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Figrefcmd=Fig. LABEL:#1

# Latency Analysis of ROS2 Multi-Node Systems

Tobias Kronauer<EMAIL_ADDRESS>Barkhausen InstitutDresdenGermany ,
Joshwa Pohlmann<EMAIL_ADDRESS>Barkhausen InstitutDresdenGermany ,
Maximilian Matthé<EMAIL_ADDRESS>Barkhausen
InstitutDresdenGermany ,  Till Smejkal<EMAIL_ADDRESS>Operating
SystemsTU DresdenGermany and  Gerhard Fettweis<EMAIL_ADDRESS>Barkhausen InstitutDresdenGermany

###### Abstract.

The Robot Operating System 2 (ROS2) targets distributed real-time systems and
is widely used in the robotics community. Especially in these systems, latency
in data processing and communication can lead to instabilities. Though being
highly configurable with respect to latency, ROS2 is often used with its
default settings.

In this paper, we investigate the end-to-end latency of ROS2 for distributed
systems with default settings and different Data Distribution Service (DDS)
middlewares. In addition, we profile the ROS2 stack and point out latency
bottlenecks. Our findings indicate that end-to-end latency strongly depends on
the used DDS middleware. Moreover, we show that ROS2 can lead to 50 % latency
overhead compared to using low-level DDS communications. Our results imply
guidelines for designing distributed ROS2 architectures and indicate
possibilities for reducing the ROS2 overhead.

distributed systems, mobile robotics, latency, profiling, ROS2

††conference: SenSys; November 2021; Coimbra Portugal††copyright: none††ccs:
Software and its engineering Application specific development
environments††ccs: Computer systems organization Robotics

##  1\. Introduction

Through the advent of robotic applications, such as autonomous driving or
household robotics, the robot operating system (ROS) emerged as one of the
most widely used software development frameworks. With more than tens of
thousands of users (OSRF, 2020b), it is widely used in academia as well as in
industry (OSRF, 2020e).

Shortcomings of ROS1, but also its popularity led to the development of its
successor, ROS2, which is developed by the Open Source Robotics Foundation
(OSRF) with many industrial contributors (OSRF, 2020c; Casini et al., 2019).
Although being under heavy development, it is already used by notable
companies (LGSVL, 2020) and the Open Source community (Gaz, 2020). Reasons for
the development of ROS2 are new use cases, e.g. multiple robots, small
embedded platforms, and real-time capability. Further, new technologies are
available such as the Data Distribution Service (DDS) (OMG, 2020). (OSRF,
2020f)

ROS2 and its predecessor share the same core concept. Therefore, we refer to
software architectures in ROS1 or ROS2 as ROS systems. Among others, a ROS
system comprises nodes, messages, and topics. A node is a software module
performing computation. As ROS features the notion of modularity, a ROS system
is usually composed of several nodes. These nodes exchange information by
passing messages. These messages only contain typed data structures that are
standard primitive data types. A message is published by a node to a given
topic, which is described by a string. Nodes that are interested in the data
contained in this message subscribe to that topic. Each node can have multiple
subscribers and publishers. (Quigley et al., 2009)

Although still using the publish/subscribe mechanism of ROS1, ROS2 builds its
transport layer on a new middleware. The middleware is an implementation of
the DDS standard (OMG, 2020) that is widely used for distributed, real-time
systems. Without changing much of the usercode of ROS1, the goal was to hide
the DDS middleware and its API to the ROS2 user as shown in
DDSAbstractionRos2. For that purpose, middleware interface modules (rmw in
short for ros middleware) were introduced. The most recent release of ROS2,
Foxy Fitzroy, supports, among others, eProsima FastRTPS, Eclipse Cyclone DDS,
and RTI Connext as DDS middleware. (OSRF, 2020d, a).

Between userland code and DDS middlware, ROS2 introduces two API layers.

Figure 1. API layout from ROS2, taken from (OSRF, 2020d).

Since it is not the main focus of the paper, we will only briefly summarize
DDS. The summary is based on the most recent DDS specification 1.4 (OMG,
2020). It describes a Data-Centric Publish-Subscribe model (DCPS) for
distributed applications enabling reliable, configurable, and real-time
capable information between information points. Similar to ROS1 and ROS2,
there are publishers that publish information of different data types. Each
publisher has a DataWriter that can be regarded as a source of information
providing data of predefined type. The subscriber, on the other hand, is
responsible for receiving the data sent by the publisher. A DataReader is
responsible for reading the information obtained by the subscriber. As in ROS,
a topic fulfills the task to connect the publisher with one or more
subscribers. A distinguishing feature of DDS is the use of quality of service
(QoS) policies. Each entity has an assigned QoS policy determining the
behavior of each entity concerning communication and discovery. There is a
huge variety of QoS parameters that can be set.

