A Computational Approach for Checking Compliance with European View and
Sunlight Exposure Criteria Eleonora Brembilla, Shervin Azadi, Pirouz Nourian

# A Computational Approach for Checking Compliance with European View and
Sunlight Exposure Criteria

missing  Eleonora Brembilla, Shervin Azadi, and Pirouz Nourian Delft
University of Technology
Email: {e.brembilla, , s.azadi-1<EMAIL_ADDRESS>Department of
Architectural Engineering & Technology,

###### Abstract

The paper presents open-source computational workflows for assessing the
“Exposure to sunlight” and “View out” criteria as defined in the European
standard EN 17037 “Daylight in Buildings”, issued by the European Committee
for Standardization. In addition to these factors, the standard document also
addresses daylight provision and protection from glare, both of which fall out
of the scope of this paper. The purpose of the standard is stated as
‘encouraging building designers to assess and ensure successfully daylit
spaces’. The standard document proposes verification methods for performing
such assessments, albeit without recommending a simulation procedure for
computing the aforementioned criteria. The workflows proposed in this paper
are arguably the first attempt to standardize these assessment methods using
de-facto open-source standard technologies currently used in practice. The
approach of this work is twofold: establish that the compliance check can be
systematically performed on a 3D model by a novel simulation tool developed by
the authors; and highlighting the additional assumptions that need to be
implemented to build a robust and unambiguous tool within existing open-source
frameworks. 111Code available at
https://github.com/shervinazadi/EN_17037_Compliance

## Key Innovations

  * •

Formulating procedures for computational assessment of EN 17037 criteria for
sunlight exposure and view out

  * •

Standardizing inputs and outputs for the proposed computational assessment
procedures

  * •

Devising Python workflows utilizing the Radiance simulation engine and
Honeybee from Ladybug Tools for running sunlight exposure and view analyses

## Practical Implications

The tool presented in this paper offers an open-source solution to check
compliance with EN 17037 criteria for “View out” and “Exposure to sunlight”.
The tool will be made available to designers, consultants and researchers.
Furthermore, the paper presents suggestions to policy-makers on how the
compliance procedures could be made more robust and better integrated into
computational design workflows.

##  I Introduction

In 2018 a new European standard on “Daylight in Buildings”, EN 17037 [1] was
introduced and ratified in all European Union countries, largely superseding
existing national daylighting standards. The document includes recommendations
for: 1) Indoor daylight provision; (2) View out; (3) Exposure to sunlight; and
(4) Protection from glare. Previous works focused mainly on the implementation
of the “Indoor daylight provision” and “Protection from glare” criteria [2, 3,
4, 5]. Instead, the proposed paper focuses on the “View out” and “Exposure to
sunlight” sections; namely, it introduces a computational approach to
facilitate compliance assessment at early design stages.

The analyses required by these two sections of the standard are exclusively
dependent on the geometrical characteristics of the building under assessment
and its surroundings. The verification procedures suggested in the standard
are largely based on geometrical measurements on 2D plan and section views.
Separate options are given for the verification via photographs – only for
existing buildings – or via rendered images. For the assessment of view
quality, the theoretical basis and a description of the advanced verification
method can be found in [6] [7], respectively. As for sunlight exposure, the
verification procedure is delineated by [8] and is based on evidence of the
benefits of direct sunlight in buildings found by [9].

We argue that being able to assess all four criteria with a single
computational tool would facilitate the uptake and application of the new
standard from early design decision-making. Additionally, being able to assess
the “View out” and “Exposure to sunlight” with procedures based on direct ray-
tracing is deemed to be more efficient than generating rendered images, and
better suited for computational design processes. The approach of this work is
twofold: establish that the compliance check can be systematically performed
on a 3D model by a novel simulation tool developed by the authors; and
highlighting the additional assumptions that need to be implemented to build a
robust and unambiguous tool within existing open-source frameworks.

Given that the verification procedures proposed in the standard document are
developed primarily for manual geometrical assessment, several challenges and
problems surfaced in developing the equivalent simulation procedures. The
present paper describes how we reinterpreted this standard for a computational
assessment based on ray-tracing. The main problems addressed in this paper are
the standardization of definitions, data models and procedures for performing
the proposed assessments. Ideally, this should be carried out in such an
unambiguous way that an algorithm can perform the assessment and put out a
conclusion without the need for a human interpreter during intermediate steps.

##  II Methods

In this section we present in detail the procedures devised to determine
target levels recommended by sections 5.2 and 5.3 of EN 17037:2018,
respectively addressing the assessments of “View out” and “Exposure to
sunlight”. The chosen performance indicators and recommended target values are
listed in Table I and explained below.

TABLE I: Performance level indicators and recommended target values for view and exposure to sunlight. | View out |  Exposure to sunlight
---|---|---
|  Horizontal sight angle |  Distance to obstructions |  Number of layers |  Sunlight hours
Min |  $\geq$14 |  $\geq$6 |  1 |  1,5
Med |  $\geq$28 |  $\geq$20 |  2 |  3
High |  $\geq$54 |  $\geq$50 |  3 |  4

The combination of the first three indicators should in principle provide a
comprehensive assessment of the quality of the view out. The overall
performance level (classified as minimum, medium or high) is equivalent to
that of the indicator that scores the lowest among the three. The horizontal
sight angle describes the width of a window as seen by an observer’s point of
view. The distance to obstructions is the distance between the interior
surface of a window and the “major” outdoor obstructions to a view of the sky.
The number of layers gives an indication of how varied the outside view is by
considering the presence of at least one of the three types of elements: a
view of the ground, a view of the landscape (natural, architectural or of the
horizon), and a view of the sky. The fourth indicator from Table I refers to
the exposure to sunlight recommendations and indicates the number of hours
during which a point on the inner the surface of a window receives direct
sunlight.

Besides the imprecision inherent in the definition of some key factors in
determining the quantity of these performance indicators, a number of
variables are left for the user/designer to decide. Among these, two were
identified as critical for understanding the variability of results: the view-
point location for the view out analysis, and the date for the sunlight
exposure analysis. The variability of performance indicators due to these two
variables was investigated using the newly developed tools and is presented in
the Result section. The following sections describe the computational approach
and the test scene used for the analysis.

###  II-A Computational tools

To maximize accessibility and ease of use, we adopted existing technical
frameworks and built on top of them. The developed toolset is primarily
available as a Python package. The simulation core utilizes the Radiance ray-
tracer [10] through the utility functions and methods of the Ladybug Tools
software [11, 12].

####  II-A1 View Out

The “Context View” recipe assesses the view of a vantage point inside the room
towards outside through a window, by computing the horizontal view angle, the
distance to outdoor obstructions, and the view layers that are visible from
that point. The standard does not constraint choosing the horizontal
positioning of the vantage point (as long as it is in the so-called utilized
area), but it limits the point height to 1.2 m for a sitting eye level and 1.7
m for a standing eye level. As in the case of sunlight exposure, the standard
proposes two methods: one based on fish-eye photographs and one geometrical
method. In the fish-eye method, it is suggested to superimpose a diagram on
the photograph, in order to measure the horizontal angle and counting the
different types of layer (sky, ground, landscape) present in the photograph.
In the geometrical method, a straight line should be drawn from the vantage
point towards the upper sill and lower sill in the section view and extended
towards the outside scene until it hits an obstacle. This line represents the
bounds of what is visible from the vantage point. Based on this drawing, the
number of visible layers can be counted. The horizontal sight angle can be
determined via a set of graphs relating the width of the window to the depth
of the room.

