived charged particles inside the acceptance in the data. The
numerical value for this constraint is obtained from the full simulation,
tuned to reproduce the observed average multiplicity per event and corrected
for differences between data and simulation in the average track
reconstruction efficiency and the fraction of tracks that are associated to a
true particle.

Figure 2 shows the posterior densities $\rho(f_{X})$ and $\rho(F_{\rm T})$ of
the cross-section fractions $f_{X}$ and the cross-section extrapolation factor
$F_{\rm T}$. The mean values of the fractions of $f_{X}$ are found to be
$f^{\rm sim}_{\rm SD}=0.21$ and $f^{\rm sim}_{\rm DD}=0.18$, consistent with
measurements at $\sqrt{s}=7$ TeV [8]. The resulting cross-section
extrapolation factor is $F_{\rm T}=1.211\pm 0.072$, which yields a total
inelastic cross-section of

$\sigma_{\rm inel}=75.4\pm 3.0(\rm exp)\pm 4.5(\rm extr)\,{\rm mb}\;,$

where the first uncertainty is due to the experimental uncertainty of the
fiducial cross-section and the second due to the cross-section extrapolation.
Summing all uncertainties in quadrature one finds $\sigma_{\rm inel}=75.4\pm
5.4$ mb.

Figure 2: Posterior densities of (left) the cross-section fractions $f_{X}$
for non-diffractive (ND) double-diffractive (DD) and single-diffractive
(SD=SDA+SDB) contributions, and (right) of the extrapolation factor $F_{\rm
T}$.

##  6 Summary and conclusions

A measurement is presented of the inelastic proton-proton cross-section with
at least one prompt long-lived charged particle with momentum $p>2$ GeV/$c$ in
the pseudorapidity range $2<\eta<5$. A particle is defined as “long-lived” if
its lifetime is larger than 30 ps, and it is prompt if it is produced directly
in the primary interaction or if none of its ancestors is long-lived. The
measurement is done with the empty-event counting method applied to unbiased
data. A total of 691 million events is analysed. The statistical uncertainty
of the overall result is negligible. The systematic uncertainty has
contributions from the integrated luminosity (4%), the unfolding parameter
(0.25%) and vertical location and extension of the luminous region and
background levels (0.05%). Adding all uncertainties not related to the
integrated luminosity in quadrature, the final result for the fiducial cross-
section is

$\sigma_{\rm acc}(\sqrt{s}=13\,{\rm TeV})=62.2\pm 0.2\pm 2.5(\rm lumi)\,{\rm
mb}\;.$

Extrapolating to the full phase space yields a total inelastic cross-section
of

$\sigma_{\rm inel}(\sqrt{s}=13\,{\rm TeV})=75.4\pm 3.0(\rm exp)\pm 4.5(\rm
extr)\,{\rm mb}\;.$

Since the publication of a measurement of the inelastic proton-proton cross-
section at a centre-of-mass energy of 7 TeV by the LHCb collaboration [15] an
improved calibration of the luminosity scale has become available [25]. The
new value of the reference cross-section for the integrated luminosity of the
data analysed for the previous measurement is 2.7% larger than the initial
estimate and the uncertainty has been reduced from 3.5% to 1.7%. With the
analysis of Ref. [15] unchanged, the updated cross-section is

$\sigma_{\rm inel}(\sqrt{s}=7\,{\rm TeV})=68.7\pm 2.1(\rm exp)\pm 4.5(\rm
extr)\,{\rm mb}\;,$

which supersedes the previous result. The experimental uncertainty is reduced
from 4.3% to 3.0% and the central value shifted up by 2.7%.

A comparison of the total inelastic cross-section measurements from proton-
proton collisions at the LHC is shown in Fig. 3. The new LHCb measurement at
$\sqrt{s}=13$ TeV is in good agreement with the measurements by the ATLAS [12]
and TOTEM [21] collaborations. In the LHC energy range the dependence of the
inelastic cross-section on $\sqrt{s}$ is well described by a power law.

Figure 3: Measurement of the total inelastic proton-proton cross-section at
the LHC at centre-of-mass energies of 2.76, 7, 8 and 13 TeV. Results are shown
from the ALICE [8], ATLAS [9, 10, 11, 12] and TOTEM [16, 17, 18, 19, 20, 21]
collaborations. For better visibility, measurements at the same energy are
drawn at slightly displaced locations. The error bars show the total
uncertainties, with positive and negative uncertainties of the respective
results independently added in quadrature. The line shows the result from a
power-law fit.