The described concept advocates the use of a distributed, modularized system.
Applications that are based on a ROS system often use a software architecture
of many nodes with well-defined interfaces (Naumann et al., 2018). Running on
localhost, shared memory and intraprocess communication may be used,
significantly reducing latency. However, for distributed systems consisting of
multiple hardware systems, this is not possible. In this work, we concentrate
on the specifics provided by ROS by default, i.e. that can be used by users
without the necessity to tweak the configuration. We consider this a viable
use case, as lots of potential users use the out-of-the-box behavior of ROS2.

Splitting the signal processing into several nodes, entails a certain latency
to the system. Since real-time capability is one of the main feature claims of
ROS2, the question arises how much latency is entailed by a system of many
nodes compared to a system that performs the same computation in a single
node. This leads to the central question of this paper: How does a ROS2 system
cope with scalability? Latency plays a critical factor for new technologies,
e.g. autonomous cars, edge cloud systems, and plenty of other applications
enabled by 5G (Lema et al., 2017; Maheshwari et al., 2018; Voigtländer et al.,
2017).

The paper is structured as follows: In RelatedWork, we will summarize
available publications that analyze ROS2 in terms of latency followed by the
description of the contribution of our work. In the succeeding section, we
will briefly explain our methodology for the latency evaluation. Results are
presented in section Evaluation. This work will be concluded with a future
outlook in Conclusion.

##  2\. Related Work

At the early stage of development, ROS2 was evaluated by (Maruyama et al.,
2016) who used an alpha version and compared it with ROS1. Messages with sizes
between 256 B and 4 MB were published at a 10 Hz rate. The authors also vary
the DDS middleware used by ROS2, i.e. RTI Connext, OpenSplice, and FastRTPS.
The number of nodes that subscribe to a certain topic another node publishes
to were varied as well. Latency, throughput via Ethernet, memory consumption,
and threads per node were chosen as measurement metrics. Additionally, the
overhead entailed by ROS2 to the latency is evaluated. They emphasize the
importance of the message size for end-to-end latencies via Ethernet with a
constant latency and ROS2 overhead until 64 KB with the QoS policy being the
major part. Further, they recommend a fragment size of 64 KB that is used by
the DDS middleware UDP protocol.

The results obtained were confirmed by (Reke et al., 2020) who evaluated ROS2
for autonomous cars on two KIA Niros with respect to real-time capability.
They figured out that the results depend on the Linux kernel. Their software
architecture is composed of 14 nodes on i7 Intel NUC. Messages were sent at a
frequency of 33 Hz and statistics of the time difference between two
communicating nodes were calculated. By using a real-time kernel for Linux the
jitter of the time difference could be significantly reduced. Using this
information, the overall car behavior was analyzed under different scenarios.

The first official ROS2 release in December 2017, Ardent Apalone, was
evaluated by (Gutiérrez et al., 2018) using a real-time Linux kernel over
Ethernet. By varying system loads, e.g. CPU load and concurrent traffic,
round-trip latency was measured. One node was launched on a normal computer,
another node was launched on an embedded device. A message was sent from the
normal computer to the embedded device that sends the message back. The
authors point out how this round-trip latency is influenced by the network and
OS stack.

The previous papers emphasize the influence of various QoS parameters and DDS
middlewares on the latency and throughput. (Morita and Matsubara, 2018)
propose an architecture that dynamically binds different DDS middlewares to
ROS2 nodes to exploit performance benefits of the DDS middlewares under
varying circumstances.

(Wang et al., 2019) focused on improving the Inter Process Communication and
compared it to the ROS2 implementation obtaining a lower latency and higher
throughput. (Kim et al., 2018) evaluated latency and throughput in combination
with encryption.

###  2.1. Contribution

To the best of the author’s knowledge, (Maruyama et al., 2016) did the most
comprehensive evaluation from a pure ROS2 perspective. Yet, the authors used a
ROS2 alpha version and there have been a couple of releases in the meantime.
Although (Reke et al., 2020) did evaluations on realistic hardware, they only
provided a brief, very high-level evaluation of their software architecture.
The evaluations were mostly constrained to two or three nodes, i.e. it was not
evaluated if the results can be scaled to a node system comprised of many
nodes.

In this paper, we answer that question and provide the user with some
guidelines to go along if the latency of a ROS system is to be decreased. For
that, we perform an intra-layer profiling to concisely evaluate the
bottlenecks in the communication in order to show possible implementation
improvements for future ROS2 releases. Since distributed systems can be
composed of different entities (robots, edge cloud, etc.), we define the use-
case of reading a sensor in one component and post-processing it afterwards in
other system components. Our parameters are then derived from this use case.
We do not focus on the DDS middlewares as there are benchmarks on the homepage
of the vendors. In addition, configuration strongly depends on the use case.