To translate this procedure into a simulation workflow, we discretize the
horizontal plane of the room at a height of 1.2 m and 1.7 m into a grid of
vantage points. Then, from each vantage point, rays are shot towards a
homogenous discretization (subdivided icosahedron) of a sphere, mapping the
distance and type of objects in all directions.

Figure 1: Context View simulation diagram.

Distance to obstructions: For all shot rays, we retrieve the distance to the
first and last intersection points. The difference between these two values
enables us to identify the rays that have passed the window. Given that the
standard specifies that the distance to outside obstructions should be
measured perpendicular to the window surface, the distance can be computed as:

$d=(\delta_{1}-\delta_{0})\mathbf{r}\cdot\mathbf{n}$ (1)

where $\mathbf{n}$ is the window surface normal, $\mathbf{r}$ is the ray
direction, $\delta_{0}$ is the distance of the vantage point to the first
intersection, and $\delta_{1}$ is the distance of the vantage point to the
last intersection.

As further elaborated in the discussion, the standard document does not
specify the nature of the scene as a geo-spatial data model. We have
pragmatically considered the maximum extent of our scene model (circa 500
metres) as the farthest intersection distance for the test case discussed
here. However, it must be noted that without specifying the extents of the
scene there might be a range of unforeseen issues arising out of such an
ambiguity in the standard document, especially for a computational assessment.
Namely, an arbitrary choice of such a distance will inevitably affect the
reproducibility of the results and thus the reliability of the standard.
Furthermore, in regions where the shape of the terrain is non-trivially
blocking the sunlight hours (e.g. because of a mountain range behind a
building, even if far away) then the results obtained as such cannot be
reliable. At such a scale, i.e. major terrain obstacles, even the curvature of
the earth will play a role. Past a certain distance, e.g. circa 8 km away from
a 4000 meters high mountain peak, it will not be visible on the horizon due to
the curvature of the earth. However, in closer ranges high mountainous ranges
can potentially block the sunlight hours.

Horizontal sight angle: To compute the horizontal sight angle, we assess the
ratio of the horizontal rays that have passed the window ($\rho$) to all the
horizontal rays ($\varrho$), i.e. the portion of a horizontal circle covered
by the window from a specific vantage point. Given that rays are shot toward a
homogenous discretization of the sphere, the horizontal sight angle can be
computed as the following:

$\beta=360\frac{\rho}{\varrho}$ (2)

View layers: On each grid point, we count the number of final ray
intersections for each object type. Consequently, we can compute how many view
layers were in the sight of each vantage point and what portion of the view
sphere is occupied by them. If these portions are beyond a certain threshold,
we can establish that the object is visible and perceivable by building
occupants. The need for such a threshold and its specification will be further
examined in the discussion section.

####  II-A2 Exposure to Sunlight

The “Exposure to Sunlight” recipe is a measure of the minimum number of hours
that sun is visible from a vantage point $P$ defined in the horizontal centre
of the window with the minimum height of 1.2 m above the floor or 0.3 m above
the sill. The standard specifies that the selected date for measurement should
be between February 1st and March 21st. To compute this measure, two methods
are proposed in the document: one based on a fish-eye photograph taken from
the vantage point, and one based on geometrical calculations. In the fisheye
method, a sun path diagram is superimposed on the photograph, so that the
number of hours that directly see the sun can be counted. In the geometrical
method, $\alpha$ is defined as the horizontal acceptance angle of the window
spanning from the right side to the left side of the window from $P$,
excluding major external obstacles. Next, the sun path for different
geographical locations can be identified via a lookup table. Finally, with the
help of the angle between window normal and North direction, the overlap
between $\alpha$ and the sun path span is determined.

Figure 2: Exposure to Sunlight simulation diagram.

It is clear that such assessment of the overlap of the sun path with the
opening of the window is extremely sensitive to the precision of drawings and
measurements. Moreover, the more complex the outdoor scene becomes, the less
feasible is to compute the effect of obstructions with this procedure.
Consequently, to translate this procedure into a simulation workflow
(illustrated in Figure 2), we computed the position of the sun throughout the
year in half an hour intervals based on the geolocation of the building. Then,
by considering the geometry of the context as obstacles we checked for a clear
sight-line from the vantage point of the window ($P$) in the direction of the
sun. Aggregating this information for each day indicates the number of
sunlight exposure hours.

###  II-B Test Scene

Two different 3D models were combined to recreate a fictitious – yet realistic
– test scene for the evaluation. For the urban environment, an existing model
of Rotterdam city centre was used [13]. Such a model includes the Blaaktoren
tower, where the Massachusetts Institute of Technology (MIT) reference office
model was inserted, namely on the third floor. The office model represents a
deep-plan, side-lit room used for benchmarking daylighting and glare analyses
[14]. Figure 3 shows the test scene and indicates the position of the office
room, as well as the sun path diagram for the coordinates of Rotterdam city
centre. The office window is oriented towards the South-East and overlooks the
view represented in Figure 4. The ‘view layers’ visible in this example are
colour-coded in a similar way to [15].

Figure 3: Bird view of the scene indicating the relative positioning of the
test-case, in red; urban surrounding in light grey; hourly sun positions, as
dark orange spheres; and bi-weekly sun paths as light orange lines. Figure 4:
Outdoor view as seen from a point within the room, at a height of 1.2 m above
the floor. From this specific viewpoint, it is possible to see all the three
‘view layers’: (1) Sky, in blue; (2) Landscape, in green (2); and (3) Ground,
in red.

## Results

###  II-C View out

The first set of results concerns the assessment of view quality. The
performance criteria related to “View Out” (number of view layers and
horizontal sight angle) were computed and visualized, for two grids of points:
one at the height of 1.2 m above the floor and the other at 1.7 m. The first
grid represents the view of a sitting person, whereas the second grid
represents the view of a standing person. The third criterion to assess view
quality – distance to obstructions – was calculated for multiple points on the
window surface, as the standard does not define a specific point for this
assessment. The minimum distance was found to be 16 m and the maximum was 351
m. If the minimum distance was to be considered, then the view performance of
this room would result in a ‘Minimum’ score. Oppositely, if the point chosen
for the assessment would result in a distance of 351 m, then the view would
score a ‘High’ performance level. The placement of the room in the urban model
and the resulting variability in obstruction distances were purely
coincidental. However, it is reasonable to expect that most rooms with a high
number of view layers will be characterised by a large variety of distances to
major obstructions. Hence, such an assessment would benefit from the
definition of a single statistical indicator that can give a meaningful
indication of the overall performance, for example, the median value of all
computed distances.

Figure 5 shows the analysis on the number of view layers for a grid at 1.7 m.
From the first plot on the left, it looks as if from almost the entire room is
possible to see all three view layers. For such a deep plan room, it is
surprising that the ground can be seen even when standing at the furthest
point from the window. What happens is that the count of view layer is equally
sensitive to very large or very small portions of each view element. That is,
even if only one ray hits, e.g., the ground, then such layer is included in
the overall count. An additional investigation was therefore conducted on the
effect of adding a minimum threshold value for a layer to be counted as
effectively part of the view. The other plots in Figure 5 illustrate how the
evaluation changes depending on the set minimum threshold. It is also possible
to notice that the back portion of the room does not see any view layer.
Although a view out of the window is always present, from those points none of
the layers covers a solid angle exceeding the defined threshold. Thus, the
introduction of such a threshold could be used to indicate when the view out
is too distant from the selected vantage point, effectively removing the need
to assess the horizontal sight angle.

