# A learning algorithm with emergent scaling behavior for classifying phase
transitions

N. Maskara<EMAIL_ADDRESS>Division of Physics, Mathematics and
Astronomy, California Institute of Technology, Pasadena, CA 91125, USA
Department of Physics, Harvard University, Cambridge, MA 02138, USA  M.
Buchhold  Division of Physics, Mathematics and Astronomy, California Institute
of Technology, Pasadena, CA 91125, USA  Institute for Theoretical Physics,
University of Cologne, Zülpicher Strasse 77, 50937, Cologne, Germany  M.
Endres  Division of Physics, Mathematics and Astronomy, California Institute
of Technology, Pasadena, CA 91125, USA  E. van Nieuwenburg  Division of
Physics, Mathematics and Astronomy, California Institute of Technology,
Pasadena, CA 91125, USA  Niels Bohr International Academy, Niels Bohr
Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen, Denmark

(August 27, 2024)

###### Abstract

Machine learning-inspired techniques have emerged as a new paradigm for
analysis of phase transitions in quantum matter. In this work, we introduce a
supervised learning algorithm for studying critical phenomena from measurement
data, which is based on iteratively training convolutional networks of
increasing complexity, and test it on the transverse field Ising chain and
$q=6$ Potts model. At the continuous Ising transition, we identify scaling
behavior in the classification accuracy, from which we infer a characteristic
classification length scale. It displays a power-law divergence at the
critical point, with a scaling exponent that matches with the diverging
correlation length. Our algorithm correctly identifies the thermodynamic phase
of the system and extracts scaling behavior from projective measurements,
independently of the basis in which the measurements are performed.
Furthermore, we show the classification length scale is absent for the $q=6$
Potts model, which has a first order transition and thus lacks a divergent
correlation length. The main intuition underlying our finding is that, for
measurement patches of sizes smaller than the correlation length, the system
appears to be at the critical point, and therefore the algorithm cannot
identify the phase from which the data was drawn.

Introduction. – Machine learning techniques have emerged as a new tool for
analyzing complex many-body systems Carrasquilla (2020); Mehta  _et al._
(2019). A particularly well-studied application of such techniques is that of
the identification and classification of phase transitions directly from data,
assuming little to no prior knowledge of the underlying physics van
Nieuwenburg  _et al._ (2017); Carrasquilla and Melko (2017); Wang (2016);
Giannetti  _et al._ (2019); Ponte and Melko (2017); Beach  _et al._ (2018);
Liu  _et al._ (2019); Wetzel and Scherzer (2017); Schäfer and Lörch (2019);
Mendes-Santos  _et al._ (2021). Recent efforts have expanded such explorations
to a diverse range of systems including disordered Venderley  _et al._ (2018);
Théveniaut and Alet (2019); van Nieuwenburg  _et al._ (2018) and topologically
ordered systems Zhang  _et al._ (2019a); Deng  _et al._ (2017); Rodriguez-
Nieva and Scheurer (2019); Balabanov and Granath (2020); Greplova  _et al._
(2019), as well as applications to experiments Rem  _et al._ (2019); Bohrdt
_et al._ (2019); Zhang  _et al._ (2019b).

An often-voiced concern, however, is that machine learning methods appear as a
black box and that it is difficult to trust neural network classification
without traditional supporting evidence. For example, in the study of phase
transitions, the phase boundary identified by a machine learning algorithm may
be affected by short-distance correlations, which turn out to be irrelevant
for the thermodynamic phase of the system Beach  _et al._ (2018). Instead,
learning algorithms should ideally focus on phase transition features which
characterize the transition, such as power-law divergences near the critical
point of a second order phase transition.

In this paper, we develop a machine learning algorithm inspired by this
fundamental feature of critical phenomena, i.e. the emergence of long-distance
correlations and scale invariance. The algorithm systematically analyzes
critical behavior near a suspected transition point, using only snapshot data,
by varying the functional form of a neural network. Specifically, we restrict
the architecture so the network can only access patches of the snapshot at a
time, and then vary the largest patch size. The resulting architecture is
similar to those in Refs Wetzel and Scherzer (2017); Szegedy  _et al._ (2014);
Lin  _et al._ (2014); Mills  _et al._ (2019); Miles  _et al._ (2020). We
observe that, under these conditions, we can extract information about the
spatial growth of correlations in the underlying data from the behavior of the
classification probabilities.

Figure 1: Conceptual illustration of our method for a 1D spin-chain. Snapshots
near a second order phase transition reveal a characteristic length scale
$\xi_{\text{corr}}$, over which spins are correlated, and which diverges at
the critical point. The modules $m^{k}$ are designed to only capture
correlations in the data up to a certain length scale $\ell_{k}$, and their
outputs are aggregated into $M^{k}$. On length scales shorter than
$\xi_{\text{corr}}$, the algorithm cannot make a firm distinction between the
two phases. As the module size is increased, the prediction $\langle
M^{k}\rangle$ is improved until $\ell_{k}\sim\xi_{\text{corr}}$, after which
it quickly saturates.

Our main result is the identification of an emergent length scale, which we
extract from classification data, and which displays scaling behavior.
Physical arguments suggest that this classification length scale reflects the
system’s correlation length, which diverges at the critical point according to
a power law with a universal exponent. We exemplify this on the one-
dimensional (1D) transverse field Ising model, whose critical exponents are
known, and compare the scaling of the physical correlation length with the
classification length. We also consider a first order transition in the two-
dimensional (2D) $q=6$ Potts model, where, in-line with expectations, no
scaling of the classification length is observed.

The learning algorithm proves quite versatile, and neither requires prior
knowledge of the structure of the order parameter nor of the measurement data.
We demonstrate this by considering projective measurements in different
measurement bases, with which the thermodynamic phase and its order parameter
cannot be readily inferred from conventional two-point correlation functions.
Nevertheless, the algorithm is capable of learning more complex correlations,
and manages to distinguish the two phases with a high degree of accuracy. This
is especially promising in light of studying phase transitions with non-local
or hidden order, for which algorithms based on purely local structures hardly
gain access.

The Algorithm. – We start by introducing a supervised learning algorithm that
allows one to systematically add complexity to a machine learning model. The
model is composed of a set of independent computational units, termed modules.
The algorithm takes and trains modules iteratively, and, by design, each new
module learns correlations in the data that the prior modules did not capture.
Conceptually, complexity is added by increasing the amount of correlations
representable by the model in each step. Here, we are interested in scaling
behaviour near critical points, so each subsequent module is designed to
capture spatial correlations at a larger length-scale.

Each module $m^{i}:\vec{x}\rightarrow\mathbb{R}$, labeled with an index $i$,
takes as input a snapshot (projective measurement) $\vec{x}$ and maps it to a
scalar. Then, we apply an aggregation function $M^{k}$ that aggregates the
outputs of the first $k$ modules $m^{1},...,m^{k}$. In practice, both the
modules and the the aggregation function are implemented through a neural
network. The modules plus the aggregation function constitute our combined
machine learning model $M^{k}(m^{1},...,m^{k}):\vec{x}\rightarrow\mathbb{R}$,
mapping an input $\vec{x}$ to a corresponding classification target $y$. This
model is then trained to minimize a classification loss function $\mathcal{L}$
using the iterative training algorithm described in pseudo-code in Algorithm
1:

input : Sequence of modules $m^{1},...,m^{l}$

input : Aggregate models $M^{k}(m^{1},...,m^{k}),k\leq l$

input : Labeled dataset $\\{(\vec{x}_{i},y_{i})\\}$

input : Loss function $\mathcal{L}$

Result: Trained set of models $\\{M^{k}\\},k=1,...,l$

for  _$k=1,...,l$_ do

train $M^{k}$ on dataset $(\vec{x}_{i},y_{i})$ by minimizing
$\mathcal{L}(y_{i},M^{k}(x_{i}))$;

freeze parameters of $m^{k}$;

Algorithm 1 Iterative Training Algorithm

To understand the intuition behind this algorithm, it is helpful to consider
an aggregation function which simply sums the module outputs,
$M^{k}(\vec{x})=\sum_{j=1}^{k}m^{k}(\vec{x})$, and a loss function like mean-
squared error, which only depends on the difference between the target dataset
and model output. In this case, the loss function can be written as

$\displaystyle\mathcal{L}\left(y_{i}-M^{k}(\vec{x}_{i})\right)=\mathcal{L}\left(\tilde{y}_{i}-m^{k}(\vec{x}_{i})\right),$
(1)

where we define an effective target
$\tilde{y}_{i}=y_{i}-\sum_{j=1}^{k-1}m^{j}(\vec{x}_{i})$. Crucially, during
the $k$-th step of training, the variational parameters (weights) of all the
modules $m^{j},j<k$ are frozen, and hence $m^{k}$ is trained only on the
residuals $\tilde{y}_{i}$ of all the prior models. These residuals are the
leftover errors from the previous training step, and each subsequent module
only learns features which prior modules did not capture. In our actual
implementation, we use a linear classifier for the aggregation function and
the binary cross-entropy for the loss function (see below). As a result, our
modules are not exclusively trained on residuals, but the intuitive picture of
subtracting prior features from the cost function still approximately holds.

Figure 2:  (a) Average classification $M^{\ell}(x)$ as a function of the TFIM
parameter $g$ and the spatial extent $\ell$ of the model. Classifiers
incorporating longer range correlations can more reliably identify the phase
of snapshots taken near the critical point, as evidenced by an increase in the
slope. (inset) Average module outputs $\langle m^{\ell}\rangle$ also exhibit
scaling with $\ell$, as one would expect from an order parameter. (b) Fitted
classification lengths $\xi_{\text{net}}$ on a log-log plot, from measurements
in the $z$ (basis $=0$), $x$ (basis $=\pi/2$), and two intermediate bases
$\cos(0.18\pi)z+\sin(0.18\pi)x$ (basis $=0.18\pi)$ and $(z+x)/\sqrt{2}$ (basis
$=\pi/4$), plotted on a log-log scale. For each basis, points are separate for
approaching $g_{c}$ from above (blue) or below (red). Data for $g$ near
$g_{c}$ is consistent with power-law behavior with exponent $\mu=1$, which are
depicted by colored dotted lines. Error bars are an estimate of the standard
deviation in the fitted $\xi_{\text{net}}$. (c) Correlation lengths
$\xi_{\text{net}}$ are extracted by fitting the classification curves $\langle
M^{\ell}\rangle_{g}$ for each value of $g$, to an inverse exponential form.
Fits are performed for classifiers with largest module size between
$2\leq\ell<20$, and are shown in the same four bases. Notice in the
intermediate bases, especially $\pi/4$, the classification curves behave
erratically at very small $\ell$, but exhibit scaling at intermediate
$\ell>5$. The resulting lengthscales extracted by the exponential fits are
consistent with universal scaling near the critical point $g\approx g_{c}$
(b).

The Network. – In this section, we’ll provide more details about our choice of
neural networks. For the modules, we develop a class of convolutional neural
networks designed to probe the spatial locality of correlations. Each module
$m^{k}$ takes the functional form

$\displaystyle m^{k}(\vec{x})$
$\displaystyle=\frac{1}{N}\sum_{j}m^{k}_{0}(\vec{x}_{j}^{\ell_{k}})$ (2)

where $m^{k}_{0}$ is a two layer neural network that acts on a subset
$\vec{x}_{j}^{\ell_{k}}$ of the data $\vec{x}$. The label $\ell_{k}$ indicates
the size of a spatial region corresponding to the subset (e.g., $\ell_{k}$
adjacent sites in a one-dimensional lattice) and the index $j$ enumerates all
$N$ regions of size $\ell_{k}$.

The aggregation function we choose is a linear classifier $LC$, acting on the
module outputs $m^{k}(\vec{x})$.

$\displaystyle M^{K}(\vec{x})$
$\displaystyle=LC\Big{(}m^{1}(\vec{x}),m^{2}(\vec{x}),...m^{K}(\vec{x})\Big{)}.$
(3)

The linear classifier is defined by
$LC(\\{m^{i}(\vec{x})\\})=\sigma(\sum_{i}w_{i}m^{i}(\vec{x})-b)$, where
$\sigma$ is the sigmoid (or logistic) function $\sigma(z)=1/(1+e^{-z})$, and
$w_{i}$ and $b$ are free parameters. The non-linearity $\sigma$ maps the
linear combination of module outputs to a value between $[0,1]$, as expected
for binary classification. The loss function we use is the binary cross
entropy, $\mathcal{L}(y_{i},M^{k}(x_{i}))=\langle y\log
M^{k}(x_{i})+(1-y)\log(1-M^{k}(x_{i}))\rangle$, where $y_{i}$ is the target
label $y_{i}\in\\{0,1\\}$ and the expectation value is taken over the training
dataset.

Choosing a linear classifier ensures that the network cannot capture
additional, spurious correlations between modules. For example, for a linear
classifier, the first module that extracts information on a $5$-site region
will be the module $m^{5}(\vec{x})$. Instead, a non-linear classifier, which
contained e.g. terms quadratic in the arguments, would also include products
of the form $m^{2}(\vec{x})m^{3}(\vec{x})$. This would include non-local
information about potentially disconnected $5$-site regions, which we exclude
on purpose. Thus, in the remainder of the text, we use $M^{\ell}$ instead of
$M^{K}$ to denote an aggregate classifier with largest convolution length
$\ell_{K}=\ell$.

The full model is naturally represented by a convolutional neural network
(CNN), which can be implemented using open source machine learning libraries
such as Keras Chollet  _et al._ (2015) or PyTorch Paszke  _et al._ (2019). The
resulting CNN architecture, with different parallel convolutional modules, is
similar to the correlation probing neural network from Ref. Miles  _et al._
(2020), the network-in-network architectures from Refs. Wetzel and Scherzer
(2017); Szegedy  _et al._ (2014); Lin  _et al._ (2014), and to the EDNN from
Ref. Mills  _et al._ (2019). However, to the best of our knowledge, scaling
the convolution size by freezing the module parameters iteratively, and
observing the response via classification accuracy to extract a lengthscale,
has not appeared before in the literature.