##  3\. Methodology

At first, we will define our use case in UseCaseDefinition, which is followed
by the description of the parameter space in ParameterSpace. Afterwards, we
will introduce measurement metrics and present our evaluation framework in
MeasurementMetrics and EvaluationFramework.

###  3.1. Use Case

We focus on the use case of a distributed system. To generalize such system,
we represent each system component (i.e. one computing node) by a single node
performing all the processing. We assume that the processing of sensor
readings and other additional calculations entail no latency, i.e. the message
is sent out with the same frequency as the sampling rate of the sensor. We
assume the communication pattern to be subsequent as this is a worst-case
scenario leading to the highest latency between sending and receiving a
message. This means, a first computing node is defined which sends out
information to another component, which, upon receiving, sends this message to
the third component, etc. The setup is depicted in EvaluationSetup. We refer
to a chain of nodes as data-processing pipeline.

###  3.2. Parameter Space

Our parameters are derived from the use case of reading a sensor and post-
processing it in a distributed fashion. The sampling frequency of the sensor
is a variable parameter. Assuming that the sensor reading node only reads the
sensor data and immediately publishes the message, this corresponds to the
publisher frequency. The data size of the sensor reading is variable as well.
In the ROS system, the payload of the message represents this quantity. The
number of nodes, which includes the start and end node in a data-processing
pipeline can be modified as well. Moreover, we can change the Quality of
Service settings. The aforementioned parameters remain constant throughout the
data-processing pipeline.

Introduced parameters are visualized.

Figure 2. Visualization of evaluation setup. Parameters are highlighted in
italic.

###  3.3. Measurement Metrics

Latency is our main measurement metric. In accordance with the previous papers
mentioned in RelatedWork, latency is defined between publishing a message in
the first node and receiving the message in the last node, i.e. the call of
the callback of the subscriber.

The focus of the evaluation is the latency entailed by the ROS system and not
by the DDS middleware. Therefore, we want to profile the call stack between
publishing and subscriber callback for evaluating the overhead of ROS2 core
and the middleware interfaces. As statistical quantity, we choose the 95 %
percentile and do not analyze the distributions as such. This means 95 % of
the calculated latencies are below this value. In general, the amount of
messages that are below a certain threshold is of interest. As this depends on
the actual use case, we decided to set this value to 95 %.

###  3.4. Evaluation Framework

In a sequence diagram, we show required code adaptions for our profiling.
Categorization is shown as well.

Figure 3. Sequence diagram of necessary adaptions to enable profiling. Notes
indicate the layers. Colored boxes highlight the profiling categories.

Relevant code to reproduce paper results can be found on GitHub (GitHub,
2021). SequenceDiagramProfiling depicts the implementation of an intra-layer
profiling for ROS2 messages. The implementation is bundled within a docker
container containing the custom ROS2 build. The latency overhead of docker is
negligible (Felter et al., 2015) provided that it is run in the host network.
For the implementation, we added a ros2profiling package providing functions
to generate timestamps since the Epoch in nanoseconds. It patches the ROS2
source tree to include timestamps into processed messages. Therefore, a
minimum message size of 128 B needs to be ensured. The timestamps correspond
to the position of the notes in SequenceDiagramProfiling in the ROS2
callstack. Timestamps are recorded when entering and leaving the method of the
layer. Arrow annotations denote the called function and asterisks indicate
placeholders for the actual function name, as this depends on the middleware.
Timestamps were categorized into the following categories:

figures/results/frequency

We evaluate the influence of the publisher frequency on the latency. Generally
speaking, latency decreases with publisher frequency and increases with
message size.

Figure 4. Investigating the influence of publisher frequency on latency with
three nodes, QoS reliability is set to BEST_EFFORT.

  * •

DDS: This category only contains latency entailed by the DDS transport via
network and by the function call to actually receive the message.

  * •

Subscriber rmw and Publisher rmw: Latency attributed to the rmw layer.
Middleware-specific conversions from ROS2 messages to DDS messages that might
require DDS utility functions but are not used for the transport of the
message itself are contained in this category.

  * •

Publisher and Subscriber ROS2 Common: Overhead entailed by ROS2 that is
independent of the middleware.

  * •

Benchmarking: This latency is entailed by code used for benchmarking the
latency.

  * •

Rclcpp Notification Delay: The time difference between the notification of DDS
to ROS2 that new data is available and triggering of its actual retrieval.

As we are interested in the ROS2 overhead and not on the over-the-network
performance, which is dictated by DDS and the network itself, latency is
measured on one machine. In addition, this approach simplifies evaluation and
test setup. Nodes of the data-processing pipeline are created in different
processes. Note that this is contrast to our use case.