Figure 5: Number of view layers visible across a grid of analysis points 1.7 m
high. ($t$) is the visibility threshold for counting a layer as visible and is
measured in steradians. The window is on the top side.

Figure 6 shows the variation in horizontal sight angle values when calculated
from different points in the room. As expected, the angle decreases as the
distance from the window increases. The maximum angle found for the reference
room is 158o and the minimum is 11o. If the point within the room with the
minimum horizontal sight angle was to be considered for the evaluation, the
room would not comply with any of the recommended performance levels. Given
that this reference office room is characterized by a deep plan, this outcome
was expected too.

Figure 6: Values of horizontal sight angles across a grid of analysis points
1.7 m high. The window is on the left side.

###  II-D Exposure to sunlight

The second set of results shows the “Exposure to sunlight” performance of the
test scene. The direct view of the sun was evaluated for the whole period
suggested by the standard, from the 1st of February to the 21st of March. The
standard requires to choose only one day within this period for the evaluation
of the cumulative number of hours of direct sunlight. In the analysed case, no
major differences were found among different days, and the number of hours
exceeded the threshold for the ‘High’ performance level independently of the
chosen day.

For this analysis, a decision on the timestep to adopt when defining sun
positions had to be taken. In Figure 7, results obtained using a one-hour
timestep are compared to those obtained using a five-minute timestep. In this
case, a timestep of one hour led to a slight underestimation of exposure hours
(-3%). More analyses are required to assess the sensitivity of this
performance criterion to the chosen timestep. In any case, specifying an exact
value in the standard document would help reducing this uncertainty and making
it more robust.

(a)

(b)

Figure 7: Solar access at the evaluation point, within the period 01/02-21/03,
for clear sky conditions. The plots show both the time at which direct
sunlight access occurs (left _y_ axis) and the cumulative number of ‘direct
sunlight hours’ per day (right _y_ axis). Plot (a) shows results when using a
1 hour time step; plot (b) shows results for a 5 minute time step.

Besides considerations on detailed parameters within the “Exposure to
Sunlight” criterion, considerations concerning the integration of this
analysis with the other criteria in the standard document are important. Such
a high incidence of direct sunlight should raise concerns about potential
glare risk. To effectively inform designers of the need for shading devices
and their optimal characteristics, the two criteria “Exposure to sunlight” and
“Protection from glare” should be assessed in parallel. However, for such
comparison to be possible, the two criteria should have more similar temporal
and spatial requirements, as highlighted in the following section.

## Discussion

The main scope of this work was to develop and present a tool that enables
designers to check compliance with EN 17037 criteria. During its development,
however, several inconsistent or missing variables were identified in the
standard document. While it is true that the tool has been tested on a very
limited number of geometries, the authors have sought to develop procedures
that can be scaled and generalised to a wide range of scenarios. We discuss
here the issues that we consider more relevant to ensure robust and consistent
assessments of EN 17037 “View out” and “Exposure to sunlight” criteria, as
well as general issues concerning all criteria in the standard. Leaving
unclear and ambiguous definitions may lead to various interpretations and
implementations by a single developer, hence to several different results and
performance assessments. We argue that the implementation of additional
parameters or thresholds should be the subject of discussion among the
simulation and lighting community, ultimately resulting in modifications to
the standard document itself.

###  II-E Standardizing a standard

The suggested methods for ensuring the recommended levels of quality in the
standard document are accompanied by a variety of 2D drawings and normative
geometric methods that are supposed to help building designers attain the
aforementioned qualities. While these drawings can be helpful in a didactic
sense, they are not directly interpretable as unambiguous procedures for
computing the values in question. The ambiguity arises specifically when
translating the manual methods given in the standard into technical ‘recipes’
that could be used for assessing 3D scenes.

The absence of rigorous mathematical specification of the criteria increases
the ambiguity of the computation procedures. As an example, when counting the
visible layers in the view out criteria, a human’s perception will discard
miniscule visible patches of layers; but in the simulation environment, the
rays will be likely to intersect with such objects. Then there has to be a
defined threshold of solid angles in steradians, to identify the visibility of
that layer unambiguously. As illustrated in Figure 6, the problem of
determining the number of visibility layers may lead to unexpected results if
such computational details are not considered in the standard definitions.

Lastly, it would be extremely valuable to consider the use of EN 17037
performance assessments within the wider field of urban and architectural
design. This becomes particularly important for the “View out” assessment,
which requires a fairly detailed description of the environment surrounding
the building under analysis. The typical data models used by building
simulation practitioners either lack semantic information (in the case of
geometric models such as Wavefront OBJ or AutoCAD DXF made by Computer
Graphics or Computer-Aided Design software) or their semantic layers do not
correspond to the ones offered by the standard (in case of geometric-semantic
data models such as gbXML and CityGML made by Building Information Modelling
software or obtained from 3D City Information Models). In both cases, there is
a need for a standardized semantic mapping between established data models and
the semantic layers proposed by the standard (‘ground’, ‘landscapes’, and
‘sky’).

###  II-F Integration among EN 17037 criteria

The two sections that were not investigated in this paper, concerned with
“Daylight sufficiency” and “Protection from glare”, proposed their own spatial
and temporal aggregators. In the daylight sufficiency part, the annual
evaluation option produces at least 8760 hourly values (of which about half
are daylight hours) for each of the points in the analysis grid. Temporally,
50% of the daylight hours should comply with the requirements. Spatially, two
target performance values are defined: 50% of the analysis grid should meet a
target illuminance (e.g., 300 lx) and 95% of the analysis grid should meet a
minimum illuminance (e.g., 100 lx). In the protection from glare part, the
annual evaluation option considers only occupied hours in a year (8:00 to
18:00, Monday to Friday), for a total of about 2600 values at each evaluated
position. Of these hours, a maximum of 5% should report a Daylight Glare
Probability lower than a target value (e.g., 0.35). The evaluation position in
the space should be decided by the designer and should correspond to the
expected worse condition, i.e., close to the facade, with the sun shining in
the occupant’s field of view.

Similar aggregators could be easily devised also for the “View out” and
“Exposure to sunlight” parts of the EN 17037 standard. The challenge lies with
the selection of the most appropriate aggregator, as for it to be a meaningful
representation of occupants’ experience, more studies on human perception of
view and sunlight would be required. Furthermore, more research is necessary
for a more complete understanding of how the four criteria recommended by the
standard interact with each other, and whether a design can achieve compliance
with multiple criteria at once.

## Conclusion

This paper presented a computational toolset developed by the authors to
assess the “Exposure to sunlight” and the “View out” criteria as defined by
the EN 17037 standard “Daylight in Buildings”. Besides illustrating the
assumptions that had to be taken when interpreting the standard requirements,
the present work aimed at suggesting more robust and unambiguous approaches
for verifying compliance to the standard criteria. The analyses were carried
out only for a single test scene, which is not necessarily representative of a
typical office or an urban context. Yet, even the application of the standard
requirements on a relatively simple room highlighted a number of issues that
can affect the generalisation – and hence the adoption – of the standard.
Among such issues, the major ones were: the absence of a defined point to
assess the distance to obstructions; a definition of “major obstructions”; a
minimum solid angle threshold to account for view layers; and, a clearer
procedure to choose the analysis day and timestep for the “Exposure to
sunlight” assessment.