## 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 (The Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania);
MinES and FASO (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),
ANR, Labex P2IO and OCEVU, and Région Auvergne-Rhône-Alpes (France), Key
Research Program of Frontier Sciences of CAS, CAS PIFI, and the Thousand
Talents Program (China), RFBR, RSF and Yandex LLC (Russia), GVA, XuntaGal and
GENCAT (Spain), Herchel Smith Fund, the Royal Society, the English-Speaking
Union and the Leverhulme Trust (United Kingdom).

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LHCb collaboration

R. Aaij43, B. Adeva39, M. Adinolfi48, Z. Ajaltouni5, S. Akar59, J. Albrecht10,
F. Alessio40, M. Alexander53, A. Alfonso Albero38, S. Ali43, G. Alkhazov31, P.
Alvarez Cartelle55, A.A. Alves Jr59, S. Amato2, S. Amerio23, Y. Amhis7, L.
An3, L. Anderlini18, G. Andreassi41, M. Andreotti17,g, J.E. Andrews60, R.B.
Appleby56, F. Archilli43, P. d’Argent12, J. Arnau Romeu6, A. Artamonov37, M.
Artuso61, E. Aslanides6, M. Atzeni42, G. Auriemma26, S. Bachmann12, J.J.
Back50, C. Baesso62, S. Baker55, V. Balagura7,b, W. Baldini17, A. Baranov35,
R.J. Barlow56, S. Barsuk7, W. Barter56, F. Baryshnikov32, V. Batozskaya29, V.
Battista41, A. Bay41, J. Beddow53, F. Bedeschi24, I. Bediaga1, A. Beiter61,
L.J. Bel43, N. Beliy63, V. Bellee41, N. Belloli21,i, K. Belous37, I.
Belyaev32,40, E. Ben-Haim8, G. Bencivenni19, S. Benson43, S. Beranek9, A.
Berezhnoy33, R. Bernet42, D. Berninghoff12, E. Bertholet8, A. Bertolin23, C.
Betancourt42, F. Betti15,40, M.O. Bettler49, M. van Beuzekom43, Ia.
Bezshyiko42, S. Bifani47, P. Billoir8, A. Birnkraut10, A. Bizzeti18,u, M.
Bjørn57, T. Blake50, F. Blanc41, S. Blusk61, V. Bocci26, T. Boettcher58, A.
Bondar36,w, N. Bondar31, S. Borghi56,40, M. Borisyak35, M. Borsato39, F.
Bossu7, M. Boubdir9, T.J.V. Bowcock54, E. Bowen42, C. Bozzi17,40, S. Braun12,
M. Brodski40, J. Brodzicka27, D. Brundu16, E. Buchanan48, C. Burr56, A.
Bursche16, J. Buytaert40, W. Byczynski40, S. Cadeddu16, H. Cai64, R.
Calabrese17,g, R. Calladine47, M. Calvi21,i, M. Calvo Gomez38,m, A.
Camboni38,m, P. Campana19, D.H. Campora Perez40, L. Capriotti56, A.
Carbone15,e, G. Carboni25, R. Cardinale20,h, A. Cardini16, P. Carniti21,i, L.
Carson52, K. Carvalho Akiba2, G. Casse54, L. Cassina21, M. Cattaneo40, G.
Cavallero20,h, R. Cenci24,t, D. Chamont7, M.G. Chapman48, M. Charles8, Ph.
Charpentier40, G. Chatzikonstantinidis47, M. Chefdeville4, S. Chen16, S.-G.
Chitic40, V. Chobanova39, M. Chrzaszcz40, A. Chubykin31, P. Ciambrone19, X.
Cid Vidal39, G. Ciezarek40, P.E.L. Clarke52, M. Clemencic40, H.V. Cliff49, J.
Closier40, V. Coco40, J. Cogan6, E. Cogneras5, V. Cogoni16,f, L. Cojocariu30,
P. Collins40, T. Colombo40, A. Comerma-Montells12, A. Contu16, G. Coombs40, S.
Coquereau38, G. Corti40, M. Corvo17,g, C.M. Costa Sobral50, B. Couturier40,
G.A. Cowan52, D.C. Craik58, A. Crocombe50, M. Cruz Torres1, R. Currie52, C.
D’Ambrosio40, F. Da Cunha Marinho2, C.L. Da Silva73, E. Dall’Occo43, J.
Dalseno48, A. Davis3, O. De Aguiar Francisco40, K. De Bruyn40, S. De Capua56,
M. De Cian12, J.M. De Miranda1, L. De Paula2, M. De Serio14,d, P. De Simone19,
C.T. Dean53, D. Decamp4, L. Del Buono8, B. Delaney49, H.-P. Dembinski11, M.
Demmer10, A. Dendek28, D. Derkach35, O. Deschamps5, F. Dettori54, B. Dey65, A.
Di Canto40, P. Di Nezza19, S. Didenko69, H. Dijkstra40, F. Dordei40, M.
Dorigo40, A. Dosil Suárez39, L. Douglas53, A. Dovbnya45, K. Dreimanis54, L.