Applications. – To investigate the scaling of the classification output of our
model, we first analyze a second order phase transition in the paradigmatic 1D
transverse field Ising model (TFIM). We then contrast this behaviour with a
first order transition in the 2D $q=6$ Potts model.

The single-parameter Hamiltonian for the 1D TFIM with open boundaries is

$\displaystyle
H(g)=-\sum_{i=1}^{L-1}\sigma_{i}^{z}\sigma_{i+1}^{z}-g\sum_{i=1}^{N}\sigma_{i}^{x},$
(4)

where $\sigma^{z,x}_{i}$ are Pauli matrices for spin $i$. At critical value
$g_{c}=1$, the ground state of this model undergoes a phase transition from a
disordered (paramagnetic) to an ordered (ferromagnetic) state, breaking the
global $\mathds{Z}_{2}$-symmetry. In what follows we focus our attention on a
region around $g=g_{c}$. To construct our dataset, we employ the matrix
product state based iTEBD algorithm Vidal (2007) to numerically determine the
ground state as a function of $g$, and sample configurations for a system size
of $L=400$. We then perform projective measurements in multiple bases,
including the $z$-basis (measuring $\sigma^{z}_{i}$ on each site), but also in
the $x$-basis (measuring $\sigma^{x}_{i}$) and in a few intermediate basis,
$\cos(\theta)\sigma^{z}_{i}+\sin(\theta)\sigma^{x}_{i}$. This is done to
illustrate that the classification algorithm does not rely on the a priori
choice of an optimal basis, which for experimental measurements may be
unknown.

Each snapshot is labelled with the phase it is drawn from, e.g. ordered
($g<g_{c}$) or disordered ($g>g_{c}$). As a convention we set the label equal
to $1$ if the snapshot $x$ is drawn from the ordered phase. The machine
learning model is then trained by minimizing the binary cross-entropy between
the labels and the prediction $M^{\ell}(x)$ (see The Network), on snapshots
drawn from the ground state of $H(g)$ at 85 different values of $g$ with 800
snapshots per $g$. Points were spread from $g=0$ to $4.4$, but concentrated in
the critical region near $g_{c}=1$, with a minimum separation of $\Delta
g=0.01$. Module outputs, $\langle m^{\ell}\rangle_{g}$, and phase
classification $\langle M^{\ell}\rangle_{g}$, are computed on a separate
validation dataset consisting of $200$ snapshots per $g$, and with a minimum
separation of $\Delta g=0.002$ in the critical region. The value of $\langle
M^{\ell}\rangle_{g}$ is a measure of how accurately one can identify the phase
of the ground state of $H(g)$ from local measurements with maximum spatial
extent $\ell$, and henceforth we call this the classification accuracy.

Empirically, we find the classification accuracy improves as the convolution
size $\ell$ is increased, with the improvement most dramatic for snapshots
drawn near $g_{c}$, as shown in Fig. 2a. To rationalize this behavior, we
notice that the problem of identifying the phase from local measurements is
intimately connected to the correlations in the ground state. At the critical
point, the ordered and disordered phases are indistinguishable, and the system
is dominated by fluctuations with a divergent correlation length
$\xi_{\text{corr}}$. This results in an ambiguous prediction $\langle
M^{\ell}\rangle_{g_{c}}=0.5$. As $g$ moves away from the critical point,
characteristic correlations, indicating one of the possible phases, start to
build up at distances larger than $\xi_{\text{corr}}$, while shorter distances
remain dominated by fluctuations. Since
$\xi_{\text{corr}}\sim|g-g_{c}|^{-\nu}$ follows a power-law, farther from the
critical point the classification accuracy improves for fixed $\ell$.
Similarly, as $\ell$ is increased, the accuracy of the classification $\langle
M^{\ell}\rangle_{g}$ will improve, saturating to either 1 or 0 depending on
$g<g_{c}$ or $g>g_{c}$ respectively.

These arguments suggest the behavior of the classification curves, $\langle
M^{\ell}\rangle_{g}$ can be used to detect a second order phase transition.
Indeed, the improvement of $M^{\ell}$ with $\ell$ is contingent upon correctly
partitioning the dataset close to the critical point, and is unique to the
critical region. Away from the critical point, the classification
probabilities saturate at some constant $\ell$ and no visible improvement for
larger $\ell$ is observed SOM .

Associated with the behavior of $\langle M^{\ell}\rangle_{g}$ is a
characteristic length scale, which we extract via an exponential fit $\langle
M^{\infty}-M^{\ell}\rangle_{g}\sim\exp(-l/\xi_{\text{net}})$, where
$\xi_{\text{net}}$ is a $g$-dependent length scale. Specifically, we set
$M^{\infty}$ to $1$ in the ordered phase and $0$ in the disordered phase, the
saturation values in an ideal, infinitely large system. It turns out to be
sufficient to consider $\ell<20$ in order to obtain convincing prediction
probabilities for datapoints with $|g-g_{c}|\geq 0.01$. For our data, which is
for an $L=400$ chain, this then emulates a thermodynamically large system. We
also exclude the smallest module ($\ell=1$), which only captures single-site
observables. The resulting fit between $2\leq\ell<20$ performs well in the
$z$-basis ( 2c). However, in different bases, specifically the intermediate
$\theta=\pi/4$ basis, the classification accuracy exhibits erratic behavior
for small $\ell$. Nevertheless, at slightly larger $\ell\approx 5$, scaling
with $\ell$ reappears, and the exponential fit extracts a meaningful length
scale $\xi_{\text{net}}$ capturing the scaling of $\langle
M^{\ell}\rangle_{g}$.

Near the phase transition, the fitted correlation length $\xi_{\text{net}}$
diverges as $g$ approaches the critical point $g_{c}$, and is well described
by a power-law (Fig. 2b). It is known that, for the 1D TFIM, the physical
correlation length scales as $\xi_{\text{corr}}$ $\sim$ $|g-g_{c}|^{-\nu}$
with $\nu=1$. Remarkably, the power-law scaling of the fitted classification
length $\xi_{\text{net}}\sim|g-g_{c}|^{-\nu_{\text{net}}}$, is consistent with
$\nu_{\text{net}}\approx\nu=1$ in any of the measured bases. This also
includes the intermediate $\theta=\pi/4$ basis, where the phases cannot be
reliably distinguished from conventional two-point or string-like correlation
functions SOM . These observations suggests that the characteristic
lengthscale we extracted by scaling the machine learning model reflects the
underlying correlation lengthscale, and hence can be used to probe the growth
of correlations near the critical point.

To contrast this, we also examine the $q=6$ Potts model, which exhibits a
first-order phase transition in temperature ($T$), and hence does not feature
a diverging correlation length at the critical point Wu (1982). As a result,
we expect that spatially local measurement data should be sufficient to
distinguish the two phases, even arbitrarily close to the transition point,
since there are no long-range critical fluctuations. Indeed, our numerical
data reflects this intuition, since the classification $\langle
M^{\ell}\rangle_{T}$ do not exhibit improvement beyond $\ell=2$ (Fig. 3),
regardless of distance to the transition point.

Figure 3:  Potts Model Data. (a) Predicted classifications $\langle
M^{\ell}\rangle_{T}$ for the $q=6$ Potts model do not exhibit scaling with
system size, reflecting the fact that the phase transition is first order. (b)
The module outputs $\langle m^{\ell}\rangle_{T}$, averaged over all snapshots
at a given temperature, are in sharp contrast to the second order transition
from Fig. 2. (c) Zooming in on the classifications $\langle
M^{\ell}\rangle_{T}$ near zero demonstrates the lack of scaling with $\ell$.

Discussion. – We have presented a flexible method for extracting a
characteristic length scale $\xi_{\text{net}}$ inferred from measurement data
via scaling of the classification $\langle M^{\ell}\rangle_{g}$. Furthermore,
$\xi_{\text{net}}$ diverges with the same scaling exponent as the physical
correlation length $\xi_{\text{corr}}$, suggesting the two quantities coincide
near the critical point. Above we gave physical arguments for why this is the
case, based on indistinguishability of the phase at short distances dominated
by critical fluctuations. These arguments are quite general, and reflect the
emergence of universality at critical points. Indeed, it is widely believed
that at the critical point, the correlation length $\xi_{\text{corr}}$ is the
sole contributor to singular, thermodynamic quantities Kardar (2007); Sachdev
(2011). As long as the model and training data are sufficient to distinguish
the two phases, the trained phase classification $\langle M^{\ell}\rangle_{g}$
should exhibit a discontinuitity at the critical point $g=g_{c}$ in the
thermodynamic limit $\ell\rightarrow\infty$, and $\xi_{\text{corr}}$ should be
the only length scale governing long-distance behavior of $\langle
M^{\ell}\rangle_{g}$, in agreement with our observations. As such, our scaling
procedure makes few assumptions about the microscopic model, and could be used
to study any system with a continuous phase transition.

Our analysis of the classification length scale $\xi_{\text{net}}$, has been
performed for relatively small module sizes $\ell<20$ compared to the size of
the system $L=400$. This mitigates any potential finite size effects and
yields a scaling of the classification only with the correlation length. In
general, however, when the system size becomes comparable to the correlation
length $\xi_{\text{corr}}\sim L$, both length scales will be relevant for
characterizing the classification curves $\langle M^{\ell}\rangle_{g}$. One
could explore scaling with both parameters, to extend our framework to finite
size systems. Such scenarios will likely be relevant for near-term quantum
simulators, where resources are limited.

The framework presented here for analyzing continuous phase transitions shows
more broadly that for classification tasks, we can probe an underlying feature
of interest by systematically varying the functional form of the models, and
measuring the response in the form of classification accuracy. In addition to
the convolutional neural networks used here, one could consider different
classes of models, including kernel methods Giannetti  _et al._ (2019); Liu
_et al._ (2020), or quantum machine learning models Cong  _et al._ (2019).
Such a concept could also be readily generalized to different kinds of order.
For example, dynamical critical exponents could be estimated by looking at
time-series data, and using a set of models which can represent observables
spanning a finite-number of time-slices van Nieuwenburg  _et al._ (2018).
Similarly, phase transitions without conventional order parameters could be
studied, perhaps by looking at loop-like observables of different sizes as in
Ref. Zhang and Kim (2017). The tools developed here are especially timely, as
quantum simulation technologies are rapidly approaching the point where exotic
phases of quantum matter can be directly studied in the lab. The ability of
our algorithm to characterize phase transitions and implicitly identify useful
correlations, directly from measurement data, makes it a promising tool for
analysis of future experiments.

###### Acknowledgements.

We thank Dolev Bluvstein, Dan Borgnia, Iris Cong, Brian Timar, and Ruben
Verresen for insightful discussions. N.M. acknowledges funding from the
Department of Energy Computational Science Graduate Fellowship under Award
Number(s) DE-SC0021110. M.B. acknowledges funding via grant DI 1745/2-1 under
DFG SPP 1929 GiRyd. This project has received funding from the European
Union’s Horizon 2020 research and innovation program under the Marie
Sklodowska-Curie grant agreement No. 847523 ‘INTERACTIONS’, and the Marie
Sklodowksa-Curie grant agreement No. 895439 ‘ConQuER’.