Furthermore, the paper discussed in more detail considerations about creating
robust definitions, models and verification procedures for computational
implementations; choosing result aggregators that more closely represent the
human’s perception of view and direct sunlight; and the need for integration
among the four criteria covered by EN 17037. The latter aspect, i.e., the
transition from simulation results to assessment labels invites further
research in the direction of congruence with green building certifications
such as BREEAM, LEED, and WELL. Furthermore, considering the demonstrated
possibility of automated computational evaluation, a reconsideration of the
evaluation paradigm from discrete labels to continuous scores would make the
standard suitable for direct application in computational design workflows,
especially for integration in objective functions for design optimization. [1]

## Acknowledgement

The authors would like to acknowledge Mostapha Roudsari’s help with
understanding the Ladybug[$+$] and Honeybee[$+$] ‘recipes’ structure.

## Supplementary Material

The source code of the toolbox is available at the following repository:
https://github.com/shervinazadi/EN_17037_Compliance. Links to supplementary
materials such as documentation, examples and online reproduction of the
presented procedure are also available in the repository.

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The fields $\Lambda$ and $\overline{\Lambda}$ seem to present a new quantum
field theory that are physically distinct to $\lambda$ and
$\overset{\>{}^{{}^{{{\neg}}}}}{\smash[t]{\lambda}}$ owing to the difference
in kinematics and mass dimensions. However, these differences turn out to be
superficial. Here, we show that the Lagrangian density $\Lambda$ and
$\overline{\Lambda}$ decomposes into a sum of two physically equivalent
Lagrangian densities of mass dimension one fields. Therefore, the field theory
as described by $\mathscr{L}_{\Lambda}$ is reducible.

To prove our statement, let us write the free Lagrangian density of
$\overset{\>{}^{{}^{{{\neg}}}}}{\smash[t]{\lambda}}$ and $\lambda$ as

$\mathscr{L}(\overset{\>{}^{{}^{{{\neg}}}}}{\smash[t]{\lambda}},\lambda)=\left(\partial^{\mu}\overset{\>{}^{{}^{{{\neg}}}}}{\smash[t]{\lambda}}\partial_{\mu}\lambda-m^{2}\overset{\>{}^{{}^{{{\neg}}}}}{\smash[t]{\lambda}}\lambda\right).$
(304)

Because of the $\overset{\>{}^{{}^{{{\neg}}}}}{\smash[t]{\lambda}}\lambda$
product, the Lagrangian density is pseudo Hermitian. Despite the pseudo-
Hermiticity, as we have shown in 2.2, the theory is local, respects Lorentz
symmetry, and the free Hamiltonian is Hermitian and positive-definite. These
features, along with the results given in sec. 3 tell us that 304 is the
correct irreducible Lagrangian density for mass dimension one fields. By
irreducible, we mean that
$\mathscr{L}(\overset{\>{}^{{}^{{{\neg}}}}}{\smash[t]{\lambda}},\lambda)$
cannot be decomposed into a sum of Lagrangian densities consisting of other
independent fields.

We will now demonstrate that $\mathscr{L}_{\Lambda}$ is reducible. For this
purpose, we first use the identity
$\overset{\>{}^{{}^{{{\neg}}}}}{\smash[t]{\lambda}}=\overline{\lambda}^{\prime}$
to rewrite
$\mathscr{L}(\overset{\>{}^{{}^{{{\neg}}}}}{\smash[t]{\lambda}},\lambda)$ as

$\displaystyle\mathscr{L}(\overset{\>{}^{{}^{{{\neg}}}}}{\smash[t]{\lambda}},\lambda)=\mathscr{L}(\overline{\lambda}^{\prime},\lambda)=\partial^{\mu}\overline{\lambda}^{\prime}\partial_{\mu}\lambda-m^{2}\overline{\lambda}^{\prime}\lambda$
(305)

Next, we add a Hermitian conjugate to
$\mathscr{L}(\overline{\lambda}^{\prime},\lambda)$ to obtain a Hermitian
Lagrangian density

$\displaystyle\mathscr{L}_{h}$
$\displaystyle=\mathscr{L}(\overline{\lambda}^{\prime},\lambda)+\mathscr{L}^{{\dagger}}(\overline{\lambda}^{\prime},\lambda)$
$\displaystyle=\left(\partial^{\mu}\overline{\lambda}^{\prime}\partial_{\mu}\lambda-m^{2}\overline{\lambda}^{\prime}\lambda\right)+\left(\partial^{\mu}\overline{\lambda}\partial_{\mu}\lambda^{\prime}-m^{2}\overline{\lambda}\lambda^{\prime}\right).$
(306)

As the first and second term in (306) are physically equivalent,
$\mathscr{L}_{h}$ is reducible. That is, for the purpose of studying mass
dimension one fields, $\mathscr{L}(\overline{\lambda}^{\prime},\lambda)$
suffices. The reason for constructing a reducible $\mathscr{L}_{h}$ is to show
that it is equal to $m\mathscr{L}_{\Lambda}$ up to total derivative terms.
Integrating $\mathscr{L}_{h}$ by parts and ignore the total derivative terms,
we obtain

$\mathscr{L}_{h}=-\overline{\lambda}^{\prime}(\partial^{\mu}\partial_{\mu}+m^{2})\lambda-\overline{\lambda}(\partial^{\mu}\partial_{\mu}+m^{2})\lambda^{\prime}.$
(307)

Using the identity

$(\partial^{\mu}\partial_{\mu}+m^{2})\mathbb{I}=(i\gamma^{\mu}\partial_{\mu}+m\mathbb{I})(-i\gamma^{\nu}\partial_{\nu}+m\mathbb{I}),$
(308)

the first term in (307) can be written as

$\displaystyle-\overline{\lambda}^{\prime}(\partial^{\mu}\partial_{\mu}+m^{2})\lambda$
$\displaystyle=-\overline{\lambda}^{\prime}(i\gamma^{\mu}\partial_{\mu}+m)(-i\gamma^{\nu}\partial_{\nu}+m)\lambda$
$\displaystyle=-\overline{\lambda}^{\prime}(i\gamma^{\mu}\partial_{\mu}+m)(-m\lambda^{\prime}+m\lambda)$
$\displaystyle=m\overline{\lambda}^{\prime}(i\gamma^{\mu}\partial_{\mu}+m)\lambda^{\prime}-m\overline{\lambda}^{\prime}(i\gamma^{\mu}\partial_{\mu}+m)\lambda$
$\displaystyle=m\overline{\lambda}^{\prime}(i\gamma^{\mu}\partial_{\mu}+m)\lambda^{\prime}-m^{2}(\overline{\lambda}^{\prime}\lambda^{\prime}+\overline{\lambda}^{\prime}\lambda)$
$\displaystyle=m\left(\overline{\lambda}^{\prime}i\gamma^{\mu}\partial_{\mu}\lambda^{\prime}-m\overline{\lambda}^{\prime}\lambda\right).$
(309)

Repeating the same calculations for the second term of $\mathscr{L}_{h}$, we
find

$\displaystyle\mathscr{L}_{h}$
$\displaystyle=m\left[\left(\overline{\lambda}^{\prime}i\gamma^{\mu}\partial_{\mu}\lambda^{\prime}-m\overline{\lambda}^{\prime}\lambda\right)+\left(\overline{\lambda}i\gamma^{\mu}\partial_{\mu}\lambda-m\overline{\lambda}\lambda^{\prime}\right)\right]$
$\displaystyle=m\mathscr{L}_{\Lambda}.$ (310)

Since $\mathscr{L}_{h}$ is reducible, it follows that $\mathscr{L}_{\Lambda}$
is also reducible.