##  4\. Evaluation

Table 1. Variable parameter values. Publisher frequency | 1, 10, …, 90, 100
---|---
Payload | 128 B, 1 KB, 10 KB, 100 KB, 500 KB
Number of Nodes | 3, 5, …, 21, 23
DDS Backend | Connext, FastRTPS, CycloneDDS
Reliability | reliable, best effort

We compare two different hardware settings, namely a desktop PC, with an Intel
i7-8700 CPU @ 3.2 GHz x 6 and 32 GB RAM. In addition, we use a Raspberry Pi 4
Model B Rev 1.1 with 4 GB RAM. Kernel versions are 5.4.0-42-generic for the
desktop PC and 5.4.0-1015-raspi for Raspberry Pi. The latest release of ROS2
at the time of writing (Foxy Fitzroy 20201211) is used as ROS2 version for our
evaluation. We set the network device as localhost with UDP as transport
layer. FastRTPS version is 2.0.1, CycloneDDS is 0.6.0, and Connext was updated
to 6.0.1 as major improvements were made during this update.

The variable parameters are listed in VariableParameterValues. We assume a
publisher frequency of maximum 100 Hz, which is realistic for e.g. time-of-
flight sensors. GPS sensors operate at an update rate of 1 Hz up to 10 Hz. We
assume an update rate for cameras up to 100 Hz. Therefore, the publisher
frequency is in a range from 1 Hz to 100 Hz with a step size of 10 Hz. As
variable QoS policies, we modify the reliability from RELIABLE to BEST_EFFORT,
since they are frequently used. The number of nodes in the data-processing
pipeline varies between three and 23 nodes with a step size of two. These
values are arbitrarily chosen.

figures/results/scalability

Scalability of a node system is evaluated for different hardwares and
payloads. System behaves approximately linear.

Figure 5. Investigation of the scalability of a node system. We used payloads
of 128 B and of 500 KB. The DDS middleware was varied. For visualization
purposes, only a few frequencies were picked. Evaluation was performed on the
desktop PC with QoS-reliability BEST_EFFORT. Upper two rows: desktop PC, lower
two rows: raspberry pi.

In all cases, we use a time duration for one configuration run of 60 seconds.
Depending on the publisher frequency, this results in a varying amount of
samples, i.e. the higher the publisher frequency the higher the amount of
samples.

The default settings of the Linux kernel are highly adaptive to the load and
other external factors. In order to inhibit idle and energy saving mechanisms,
which add additional noise to the latency measured, we change the kernel
parameters: the scaling governor is set to userspace and core frequencies are
set to their maximum value. We deactivate the CPU idle by passing
cpuidle.off=1 as a kernel parameter. The option no_hz disables the scheduler
tick if no work is to be done on that CPU, which is why we deactivate it. For
the desktop PC, we turn off hyperthreading.

###  4.1. Evaluation of Publisher Frequency

We use three nodes with a publisher frequency between 1 Hz and 100 Hz as
depicted in InfluencePublisherFrequency. This corresponds to a ping-pong
scenario. While sticking to the QoS reliability to BEST_EFFORT, we use all
possible payload sizes.

In the case of the desktop PC, for all DDS middlewares, we can see that
latency decreases with increased frequency. This might be due to (unknown)
energy saving features in other hardware devices or reprioritized thread
scheduling. Further, we can see that the obtained latencies for 128 B, 1 KB,
10 KB are equal, but increase for 100 KB and 500 KB. This can be explained by
the maximum UDP packet size of 64 KB which incurs fragmentation for large
payloads. This additional overhead differs with the employed middleware.
FastRTPS is slighty faster than Connext, whereas CycloneDDS entails the
highest latency.

In the case of the Raspberry Pi, we can see that the latency decreases with
the frequency as well, except for CycloneDDS with 1 Hz. This can be due to low
amount of samples. In addition, we can see a certain plateau between 10 Hz and
40 Hz for 500 KB. In general, the latency obtained is significantly higher
than for the desktop PC.

figures/results/profiling

Results of profiling are shown. Most of the latency can be attributed to delay
between notification and message retrieval for small message sizes. For larger
message sizes, major latency contribution can be attributed to the DDS
middleware.

Figure 6. Categorization of intra-process profiling of different latencies.
Evaluation was performed with QoS reliability BEST_EFFORT. Frequency is 100 Hz
for the desktop PC and message size 500 KB. Concerning Raspberry Pi, frequency
is 50 Hz and 100 KB. The latter one was fixed to these values, as a major
amount of the sent messages was lost for higher payload and frequency.

###  4.2. Evaluation of Scalability

We evaluate the latency from starting to end node for the data-processing
pipeline ranging from 3 to 23 nodes. As payload, we use 128 B and 500 KB. For
visualization purposes, we restrict ourselves to a subset of the evaluated
frequencies. Results are shown in Scalability.