## References

  * Carrasquilla (2020) J. Carrasquilla, Advances in Physics: X 5, 1797528 (2020), publisher: Taylor & Francis _eprint: https://doi.org/10.1080/23746149.2020.1797528.
  * Mehta  _et al._ (2019) P. Mehta, M. Bukov, C.-H. Wang, A. G. R. Day, C. Richardson, C. K. Fisher, and D. J. Schwab, Physics Reports 810, 1 (2019).
  * van Nieuwenburg  _et al._ (2017) E. van Nieuwenburg, Y.-H. Liu, and S. Huber, Nature Physics 13, 435 (2017).
  * Carrasquilla and Melko (2017) J. Carrasquilla and R. G. Melko, Nature Physics 13, 431 (2017).
  * Wang (2016) L. Wang, Physical Review B 94, 195105 (2016).
  * Giannetti  _et al._ (2019) C. Giannetti, B. Lucini, and D. Vadacchino, Nuclear Physics B 944, 114639 (2019), arXiv: 1812.06726.
  * Ponte and Melko (2017) P. Ponte and R. G. Melko, Physical Review B 96, 205146 (2017), arXiv: 1704.05848.
  * Beach  _et al._ (2018) M. J. S. Beach, A. Golubeva, and R. G. Melko, Physical Review B 97, 045207 (2018), arXiv: 1710.09842.
  * Liu  _et al._ (2019) K. Liu, J. Greitemann, and L. Pollet, Physical Review B 99, 104410 (2019), arXiv: 1810.05538.
  * Wetzel and Scherzer (2017) S. J. Wetzel and M. Scherzer, Physical Review B 96, 184410 (2017), arXiv: 1705.05582.
  * Schäfer and Lörch (2019) F. Schäfer and N. Lörch, Physical Review E 99, 062107 (2019), arXiv: 1812.00895.
  * Mendes-Santos  _et al._ (2021) T. Mendes-Santos, X. Turkeshi, M. Dalmonte, and A. Rodriguez, Physical Review X 11 (2021), 10.1103/PhysRevX.11.011040.
  * Venderley  _et al._ (2018) J. Venderley, V. Khemani, and E.-A. Kim, Physical Review Letters 120, 257204 (2018), arXiv: 1711.00020.
  * Théveniaut and Alet (2019) H. Théveniaut and F. Alet, arXiv:1904.13165 [cond-mat] (2019), arXiv: 1904.13165.
  * van Nieuwenburg  _et al._ (2018) E. van Nieuwenburg, E. Bairey, and G. Refael, Physical Review B 98, 060301 (2018), publisher: American Physical Society.
  * Zhang  _et al._ (2019a) W. Zhang, L. Wang, and Z. Wang, Physical Review B 99, 054208 (2019a).
  * Deng  _et al._ (2017) D.-L. Deng, X. Li, and S. Das Sarma, Physical Review B 96, 195145 (2017).
  * Rodriguez-Nieva and Scheurer (2019) J. F. Rodriguez-Nieva and M. S. Scheurer, Nature Physics 15, 790 (2019).
  * Balabanov and Granath (2020) O. Balabanov and M. Granath, arXiv:2008.07268 (2020), arXiv: 2008.07268.
  * Greplova  _et al._ (2019) E. Greplova, A. Valenti, G. Boschung, F. Schäfer, N. Lörch, and S. Huber, arXiv:1910.10124 [cond-mat, physics:quant-ph] (2019), arXiv: 1910.10124.
  * Rem  _et al._ (2019) B. S. Rem, N. Käming, M. Tarnowski, L. Asteria, N. Fläschner, C. Becker, K. Sengstock, and C. Weitenberg, Nature Physics 15, 917 (2019), number: 9 Publisher: Nature Publishing Group.
  * Bohrdt  _et al._ (2019) A. Bohrdt, C. S. Chiu, G. Ji, M. Xu, D. Greif, M. Greiner, E. Demler, F. Grusdt, and M. Knap, Nature Physics 15, 921 (2019), number: 9 Publisher: Nature Publishing Group.
  * Zhang  _et al._ (2019b) Y. Zhang, A. Mesaros, K. Fujita, S. D. Edkins, M. H. Hamidian, K. Ch’ng, H. Eisaki, S. Uchida, J. C. S. Davis, E. Khatami, and et al., Nature 570, 484–490 (2019b).
  * Szegedy  _et al._ (2014) C. Szegedy, W. Liu, Y. Jia, P. Sermanet, S. Reed, D. Anguelov, D. Erhan, V. Vanhoucke, and A. Rabinovich, arXiv:1409.4842 [cs] (2014), arXiv: 1409.4842.
  * Lin  _et al._ (2014) M. Lin, Q. Chen, and S. Yan, arXiv:1312.4400 [cs] (2014), arXiv: 1312.4400.
  * Mills  _et al._ (2019) K. Mills, K. Ryczko, I. Luchak, A. Domurad, C. Beeler, and I. Tamblyn, Chemical Science 10, 4129 (2019), publisher: The Royal Society of Chemistry.
  * Miles  _et al._ (2020) C. Miles, A. Bohrdt, R. Wu, C. Chiu, M. Xu, G. Ji, M. Greiner, K. Q. Weinberger, E. Demler, and E.-A. Kim, arXiv:2011.03474 [cond-mat, physics:physics] (2020), arXiv: 2011.03474.
  * Chollet  _et al._ (2015) F. Chollet _et al._ , “Keras,” https://keras.io (2015).
  * Paszke  _et al._ (2019) A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga, A. Desmaison, A. Kopf, E. Yang, Z. DeVito, M. Raison, A. Tejani, S. Chilamkurthy, B. Steiner, L. Fang, J. Bai, and S. Chintala, in  _Advances in Neural Information Processing Systems 32_, edited by H. Wallach, H. Larochelle, A. Beygelzimer, F. d’ Alché-Buc, E. Fox, and R. Garnett (Curran Associates, Inc., 2019) pp. 8024–8035.
  * Vidal (2007) G. Vidal, Physical Review Letters 98, 070201 (2007).
  * (31) “Supplemental material,” .
  * Wu (1982) F. Y. Wu, Rev. Mod. Phys. 54, 235 (1982).
  * Kardar (2007) M. Kardar,  _Statistical physics of fields_ (Cambridge University Press, Cambridge ; New York, 2007) oCLC: ocn123113789.
  * Sachdev (2011) S. Sachdev,  _Quantum phase transitions_ , second ed. ed. (Cambridge University Press, Cambridge, 2011).
  * Liu  _et al._ (2020) K. Liu, N. Sadoune, N. Rao, J. Greitemann, and L. Pollet, arXiv:2004.14415 [cond-mat, physics:physics] (2020), arXiv: 2004.14415.
  * Cong  _et al._ (2019) I. Cong, S. Choi, and M. D. Lukin, Nature Physics 15, 1273–1278 (2019).
  * Zhang and Kim (2017) Y. Zhang and E.-A. Kim, Physical Review Letters 118, 216401 (2017), arXiv: 1611.01518.
  * Pfeuty (1970) P. Pfeuty, Annals of Physics 57, 79 (1970).

Supplementary material for “A learning algorithm with emergent scaling
behavior for classifying phase transitions”

##  I Network architecture

In this section, we provide a few additional details on our neural network
implementation. As explained in the main text, each module $m^{k}$ is a two
layer convolutional neural network. The first convolution takes an $\ell_{k}$
sized input to a vector of $4\ell_{k}$ features, and applies a ReLU non-
linearity defined by $\text{ReLU}(x)=\max(0,x)$. Then, the second convolution
collapses the $4\ell_{k}$ features into a single value, and applies a tanh
activation function $\tanh(x)=\frac{e^{x}-e^{-x}}{e^{x}+e^{-x}}$. The module
outputs are then combined using a linear classifier, described in the main
text. The network architecture for the third iteration $k=3$ is shown in Fig.
S3. Note that in our implementation, for the first module $m^{1}$ we only
apply a single convolution layer with linear activation, which can approximate
all mappings from a binary input to a real valued output.

##  II Correlation functions in different basis

Here, we discuss correlations functions of the TFIM in different measurement
basis. Conventionally two helpful correlation functions in the Ising model are
the two-point correlation function
$C_{2}(l)=\langle\sigma^{z}_{m+l}\sigma^{z}_{m}\rangle$ and the string
(parity) order correlation function
$C_{s}(l)=\langle\prod_{m=1}^{l}\sigma^{x}_{m}\rangle$, which both are sharp
indicators for the ordered (disordered) phase Pfeuty (1970). Note that the
parity correlation relies on the fact that the iTEBD algorithm prepares the
true ground state, which in a finite system is the superposition of the two
short-range correlated ground states.

Generalized to an arbitrary measurement basis, which we parametrize with the
angle $\theta$, the two-point correlation function
$C_{2}^{\theta}(l)=\langle\sigma^{\theta}_{m+l}\sigma^{\theta}_{m}\rangle$ and
the string order correlation function
$C_{s}^{\theta}(l)=\langle\prod_{m=1}^{l}\sigma^{\theta}_{m}\rangle$ are
expressed as functions of the spin
$\sigma^{\theta}_{l}=\cos(\theta)\sigma^{z}_{l}+\sin(\theta)\sigma^{x}_{l}$.
For $\theta=0$ this corresponds to correlation functions measured in the $z$
basis while $\theta=\frac{\pi}{2}$ correspond to measurements in the $x$
basis. We also consider intermediate bases with $\theta=0.18\pi,\pi/4$, and
$0.32\pi$.

Correlation functions like $C_{2}^{\theta},C_{s}^{\theta}$ can be
reconstructed from individual snapshots (projective measurements) by averaging
over many different positions (due to translational invariance), and are thus
accessible to the machine learning algorithm as well. Furthermore, in the $z$
and $x$ bases, these are sharp identifiers of the corresponding phase, and
also witness the scaling with distance $l$. It is therefore likely that the
algorithm learns (a variant of) these correlation functions. However, these
are two of the simplest correlations functions one can consider, and most
generally the network can capture any linear combination of correlation
functions constructed from $\sigma^{\theta}$.

In Fig. S2, we display the correlation functions
$C^{\theta}_{2},C^{\theta}_{s}$ for a set of angles $\theta$, obtained from
the ground state for different values of $g$. We observe that in the
intermediate bases, the contrast in these correlation functions on the two
sides of the transition is reduced. Most strikingly at $\theta=\frac{\pi}{4}$,
both correlation functions appear identical away from the critical point, and
only change qualitatively close to $g=g_{c}$. Thus, the two phases are not
readily distinguishable by studying these two “conventional” correlation
functions in this basis, yet the algorithm learns to distinguish them
successfully.

##  III Different labellings

In the main text, we always partition our data into ordered (1) and disordered
(0) based on knowledge of the critical point $g_{c}$. However, in many
experimental settings, the critical point may not be known a priori. Hence, in
this section, we present some results where a different threshold $g_{th}$ was
used to partition the data. Specifically, we chose $g_{th}=1.05$, label
snapshots from $g<g_{th}$ ordered, snapshots with $g>g_{th}$ disordered, and
repeat the same training procedures. However, when we look at the
classification $\langle M^{\ell}\rangle$ on a validation set, we see the the
accuracy stops improving beyond $\ell\approx 6$, see Fig. S1. This likely
reflects the finite correlation length at $g_{th}=1.05$, versus the divergent
correlation at $g=1.00$, which is what enabled improvement at larger $\ell$ in
main text Fig. 2. This also suggests that scaling of $M^{\ell}$ could be
combined with confusion methods van Nieuwenburg  _et al._ (2017) to aide in
identification of critical points.

Figure S1: Classifications curves for the incorrectly chosen partition
$g_{th}=1.05$. Notice that the classification improves as we increase $\ell$
for $\ell<5$, but then saturates and stops improving. This is likely a
reflection of the finite correlation length at $g_{th}=1.05$.  Figure S2: Two-
point correlation function $C^{\theta}_{2}(l)$ (top row) and string order
correlation function $C^{\theta}_{s}(l)$ (bottom row) obtained from the ground
state of the TFIM in different measurement basis (parametrized by $\theta$).
We see that $C_{2}(l)$ exhibits scaling with $l$ in the $z$ basis, but not in
the $x$ basis, while the opposite is true for $C_{s}(l)$. Away from the
critical point, depending on the angle $\theta$, at least one of the two
correlation functions unambiguously distinguishes the two phases. An exception
is the peculiar behavior at $\theta=\frac{\pi}{4}$, which we discuss in the
text. Figure S3: Network architecture at the third iteration, calculating the
function denoted $M^{3}$. The three modules $m^{1},m^{2},m^{3}$ are
convolutional layers, added in parallel, and are combined by a standard linear
classifier. The Lambda layer is a custom layer, added to simulate convolutions
which wrap around the periodic boundaries. The activation function for the
first convolution (conv1d_1,conv1d_3) is a ReLU, while the activation for the
second convolution (conv1d_2,conv1d_4) is tanh. The final dense layer has a
sigmoid activation. Higher iterations have more modules added in parallel. For
the Potts model, an equivalent architecture but with 2D convolutions was used.


Arcidiaconoa,c0000-0001-5904-142X, S. Argiroa,b0000-0003-2150-3750, M.
Arneodoa,c0000-0002-7790-7132, N. Bartosika0000-0002-7196-2237, R.
Bellana,b0000-0002-2539-2376, A. Belloraa,b0000-0002-2753-5473, J. Berenguer
Antequeraa,b0000-0003-3153-0891, C. Biinoa0000-0002-1397-7246, N.
Cartigliaa0000-0002-0548-9189, M. Costaa,b0000-0003-0156-0790, R.
Covarellia,b0000-0003-1216-5235, N. Demariaa0000-0003-0743-9465, M.
Grippoa,b0000-0003-0770-269X, B. Kiania,b0000-0002-1202-7652, F.
Leggera0000-0003-1400-0709, C. Mariottia0000-0002-6864-3294, S.
Masellia0000-0001-9871-7859, A. Meccaa,b0000-0003-2209-2527, E.
Migliorea,b0000-0002-2271-5192, E. Monteila,b0000-0002-2350-213X, M.
Montenoa0000-0002-3521-6333, M.M. Obertinoa,b0000-0002-8781-8192, G.
Ortonaa0000-0001-8411-2971, L. Pachera,b0000-0003-1288-4838, N.
Pastronea0000-0001-7291-1979, M. Pelliccionia0000-0003-4728-6678, M.
Ruspaa,c0000-0002-7655-3475, K. Shchelinaa0000-0003-3742-0693, F.
Sivieroa,b0000-0002-4427-4076, V. Solaa0000-0001-6288-951X, A.
Solanoa,b0000-0002-2971-8214, D. Soldia,b0000-0001-9059-4831, A.
Staianoa0000-0003-1803-624X, M. Tornagoa,b0000-0001-6768-1056, D.
Trocinoa0000-0002-2830-5872, G. Umoreta,b0000-0002-6674-7874, A.
Vagnerinia,b0000-0001-8730-5031

INFN Sezione di Trieste a, Università di Trieste b, Trieste, Italy S.
Belfortea0000-0001-8443-4460, V. Candelisea,b0000-0002-3641-5983, M.
Casarsaa0000-0002-1353-8964, F. Cossuttia0000-0001-5672-214X, A. Da
Rolda,b0000-0003-0342-7977, G. Della Riccaa,b0000-0003-2831-6982, G.
Sorrentinoa,b0000-0002-2253-819X

Kyungpook National University, Daegu, Korea S. Dogra0000-0002-0812-0758, C.
Huh0000-0002-8513-2824, B. Kim0000-0002-9539-6815, D.H.
Kim0000-0002-9023-6847, G.N. Kim0000-0002-3482-9082, J. Kim, J.
Lee0000-0002-5351-7201, S.W. Lee0000-0002-1028-3468, C.S.
Moon0000-0001-8229-7829, Y.D. Oh0000-0002-7219-9931, S.I.
Pak0000-0002-1447-3533, S. Sekmen0000-0003-1726-5681, Y.C.
Yang0000-0003-1009-4621

Chonnam National University, Institute for Universe and Elementary Particles,
Kwangju, Korea H. Kim0000-0001-8019-9387, D.H. Moon0000-0002-5628-9187

Hanyang University, Seoul, Korea E. Asilar0000-0001-5680-599X, B.
Francois0000-0002-2190-9059, T.J. Kim0000-0001-8336-2434, J.
Park0000-0002-4683-6669

Korea University, Seoul, Korea S. Cho, S. Choi0000-0001-6225-9876, B.
Hong0000-0002-2259-9929, K. Lee, K.S. Lee0000-0002-3680-7039, J. Lim, J. Park,
S.K. Park, J. Yoo0000-0003-0463-3043

Kyung Hee University, Department of Physics, Seoul, Korea J.
Goh0000-0002-1129-2083, A. Gurtu0000-0002-7155-003X