##  Appendix B The solution for $\boldsymbol{\eta}$

To solve $\eta$, let us start with

$\eta_{a}=e^{i\theta_{12}N_{12}}e^{i\theta_{34}N_{34}},$ (311)

where

$\displaystyle N_{12}$ $\displaystyle=\int
d^{3}p\left[a^{{\dagger}}(\mbox{\boldmath$\displaystyle\bm{p}$},2)a(\mbox{\boldmath$\displaystyle\bm{p}$},1)-a^{{\dagger}}(\mbox{\boldmath$\displaystyle\bm{p}$},1)a(\mbox{\boldmath$\displaystyle\bm{p}$},2)\right],$
(312) $\displaystyle N_{34}$ $\displaystyle=\int
d^{3}p\left[a^{{\dagger}}(\mbox{\boldmath$\displaystyle\bm{p}$},4)a(\mbox{\boldmath$\displaystyle\bm{p}$},3)-a^{{\dagger}}(\mbox{\boldmath$\displaystyle\bm{p}$},3)a(\mbox{\boldmath$\displaystyle\bm{p}$},4)\right].$
(313)

Acting $\eta_{a}$ on the state $|p,\tau,a\rangle$, we get

$\displaystyle\eta_{a}|p,1,a\rangle$
$\displaystyle=\cos\theta_{12}|p,1,a\rangle+i\sin\theta_{12}|p,2,a\rangle,$
(314) $\displaystyle\eta_{a}|p,2,a\rangle$
$\displaystyle=\cos\theta_{12}|p,2,a\rangle-i\sin\theta_{12}|p,1,a\rangle,$
(315) $\displaystyle\eta_{a}|p,3,a\rangle$
$\displaystyle=\cos\theta_{34}|p,3,a\rangle+i\sin\theta_{12}|p,4,a\rangle,$
(316) $\displaystyle\eta_{a}|p,4,a\rangle$
$\displaystyle=\cos\theta_{34}|p,4,a\rangle-i\sin\theta_{12}|p,3,a\rangle.$
(317)

Similarly, we take

$\eta_{b}=e^{i\phi_{12}M_{12}}e^{i\phi_{34}M_{34}},$ (318)

where

$\displaystyle M_{12}$ $\displaystyle=\int
d^{3}p\left[b^{{\dagger}}(\mbox{\boldmath$\displaystyle\bm{p}$},2)b(\mbox{\boldmath$\displaystyle\bm{p}$},1)-b^{{\dagger}}(\mbox{\boldmath$\displaystyle\bm{p}$},1)b(\mbox{\boldmath$\displaystyle\bm{p}$},2)\right],$
(319) $\displaystyle M_{34}$ $\displaystyle=\int
d^{3}p\left[b^{{\dagger}}(\mbox{\boldmath$\displaystyle\bm{p}$},4)b(\mbox{\boldmath$\displaystyle\bm{p}$},3)-b^{{\dagger}}(\mbox{\boldmath$\displaystyle\bm{p}$},3)b(\mbox{\boldmath$\displaystyle\bm{p}$},4)\right],$
(320)

to obtain

$\displaystyle\eta_{b}|p,1,b\rangle$
$\displaystyle=\cos\phi_{12}|p,1,b\rangle+i\sin\phi_{12}|p,2,b\rangle,$ (321)
$\displaystyle\eta_{b}|p,2,b\rangle$
$\displaystyle=\cos\phi_{12}|p,2,b\rangle-i\sin\phi_{12}|p,1,b\rangle,$ (322)
$\displaystyle\eta_{b}|p,3,b\rangle$
$\displaystyle=\cos\phi_{34}|p,3,b\rangle+i\sin\phi_{34}|p,4,b\rangle,$ (323)
$\displaystyle\eta_{b}|p,4,b\rangle$
$\displaystyle=\cos\phi_{34}|p,4,b\rangle-i\sin\phi_{34}|p,3,b\rangle.$ (324)

Define

$\eta_{ab}=\eta_{a}\eta_{b}.$ (325)

Because $\eta_{a}|0\rangle=|0\rangle$, $\eta_{b}|0\rangle=|0\rangle$ and
$[\eta_{a},\eta_{b}]=0$, the actions of $\eta_{ab}$ on the states are
identical to (314-317) and (321-324). Next, we note

$\displaystyle\left(\eta_{ab}-\eta^{-1}_{ab}\right)|p,1,a\rangle$
$\displaystyle=+2i\sin\theta_{12}|p,2,a\rangle,$ (326)
$\displaystyle\left(\eta_{ab}-\eta^{-1}_{ab}\right)|p,2,a\rangle$
$\displaystyle=-2i\sin\theta_{12}|p,1,a\rangle,$ (327)
$\displaystyle\left(\eta_{ab}-\eta^{-1}_{ab}\right)|p,3,a\rangle$
$\displaystyle=+2i\sin\theta_{34}|p,4,a\rangle,$ (328)
$\displaystyle\left(\eta_{ab}-\eta^{-1}_{ab}\right)|p,4,a\rangle$
$\displaystyle=-2i\sin\theta_{34}|p,3,a\rangle,$ (329)

and

$\displaystyle\left(\eta_{ab}-\eta^{-1}_{ab}\right)|p,1,b\rangle$
$\displaystyle=-2i\sin\phi_{12}|p,2,b\rangle,$ (330)
$\displaystyle\left(\eta_{ab}-\eta^{-1}_{ab}\right)|p,2,b\rangle$
$\displaystyle=+2i\sin\phi_{12}|p,1,b\rangle,$ (331)
$\displaystyle\left(\eta_{ab}-\eta^{-1}_{ab}\right)|p,3,b\rangle$
$\displaystyle=-2i\sin\phi_{34}|p,4,b\rangle,$ (332)
$\displaystyle\left(\eta_{ab}-\eta^{-1}_{ab}\right)|p,4,b\rangle$
$\displaystyle=+2i\sin\phi_{34}|p,3,b\rangle.$ (333)

Therefore, the solution for $\eta$ is given by

$\eta=\frac{1}{2}\left(\eta_{ab}-\eta^{-1}_{ab}\right)$ (334)

with

$\theta_{12}=-\theta_{34}=\frac{\pi}{2},\quad\phi_{12}=-\phi_{34}=\frac{\pi}{2},$
(335)

where

$\eta_{ab}=\exp\left\\{\frac{i\pi}{2}\int
d^{3}p\sum_{\tau}\epsilon(\tau)\left[a^{{\dagger}}(\mbox{\boldmath$\displaystyle\bm{p}$},\rho(\tau))a(\mbox{\boldmath$\displaystyle\bm{p}$},\tau)+b^{{\dagger}}(\mbox{\boldmath$\displaystyle\bm{p}$},\rho(\tau))b(\mbox{\boldmath$\displaystyle\bm{p}$},\tau)\right]\right\\},$
(336)

and

$\epsilon(1)=-\epsilon(2)=\epsilon(3)=-\epsilon(4)=1.$ (337)

###### Acknowledgements.

GBG thanks FAPESP (2021/12126-5) for financial support and Dharam Vir
Ahluwalia for his great scientific legacy. He dedicates this work to the
memory of Dharam Vir Ahluwalia. JMHS thanks CNPq, Brazil for financial support
through grant number 307641/2022-8. CYL thanks James Brister, Chou-Man Sou,
Zheng Sun, Wenqi Yu and Siyi Zhou for useful discussions. CYL is supported by
The Sichuan University Post-doctoral Research Fund No. 2022SCU12119. BMP
thanks CNPq for partial support.