We can observe the same pattern as in InfluencePublisherFrequency: the latency
decreases if the frequency is increased. This effect is intensified with the
length of the data-processing pipeline. As far as the desktop PC is concerned,
for a payload of 128 B, the results indicate a linear relationship between the
number of nodes and latency. The outliers may occur due to too few samples,
which is the case for lower frequencies. It needs to be further investigated
if the relationship will be more linear if the number of samples is larger.

Similar results were observed for the Raspberry Pi, whereas differences in
latency with regard to frequency are more apparent. Although some linearity
can be observed, more fluctuations occur. Interestingly, for Connext with 128
B and a frequency of 100 Hz, latency increases nonlinear for high node count.
Regarding message size, we restricted ourselves to 100 KB as plenty of
messages (roughly 30 %) were lost for 500 KB. In Scalability, we can see for
all middlewares the same pattern: for frequencies higher than 50 Hz, latency
increases extremely at 13 or 17 nodes. Hence, the raspberry pi seems to be
overloaded in this area.

###  4.3. Profiling

The following findings apply for both hardwares: for a payload of 128 B, the
largest amount of latency can be attributed to the categories DDS and Rclcpp
Notification Delay as seen in Profiling. The overhead of ROS2 compared to raw
DDS amounts up to 50 % for small messages. Using a payload of 500 KB, one can
clearly see that for all middlewares, the major part of the latency is due to
the DDS middleware. As we focus on possible overhead reductions of ROS2 in
this paper, we assume that the DDS middlewares cannot be changed. Thus, we can
observe that major performance improvements can be obtained for the category
Rclcpp Notification Delay.

In addition, we can observe for the Raspberry Pi different conclusions for
latency compared to the desktop PC: We can observe that Connext and CycloneDDS
yield comparable results, whereas FastRTPS is significantly faster, which is
different to the desktop PC. As for higher payload lots of messages were lost,
we restricted ourselves to 100 Kb and 50 Hz.

###  4.4. Influence of QoS Reliability

In the last sections, the QoS reliability policy was set to BEST_EFFORT and
kept as a constant parameter. We pick the highest possible throughput and
calculate the relative deviation between the 95 % percentile of the latencies
obtained with the QoS policy BEST_EFFORT and RELIABLE. In our setup, using
RELIABLE transmission imposed a latency overhead of up to 15 %, cf. QoS.

figures/results/qos

The relative difference in latency between BEST_EFFORT and RELIABLE can reach
up to 15 %.

Figure 7. Evaluation of influence of QoS reliability settings on latency. For
the desktop PC, we choose 500 KB and 100 Hz. In the case of Raspberry Pi, we
have a payload of 100 KB and a publisher frequency of 50 Hz.

##  5\. Conclusion and Future Outlook

The goal of this paper was to provide the reader with simple guidelines if
ROS2 is used for distributed systems. Given our parameter set, we discovered
the following rules of thumb:

  * •

With a payload higher than the fragmentation size of UDP (here, 64 KB),
latency increases with the payload size.

  * •

The higher the frequency, the lower the latency.

  * •

Linearity with minor fluctuations for the 95 % percentile of latency with
respect to node count could be observed.

  * •

Latency critically depends on the hardware used and the parameter settings. No
middleware yields the lowest latency in all cases.

  * •

DDS middleware and the delay between message notification and message
retrieval by ROS2 contribute the biggest portions to the overall latency.

  * •

Latency is larger on Raspberry Pi and fluctuation in latency are more
significant compared to the desktop PC. However, middlewares perform
differently on the Raspberry Pi compared to the desktop PC.

During our evaluation, we observe that latency highly depends on energy saving
features of the OS and the hardware. Our main focus was on the CPU. However,
energy saving features of the NIC, e.g., might play an important role. This
needs to be taken carefully into consideration if latency is to be mitigated
for real-time critical applications. Further, a real-time kernel could be
chosen.

In future work, one might consider an evaluation in a more realistic setup,
i.e. with distributed systems. Network effects could be better evaluated.
Aside from the 95 percentile, one could verify if the latencies of the
messages follow a certain distribution. The obtained information could then be
used as an additional uncertainty for state estimation and incorporated into
the Consensus Kalman Filter.

Although the amount of lost messages was negligible, differences between
different DDS middlewares could be observed. This could be analyzed as well.

###### Acknowledgements.

This research was co-financed by public funding of the state of Saxony,
Germany. We thank RTI for the license and support.