Dufour43, G. Dujany8, P. Durante40, J.M. Durham73, D. Dutta56, R.
Dzhelyadin37, M. Dziewiecki12, A. Dziurda40, A. Dzyuba31, S. Easo51, U.
Egede55, V. Egorychev32, S. Eidelman36,w, S. Eisenhardt52, U. Eitschberger10,
R. Ekelhof10, L. Eklund53, S. Ely61, A. Ene30, S. Escher9, S. Esen12, H.M.
Evans49, T. Evans57, A. Falabella15, N. Farley47, S. Farry54, D.
Fazzini21,40,i, L. Federici25, G. Fernandez38, P. Fernandez Declara40, A.
Fernandez Prieto39, F. Ferrari15, L. Ferreira Lopes41, F. Ferreira Rodrigues2,
M. Ferro-Luzzi40, S. Filippov34, R.A. Fini14, M. Fiorini17,g, M. Firlej28, C.
Fitzpatrick41, T. Fiutowski28, F. Fleuret7,b, M. Fontana16,40, F.
Fontanelli20,h, R. Forty40, V. Franco Lima54, M. Frank40, C. Frei40, J.
Fu22,q, W. Funk40, C. Färber40, E. Gabriel52, A. Gallas Torreira39, D.
Galli15,e, S. Gallorini23, S. Gambetta52, M. Gandelman2, P. Gandini22, Y.
Gao3, L.M. Garcia Martin71, J. García Pardiñas39, J. Garra Tico49, L.
Garrido38, D. Gascon38, C. Gaspar40, L. Gavardi10, G. Gazzoni5, D. Gerick12,
E. Gersabeck56, M. Gersabeck56, T. Gershon50, Ph. Ghez4, S. Gianì41, V.
Gibson49, O.G. Girard41, L. Giubega30, K. Gizdov52, V.V. Gligorov8, D.
Golubkov32, A. Golutvin55,69, A. Gomes1,a, I.V. Gorelov33, C. Gotti21,i, E.
Govorkova43, J.P. Grabowski12, R. Graciani Diaz38, L.A. Granado Cardoso40, E.
Graugés38, E. Graverini42, G. Graziani18, A. Grecu30, R. Greim43, P.
Griffith16, L. Grillo56, L. Gruber40, B.R. Gruberg Cazon57, O. Grünberg67, E.
Gushchin34, Yu. Guz37, T. Gys40, C. Göbel62, T. Hadavizadeh57, C.
Hadjivasiliou5, G. Haefeli41, C. Haen40, S.C. Haines49, B. Hamilton60, X.
Han12, T.H. Hancock57, S. Hansmann-Menzemer12, N. Harnew57, S.T. Harnew48, C.
Hasse40, M. Hatch40, J. He63, M. Hecker55, K. Heinicke10, A. Heister9, K.
Hennessy54, L. Henry71, E. van Herwijnen40, M. Heß67, A. Hicheur2, D. Hill57,
P.H. Hopchev41, W. Hu65, W. Huang63, Z.C. Huard59, W. Hulsbergen43, T.
Humair55, M. Hushchyn35, D. Hutchcroft54, P. Ibis10, M. Idzik28, P. Ilten47,
R. Jacobsson40, J. Jalocha57, E. Jans43, A. Jawahery60, F. Jiang3, M. John57,
D. Johnson40, C.R. Jones49, C. Joram40, B. Jost40, N. Jurik57, S. Kandybei45,
M. Karacson40, J.M. Kariuki48, S. Karodia53, N. Kazeev35, M. Kecke12, F.
Keizer49, M. Kelsey61, M. Kenzie49, T. Ketel44, E. Khairullin35, B. Khanji12,
C. Khurewathanakul41, K.E. Kim61, T. Kirn9, S. Klaver19, K. Klimaszewski29, T.
Klimkovich11, S. Koliiev46, M. Kolpin12, R. Kopecna12, P. Koppenburg43, S.
Kotriakhova31, M. Kozeiha5, L. Kravchuk34, M. Kreps50, F. Kress55, P.
Krokovny36,w, W. Krupa28, W. Krzemien29, W. Kucewicz27,l, M. Kucharczyk27, V.
Kudryavtsev36,w, A.K. Kuonen41, T. Kvaratskheliya32,40, D. Lacarrere40, G.
Lafferty56, A. Lai16, G. Lanfranchi19, C. Langenbruch9, T. Latham50, C.
Lazzeroni47, R. Le Gac6, A. Leflat33,40, J. Lefrançois7, R. Lefèvre5, F.
Lemaitre40, E. Lemos Cid39, P. Lenisa17, O. Leroy6, T. Lesiak27, B.
Leverington12, P.-R. Li63, T. Li3, Y. Li7, Z. Li61, X. Liang61, T.
Likhomanenko68, R. Lindner40, F. Lionetto42, V. Lisovskyi7, X. Liu3, D. Loh50,
A. Loi16, I. Longstaff53, J.H. Lopes2, D. Lucchesi23,o, M. Lucio Martinez39,
A. Lupato23, E. Luppi17,g, O. Lupton40, A. Lusiani24, X. Lyu63, F. Machefert7,
F. Maciuc30, V. Macko41, P. Mackowiak10, S. Maddrell-Mander48, O. Maev31,40,
K. Maguire56, D. Maisuzenko31, M.W. Majewski28, S. Malde57, B. Malecki27, A.
Malinin68, T. Maltsev36,w, G. Manca16,f, G. Mancinelli6, D. Marangotto22,q, J.