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Berryhill0000-0002-8124-3033, P.C. Bhat, K. Burkett0000-0002-2284-4744, J.N.
Butler, A. Canepa, G.B. Cerati0000-0003-3548-0262, H.W.K.
Cheung0000-0001-6389-9357, F. Chlebana, M. Cremonesi, K.F. Di
Petrillo0000-0001-8001-4602, V.D. Elvira0000-0003-4446-4395, Y. Feng, J.
Freeman, Z. Gecse, L. Gray, D. Green, S. Grünendahl0000-0002-4857-0294, O.
Gutsche0000-0002-8015-9622, R.M. Harris0000-0003-1461-3425, R. Heller, T.C.
Herwig0000-0002-4280-6382, J. Hirschauer0000-0002-8244-0805, B.
Jayatilaka0000-0001-7912-5612, S. Jindariani, M. Johnson, U. Joshi, T.
Klijnsma0000-0003-1675-6040, B. Klima0000-0002-3691-7625, K.H.M. Kwok, S.
Lammel0000-0003-0027-635X, D. Lincoln0000-0002-0599-7407, R. Lipton, T. Liu,
C. Madrid, K. Maeshima, C. Mantilla0000-0002-0177-5903, D. Mason, P.
McBride0000-0001-6159-7750, P. Merkel, S. Mrenna0000-0001-8731-160X, S.
Nahn0000-0002-8949-0178, V. O’Dell, V. Papadimitriou, K.
Pedro0000-0003-2260-9151, C. Pena570000-0002-4500-7930, O. Prokofyev, F.
Ravera0000-0003-3632-0287, A. Reinsvold Hall0000-0003-1653-8553, L.
Ristori0000-0003-1950-2492, B. Schneider0000-0003-4401-8336, E. Sexton-
Kennedy0000-0001-9171-1980, N. Smith0000-0002-0324-3054, A.
Soha0000-0002-5968-1192, W.J. Spalding0000-0002-7274-9390, L. Spiegel, S.
Stoynev0000-0003-4563-7702, J. Strait0000-0002-7233-8348, L.
Taylor0000-0002-6584-2538, S. Tkaczyk, N.V. Tran0000-0002-8440-6854, L.
Uplegger0000-0002-9202-803X, E.W. Vaandering0000-0003-3207-6950, H.A.
Weber0000-0002-5074-0539 University of Florida, Gainesville, Florida, USA D.
Acosta0000-0001-5367-1738, P. Avery, D. Bourilkov0000-0003-0260-4935, L.
Cadamuro0000-0001-8789-610X, V. Cherepanov, F. Errico0000-0001-8199-370X, R.D.
Field, D. Guerrero, B.M. Joshi0000-0002-4723-0968, M. Kim, E. Koenig, J.
Konigsberg0000-0001-6850-8765, A. Korytov, K.H. Lo, K.
Matchev0000-0003-4182-9096, N. Menendez0000-0002-3295-3194, G.
Mitselmakher0000-0001-5745-3658, A. Muthirakalayil Madhu, N. Rawal, D.
Rosenzweig, S. Rosenzweig, K. Shi0000-0002-2475-0055, J.
Sturdy0000-0002-4484-9431, J. Wang0000-0003-3879-4873, E.
Yigitbasi0000-0002-9595-2623, X. Zuo Florida State University, Tallahassee,
Florida, USA T. Adams0000-0001-8049-5143, A. Askew0000-0002-7172-1396, R.
Habibullah0000-0002-3161-8300, V. Hagopian, 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. Butalla, T. Elkafrawy150000-0001-9930-6445, 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. Adams, H.
Becerril Gonzalez0000-0001-5387-712X, R. Cavanaugh0000-0001-7169-3420, X.
Chen0000-0002-8157-1328, S. Dittmer, O. Evdokimov0000-0002-1250-8931, C.E.
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Oh0000-0003-0744-1063, T. Roy, S. Rudrabhatla, M.B. Tonjes0000-0002-2617-9315,
N. Varelas0000-0002-9397-5514, J. Viinikainen0000-0003-2530-4265, X. Wang, Z.
Wu0000-0003-2165-9501, Z. Ye0000-0001-6091-6772 The University of Iowa, Iowa
City, Iowa, USA M. Alhusseini0000-0002-9239-470X, K.
Dilsiz900000-0003-0138-3368, R.P. Gandrajula0000-0001-9053-3182, O.K.
Köseyan0000-0001-9040-3468, J.-P. Merlo, A. Mestvirishvili91, J. Nachtman, H.
Ogul920000-0002-5121-2893, Y. Onel0000-0002-8141-7769, A. Penzo, C. Snyder, E.
Tiras930000-0002-5628-7464 Johns Hopkins University, Baltimore, Maryland, USA
O. Amram0000-0002-3765-3123, B. Blumenfeld0000-0003-1150-1735, L.
Corcodilos0000-0001-6751-3108, J. Davis, M. Eminizer0000-0003-4591-2225, A.V.
Gritsan0000-0002-3545-7970, S. Kyriacou, P. Maksimovic0000-0002-2358-2168, J.
Roskes0000-0001-8761-0490, M. Swartz, T.Á. Vámi0000-0002-0959-9211 The
University of Kansas, Lawrence, Kansas, USA A. Abreu, J. Anguiano, C.
Baldenegro Barrera0000-0002-6033-8885, P. Baringer0000-0002-3691-8388, A.
Bean0000-0001-5967-8674, A. Bylinkin0000-0001-6286-120X, Z. Flowers, T.
Isidori, S. Khalil0000-0001-8630-8046, J. King, G.
Krintiras0000-0002-0380-7577, A. Kropivnitskaya0000-0002-8751-6178, M.
Lazarovits, C. Lindsey, J. Marquez, N. Minafra0000-0003-4002-1888, M.
Murray0000-0001-7219-4818, M. Nickel, C. Rogan0000-0002-4166-4503, C. Royon,
R. Salvatico0000-0002-2751-0567, S. Sanders, E. Schmitz, C.
Smith0000-0003-0505-0528, J.D. Tapia Takaki0000-0002-0098-4279, 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. Rebassoo, D. Wright
University of Maryland, College Park, Maryland, USA E. Adams, A. Baden, 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. Kellogg, T.
Koeth, A.C. Mignerey, S. Nabili, M. Seidel0000-0003-3550-6151, A.
Skuja0000-0002-7312-6339, L. Wang, K. Wong0000-0002-9698-1354 Massachusetts
Institute of Technology, Cambridge, Massachusetts, USA D. Abercrombie, G.
Andreassi, R. Bi, S. Brandt, W. Busza0000-0002-3831-9071, I.A. Cali, Y.
Chen0000-0003-2582-6469, M. D’Alfonso0000-0002-7409-7904, J. Eysermans, C.
Freer0000-0002-7967-4635, G. Gomez Ceballos, M. Goncharov, P. Harris, M. Hu,
M. Klute0000-0002-0869-5631, D. Kovalskyi0000-0002-6923-293X, J. Krupa, Y.-J.
Lee0000-0003-2593-7767, B. Maier, C. Mironov0000-0002-8599-2437, C.
Paus0000-0002-6047-4211, D. Rankin0000-0001-8411-9620, C.
Roland0000-0002-7312-5854, G. Roland, Z. Shi0000-0001-5498-8825, G.S.F.
Stephans0000-0003-3106-4894, K. Tatar0000-0002-6448-0168, 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, P. Hansen, J. Hiltbrand, Sh.
Jain0000-0003-1770-5309, M. Krohn, Y. Kubota, J. Mans0000-0003-2840-1087, M.
Revering, R. Rusack0000-0002-7633-749X, R. Saradhy, N.
Schroeder0000-0002-8336-6141, N. Strobbe0000-0001-8835-8282, M.A. Wadud
University of Nebraska-Lincoln, Lincoln, Nebraska, USA K.
Bloom0000-0002-4272-8900, M. Bryson, S. Chauhan0000-0002-6544-5794, D.R.
Claes, C. Fangmeier, L. Finco0000-0002-2630-5465, F. Golf0000-0003-3567-9351,
C. Joo, I. Kravchenko0000-0003-0068-0395, M. Musich, I. Reed, J.E. Siado, G.R.