## References

  * (1)
  * Gaz (2020) 2020 (accessed August 17, 2020).  _gazebo_ros2_control_.  https://github.com/gazebo_ros2_control
  * Casini et al. (2019) Daniel Casini, Tobias Blaß, Ingo Lütkebohle, and Björn B. Brandenburg. 2019.  Response-Time Analysis of ROS 2 Processing Chains Under Reservation-Based Scheduling. In _31st Euromicro Conference on Real-Time Systems (ECRTS 2019)_ _(Leibniz International Proceedings in Informatics (LIPIcs), Vol. 133)_ , Sophie Quinton (Ed.). Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, 6:1–6:23.  https://doi.org/10.4230/LIPIcs.ECRTS.2019.6
  * Felter et al. (2015) W. Felter, A. Ferreira, R. Rajamony, and J. Rubio. 2015.  An updated performance comparison of virtual machines and Linux containers. In _2015 IEEE International Symposium on Performance Analysis of Systems and Software (ISPASS)_. 171–172.
  * GitHub (2021) GitHub. 2021 (accessed June 06, 2021).  _BI GitHub Projects_.  https://github.com/orgs/Barkhausen-Institut/projects
  * Gutiérrez et al. (2018) Carlos San Vicente Gutiérrez, Lander Usategui San Juan, Irati Zamalloa Ugarte, and Víctor Mayoral Vilches. 2018\.  Towards a distributed and real-time framework for robots: Evaluation of ROS 2.0 communications for real-time robotic applications.  _arXiv:1809.02595 [cs]_ (Sept. 2018).  http://arxiv.org/abs/1809.02595 arXiv: 1809.02595.
  * Kim et al. (2018) Jongkil Kim, Jonathon M. Smereka, Calvin Cheung, Surya Nepal, and Marthie Grobler. 2018.  Security and Performance Considerations in ROS 2: A Balancing Act.  _arXiv:1809.09566 [cs]_ (Sept. 2018).  http://arxiv.org/abs/1809.09566
  * Lema et al. (2017) Maria A Lema, Andres Laya, Toktam Mahmoodi, Maria Cuevas, Joachim Sachs, Jan Markendahl, and Mischa Dohler. 2017.  Business case and technology analysis for 5G low latency applications.  _IEEE Access_ 5 (2017), 5917–5935.
  * LGSVL (2020) LGSVL. 2020 (accessed August 17, 2020).  _LGSVL Simulator_.  https://www.lgsvlsimulator.com/
  * Maheshwari et al. (2018) S. Maheshwari, D. Raychaudhuri, I. Seskar, and F. Bronzino. 2018.  Scalability and Performance Evaluation of Edge Cloud Systems for Latency Constrained Applications. In _2018 IEEE/ACM Symposium on Edge Computing (SEC)_. 286–299.
  * Maruyama et al. (2016) Yuya Maruyama, Shinpei Kato, and Takuya Azumi. 2016\.  Exploring the performance of ROS2. In _Proceedings of the 13th International Conference on Embedded Software - EMSOFT ’16_. ACM Press, Pittsburgh, Pennsylvania, 1–10.  https://doi.org/10.1145/2968478.2968502
  * Morita and Matsubara (2018) Ren Morita and Katsuya Matsubara. 2018.  Dynamic Binding a Proper DDS Implementation for Optimizing Inter-Node Communication in ROS2. In _2018 IEEE 24th International Conference on Embedded and Real-Time Computing Systems and Applications (RTCSA)_. 246–247.  https://doi.org/10.1109/RTCSA.2018.00043 ISSN: 2325-1301.
  * Naumann et al. (2018) M. Naumann, F. Poggenhans, M. Lauer, and C. Stiller. 2018.  CoInCar-Sim: An Open-Source Simulation Framework for Cooperatively Interacting Automobiles. In _2018 IEEE Intelligent Vehicles Symposium (IV)_. 1–6.
  * OMG (2020) OMG. 2015 (accessed August 17, 2020).  _Data Distribution Service_.  https://www.omg.org/spec/DDS/
  * OSRF (2020b) OSRF. 2019 (accessed August 17, 2020)b.  _Community Metrics Report_.  http://download.ros.org/downloads/metrics/metrics-report-2019-07.pdf
  * OSRF (2020d) OSRF. 2019 (accessed August 17, 2020)d.  _ROS on DDS_.  https://design.ros2.org/articles/ros_on_dds.html
  * OSRF (2020a) OSRF. 2020 (accessed August 17, 2020)a.  _About different ROS 2 DDS/RTPS vendors_.  https://index.ros.org/doc/ros2/Concepts/DDS-and-ROS-middleware-implementations/
  * OSRF (2020c) OSRF. 2020 (accessed August 17, 2020)c.  _Project Governance_.  https://index.ros.org/doc/ros2/Governance/#governance
  * OSRF (2020e) OSRF. 2020 (accessed August 17, 2020)e.  _ROS Robots_.  https://robots.ros.org/
  * OSRF (2020f) OSRF. 2020 (accessed August 17, 2020)f.  _Why ROS 2?_ https://design.ros2.org/articles/why_ros2.html
  * Quigley et al. (2009) Morgan Quigley, Ken Conley, Brian Gerkey, Josh Faust, Tully Foote, Jeremy Leibs, Rob Wheeler, and Andrew Y Ng. 2009\.  ROS: an open-source Robot Operating System. In _ICRA workshop on open source software_ , Vol. 3. Kobe, Japan, 5.
  * Reke et al. (2020) Michael Reke, Daniel Peter, Joschua Schulte-Tigges, Stefan Schiffer, Alexander Ferrein, Thomas Walter, and Dominik Matheis. 2020\.  A Self-Driving Car Architecture in ROS2. In _2020 International SAUPEC/RobMech/PRASA Conference_. 1–6.  https://doi.org/10.1109/SAUPEC/RobMech/PRASA48453.2020.9041020
  * Voigtländer et al. (2017) F. Voigtländer, A. Ramadan, J. Eichinger, C. Lenz, D. Pensky, and A. Knoll. 2017\.  5G for Robotics: Ultra-Low Latency Control of Distributed Robotic Systems. In _2017 International Symposium on Computer Science and Intelligent Controls (ISCSIC)_. 69–72.
  * Wang et al. (2019) Yu-Ping Wang, Wende Tan, Xu-Qiang Hu, Dinesh Manocha, and Shi-Min Hu. 2019.  TZC: Efficient Inter-Process Communication for Robotics Middleware with Partial Serialization. In _2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)_. 7805–7812.  https://doi.org/10.1109/IROS40897.2019.8968462 ISSN: 2153-0866.