Sejong University, Seoul, Korea H. S. Kim0000-0002-6543-9191, Y. Kim

Seoul National University, Seoul, Korea J. Almond, J.H. Bhyun, J.
Choi0000-0002-2483-5104, S. Jeon0000-0003-1208-6940, J.S. Kim, J.
Kim0000-0001-9876-6642, S. Ko0000-0003-4377-9969, H. Kwon0009-0002-5165-5018,
H. Lee0000-0002-1138-3700, S. Lee, B.H. Oh, M. Oh0000-0003-2618-9203, S.B.
Oh0000-0003-0710-4956, H. Seo0000-0002-3932-0605, U.K. Yang, I.
Yoon0000-0002-3491-8026

University of Seoul, Seoul, Korea W. Jang0000-0002-1571-9072, D.Y. Kang, Y.
Kang0000-0001-6079-3434, S. Kim, B. Ko, J.S.H. Lee0000-0002-2153-1519, Y. Lee,
J.A. Merlin, I.C. Park0000-0003-4510-6776, Y. Roh, M.S.
Ryu0000-0002-1855-180X, D. Song, Watson, I.J.0000-0003-2141-3413, S.
Yang0000-0001-6905-6553

Yonsei University, Department of Physics, Seoul, Korea S.
Ha0000-0003-2538-1551, H.D. Yoo0000-0002-3892-3500

Sungkyunkwan University, Suwon, Korea M. Choi, H. Lee, Y.
Lee0000-0002-4000-5901, I. Yu0000-0003-1567-5548

College of Engineering and Technology, American University of the Middle East
(AUM), Dasman, Kuwait T. Beyrouthy, Y. Maghrbi0000-0002-4960-7458

Riga Technical University, Riga, Latvia K. Dreimanis0000-0003-0972-5641, V.
Veckalns520000-0003-3676-9711

Vilnius University, Vilnius, Lithuania M. Ambrozas0000-0003-2449-0158, A.
Carvalho Antunes De Oliveira0000-0003-2340-836X, A.
Juodagalvis0000-0002-1501-3328, A. Rinkevicius0000-0002-7510-255X, G.
Tamulaitis0000-0002-2913-9634

National Centre for Particle Physics, Universiti Malaya, Kuala Lumpur,
Malaysia N. Bin Norjoharuddeen0000-0002-8818-7476, S.Y.
Hoh530000-0003-3233-5123, Z. Zolkapli

Universidad de Sonora (UNISON), Hermosillo, Mexico J.F.
Benitez0000-0002-2633-6712, A. Castaneda Hernandez0000-0003-4766-1546, H.A.
Encinas Acosta, L.G. Gallegos Maríñez, M. León Coello0000-0002-3761-911X, J.A.
Murillo Quijada0000-0003-4933-2092, A. Sehrawat0000-0002-6816-7814, L.
Valencia Palomo0000-0002-8736-440X

Centro de Investigacion y de Estudios Avanzados del IPN, Mexico City, Mexico
G. Ayala0000-0002-8294-8692, H. Castilla-Valdez0009-0005-9590-9958, E. De La
Cruz-Burelo0000-0002-7469-6974, I. Heredia-De La Cruz540000-0002-8133-6467, R.
Lopez-Fernandez0000-0002-2389-4831, C.A. Mondragon Herrera, D.A. Perez
Navarro0000-0001-9280-4150, R. Reyes-Almanza0000-0002-4600-7772, A. Sánchez
Hernández0000-0001-9548-0358

Universidad Iberoamericana, Mexico City, Mexico C. Oropeza
Barrera0000-0001-9724-0016, F. Vazquez Valencia

Benemerita Universidad Autonoma de Puebla, Puebla, Mexico I.
Pedraza0000-0002-2669-4659, H.A. Salazar Ibarguen0000-0003-4556-7302, C. Uribe
Estrada0000-0002-2425-7340

University of Montenegro, Podgorica, Montenegro I. Bubanja, J. Mijuskovic55,
N. Raicevic0000-0002-2386-2290

University of Auckland, Auckland, New Zealand D. Krofcheck0000-0001-5494-7302

University of Canterbury, Christchurch, New Zealand P.H.
Butler0000-0001-9878-2140

National Centre for Physics, Quaid-I-Azam University, Islamabad, Pakistan A.
Ahmad0000-0002-4770-1897, M.I. Asghar, A. Awais0000-0003-3563-257X, M.I.M.
Awan, M. Gul0000-0002-5704-1896, H.R. Hoorani0000-0002-0088-5043, W.A.
Khan0000-0003-0488-0941, M.A. Shah, M. Shoaib0000-0001-6791-8252, M.
Waqas0000-0002-3846-9483

AGH University of Science and Technology Faculty of Computer Science,
Electronics and Telecommunications, Krakow, Poland V. Avati, L.
Grzanka0000-0002-3599-854X, M. Malawski0000-0001-6005-0243

National Centre for Nuclear Research, Swierk, Poland H.
Bialkowska0000-0002-5956-6258, M. Bluj0000-0003-1229-1442, B.
Boimska0000-0002-4200-1541, M. Górski0000-0003-2146-187X, M.
Kazana0000-0002-7821-3036, M. Szleper0000-0002-1697-004X, P.
Zalewski0000-0003-4429-2888

Institute of Experimental Physics, Faculty of Physics, University of Warsaw,
Warsaw, Poland K. Bunkowski0000-0001-6371-9336, K. Doroba0000-0002-7818-2364,
A. Kalinowski0000-0002-1280-5493, M. Konecki0000-0001-9482-4841, J.
Krolikowski0000-0002-3055-0236

Laboratório de Instrumentação e Física Experimental de Partículas, Lisboa,
Portugal M. Araujo0000-0002-8152-3756, P. Bargassa0000-0001-8612-3332, D.
Bastos0000-0002-7032-2481, A. Boletti0000-0003-3288-7737, P.
Faccioli0000-0003-1849-6692, M. Gallinaro0000-0003-1261-2277, J.
Hollar0000-0002-8664-0134, N. Leonardo0000-0002-9746-4594, T.
Niknejad0000-0003-3276-9482, M. Pisano0000-0002-0264-7217, J.
Seixas0000-0002-7531-0842, O. Toldaiev0000-0002-8286-8780, J.
Varela0000-0003-2613-3146

VINCA Institute of Nuclear Sciences, University of Belgrade, Belgrade, Serbia
P. Adzic560000-0002-5862-7397, M. Dordevic0000-0002-8407-3236, P.
Milenovic0000-0001-7132-3550, J. Milosevic0000-0001-8486-4604

Centro de Investigaciones Energéticas Medioambientales y Tecnológicas
(CIEMAT), Madrid, Spain M. Aguilar-Benitez, J. Alcaraz
Maestre0000-0003-0914-7474, A. Álvarez Fernández0000-0003-1525-4620, I.
Bachiller, M. Barrio Luna, C.A. Carrillo Montoya0000-0002-6245-6535, M.
Cepeda0000-0002-6076-4083, M. Cerrada0000-0003-0112-1691, N.
Colino0000-0002-3656-0259, B. De La Cruz0000-0001-9057-5614, A. Delgado
Peris0000-0002-8511-7958, Cristina F. Bedoya0000-0001-8057-9152, J.P.
Fernández Ramos0000-0002-0122-313X, J. Flix0000-0003-2688-8047, M.C.
Fouz0000-0003-2950-976X, O. Gonzalez Lopez0000-0002-4532-6464, S. Goy
Lopez0000-0001-6508-5090, J.M. Hernandez0000-0001-6436-7547, M.I.
Josa0000-0002-4985-6964, J. León Holgado0000-0002-4156-6460, D.
Moran0000-0002-1941-9333, Á. Navarro Tobar0000-0003-3606-1780, C. Perez
Dengra0000-0003-2821-4249, A. Pérez-Calero Yzquierdo0000-0003-3036-7965, J.
Puerta Pelayo0000-0001-7390-1457, I. Redondo0000-0003-3737-4121, L. Romero, S.
Sánchez Navas0000-0001-6129-9059, L. Urda Gómez0000-0002-7865-5010, C.
Willmott

Universidad Autónoma de Madrid, Madrid, Spain J.F. de
Trocóniz0000-0002-0798-9806

Universidad de Oviedo, Instituto Universitario de Ciencias y Tecnologías
Espaciales de Asturias (ICTEA), Oviedo, Spain B. Alvarez
Gonzalez0000-0001-7767-4810, J. Cuevas0000-0001-5080-0821, J. Fernandez
Menendez0000-0002-5213-3708, S. Folgueras0000-0001-7191-1125, I. Gonzalez
Caballero0000-0002-8087-3199, J.R. González Fernández0000-0002-4825-8188, E.
Palencia Cortezon0000-0001-8264-0287, C. Ramón Álvarez0000-0003-1175-0002, V.
Rodríguez Bouza0000-0002-7225-7310, A. Soto Rodríguez0000-0002-2993-8663, A.
Trapote0000-0002-4030-2551, N. Trevisani0000-0002-5223-9342, C. Vico
Villalba0000-0002-1905-1874

Instituto de Física de Cantabria (IFCA), CSIC-Universidad de Cantabria,
Santander, Spain J.A. Brochero Cifuentes0000-0003-2093-7856, I.J.
Cabrillo0000-0002-0367-4022, A. Calderon0000-0002-7205-2040, J. Duarte
Campderros0000-0003-0687-5214, C. Fernandez Madrazo0000-0001-9748-4336, P.J.
Fernández Manteca0000-0003-2566-7496, M. Fernandez0000-0002-4824-1087, A.
García Alonso, G. Gomez0000-0002-1077-6553, C. Martinez
Rivero0000-0002-3224-956X, P. Martinez Ruiz del Arbol0000-0002-7737-5121, P.
Matorras Cuevas0000-0001-7481-7273, F. Matorras0000-0003-4295-5668, J. Piedra
Gomez0000-0002-9157-1700, C. Prieels, A. Ruiz-Jimeno0000-0002-3639-0368, L.
Scodellaro0000-0002-4974-8330, I. Vila0000-0002-6797-7209, J.M. Vizan
Garcia0000-0002-6823-8854

University of Colombo, Colombo, Sri Lanka D.D.C.
Wickramarathna0000-0002-6941-8478, B. Kailasapathy570000-0003-2424-1303, M.K.
Jayananda, D.U.J. Sonnadara0000-0001-7862-2537

University of Ruhuna, Department of Physics, Matara, Sri Lanka W.G.D.
Dharmaratna0000-0002-6366-837X, K. Liyanage0000-0002-3792-7665, N.
Perera0000-0002-4747-9106, N. Wickramage0000-0001-7760-3537

CERN, European Organization for Nuclear Research, Geneva, Switzerland T.K.
Aarrestad0000-0002-7671-243X, D. Abbaneo0000-0001-9416-1742, J.
Alimena0000-0001-6030-3191, E. Auffray0000-0001-8540-1097, G.
Auzinger0000-0001-7077-8262, J. Baechler, P.
Baillon${}^{\textrm{\textdagger}}$, D. Barney0000-0002-4927-4921, J.
Bendavid0000-0002-7907-1789, M. Bianco0000-0002-8336-3282, B.
Bilin0000-0003-1439-7128, A. Bocci0000-0002-6515-5666, C.
Caillol0000-0002-5642-3040, T. Camporesi0000-0001-5066-1876, M. Capeans
Garrido0000-0001-7727-9175, G. Cerminara0000-0002-2897-5753, N.
Chernyavskaya0000-0002-2264-2229, S.S. Chhibra0000-0002-1643-1388, S.
Choudhury, M. Cipriani0000-0002-0151-4439, L. Cristella0000-0002-4279-1221, D.
d’Enterria0000-0002-5754-4303, A. Dabrowski0000-0003-2570-9676, A.
David0000-0001-5854-7699, A. De Roeck0000-0002-9228-5271, M.M.
Defranchis0000-0001-9573-3714, M. Deile0000-0001-5085-7270, M. Dobson, M.
Dünser0000-0002-8502-2297, N. Dupont, A. Elliott-Peisert, F. Fallavollita58,
A. Florent0000-0001-6544-3679, L. Forthomme0000-0002-3302-336X, G.
Franzoni0000-0001-9179-4253, W. Funk0000-0003-0422-6739, S.
Ghosh0000-0001-6717-0803, S. Giani, D. Gigi, K. Gill, F.
Glege0000-0002-4526-2149, L. Gouskos0000-0002-9547-7471, E.
Govorkova0000-0003-1920-6618, M. Haranko0000-0002-9376-9235, J.
Hegeman0000-0002-2938-2263, V. Innocente0000-0003-3209-2088, T.
James0000-0002-3727-0202, P. Janot0000-0001-7339-4272, J.
Kaspar0000-0001-5639-2267, J. Kieseler0000-0003-1644-7678, M.
Komm0000-0002-7669-4294, N. Kratochwil0000-0001-5297-1878, C.
Lange0000-0002-3632-3157, S. Laurila0000-0001-7507-8636, P.
Lecoq0000-0002-3198-0115, A. Lintuluoto0000-0002-0726-1452, C.
Lourenço0000-0003-0885-6711, B. Maier0000-0001-5270-7540, L.
Malgeri0000-0002-0113-7389, S. Mallios, M. Mannelli0000-0003-3748-8946, A.C.
Marini0000-0003-2351-0487, F. Meijers0000-0002-6530-3657, S.
Mersi0000-0003-2155-6692, E. Meschi0000-0003-4502-6151, F.
Moortgat0000-0001-7199-0046, M. Mulders0000-0001-7432-6634, S. Orfanelli, L.
Orsini, F. Pantaleo0000-0003-3266-4357, E. Perez, M.
Peruzzi0000-0002-0416-696X, A. Petrilli0000-0003-0887-1882, G.
Petrucciani0000-0003-0889-4726, A. Pfeiffer0000-0001-5328-448X, M.
Pierini0000-0003-1939-4268, D. Piparo0009-0006-6958-3111, M.
Pitt0000-0003-2461-5985, H. Qu0000-0002-0250-8655, T. Quast, D.
Rabady0000-0001-9239-0605, A. Racz, G. Reales Gutiérrez, M.
Rovere0000-0001-8048-1622, H. Sakulin0000-0003-2181-7258, J. Salfeld-
Nebgen0000-0003-3879-5622, S. Scarfi, M. Selvaggi0000-0002-5144-9655, A.
Sharma0000-0002-9860-1650, P. Silva0000-0002-5725-041X, W.
Snoeys0000-0003-3541-9066, P. Sphicas590000-0002-5456-5977, A.G. Stahl
Leiton0000-0002-5397-252X, S. Summers0000-0003-4244-2061, K.
Tatar0000-0002-6448-0168, V.R. Tavolaro0000-0003-2518-7521, D. Treille, P.
Tropea0000-0003-1899-2266, A. Tsirou, J. Wanczyk600000-0002-8562-1863, K.A.
Wozniak0000-0002-4395-1581, W.D. Zeuner