Snow${}^{\textrm{\textdagger}}$, W. Tabb, F. Yan 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. Kharchilava, C. McLean0000-0002-7450-4805, D.
Nguyen, 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. Barberis, Y. Haddad0000-0003-4916-7752,
A. Hortiangtham, J. Li0000-0001-5245-2074, G. Madigan, B.
Marzocchi0000-0001-6687-6214, D.M. Morse0000-0003-3163-2169, V. Nguyen, T.
Orimoto0000-0002-8388-3341, A. Parker, L. Skinnari0000-0002-2019-6755, A.
Tishelman-Charny, T. Wamorkar, 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. Hahn, Y. Liu,
N. Odell, M.H. Schmitt0000-0003-0814-3578, M. Velasco University of Notre
Dame, Notre Dame, Indiana, USA R. Band0000-0003-4873-0523, R. Bucci, A.
Das0000-0001-9115-9698, N. Dev0000-0003-2792-0491, R.
Goldouzian0000-0002-0295-249X, M. Hildreth, K. Hurtado
Anampa0000-0002-9779-3566, C. Jessop0000-0002-6885-3611, K.
Lannon0000-0002-9706-0098, J. Lawrence, N. Loukas0000-0003-0049-6918, D.
Lutton, N. Marinelli, I. Mcalister, T. McCauley0000-0001-6589-8286, F. Meng,
K. Mohrman, Y. Musienko49, R. Ruchti, P. Siddireddy, A. Townsend, M. Wayne, A.
Wightman, M. Wolf0000-0002-6997-6330, M. Zarucki0000-0003-1510-5772, L. Zygala
The Ohio State University, Columbus, Ohio, USA B. Bylsma, B. Cardwell, L.S.
Durkin0000-0002-0477-1051, B. Francis0000-0002-1414-6583, C.
Hill0000-0003-0059-0779, M. Nunez Ornelas0000-0003-2663-7379, K. Wei, B.L.
Winer, 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. Dezoort, P. Elmer0000-0001-6830-3356, A.
Frankenthal0000-0002-2583-5982, B. Greenberg0000-0002-4922-1934, N. Haubrich,
S. Higginbotham, A. Kalogeropoulos0000-0003-3444-0314, G. Kopp, S.
Kwan0000-0002-5308-7707, D. Lange, M.T. Lucchini0000-0002-7497-7450, D.
Marlow0000-0002-6395-1079, K. Mei0000-0003-2057-2025, I. Ojalvo, J.
Olsen0000-0002-9361-5762, C. Palmer0000-0003-0510-141X, 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. Bakshi, 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, S. Karmarkar, M. Liu, G. Negro, N.
Neumeister0000-0003-2356-1700, G. Paspalaki, C.C. Peng, S.
Piperov0000-0002-9266-7819, A. Purohit, J.F. Schulte0000-0003-4421-680X, M.
Stojanovic16, 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. Parashar Rice
University, Houston, Texas, USA A. Baty0000-0001-5310-3466, 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. Li,
B.P. Padley0000-0002-3572-5701, R. Redjimi, W. Shi0000-0002-8102-9002, A.G.
Stahl Leiton0000-0002-5397-252X, S. Yang0000-0002-2075-8631, L. Zhang, Y.
Zhang0000-0002-6812-761X University of Rochester, Rochester, New York, USA A.
Bodek0000-0003-0409-0341, P. de Barbaro, 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. Khukhunaishvili, E. Ranken, R. Taus Rutgers,
The State University of New Jersey, Piscataway, New Jersey, USA B. Chiarito,
J.P. Chou0000-0001-6315-905X, A. Gandrakota0000-0003-4860-3233, Y.
Gershtein0000-0002-4871-5449, E. Halkiadakis0000-0002-3584-7856, A. Hart, M.
Heindl0000-0002-2831-463X, O. Karacheban230000-0002-2785-3762, I. Laflotte, A.
Lath0000-0003-0228-9760, R. Montalvo, K. Nash, M. Osherson, S.
Salur0000-0002-4995-9285, S. Schnetzer, S. Somalwar0000-0002-8856-7401, R.
Stone, 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. Spanier0000-0002-8438-3197 Texas A&M
University, College Station, Texas, USA O. Bouhali940000-0001-7139-7322, M.
Dalchenko0000-0002-0137-136X, A. Delgado0000-0003-3453-7204, R. Eusebi, J.
Gilmore, T. Huang, T. Kamon95, H. Kim0000-0003-4986-1728, S.
Luo0000-0003-3122-4245, S. Malhotra, R. Mueller, D. Overton, D.
Rathjens0000-0002-8420-1488, A. Safonov0000-0001-9497-5471 Texas Tech
University, Lubbock, Texas, USA N. Akchurin, J. Damgov, V. Hegde, S. Kunori,
K. Lamichhane, S.W. Lee0000-0002-3388-8339, T. Mengke, S.
Muthumuni0000-0003-0432-6895, T. Peltola0000-0002-4732-4008, I. Volobouev, Z.
Wang, A. Whitbeck Vanderbilt University, Nashville, Tennessee, USA E.
Appelt0000-0003-3389-4584, S. Greene, A. Gurrola0000-0002-2793-4052, W. Johns,
A. Melo, H. Ni, K. Padeken0000-0001-7251-9125, F. Romeo0000-0002-1297-6065, P.
Sheldon0000-0003-1550-5223, S. Tuo, J. Velkovska0000-0003-1423-5241 University
of Virginia, Charlottesville, Virginia, USA M.W. Arenton0000-0002-6188-1011,
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. Li, C.
Neu0000-0003-3644-8627, B. Tannenwald0000-0002-5570-8095, S.
White0000-0002-6181-4935, E. Wolfe0000-0001-6553-4933 Wayne State University,
Detroit, Michigan, USA N. Poudyal0000-0003-4278-3464 University of Wisconsin -
Madison, Madison, WI, Wisconsin, USA K. Black0000-0001-7320-5080, T.
Bose0000-0001-8026-5380, J. Buchanan0000-0001-8207-5556, C. Caillol, S.
Dasu0000-0001-5993-9045, I. De Bruyn0000-0003-1704-4360, P.
Everaerts0000-0003-3848-324X, F. Fienga0000-0001-5978-4952, C. Galloni, H. He,
M. Herndon0000-0003-3043-1090, A. Hervé, U. Hussain, A. Lanaro, A. Loeliger,
R. Loveless, J. Madhusudanan Sreekala0000-0003-2590-763X, A. Mallampalli, A.
Mohammadi, D. Pinna, A. Savin, V. Shang, V. Sharma0000-0003-1287-1471, W.H.
Smith0000-0003-3195-0909, D. Teague, S. Trembath-Reichert, W.
Vetens0000-0003-1058-1163 †: Deceased
1: Also at TU Wien, Wien, Austria
2: Also at Institute of Basic and Applied Sciences, Faculty of Engineering,
Arab Academy for Science, Technology and Maritime Transport, Alexandria, Egypt
3: Also at Université Libre de Bruxelles, Bruxelles, Belgium
4: Also at Universidade Estadual de Campinas, Campinas, Brazil
5: Also at Federal University of Rio Grande do Sul, Porto Alegre, Brazil
6: Also at University of Chinese Academy of Sciences, Beijing, China
7: Also at Department of Physics, Tsinghua University, Beijing, China
8: Also at UFMS, Nova Andradina, Brazil
9: Also at Nanjing Normal University Department of Physics, Nanjing, China
10: Now at The University of Iowa, Iowa City, Iowa, USA