# Light vector mediators at direct detection experiments

Valentina De Romeri<EMAIL_ADDRESS>Instituto de Física Corpuscular
(CSIC-Universitat de València), Parc Científic UV C/ Catedrático José Beltrán,
2 E-46980 Paterna (Valencia) - Spain  Dimitrios K. Papoulias
<EMAIL_ADDRESS>Department of Physics, National and Kapodistrian
University of Athens, Zografou Campus GR-15772 Athens, Greece  Christoph A.
Ternes<EMAIL_ADDRESS>Istituto Nazionale di Fisica Nucleare
(INFN), Laboratori Nazionali del Gran Sasso, 67100 Assergi, L’Aquila (AQ),
Italy

###### Abstract

Solar neutrinos induce elastic neutrino-electron scattering in dark matter
direct detection experiments, resulting in detectable event rates at current
facilities. We analyze recent data from the XENONnT, LUX-ZEPLIN, and PandaX-4T
experiments and we derive stringent constraints on several $U(1)^{\prime}$
extensions of the Standard Model, accommodating new neutrino-electron
interactions. We provide bounds on the relevant coupling and mass of light
vector mediators for a variety of models, including the anomaly-free $B-L$
model, lepton flavor-dependent interactions like $L_{\alpha}-L_{\beta}$,
$B-2L_{e}-L_{\mu,\tau}$, $B-3L_{\alpha}$, and $B+2L_{\mu}+2L_{\tau}$ models.
We compare our results with other limits obtained in the literature from both
terrestrial and astrophysical experiments. Finally, we present forecasts for
improving current bounds with a future experiment like DARWIN.

light mediators, dark matter detectors, neutrinos

###### Contents

  1. I Introduction
  2. II Theoretical framework
    1. II.1 E$\nu$ES in the Standard Model
    2. II.2 E$\nu$ES in models with an extra $U(1)^{\prime}$ symmetry
  3. III Data analysis
    1. III.1 Current experiments
    2. III.2 DARWIN sensitivity
  4. IV Results
  5. V Conclusions

##  I Introduction

Dark Matter (DM) Direct Detection (DD) experiments [1, 2], although primarily
designed for DM searches, have been recently recognized as favorable
facilities to probe new physics beyond the weakly interacting massive
particles (WIMPs) paradigm [3]. Indeed, and despite the so far eluding WIMP
detection, the latest generation of DM DD experiments — including low-
threshold dual-phase liquid xenon (LXe) detectors developed by the XENON
(Italy) [4, 5, 6], LUX-ZEPLIN (LZ) in the USA [7, 8, 9], and PandaX (China)
[10, 11, 12] collaborations — have reached world-leading sensitivities also on
alternative physics beyond the SM (BSM), for instance boosted-DM scenarios
[13, 14], dark photons [15], axion-like particles [16], novel hidden sectors
[17] and gravitational waves [18]. The physics program of DD facilities will
continue and intensify with next-generation detectors [3, 19, 20] such as
those planned by the DARWIN Collaboration [21] that aspire to achieve very low
sensitivities leveraging its multi-ton exposure, low background and low
threshold. Towards this purpose the XLZD Consortium (XENON, LZ, DARWIN) aims
to develop a 60-ton LXe detector in the next decade [22] that will probe WIMPs
down to the neutrino fog. At the same time, further advances based on liquid
argon (LAr) technology are currently under development by the Global Argon
Dark Matter Collaboration (GADMC) [23], with near-term activities focusing on
the construction of the DarkSide-20k detector at Laboratori Nazionali del Gran
Sasso (LNGS), and the ultimate goal being the construction of a 300-ton argon
detector.