Paul Scherrer Institut, Villigen, Switzerland L.
Caminada610000-0001-5677-6033, A. Ebrahimi0000-0003-4472-867X, W.
Erdmann0000-0001-9964-249X, R. Horisberger0000-0002-5594-1321, Q.
Ingram0000-0002-9576-055X, H.C. Kaestli0000-0003-1979-7331, D.
Kotlinski0000-0001-5333-4918, M. Missiroli610000-0002-1780-1344, L.
Noehte610000-0001-6125-7203, T. Rohe0009-0005-6188-7754

ETH Zurich - Institute for Particle Physics and Astrophysics (IPA), Zurich,
Switzerland K. Androsov600000-0003-2694-6542, M. Backhaus0000-0002-5888-2304,
P. Berger, A. Calandri0000-0001-7774-0099, A. De Cosa0000-0003-2533-2856, G.
Dissertori0000-0002-4549-2569, M. Dittmar, M. Donegà0000-0001-9830-0412, C.
Dorfer0000-0002-2163-442X, F. Eble0009-0002-0638-3447, K.
Gedia0009-0006-0914-7684, F. Glessgen0000-0001-5309-1960, T.A. Gómez
Espinosa0000-0002-9443-7769, C. Grab0000-0002-6182-3380, D.
Hits0000-0002-3135-6427, W. Lustermann0000-0003-4970-2217, A.-M.
Lyon0009-0004-1393-6577, R.A. Manzoni0000-0002-7584-5038, L.
Marchese0000-0001-6627-8716, C. Martin Perez0000-0003-1581-6152, M.T.
Meinhard0000-0001-9279-5047, F. Nessi-Tedaldi0000-0002-4721-7966, J.
Niedziela0000-0002-9514-0799, F. Pauss0000-0002-3752-4639, V.
Perovic0009-0002-8559-0531, S. Pigazzini0000-0002-8046-4344, M.G.
Ratti0000-0003-1777-7855, M. Reichmann0000-0002-6220-5496, C.
Reissel0000-0001-7080-1119, T. Reitenspiess0000-0002-2249-0835, B.
Ristic0000-0002-8610-1130, D. Ruini, D.A. Sanz Becerra0000-0002-6610-4019, J.
Steggemann600000-0003-4420-5510, R. Wallny0000-0001-8038-1613

Universität Zürich, Zurich, Switzerland C. Amsler620000-0002-7695-501X, P.
Bärtschi0000-0002-8842-6027, C. Botta0000-0002-8072-795X, D. Brzhechko, M.F.
Canelli0000-0001-6361-2117, K. Cormier0000-0001-7873-3579, A. De
Wit0000-0002-5291-1661, R. Del Burgo, J.K. Heikkilä0000-0002-0538-1469, M.
Huwiler0000-0002-9806-5907, W. Jin0009-0009-8976-7702, A.
Jofrehei0000-0002-8992-5426, B. Kilminster0000-0002-6657-0407, S.
Leontsinis0000-0002-7561-6091, S.P. Liechti0000-0002-1192-1628, A.
Macchiolo0000-0003-0199-6957, P. Meiring, V.M. Mikuni0000-0002-1579-2421, U.
Molinatti0000-0002-9235-3406, I. Neutelings0009-0002-6473-1403, A.
Reimers0000-0002-9438-2059, P. Robmann, S. Sanchez Cruz0000-0002-9991-195X, K.
Schweiger0000-0002-5846-3919, M. Senger0000-0002-1992-5711, Y.
Takahashi0000-0001-5184-2265

National Central University, Chung-Li, Taiwan C. Adloff63, C.M. Kuo, W. Lin,
A. Roy0000-0002-5622-4260, T. Sarkar380000-0003-0582-4167, S.S.
Yu0000-0002-6011-8516

National Taiwan University (NTU), Taipei, Taiwan L. Ceard, Y.
Chao0000-0002-5976-318X, K.F. Chen0000-0003-1304-3782, P.H.
Chen0000-0002-0468-8805, P.s. Chen, H. Cheng0000-0001-6456-7178, W.-S.
Hou0000-0002-4260-5118, Y.y. Li0000-0003-3598-556X, R.-S.
Lu0000-0001-6828-1695, E. Paganis0000-0002-1950-8993, A. Psallidas, A. Steen,
H.y. Wu, E. Yazgan0000-0001-5732-7950, P.r. Yu

Chulalongkorn University, Faculty of Science, Department of Physics, Bangkok,
Thailand B. Asavapibhop0000-0003-1892-7130, C.
Asawatangtrakuldee0000-0003-2234-7219, N. Srimanobhas0000-0003-3563-2959

Çukurova University, Physics Department, Science and Art Faculty, Adana,
Turkey F. Boran0000-0002-3611-390X, S. Damarseckin640000-0003-4427-6220, Z.S.
Demiroglu0000-0001-7977-7127, F. Dolek0000-0001-7092-5517, I.
Dumanoglu650000-0002-0039-5503, E. Eskut, Y. Guler660000-0001-7598-5252, E.
Gurpinar Guler660000-0002-6172-0285, C. Isik, O. Kara, A. Kayis
Topaksu0000-0002-3169-4573, U. Kiminsu0000-0001-6940-7800, G.
Onengut0000-0002-6274-4254, K. Ozdemir67, A. Polatoz, A.E.
Simsek0000-0002-9074-2256, B. Tali680000-0002-7447-5602, U.G.
Tok0000-0002-3039-021X, S. Turkcapar0000-0003-2608-0494, I.S.
Zorbakir0000-0002-5962-2221

Middle East Technical University, Physics Department, Ankara, Turkey G.
Karapinar, K. Ocalan690000-0002-8419-1400, M. Yalvac700000-0003-4915-9162

Bogazici University, Istanbul, Turkey B. Akgun0000-0001-8888-3562, I.O.
Atakisi0000-0002-9231-7464, E. Gülmez0000-0002-6353-518X, M.
Kaya710000-0003-2890-4493, O. Kaya720000-0002-8485-3822, Ö.
Özçelik0000-0003-3227-9248, S. Tekten730000-0002-9624-5525, E.A.
Yetkin740000-0002-9007-8260

Istanbul Technical University, Istanbul, Turkey A. Cakir0000-0002-8627-7689,
K. Cankocak650000-0002-3829-3481, Y. Komurcu0000-0002-7084-030X, S.
Sen750000-0001-7325-1087

Istanbul University, Istanbul, Turkey S. Cerci680000-0002-8702-6152, I.
Hos760000-0002-7678-1101, B. Isildak770000-0002-0283-5234, B.
Kaynak0000-0003-3857-2496, S. Ozkorucuklu0000-0001-5153-9266, H.
Sert0000-0003-0716-6727, C. Simsek, D. Sunar Cerci680000-0002-5412-4688, C.
Zorbilmez0000-0002-5199-061X

Institute for Scintillation Materials of National Academy of Science of
Ukraine, Kharkiv, Ukraine B. Grynyov0000-0002-3299-9985

National Science Centre, Kharkiv Institute of Physics and Technology, Kharkiv,
Ukraine L. Levchuk0000-0001-5889-7410

University of Bristol, Bristol, United Kingdom D. Anthony0000-0002-5016-8886,
E. Bhal0000-0003-4494-628X, S. Bologna, J.J. Brooke0000-0003-2529-0684, A.
Bundock0000-0002-2916-6456, E. Clement0000-0003-3412-4004, D.
Cussans0000-0001-8192-0826, H. Flacher0000-0002-5371-941X, M. Glowacki, J.
Goldstein0000-0003-1591-6014, G.P. Heath, H.F. Heath0000-0001-6576-9740, L.
Kreczko0000-0003-2341-8330, B. Krikler0000-0001-9712-0030, S.
Paramesvaran0000-0003-4748-8296, S. Seif El Nasr-Storey, V.J.
Smith0000-0003-4543-2547, N. Stylianou780000-0002-0113-6829, K. Walkingshaw
Pass, R. White0000-0001-5793-526X

Rutherford Appleton Laboratory, Didcot, United Kingdom K.W.
Bell0000-0002-2294-5860, A. Belyaev790000-0002-1733-4408, C.
Brew0000-0001-6595-8365, R.M. Brown0000-0002-6728-0153, D.J.A.
Cockerill0000-0003-2427-5765, C. Cooke0000-0003-3730-4895, K.V. Ellis, K.
Harder0000-0002-2965-6973, S. Harper0000-0001-5637-2653, M.-L.
Holmberg800000-0002-9473-5985, J. Linacre0000-0001-7555-652X, K. Manolopoulos,
D.M. Newbold0000-0002-9015-9634, E. Olaiya, D. Petyt0000-0002-2369-4469, T.
Reis0000-0003-3703-6624, T. Schuh, C.H. Shepherd-
Themistocleous0000-0003-0551-6949, I.R. Tomalin, T.
Williams0000-0002-8724-4678

Imperial College, London, United Kingdom R. Bainbridge0000-0001-9157-4832, P.
Bloch0000-0001-6716-979X, S. Bonomally, J. Borg0000-0002-7716-7621, S. Breeze,
O. Buchmuller, V. Cepaitis0000-0002-4809-4056, G.S.
Chahal810000-0003-0320-4407, D. Colling0000-0001-9959-4977, P.
Dauncey0000-0001-6839-9466, G. Davies0000-0001-8668-5001, M. Della
Negra0000-0001-6497-8081, S. Fayer, G. Fedi0000-0001-9101-2573, G.
Hall0000-0002-6299-8385, M.H. Hassanshahi0000-0001-6634-4517, G.
Iles0000-0002-1219-5859, J. Langford0000-0002-3931-4379, L.
Lyons0000-0001-7945-9188, A.-M. Magnan0000-0002-4266-1646, S. Malik, A.
Martelli0000-0003-3530-2255, D.G. Monk0000-0002-8377-1999, J.
Nash820000-0003-0607-6519, M. Pesaresi, B.C. Radburn-Smith0000-0003-1488-9675,
D.M. Raymond, A. Richards, A. Rose0000-0002-9773-550X, E.
Scott0000-0003-0352-6836, C. Seez0000-0002-1637-5494, A. Shtipliyski, A.
Tapper0000-0003-4543-864X, K. Uchida0000-0003-0742-2276, T.
Virdee210000-0001-7429-2198, M. Vojinovic0000-0001-8665-2808, N.
Wardle0000-0003-1344-3356, S.N. Webb0000-0003-4749-8814, D. Winterbottom

Brunel University, Uxbridge, United Kingdom K. Coldham, J.E.
Cole0000-0001-5638-7599, A. Khan, P. Kyberd0000-0002-7353-7090, I.D.
Reid0000-0002-9235-779X, L. Teodorescu, S. Zahid0000-0003-2123-3607

Baylor University, Waco, Texas, USA S. Abdullin0000-0003-4885-6935, A.
Brinkerhoff0000-0002-4819-7995, B. Caraway0000-0002-6088-2020, J.
Dittmann0000-0002-1911-3158, K. Hatakeyama0000-0002-6012-2451, A.R.
Kanuganti0000-0002-0789-1200, B. McMaster0000-0002-4494-0446, M.
Saunders0000-0003-1572-9075, S. Sawant0000-0002-1981-7753, C.
Sutantawibul0000-0003-0600-0151, J. Wilson0000-0002-5672-7394

Catholic University of America, Washington, DC, USA R.
Bartek0000-0002-1686-2882, A. Dominguez0000-0002-7420-5493, R.
Uniyal0000-0001-7345-6293, A.M. Vargas Hernandez0000-0002-8911-7197

The University of Alabama, Tuscaloosa, Alabama, USA A.
Buccilli0000-0001-6240-8931, S.I. Cooper0000-0002-4618-0313, D. Di
Croce0000-0002-1122-7919, S.V. Gleyzer0000-0002-6222-8102, C.
Henderson0000-0002-6986-9404, C.U. Perez0000-0002-6861-2674, P.
Rumerio830000-0002-1702-5541, C. West0000-0003-4460-2241

Boston University, Boston, Massachusetts, USA A. Akpinar0000-0001-7510-6617,
A. Albert0000-0003-2369-9507, D. Arcaro0000-0001-9457-8302, C.
Cosby0000-0003-0352-6561, Z. Demiragli0000-0001-8521-737X, C.
Erice0000-0002-6469-3200, E. Fontanesi0000-0002-0662-5904, D.
Gastler0009-0000-7307-6311, S. May0000-0002-6351-6122, J.
Rohlf0000-0001-6423-9799, K. Salyer0000-0002-6957-1077, D.
Sperka0000-0002-4624-2019, D. Spitzbart0000-0003-2025-2742, I.
Suarez0000-0002-5374-6995, A. Tsatsos0000-0001-8310-8911, S.
Yuan0000-0002-2029-024X

Brown University, Providence, Rhode Island, USA G. Benelli0000-0003-4461-8905,
B. Burkle0000-0003-1645-822X, X. Coubez23, D. Cutts0000-0003-1041-7099, M.
Hadley0000-0002-7068-4327, U. Heintz0000-0002-7590-3058, J.M.
Hogan840000-0002-8604-3452, T. Kwon0000-0001-9594-6277, G.
Landsberg0000-0002-4184-9380, K.T. Lau0000-0003-1371-8575, D. Li, M. Lukasik,
J. Luo0000-0002-4108-8681, M. Narain, N. Pervan, S.
Sagir850000-0002-2614-5860, F. Simpson0000-0001-8944-9629, E.
Usai0000-0001-9323-2107, W.Y. Wong, X. Yan0000-0002-6426-0560, D.
Yu0000-0001-5921-5231, W. Zhang