11: Also at Institute for Theoretical and Experimental Physics named by A.I.
Alikhanov of NRC ‘Kurchatov Institute’, Moscow, Russia
12: Also at Joint Institute for Nuclear Research, Dubna, Russia
13: Also at Helwan University, Cairo, Egypt
14: Now at Zewail City of Science and Technology, Zewail, Egypt
15: Also at Ain Shams University, Cairo, Egypt
16: Also at Purdue University, West Lafayette, Indiana, USA
17: Also at Université de Haute Alsace, Mulhouse, France
18: Also at Erzincan Binali Yildirim University, Erzincan, Turkey
19: Also at CERN, European Organization for Nuclear Research, Geneva,
Switzerland
20: Also at RWTH Aachen University, III. Physikalisches Institut A, Aachen,
Germany
21: Also at University of Hamburg, Hamburg, Germany
22: Also at Isfahan University of Technology, Isfahan, Iran
23: Also at Brandenburg University of Technology, Cottbus, Germany
24: Also at Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State
University, Moscow, Russia
25: Also at Physics Department, Faculty of Science, Assiut University, Assiut,
Egypt
26: Also at Karoly Robert Campus, MATE Institute of Technology, Gyongyos,
Hungary
27: Also at Institute of Physics, University of Debrecen, Debrecen, Hungary
28: Also at Institute of Nuclear Research ATOMKI, Debrecen, Hungary
29: Also at MTA-ELTE Lendület CMS Particle and Nuclear Physics Group, Eötvös
Loránd University, Budapest, Hungary
30: Also at Wigner Research Centre for Physics, Budapest, Hungary
31: Also at IIT Bhubaneswar, Bhubaneswar, India
32: Also at Institute of Physics, Bhubaneswar, India
33: Also at G.H.G. Khalsa College, Punjab, India
34: Also at Shoolini University, Solan, India
35: Also at University of Hyderabad, Hyderabad, India
36: Also at University of Visva-Bharati, Santiniketan, India
37: Also at Indian Institute of Technology (IIT), Mumbai, India
38: Also at Deutsches Elektronen-Synchrotron, Hamburg, Germany
39: Also at Sharif University of Technology, Tehran, Iran
40: Also at Department of Physics, University of Science and Technology of
Mazandaran, Behshahr, Iran
41: Now at INFN Sezione di Bari, Università di Bari, Politecnico di Bari,
Bari, Italy
42: Also at Italian National Agency for New Technologies, Energy and
Sustainable Economic Development, Bologna, Italy
43: Also at Centro Siciliano di Fisica Nucleare e di Struttura Della Materia,
Catania, Italy
44: Also at Università di Napoli ’Federico II’, Napoli, Italy
45: Also at Consiglio Nazionale delle Ricerche - Istituto Officina dei
Materiali, Perugia, Italy
46: Also at Riga Technical University, Riga, Latvia
47: Also at Consejo Nacional de Ciencia y Tecnología, Mexico City, Mexico
48: Also at IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France
49: Also at Institute for Nuclear Research, Moscow, Russia
50: Now at National Research Nuclear University ’Moscow Engineering Physics
Institute’ (MEPhI), Moscow, Russia
51: Also at Institute of Nuclear Physics of the Uzbekistan Academy of
Sciences, Tashkent, Uzbekistan
52: Also at St. Petersburg Polytechnic University, St. Petersburg, Russia
53: Also at University of Florida, Gainesville, Florida, USA
54: Also at Imperial College, London, United Kingdom
55: Also at Moscow Institute of Physics and Technology, Moscow, Russia
56: Also at P.N. Lebedev Physical Institute, Moscow, Russia
57: Also at California Institute of Technology, Pasadena, California, USA
58: Also at Budker Institute of Nuclear Physics, Novosibirsk, Russia
59: Also at Faculty of Physics, University of Belgrade, Belgrade, Serbia
60: Also at Trincomalee Campus, Eastern University, Sri Lanka, Nilaveli, Sri
Lanka
61: Also at INFN Sezione di Pavia, Università di Pavia, Pavia, Italy
62: Also at National and Kapodistrian University of Athens, Athens, Greece
63: Also at Ecole Polytechnique Fédérale Lausanne, Lausanne, Switzerland
64: Also at Universität Zürich, Zurich, Switzerland
65: Also at Stefan Meyer Institute for Subatomic Physics, Vienna, Austria
66: Also at Laboratoire d’Annecy-le-Vieux de Physique des Particules,
IN2P3-CNRS, Annecy-le-Vieux, France
67: Also at Şırnak University, Sirnak, Turkey
68: Also at Near East University, Research Center of Experimental Health
Science, Nicosia, Turkey
69: Also at Konya Technical University, Konya, Turkey
70: Also at Istanbul University - Cerrahpasa, Faculty of Engineering,
Istanbul, Turkey
71: Also at Piri Reis University, Istanbul, Turkey
72: Also at Adiyaman University, Adiyaman, Turkey
73: Also at Ozyegin University, Istanbul, Turkey
74: Also at Izmir Institute of Technology, Izmir, Turkey
75: Also at Necmettin Erbakan University, Konya, Turkey
76: Also at Bozok Universitetesi Rektörlügü, Yozgat, Turkey
77: Also at Marmara University, Istanbul, Turkey
78: Also at Milli Savunma University, Istanbul, Turkey
79: Also at Kafkas University, Kars, Turkey
80: Also at Istanbul Bilgi University, Istanbul, Turkey
81: Also at Hacettepe University, Ankara, Turkey
82: Also at Rutherford Appleton Laboratory, Didcot, United Kingdom
83: Also at Vrije Universiteit Brussel, Brussel, Belgium
84: Also at School of Physics and Astronomy, University of Southampton,
Southampton, United Kingdom
85: Also at IPPP Durham University, Durham, United Kingdom
86: Also at Monash University, Faculty of Science, Clayton, Australia
87: Also at Università di Torino, Torino, Italy
88: Also at Bethel University, St. Paul, Minneapolis, USA
89: Also at Karamanoğlu Mehmetbey University, Karaman, Turkey
90: Also at Bingol University, Bingol, Turkey
91: Also at Georgian Technical University, Tbilisi, Georgia
92: Also at Sinop University, Sinop, Turkey
93: Also at Erciyes University, Kayseri, Turkey
94: Also at Texas A&M University at Qatar, Doha, Qatar
95: Also at Kyungpook National University, Daegu, Korea