Maratas5,v, J.F. Marchand4, U. Marconi15, C. Marin Benito38, M. Marinangeli41,
P. Marino41, J. Marks12, G. Martellotti26, M. Martin6, M. Martinelli41, D.
Martinez Santos39, F. Martinez Vidal71, A. Massafferri1, R. Matev40, A.
Mathad50, Z. Mathe40, C. Matteuzzi21, A. Mauri42, E. Maurice7,b, B. Maurin41,
A. Mazurov47, M. McCann55,40, A. McNab56, R. McNulty13, J.V. Mead54, B.
Meadows59, C. Meaux6, F. Meier10, N. Meinert67, D. Melnychuk29, M. Merk43, A.
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Minzoni17, D.S. Mitzel12, A. Mogini8, J. Molina Rodriguez1,y, T. Mombächer10,
I.A. Monroy66, S. Monteil5, M. Morandin23, G. Morello19, M.J. Morello24,t, O.
Morgunova68, J. Moron28, A.B. Morris52, R. Mountain61, F. Muheim52, M.
Mulder43, D. Müller40, J. Müller10, K. Müller42, V. Müller10, P. Naik48, T.
Nakada41, R. Nandakumar51, A. Nandi57, I. Nasteva2, M. Needham52, N. Neri22,
S. Neubert12, N. Neufeld40, M. Neuner12, T.D. Nguyen41, C. Nguyen-Mau41,n, S.
Nieswand9, R. Niet10, N. Nikitin33, A. Nogay68, D.P. O’Hanlon15, A.
Oblakowska-Mucha28, V. Obraztsov37, S. Ogilvy19, R. Oldeman16,f, C.J.G.
Onderwater72, A. Ossowska27, J.M. Otalora Goicochea2, P. Owen42, A.
Oyanguren71, P.R. Pais41, A. Palano14, M. Palutan19,40, G. Panshin70, A.
Papanestis51, M. Pappagallo52, L.L. Pappalardo17,g, W. Parker60, C. Parkes56,
G. Passaleva18,40, A. Pastore14, M. Patel55, C. Patrignani15,e, A. Pearce40,
A. Pellegrino43, G. Penso26, M. Pepe Altarelli40, S. Perazzini40, D.
Pereima32, P. Perret5, L. Pescatore41, K. Petridis48, A. Petrolini20,h, A.
Petrov68, M. Petruzzo22,q, B. Pietrzyk4, G. Pietrzyk41, M. Pikies27, D.
Pinci26, F. Pisani40, A. Pistone20,h, A. Piucci12, V. Placinta30, S.
Playfer52, M. Plo Casasus39, F. Polci8, M. Poli Lener19, A. Poluektov50, N.
Polukhina69, I. Polyakov61, E. Polycarpo2, G.J. Pomery48, S. Ponce40, A.
Popov37, D. Popov11,40, S. Poslavskii37, C. Potterat2, E. Price48, J.
Prisciandaro39, C. Prouve48, V. Pugatch46, A. Puig Navarro42, H. Pullen57, G.
Punzi24,p, W. Qian63, J. Qin63, R. Quagliani8, B. Quintana5, B. Rachwal28,
J.H. Rademacker48, M. Rama24, M. Ramos Pernas39, M.S. Rangel2, I. Raniuk45,†,
F. Ratnikov35,x, G. Raven44, M. Ravonel Salzgeber40, M. Reboud4, F. Redi41, S.
Reichert10, A.C. dos Reis1, C. Remon Alepuz71, V. Renaudin7, S. Ricciardi51,
S. Richards48, K. Rinnert54, P. Robbe7, A. Robert8, A.B. Rodrigues41, E.
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Rollings57, V. Romanovskiy37, A. Romero Vidal39,40, M. Rotondo19, M.S.
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B. Sciascia19, A. Sciubba26,k, A. Semennikov32, E.S. Sepulveda8, A. Sergi47,
N. Serra42, J. Serrano6, L. Sestini23, P. Seyfert40, M. Shapkin37, Y.
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R. Silva Coutinho42, L. Silva de Oliveira2, G. Simi23,o, S. Simone14,d, N.
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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
4Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, IN2P3-LAPP, Annecy,
France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France
7LAL, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, 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
17Universita e INFN, 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 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 RAS),
Moscow, Russia
35Yandex School of Data Analysis, Moscow, Russia
36Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia
37Institute for High Energy Physics (IHEP), Protvino, Russia
38ICCUB, Universitat de Barcelona, Barcelona, Spain
39Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de
Santiago de Compostela, Santiago de Compostela, Spain
40European Organization for Nuclear Research (CERN), Geneva, Switzerland
41Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL),
Lausanne, Switzerland
42Physik-Institut, Universität Zürich, Zürich, Switzerland
43Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
44Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
45NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
46Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
47University of Birmingham, Birmingham, United Kingdom
48H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
49Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
50Department of Physics, University of Warwick, Coventry, United Kingdom
51STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
52School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
53School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
54Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
55Imperial College London, London, United Kingdom
56School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
57Department of Physics, University of Oxford, Oxford, United Kingdom
58Massachusetts Institute of Technology, Cambridge, MA, United States
59University of Cincinnati, Cincinnati, OH, United States
60University of Maryland, College Park, MD, United States
61Syracuse University, Syracuse, NY, United States
62Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
63University of Chinese Academy of Sciences, Beijing, China, associated to 3
64School of Physics and Technology, Wuhan University, Wuhan, China, associated
to 3
65Institute of Particle Physics, Central China Normal University, Wuhan,
Hubei, China, associated to 3
66Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 8
67Institut für Physik, Universität Rostock, Rostock, Germany, associated to 12
68National Research Centre Kurchatov Institute, Moscow, Russia, associated to
32
69National University of Science and Technology MISIS, Moscow, Russia,
associated to 32
70National Research Tomsk Polytechnic University, Tomsk, Russia, associated to
32
71Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia -
CSIC, Valencia, Spain, associated to 38
72Van Swinderen Institute, University of Groningen, Groningen, The
Netherlands, associated to 43
73Los Alamos National Laboratory (LANL), Los Alamos, United States, associated
to 61

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 Genova, Genova, Italy
iUniversità di Milano Bicocca, Milano, Italy
jUniversità di Roma Tor Vergata, Roma, Italy
kUniversità di Roma La Sapienza, Roma, Italy
lAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
mLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
nHanoi University of Science, Hanoi, Vietnam
oUniversità di Padova, Padova, Italy
pUniversità di Pisa, Pisa, Italy
qUniversità degli Studi di Milano, Milano, Italy
rUniversità di Urbino, Urbino, Italy
sUniversità della Basilicata, Potenza, Italy
tScuola Normale Superiore, Pisa, Italy
uUniversità di Modena e Reggio Emilia, Modena, Italy
vIligan Institute of Technology (IIT), Iligan, Philippines
wNovosibirsk State University, Novosibirsk, Russia
xNational Research University Higher School of Economics, Moscow, Russia
yEscuela Agrícola Panamericana, San Antonio de Oriente, Honduras
†Deceased