University of California, Davis, Davis, California, USA J.
Bonilla0000-0002-6982-6121, C. Brainerd0000-0002-9552-1006, R.
Breedon0000-0001-5314-7581, M. Calderon De La Barca
Sanchez0000-0001-9835-4349, M. Chertok0000-0002-2729-6273, J.
Conway0000-0003-2719-5779, P.T. Cox0000-0003-1218-2828, R.
Erbacher0000-0001-7170-8944, G. Haza0009-0001-1326-3956, F.
Jensen0000-0003-3769-9081, O. Kukral0009-0007-3858-6659, R. Lander, G.
Mocellin0000-0002-1531-3478, M. Mulhearn0000-0003-1145-6436, D.
Pellett0009-0000-0389-8571, B. Regnery0000-0003-1539-923X, D.
Taylor0000-0002-4274-3983, Y. Yao0000-0002-5990-4245, F.
Zhang0000-0002-6158-2468

University of California, Los Angeles, California, USA M.
Bachtis0000-0003-3110-0701, R. Cousins0000-0002-5963-0467, A.
Datta0000-0003-2695-7719, D. Hamilton0000-0002-5408-169X, J.
Hauser0000-0002-9781-4873, M. Ignatenko0000-0001-8258-5863, M.A.
Iqbal0000-0001-8664-1949, T. Lam0000-0002-0862-7348, W.A.
Nash0009-0004-3633-8967, S. Regnard0000-0002-9818-6725, D.
Saltzberg0000-0003-0658-9146, B. Stone0000-0002-9397-5231, V.
Valuev0000-0002-0783-6703

University of California, Riverside, Riverside, California, USA Y. Chen, R.
Clare0000-0003-3293-5305, J.W. Gary0000-0003-0175-5731, M. Gordon, G.
Hanson0000-0002-7273-4009, G. Karapostoli0000-0002-4280-2541, O.R.
Long0000-0002-2180-7634, N. Manganelli0000-0002-3398-4531, W.
Si0000-0002-5879-6326, S. Wimpenny, Y. Zhang

University of California, San Diego, La Jolla, California, USA J.G. Branson,
P. Chang0000-0002-2095-6320, S. Cittolin, S. Cooperstein0000-0003-0262-3132,
D. Diaz0000-0001-6834-1176, J. Duarte0000-0002-5076-7096, R.
Gerosa0000-0001-8359-3734, L. Giannini0000-0002-5621-7706, J.
Guiang0000-0002-2155-8260, R. Kansal0000-0003-2445-1060, V.
Krutelyov0000-0002-1386-0232, R. Lee0009-0000-4634-0797, J.
Letts0000-0002-0156-1251, M. Masciovecchio0000-0002-8200-9425, F.
Mokhtar0000-0003-2533-3402, M. Pieri0000-0003-3303-6301, B.V. Sathia
Narayanan0000-0003-2076-5126, V. Sharma0000-0003-1736-8795, M.
Tadel0000-0001-8800-0045, F. Würthwein0000-0001-5912-6124, Y.
Xiang0000-0003-4112-7457, A. Yagil0000-0002-6108-4004

University of California, Santa Barbara - Department of Physics, Santa
Barbara, California, USA N. Amin, C. Campagnari0000-0002-8978-8177, M.
Citron0000-0001-6250-8465, G. Collura0000-0002-4160-1844, A.
Dorsett0000-0001-5349-3011, V. Dutta0000-0001-5958-829X, J.
Incandela0000-0001-9850-2030, M. Kilpatrick0000-0002-2602-0566, J.
Kim0000-0002-2072-6082, B. Marsh, H. Mei0000-0002-9838-8327, M.
Oshiro0000-0002-2200-7516, M. Quinnan0000-0003-2902-5597, J.
Richman0000-0002-5189-146X, U. Sarica0000-0002-1557-4424, F.
Setti0000-0001-9800-7822, J. Sheplock0000-0002-8752-1946, P. Siddireddy, D.
Stuart0000-0002-4965-0747, S. Wang0000-0001-7887-1728

California Institute of Technology, Pasadena, California, USA A.
Bornheim0000-0002-0128-0871, O. Cerri, I. Dutta0000-0003-0953-4503, J.M.
Lawhorn0000-0002-8597-9259, N. Lu0000-0002-2631-6770, J.
Mao0009-0002-8988-9987, H.B. Newman0000-0003-0964-1480, T. Q.
Nguyen0000-0003-3954-5131, M. Spiropulu0000-0001-8172-7081, J.R.
Vlimant0000-0002-9705-101X, C. Wang0000-0002-0117-7196, S.
Xie0000-0003-2509-5731, Z. Zhang0000-0002-1630-0986, R.Y.
Zhu0000-0003-3091-7461

Carnegie Mellon University, Pittsburgh, Pennsylvania, USA J.
Alison0000-0003-0843-1641, S. An0000-0002-9740-1622, M.B.
Andrews0000-0001-5537-4518, P. Bryant0000-0001-8145-6322, T.
Ferguson0000-0001-5822-3731, A. Harilal0000-0001-9625-1987, C.
Liu0000-0002-3100-7294, T. Mudholkar0000-0002-9352-8140, M.
Paulini0000-0002-6714-5787, A. Sanchez0000-0002-5431-6989, W.
Terrill0000-0002-2078-8419

University of Colorado Boulder, Boulder, Colorado, USA J.P.
Cumalat0000-0002-6032-5857, W.T. Ford0000-0001-8703-6943, A.
Hassani0009-0008-4322-7682, G. Karathanasis0000-0001-5115-5828, E. MacDonald,
R. Patel, A. Perloff0000-0001-5230-0396, C. Savard0009-0000-7507-0570, N.
Schonbeck0009-0008-3430-7269, K. Stenson0000-0003-4888-205X, K.A.
Ulmer0000-0001-6875-9177, S.R. Wagner0000-0002-9269-5772, N.
Zipper0000-0002-4805-8020

Cornell University, Ithaca, New York, USA J. Alexander0000-0002-2046-342X, S.
Bright-Thonney0000-0003-1889-7824, X. Chen0000-0002-8157-1328, Y.
Cheng0000-0002-2602-935X, D.J. Cranshaw0000-0002-7498-2129, J.
Fan0009-0003-3728-9960, X. Fan0000-0003-2067-0127, D.
Gadkari0000-0002-6625-8085, S. Hogan0000-0003-3657-2281, J.
Monroy0000-0002-7394-4710, J.R. Patterson0000-0002-3815-3649, D.
Quach0000-0002-1622-0134, J. Reichert0000-0003-2110-8021, M.
Reid0000-0001-7706-1416, A. Ryd0000-0001-5849-1912, J.
Thom0000-0002-4870-8468, P. Wittich0000-0002-7401-2181, R.
Zou0000-0002-0542-1264

Fermi National Accelerator Laboratory, Batavia, Illinois, USA M.
Albrow0000-0001-7329-4925, M. Alyari0000-0001-9268-3360, G.
Apollinari0000-0002-5212-5396, A. Apresyan0000-0002-6186-0130, A.
Apyan0000-0002-9418-6656, L.A.T. Bauerdick0000-0002-7170-9012, D.
Berry0000-0002-5383-8320, J. Berryhill0000-0002-8124-3033, P.C.
Bhat0000-0003-3370-9246, K. Burkett0000-0002-2284-4744, J.N.
Butler0000-0002-0745-8618, A. Canepa0000-0003-4045-3998, G.B.
Cerati0000-0003-3548-0262, H.W.K. Cheung0000-0001-6389-9357, F.
Chlebana0000-0002-8762-8559, K.F. Di Petrillo0000-0001-8001-4602, J.
Dickinson0000-0001-5450-5328, V.D. Elvira0000-0003-4446-4395, Y.
Feng0000-0003-2812-338X, J. Freeman0000-0002-3415-5671, A.
Gandrakota0000-0003-4860-3233, Z. Gecse0009-0009-6561-3418, L.
Gray0000-0002-6408-4288, D. Green, S. Grünendahl0000-0002-4857-0294, O.
Gutsche0000-0002-8015-9622, R.M. Harris0000-0003-1461-3425, R.
Heller0000-0002-7368-6723, T.C. Herwig0000-0002-4280-6382, J.
Hirschauer0000-0002-8244-0805, B. Jayatilaka0000-0001-7912-5612, S.
Jindariani0009-0000-7046-6533, M. Johnson0000-0001-7757-8458, U.
Joshi0000-0001-8375-0760, T. Klijnsma0000-0003-1675-6040, B.
Klima0000-0002-3691-7625, K.H.M. Kwok0000-0002-8693-6146, S.
Lammel0000-0003-0027-635X, D. Lincoln0000-0002-0599-7407, R.
Lipton0000-0002-6665-7289, T. Liu0009-0007-6522-5605, C.
Madrid0000-0003-3301-2246, K. Maeshima0009-0000-2822-897X, C.
Mantilla0000-0002-0177-5903, D. Mason0000-0002-0074-5390, P.
McBride0000-0001-6159-7750, P. Merkel0000-0003-4727-5442, S.
Mrenna0000-0001-8731-160X, S. Nahn0000-0002-8949-0178, J.
Ngadiuba0000-0002-0055-2935, V. Papadimitriou0000-0002-0690-7186, N.
Pastika0009-0006-0993-6245, K. Pedro0000-0003-2260-9151, C.
Pena860000-0002-4500-7930, F. Ravera0000-0003-3632-0287, A. Reinsvold
Hall870000-0003-1653-8553, L. Ristori0000-0003-1950-2492, E. Sexton-
Kennedy0000-0001-9171-1980, N. Smith0000-0002-0324-3054, A.
Soha0000-0002-5968-1192, L. Spiegel0000-0001-9672-1328, J.
Strait0000-0002-7233-8348, L. Taylor0000-0002-6584-2538, S.
Tkaczyk0000-0001-7642-5185, N.V. Tran0000-0002-8440-6854, L.
Uplegger0000-0002-9202-803X, E.W. Vaandering0000-0003-3207-6950, H.A.
Weber0000-0002-5074-0539, I. Zoi0000-0002-5738-9446

University of Florida, Gainesville, Florida, USA P. Avery0000-0003-0609-627X,
D. Bourilkov0000-0003-0260-4935, L. Cadamuro0000-0001-8789-610X, V.
Cherepanov0000-0002-6748-4850, R.D. Field, D. Guerrero0000-0001-5552-5400, M.
Kim, E. Koenig0000-0002-0884-7922, J. Konigsberg0000-0001-6850-8765, A.
Korytov0000-0001-9239-3398, K.H. Lo, K. Matchev0000-0003-4182-9096, N.
Menendez0000-0002-3295-3194, G. Mitselmakher0000-0001-5745-3658, A.
Muthirakalayil Madhu0000-0003-1209-3032, N. Rawal0000-0002-7734-3170, D.
Rosenzweig0000-0002-3687-5189, S. Rosenzweig0000-0002-5613-1507, K.
Shi0000-0002-2475-0055, J. Wang0000-0003-3879-4873, Z. Wu0000-0003-2165-9501,
E. Yigitbasi0000-0002-9595-2623, X. Zuo0000-0002-0029-493X

Florida State University, Tallahassee, Florida, USA T.
Adams0000-0001-8049-5143, A. Askew0000-0002-7172-1396, R.
Habibullah0000-0002-3161-8300, V. Hagopian0000-0002-3791-1989, K.F. Johnson,
R. Khurana, T. Kolberg0000-0002-0211-6109, G. Martinez, H.
Prosper0000-0002-4077-2713, C. Schiber, O. Viazlo0000-0002-2957-0301, R.
Yohay0000-0002-0124-9065, J. Zhang

Florida Institute of Technology, Melbourne, Florida, USA M.M.
Baarmand0000-0002-9792-8619, S. Butalla0000-0003-3423-9581, T.
Elkafrawy880000-0001-9930-6445, M. Hohlmann0000-0003-4578-9319, R. Kumar
Verma0000-0002-8264-156X, D. Noonan0000-0002-3932-3769, M. Rahmani, F.
Yumiceva0000-0003-2436-5074

University of Illinois at Chicago (UIC), Chicago, Illinois, USA M.R.
Adams0000-0001-8493-3737, H. Becerril Gonzalez0000-0001-5387-712X, R.
Cavanaugh0000-0001-7169-3420, S. Dittmer0000-0002-5359-9614, O.
Evdokimov0000-0002-1250-8931, C.E. Gerber0000-0002-8116-9021, D.J.
Hofman0000-0002-2449-3845, A.H. Merrit0000-0003-3922-6464, C.
Mills0000-0001-8035-4818, G. Oh0000-0003-0744-1063, T. Roy0000-0001-7299-7653,
S. Rudrabhatla0000-0002-7366-4225, M.B. Tonjes0000-0002-2617-9315, N.
Varelas0000-0002-9397-5514, J. Viinikainen0000-0003-2530-4265, X.
Wang0000-0003-2792-8493, Z. Ye0000-0001-6091-6772

The University of Iowa, Iowa City, Iowa, USA M. Alhusseini0000-0002-9239-470X,
K. Dilsiz890000-0003-0138-3368, L. Emediato, R.P.
Gandrajula0000-0001-9053-3182, O.K. Köseyan0000-0001-9040-3468, J.-P. Merlo,
A. Mestvirishvili900000-0002-8591-5247, J. Nachtman0000-0003-3951-3420, H.
Ogul910000-0002-5121-2893, Y. Onel0000-0002-8141-7769, A.
Penzo0000-0003-3436-047X, C. Snyder, E. Tiras920000-0002-5628-7464

Johns Hopkins University, Baltimore, Maryland, USA O.
Amram0000-0002-3765-3123, B. Blumenfeld0000-0003-1150-1735, L.
Corcodilos0000-0001-6751-3108, J. Davis0000-0001-6488-6195, A.V.
Gritsan0000-0002-3545-7970, S. Kyriacou0000-0002-9254-4368, P.
Maksimovic0000-0002-2358-2168, J. Roskes0000-0001-8761-0490, M.
Swartz0000-0002-0286-5070, T.Á. Vámi0000-0002-0959-9211

The University of Kansas, Lawrence, Kansas, USA A. Abreu0000-0002-9000-2215,
J. Anguiano0000-0002-7349-350X, P. Baringer0000-0002-3691-8388, A.
Bean0000-0001-5967-8674, Z. Flowers0000-0001-8314-2052, T.
Isidori0000-0002-7934-4038, S. Khalil0000-0001-8630-8046, J.
King0000-0001-9652-9854, G. Krintiras0000-0002-0380-7577, A.
Kropivnitskaya0000-0002-8751-6178, M. Lazarovits0000-0002-5565-3119, C. Le
Mahieu0000-0001-5924-1130, C. Lindsey, J. Marquez0000-0003-3887-4048, N.
Minafra0000-0003-4002-1888, M. Murray0000-0001-7219-4818, M.
Nickel0000-0003-0419-1329, C. Rogan0000-0002-4166-4503, C.
Royon0000-0002-7672-9709, R. Salvatico0000-0002-2751-0567, S.
Sanders0000-0002-9491-6022, E. Schmitz0000-0002-2484-1774, C.
Smith0000-0003-0505-0528, Q. Wang0000-0003-3804-3244, Z. Warner, J.
Williams0000-0002-9810-7097, G. Wilson0000-0003-0917-4763

Kansas State University, Manhattan, Kansas, USA S. Duric, A.
Ivanov0000-0002-9270-5643, K. Kaadze0000-0003-0571-163X, D. Kim, Y.
Maravin0000-0002-9449-0666, T. Mitchell, A. Modak, K. Nam

Lawrence Livermore National Laboratory, Livermore, California, USA F.
Rebassoo0000-0001-8934-9329, D. Wright0000-0002-3586-3354

University of Maryland, College Park, Maryland, USA E.
Adams0000-0003-2809-2683, A. Baden0000-0002-6159-3861, O. Baron, A.
Belloni0000-0002-1727-656X, S.C. Eno0000-0003-4282-2515, N.J.
Hadley0000-0002-1209-6471, S. Jabeen0000-0002-0155-7383, R.G.
Kellogg0000-0001-9235-521X, T. Koeth0000-0002-0082-0514, Y.
Lai0000-0002-7795-8693, S. Lascio0000-0001-8579-5874, A.C.
Mignerey0000-0001-5164-6969, S. Nabili0000-0002-6893-1018, C.
Palmer0000-0002-5801-5737, M. Seidel0000-0003-3550-6151, A.
Skuja0000-0002-7312-6339, L. Wang0000-0003-3443-0626, K.
Wong0000-0002-9698-1354

Massachusetts Institute of Technology, Cambridge, Massachusetts, USA D.
Abercrombie, G. Andreassi, R. Bi, W. Busza0000-0002-3831-9071, I.A.
Cali0000-0002-2822-3375, Y. Chen0000-0003-2582-6469, M.
D’Alfonso0000-0002-7409-7904, J. Eysermans0000-0001-6483-7123, C.
Freer0000-0002-7967-4635, G. Gomez-Ceballos0000-0003-1683-9460, M. Goncharov,
P. Harris, M. Hu0000-0003-2858-6931, M. Klute0000-0002-0869-5631, D.
Kovalskyi0000-0002-6923-293X, J. Krupa0000-0003-0785-7552, Y.-J.
Lee0000-0003-2593-7767, K. Long0000-0003-0664-1653, C.
Mironov0000-0002-8599-2437, C. Paus0000-0002-6047-4211, D.
Rankin0000-0001-8411-9620, C. Roland0000-0002-7312-5854, G.
Roland0000-0001-8983-2169, Z. Shi0000-0001-5498-8825, G.S.F.
Stephans0000-0003-3106-4894, J. Wang, Z. Wang0000-0002-3074-3767, B.
Wyslouch0000-0003-3681-0649

University of Minnesota, Minneapolis, Minnesota, USA R.M. Chatterjee, A.
Evans0000-0002-7427-1079, J. Hiltbrand0000-0003-1691-5937, Sh.
Jain0000-0003-1770-5309, B.M. Joshi0000-0002-4723-0968, M.
Krohn0000-0002-1711-2506, Y. Kubota0000-0001-6146-4827, J.
Mans0000-0003-2840-1087, M. Revering0000-0001-5051-0293, R.
Rusack0000-0002-7633-749X, R. Saradhy0000-0001-8720-293X, N.
Schroeder0000-0002-8336-6141, N. Strobbe0000-0001-8835-8282, M.A.
Wadud0000-0002-0653-0761

University of Nebraska-Lincoln, Lincoln, Nebraska, USA K.
Bloom0000-0002-4272-8900, M. Bryson, S. Chauhan0000-0002-6544-5794, D.R.
Claes0000-0003-4198-8919, C. Fangmeier0000-0002-5998-8047, L.
Finco0000-0002-2630-5465, F. Golf0000-0003-3567-9351, C.
Joo0000-0002-5661-4330, I. Kravchenko0000-0003-0068-0395, I.
Reed0000-0002-1823-8856, J.E. Siado0000-0002-9757-470X, G.R.
Snow${}^{\textrm{\textdagger}}$, W. Tabb0000-0002-9542-4847, A.
Wightman0000-0001-6651-5320, F. Yan0000-0002-4042-0785, A.G.
Zecchinelli0000-0001-8986-278X

State University of New York at Buffalo, Buffalo, New York, USA G.
Agarwal0000-0002-2593-5297, H. Bandyopadhyay0000-0001-9726-4915, L.
Hay0000-0002-7086-7641, I. Iashvili0000-0003-1948-5901, A.
Kharchilava0000-0002-3913-0326, C. McLean0000-0002-7450-4805, D.
Nguyen0000-0002-5185-8504, J. Pekkanen0000-0002-6681-7668, S.
Rappoccio0000-0002-5449-2560, A. Williams0000-0003-4055-6532

Northeastern University, Boston, Massachusetts, USA G.
Alverson0000-0001-6651-1178, E. Barberis0000-0002-6417-5913, Y.
Haddad0000-0003-4916-7752, Y. Han0000-0002-3510-6505, A. Hortiangtham, A.
Krishna0000-0002-4319-818X, J. Li0000-0001-5245-2074, J.
Lidrych0000-0003-1439-0196, G. Madigan0000-0001-8796-5865, B.
Marzocchi0000-0001-6687-6214, D.M. Morse0000-0003-3163-2169, V.
Nguyen0000-0003-1278-9208, T. Orimoto0000-0002-8388-3341, A.
Parker0000-0002-9421-3335, L. Skinnari0000-0002-2019-6755, A. Tishelman-
Charny0000-0002-7332-5098, T. Wamorkar0000-0001-5551-5456, B.
Wang0000-0003-0796-2475, A. Wisecarver, D. Wood0000-0002-6477-801X

Northwestern University, Evanston, Illinois, USA S.
Bhattacharya0000-0002-0526-6161, J. Bueghly, Z. Chen0000-0003-4521-6086, A.
Gilbert0000-0001-7560-5790, T. Gunter0000-0002-7444-5622, K.A.
Hahn0000-0001-7892-1676, Y. Liu0000-0002-5588-1760, N.
Odell0000-0001-7155-0665, M.H. Schmitt0000-0003-0814-3578, M. Velasco

University of Notre Dame, Notre Dame, Indiana, USA R. Band0000-0003-4873-0523,
R. Bucci, M. Cremonesi, A. Das0000-0001-9115-9698, R.
Goldouzian0000-0002-0295-249X, M. Hildreth0000-0002-4454-3934, K. Hurtado
Anampa0000-0002-9779-3566, C. Jessop0000-0002-6885-3611, K.
Lannon0000-0002-9706-0098, J. Lawrence, N. Loukas0000-0003-0049-6918, L.
Lutton0000-0002-3212-4505, J. Mariano, N. Marinelli, I. Mcalister, T.
McCauley0000-0001-6589-8286, C. Mcgrady0000-0002-8821-2045, K. Mohrman, C.
Moore0000-0002-8140-4183, Y. Musienko140009-0006-3545-1938, R.
Ruchti0000-0002-3151-1386, A. Townsend0000-0002-3696-689X, M.
Wayne0000-0001-8204-6157, M. Zarucki0000-0003-1510-5772, L.
Zygala0000-0001-9665-7282

The Ohio State University, Columbus, Ohio, USA B. Bylsma, L.S.
Durkin0000-0002-0477-1051, B. Francis0000-0002-1414-6583, C.
Hill0000-0003-0059-0779, A. Lesauvage0000-0003-3437-7845, M. Nunez
Ornelas0000-0003-2663-7379, K. Wei, B.L. Winer0000-0001-9980-4698, B. R.
Yates0000-0001-7366-1318

Princeton University, Princeton, New Jersey, USA F.M.
Addesa0000-0003-0484-5804, B. Bonham0000-0002-2982-7621, P.
Das0000-0002-9770-1377, G. Dezoort0000-0002-5890-0445, P.
Elmer0000-0001-6830-3356, A. Frankenthal0000-0002-2583-5982, B.
Greenberg0000-0002-4922-1934, N. Haubrich0000-0002-7625-8169, S.
Higginbotham0000-0002-4436-5461, A. Kalogeropoulos0000-0003-3444-0314, G.
Kopp0000-0001-8160-0208, S. Kwan0000-0002-5308-7707, D.
Lange0000-0002-9086-5184, D. Marlow0000-0002-6395-1079, K.
Mei0000-0003-2057-2025, I. Ojalvo0000-0003-1455-6272, J.
Olsen0000-0002-9361-5762, D. Stickland0000-0003-4702-8820, C.
Tully0000-0001-6771-2174

University of Puerto Rico, Mayaguez, Puerto Rico, USA S.
Malik0000-0002-6356-2655, S. Norberg

Purdue University, West Lafayette, Indiana, USA A.S.
Bakshi0000-0002-2857-6883, V.E. Barnes0000-0001-6939-3445, R.
Chawla0000-0003-4802-6819, S. Das0000-0001-6701-9265, L. Gutay, M.
Jones0000-0002-9951-4583, A.W. Jung0000-0003-3068-3212, D.
Kondratyev0000-0002-7874-2480, A.M. Koshy, M. Liu0000-0001-9012-395X, G.
Negro, N. Neumeister0000-0003-2356-1700, G. Paspalaki0000-0001-6815-1065, S.
Piperov0000-0002-9266-7819, A. Purohit0000-0003-0881-612X, J.F.
Schulte0000-0003-4421-680X, M. Stojanovic0000-0002-1542-0855, J.
Thieman0000-0001-7684-6588, F. Wang0000-0002-8313-0809, R.
Xiao0000-0001-7292-8527, W. Xie0000-0003-1430-9191

Purdue University Northwest, Hammond, Indiana, USA J.
Dolen0000-0003-1141-3823, N. Parashar0009-0009-1717-0413

Rice University, Houston, Texas, USA D. Acosta0000-0001-5367-1738, A.
Baty0000-0001-5310-3466, T. Carnahan0000-0001-7492-3201, M. Decaro, S.
Dildick0000-0003-0554-4755, K.M. Ecklund0000-0002-6976-4637, S. Freed, P.
Gardner, F.J.M. Geurts0000-0003-2856-9090, A. Kumar0000-0002-5180-6595, W.
Li0000-0003-4136-3409, B.P. Padley0000-0002-3572-5701, R. Redjimi, J.
Rotter0009-0009-4040-7407, W. Shi0000-0002-8102-9002, S.
Yang0000-0002-2075-8631, L. Zhang93, Y. Zhang0000-0002-6812-761X

University of Rochester, Rochester, New York, USA A. Bodek0000-0003-0409-0341,
P. de Barbaro0000-0002-5508-1827, R. Demina0000-0002-7852-167X, J.L.
Dulemba0000-0002-9842-7015, C. Fallon, T. Ferbel0000-0002-6733-131X, M.
Galanti, A. Garcia-Bellido0000-0002-1407-1972, O.
Hindrichs0000-0001-7640-5264, A. Khukhunaishvili0000-0002-3834-1316, E.
Ranken0000-0001-7472-5029, R. Taus0000-0002-5168-2932, G.P. Van
Onsem0000-0002-1664-2337

The Rockefeller University, New York, New York, USA K.
Goulianos0000-0002-6230-9535

Rutgers, The State University of New Jersey, Piscataway, New Jersey, USA B.
Chiarito, J.P. Chou0000-0001-6315-905X, Y. Gershtein0000-0002-4871-5449, E.
Halkiadakis0000-0002-3584-7856, A. Hart0000-0003-2349-6582, M.
Heindl0000-0002-2831-463X, O. Karacheban250000-0002-2785-3762, I.
Laflotte0000-0002-7366-8090, A. Lath0000-0003-0228-9760, R. Montalvo, K. Nash,
M. Osherson0000-0002-9760-9976, S. Salur0000-0002-4995-9285, S. Schnetzer, S.
Somalwar0000-0002-8856-7401, R. Stone0000-0001-6229-695X, S.A.
Thayil0000-0002-1469-0335, S. Thomas, H. Wang0000-0002-3027-0752

University of Tennessee, Knoxville, Tennessee, USA H. Acharya, A.G.
Delannoy0000-0003-1252-6213, S. Fiorendi0000-0003-3273-9419, T.
Holmes0000-0002-3959-5174, S. Spanier0000-0002-7049-4646

Texas A&M University, College Station, Texas, USA O.
Bouhali940000-0001-7139-7322, M. Dalchenko0000-0002-0137-136X, A.
Delgado0000-0003-3453-7204, R. Eusebi0000-0003-3322-6287, J.
Gilmore0000-0001-9911-0143, T. Huang0000-0002-0793-5664, T.
Kamon950000-0001-5565-7868, H. Kim0000-0003-4986-1728, S.
Luo0000-0003-3122-4245, S. Malhotra, R. Mueller0000-0002-6723-6689, D.
Overton0009-0009-0648-8151, D. Rathjens0000-0002-8420-1488, A.
Safonov0000-0001-9497-5471

Texas Tech University, Lubbock, Texas, USA N. Akchurin0000-0002-6127-4350, J.
Damgov0000-0003-3863-2567, V. Hegde0000-0003-4952-2873, K.
Lamichhane0000-0003-0152-7683, S.W. Lee0000-0002-3388-8339, T. Mengke, S.
Muthumuni0000-0003-0432-6895, T. Peltola0000-0002-4732-4008, I.
Volobouev0000-0002-2087-6128, Z. Wang, A. Whitbeck0000-0003-4224-5164

Vanderbilt University, Nashville, Tennessee, USA E. Appelt0000-0003-3389-4584,
S. Greene, A. Gurrola0000-0002-2793-4052, W. Johns0000-0001-5291-8903, A.
Melo0000-0003-3473-8858, F. Romeo0000-0002-1297-6065, P.
Sheldon0000-0003-1550-5223, S. Tuo0000-0001-6142-0429, J.
Velkovska0000-0003-1423-5241

University of Virginia, Charlottesville, Virginia, USA M.W.
Arenton0000-0002-6188-1011, B. Cardwell0000-0001-5553-0891, B.
Cox0000-0003-3752-4759, G. Cummings0000-0002-8045-7806, J.
Hakala0000-0001-9586-3316, R. Hirosky0000-0003-0304-6330, M.
Joyce0000-0003-1112-5880, A. Ledovskoy0000-0003-4861-0943, A.
Li0000-0002-4547-116X, C. Neu0000-0003-3644-8627, C.E. Perez
Lara0000-0003-0199-8864, B. Tannenwald0000-0002-5570-8095, S.
White0000-0002-6181-4935

Wayne State University, Detroit, Michigan, USA N. Poudyal0000-0003-4278-3464

University of Wisconsin - Madison, Madison, Wisconsin, USA S.
Banerjee0000-0001-7880-922X, K. Black0000-0001-7320-5080, T.
Bose0000-0001-8026-5380, S. Dasu0000-0001-5993-9045, I. De
Bruyn0000-0003-1704-4360, P. Everaerts0000-0003-3848-324X, C. Galloni, H.
He0009-0008-3906-2037, M. Herndon0000-0003-3043-1090, A.
Herve0000-0002-1959-2363, U. Hussain, A. Lanaro, A.
Loeliger0000-0002-5017-1487, R. Loveless0000-0002-2562-4405, J. Madhusudanan
Sreekala0000-0003-2590-763X, A. Mallampalli0000-0002-3793-8516, A.
Mohammadi0000-0001-8152-927X, D. Pinna, A. Savin, V. Shang0000-0002-1436-6092,
V. Sharma0000-0003-1287-1471, W.H. Smith0000-0003-3195-0909, D. Teague, S.
Trembath-Reichert, W. Vetens0000-0003-1058-1163

Authors affiliated with an institute or an international laboratory covered by
a cooperation agreement with CERN S. Afanasiev, V. Andreev0000-0002-5492-6920,
Yu. Andreev0000-0002-7397-9665, T. Aushev0000-0002-6347-7055, M.
Azarkin0000-0002-7448-1447, A. Babaev0000-0001-8876-3886, A.
Belyaev0000-0003-1692-1173, V. Blinov96, E. Boos0000-0002-0193-5073, V.
Borshch0000-0002-5479-1982, D. Budkouski0000-0002-2029-1007, M.
Chadeeva960000-0003-1814-1218, V. Chekhovsky, A. Dermenev0000-0001-5619-376X,
T. Dimova960000-0002-9560-0660, I. Dremin0000-0001-7451-247X, M.
Dubinin860000-0002-7766-7175, L. Dudko0000-0002-4462-3192, V. Epshteyn, A.
Ershov0000-0001-5779-142X, G. Gavrilov0000-0001-9689-7999, V.
Gavrilov0000-0002-9617-2928, S. Gninenko0000-0001-6495-7619, V.
Golovtcov0000-0002-0595-0297, N. Golubev0000-0002-9504-7754, I. Golutvin, I.
Gorbunov0000-0003-3777-6606, A. Gribushin0000-0002-5252-4645, Y.
Ivanov0000-0001-5163-7632, V. Ivanchenko0000-0002-1844-5433, V.
Kachanov0000-0002-3062-010X, A. Kaminskiy97, L. Kardapoltsev96, V.
Karjavine0000-0002-5326-3854, A. Karneyeu0000-0001-9983-1004, V.
Kim960000-0001-7161-2133, M. Kirakosyan, D. Kirpichnikov0000-0002-7177-077X,
M. Kirsanov0000-0002-8879-6538, V. Klyukhin0000-0002-8577-6531, O.
Kodolova980000-0003-1342-4251, D. Konstantinov0000-0001-6673-7273, V.
Korenkov0000-0002-2342-7862, A. Kozyrev960000-0003-0684-9235, N.
Krasnikov0000-0002-8717-6492, E. Kuznetsova99, A. Lanev0000-0001-8244-7321, A.
Litomin, N. Lychkovskaya0000-0001-5084-9019, V. Makarenko0000-0002-8406-8605,
A. Malakhov0000-0001-8569-8409, V. Matveev960000-0002-2745-5908, V.
Murzin0000-0002-0554-4627, A. Nikitenko1000000-0002-1933-5383, S.
Obraztsov0009-0001-1152-2758, V. Okhotnikov0000-0003-3088-0048, V.
Oreshkin0000-0003-4749-4995, A. Oskin, I. Ovtin960000-0002-2583-1412, V.
Palichik0009-0008-0356-1061, P. Parygin0000-0001-6743-3781, A. Pashenkov, V.
Perelygin0009-0005-5039-4874, S. Petrushanko0000-0003-0210-9061, G.
Pivovarov0000-0001-6435-4463, S. Polikarpov960000-0001-6839-928X, V. Popov, E.
Popova0000-0001-7556-8969, O. Radchenko960000-0001-7116-9469, M.
Savina0000-0002-9020-7384, V. Savrin0009-0000-3973-2485, D.
Selivanova0000-0002-7031-9434, V. Shalaev0000-0002-2893-6922, S.
Shmatov0000-0001-5354-8350, S. Shulha0000-0002-4265-928X, Y.
Skovpen960000-0002-3316-0604, S. Slabospitskii0000-0001-8178-2494, I. Smirnov,
V. Smirnov, D. Sosnov0000-0002-7452-8380, A. Stepennov0000-0001-7747-6582, V.
Sulimov0009-0009-8645-6685, E. Tcherniaev0000-0002-3685-0635, A.
Terkulov0000-0003-4985-3226, O. Teryaev0000-0001-7002-9093, M.
Toms0000-0002-7703-3973, A. Toropin0000-0002-2106-4041, L.
Uvarov0000-0002-7602-2527, A. Uzunian0000-0002-7007-9020, E.
Vlasov0000-0002-8628-2090, S. Volkov, A. Vorobyev, N.
Voytishin0000-0001-6590-6266, B.S. Yuldashev101, A.
Zarubin0000-0002-1964-6106, I. Zhizhin0000-0001-6171-9682, A.
Zhokin0000-0001-7178-5907

†: Deceased
1Also at YEREVAN STATE UNIVERSITY, Yerevan, Armenia
2Also at TU Wien, Vienna, Austria
3Also at Institute of Basic and Applied Sciences, Faculty of Engineering, Arab
Academy for Science, Technology and Maritime Transport, Alexandria, Egypt
4Also at Université Libre de Bruxelles, Bruxelles, Belgium
5Also at Universidade Estadual de Campinas, Campinas, Brazil
6Also at Federal University of Rio Grande do Sul, Porto Alegre, Brazil
7Also at UFMS, Nova Andradina, Brazil
8Also at The University of the State of Amazonas, Manaus, Brazil
9Also at University of Chinese Academy of Sciences, Beijing, China
10Also at Department of Physics, Tsinghua University, Beijing, China
11Also at Nanjing Normal University Department of Physics, Nanjing, China
12Now at The University of Iowa, Iowa City, Iowa, USA
13Also at University of Chinese Academy of Sciences, Beijing, China
14Also at an institute or an international laboratory covered by a cooperation
agreement with CERN
15Also at Cairo University, Cairo, Egypt
16Also at Suez University, Suez, Egypt
17Now at British University in Egypt, Cairo, Egypt
18Also at Purdue University, West Lafayette, Indiana, USA
19Also at Université de Haute Alsace, Mulhouse, France
20Also at Erzincan Binali Yildirim University, Erzincan, Turkey
21Also at CERN, European Organization for Nuclear Research, Geneva,
Switzerland
22Also at University of Hamburg, Hamburg, Germany
23Also at RWTH Aachen University, III. Physikalisches Institut A, Aachen,
Germany
24Also at Isfahan University of Technology, Isfahan, Iran
25Also at Brandenburg University of Technology, Cottbus, Germany
26Also at Forschungszentrum Jülich, Juelich, Germany
27Also at Physics Department, Faculty of Science, Assiut University, Assiut,
Egypt
28Also at Karoly Robert Campus, MATE Institute of Technology, Gyongyos,
Hungary
29Also at Institute of Physics, University of Debrecen, Debrecen, Hungary
30Also at Institute of Nuclear Research ATOMKI, Debrecen, Hungary
31Now at Universitatea Babes-Bolyai - Facultatea de Fizica, Cluj-Napoca,
Romania
32Also at MTA-ELTE Lendület CMS Particle and Nuclear Physics Group, Eötvös
Loránd University, Budapest, Hungary
33Also at Faculty of Informatics, University of Debrecen, Debrecen, Hungary
34Also at Wigner Research Centre for Physics, Budapest, Hungary
35Also at Punjab Agricultural University, Ludhiana, India
36Also at UPES - University of Petroleum and Energy Studies, Dehradun, India
37Also at University of Hyderabad, Hyderabad, India
38Also at University of Visva-Bharati, Santiniketan, India
39Also at Indian Institute of Science (IISc), Bangalore, India
40Also at Indian Institute of Technology (IIT), Mumbai, India
41Also at IIT Bhubaneswar, Bhubaneswar, India
42Also at Institute of Physics, Bhubaneswar, India
43Also at Department of Electrical and Computer Engineering, Isfahan
University of Technology, Isfahan, Iran
44Also at Sharif University of Technology, Tehran, Iran
45Also at Department of Physics, University of Science and Technology of
Mazandaran, Behshahr, Iran
46Also at Helwan University, Cairo, Egypt
47Also at Italian National Agency for New Technologies, Energy and Sustainable
Economic Development, Bologna, Italy
48Also at Centro Siciliano di Fisica Nucleare e di Struttura Della Materia,
Catania, Italy
49Also at Scuola Superiore Meridionale, Università di Napoli ’Federico II’,
Napoli, Italy
50Also at Università di Napoli ’Federico II’, Napoli, Italy
51Also at Consiglio Nazionale delle Ricerche - Istituto Officina dei
Materiali, Perugia, Italy
52Also at Riga Technical University, Riga, Latvia
53Also at Department of Applied Physics, Faculty of Science and Technology,
Universiti Kebangsaan Malaysia, Bangi, Malaysia
54Also at Consejo Nacional de Ciencia y Tecnología, Mexico City, Mexico
55Also at IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France
56Also at Faculty of Physics, University of Belgrade, Belgrade, Serbia
57Also at Trincomalee Campus, Eastern University, Sri Lanka, Nilaveli, Sri
Lanka
58Also at INFN Sezione di Pavia, Università di Pavia, Pavia, Italy
59Also at National and Kapodistrian University of Athens, Athens, Greece
60Also at Ecole Polytechnique Fédérale Lausanne, Lausanne, Switzerland
61Also at Universität Zürich, Zurich, Switzerland
62Also at Stefan Meyer Institute for Subatomic Physics, Vienna, Austria
63Also at Laboratoire d’Annecy-le-Vieux de Physique des Particules,
IN2P3-CNRS, Annecy-le-Vieux, France
64Also at Şırnak University, Sirnak, Turkey
65Also at Near East University, Research Center of Experimental Health
Science, Mersin, Turkey
66Also at Konya Technical University, Konya, Turkey
67Also at Piri Reis University, Istanbul, Turkey
68Also at Adiyaman University, Adiyaman, Turkey
69Also at Necmettin Erbakan University, Konya, Turkey
70Also at Bozok Universitetesi Rektörlügü, Yozgat, Turkey
71Also at Marmara University, Istanbul, Turkey
72Also at Milli Savunma University, Istanbul, Turkey
73Also at Kafkas University, Kars, Turkey
74Also at Istanbul Bilgi University, Istanbul, Turkey
75Also at Hacettepe University, Ankara, Turkey
76Also at Istanbul University - Cerrahpasa, Faculty of Engineering, Istanbul,
Turkey
77Also at Ozyegin University, Istanbul, Turkey
78Also at Vrije Universiteit Brussel, Brussel, Belgium
79Also at School of Physics and Astronomy, University of Southampton,
Southampton, United Kingdom
80Also at University of Bristol, Bristol, United Kingdom
81Also at IPPP Durham University, Durham, United Kingdom
82Also at Monash University, Faculty of Science, Clayton, Australia
83Also at Università di Torino, Torino, Italy
84Also at Bethel University, St. Paul, Minnesota, USA
85Also at Karamanoğlu Mehmetbey University, Karaman, Turkey
86Also at California Institute of Technology, Pasadena, California, USA
87Also at United States Naval Academy, Annapolis, Maryland, USA
88Also at Ain Shams University, Cairo, Egypt
89Also at Bingol University, Bingol, Turkey
90Also at Georgian Technical University, Tbilisi, Georgia
91Also at Sinop University, Sinop, Turkey
92Also at Erciyes University, Kayseri, Turkey
93Also at Institute of Modern Physics and Key Laboratory of Nuclear Physics
and Ion-beam Application (MOE) - Fudan University, Shanghai, China
94Also at Texas A&M University at Qatar, Doha, Qatar
95Also at Kyungpook National University, Daegu, Korea
96Also at another institute or international laboratory covered by a
cooperation agreement with CERN
97Also at INFN Sezione di Padova, Università di Padova, Padova, Italy;
Università di Trento, Trento, Italy
98Also at Yerevan Physics Institute, Yerevan, Armenia
99Now at University of Florida, Gainesville, Florida, USA
100Also at Imperial College, London, United Kingdom
101Also at Institute of Nuclear Physics of the Uzbekistan Academy of Sciences,
Tashkent, Uzbekistan