At present, the large fiducial volumes of LXe detectors available at the
XENONnT (5.9 ton), LZ (5.5 ton) and PandaX-4T (3.7 ton) experiments have
already allowed the collaborations to accumulate exposures of 1.16, 0.90, and
0.63 ton $\times$ year, respectively, in a rather short amount of data-
collection time during their first run. This, together with their extremely
low-threshold capabilities has prompted an impressive flourishing of
theoretical activity in the search for new physics, inspiring an exhaustive
number of phenomenological analyses.

Strikingly, the increase in target size and sensitivity of current DD
detectors has opened a whole new window for the observation of the scattering
of solar neutrinos. While constituting an irreducible background for DM
searches, through the so-called $\nu-$floor [24] or fog [25], sizable fluxes
of solar neutrinos also provide new opportunities for probing neutrino
properties [26, 27, 28] and new physics connected to the neutrino sector [29,
30, 31, 32, 33, 34, 35, 36].

Neutrinos coming from the Sun can induce elastic neutrino-electron scattering
(E$\nu$ES) and coherent elastic neutrino-nucleus scattering (CE$\nu$NS) events
in DM DD experiments, both having a strong degeneracy with the corresponding
DM-electron [32, 37] and DM-nucleus signals [38]. Given the current detector
technology, for E$\nu$ES (CE$\nu$NS) only the $pp$ and 7Be (8B) components of
the total solar neutrino flux contribute significantly to the detectable event
rates. However, since the CE$\nu$NS rate is suppressed at current detectors
due to threshold limitations, solar neutrinos at DM DD experiments are
currently detected mainly through E$\nu$ES.

In this work we are interested in determining the potential of current DM DD
experiments, namely XENONnT, LZ and PandaX-4T in probing new physics in the
neutrino sector through E$\nu$ES induced by solar neutrinos. Analyses along
this line have been done previously to investigate neutrino properties and BSM
interactions. These include, for instance, neutrino electromagnetic properties
such as effective [26, 28] and fundamental [39] neutrino magnetic moments.
Future data from e.g. a DARWIN-type experiment will allow for precision
searches of electroweak and oscillation parameters as detailed in Ref. [21],
while the possibility of probing flavor-dependent radiative corrections to
CE$\nu$NS has been explored in Ref. [40]. Neutrino nonstandard interactions
(NSI) have been addressed in Ref. [41] using existing data (XENONnT and LZ)
and providing forecasts for DARWIN, complementing the NSI landscape probed by
CE$\nu$NS experiments and oscillation searches.

Going one step beyond effective NSI, our goal is to explore new neutrino
interactions mediated by light vector bosons, that can arise in several
motivated $U(1)^{\prime}$ [42] extensions of the SM. We will focus on light
vector mediators, that are expected to generate spectral distortions, through
an increase of the E$\nu$ES differential cross section, for sufficiently small
mediator masses and low recoil energies. DM DD experiments, characterised by
low-energy thresholds, are suitable facilities to probe such spectral features
[43, 44, 15]. We will focus on several BSM models with an extended gauge
sector, namely an additional $U(1)^{\prime}$ symmetry. These will include: the
anomaly-free $B-L$ model [42, 45, 46], $B$ being the baryon number and $L$ the
total lepton number; lepton flavor-dependent interactions like the
$L_{e}-L_{\mu}$, $L_{\mu}-L_{\tau}$ and $L_{e}-L_{\tau}$ [47, 48, 49, 50]
$U(1)^{\prime}$ models, also free of quantum anomalies; the $B-2L_{e}-L_{\mu}$
and $B-2L_{e}-L_{\tau}$ models [51, 52], where leptons have generation-
dependent charges under the $U(1)^{\prime}$ symmetry; the $B-3L_{e}$ [53, 51,
54, 55, 52], $B-3L_{\mu}$ and $B-3L_{\tau}$ scenarios [56, 57, 58, 59, 60, 55,
51, 54] and $L_{e}+2L_{\mu}+2L_{\tau}$ [54].

There is a number of previous works involving light-mediator analyses of DM DD
data: Ref. [39] analyzed general light mediators exploiting recent data from
the LZ [9] and XENONnT [6] experiments, while Ref. [61] performed a similar
study employing recent data by the PandaX-II [62] experiment. Reference [63]
set constraints on general neutrino interactions using SENSEI, Edelweiss, and
SuperCDMS data and as well as projections for future experiments. These
studies complement bounds inferred using CE$\nu$NS data by COHERENT [64] and
E$\nu$ES data at Borexino [65], as well as forecasts for the DUNE near
detector [66]. Additional studies have focused on anomaly-free $U(1)^{\prime}$
models. For instance, Ref. [67] explored the implications of XENONnT and
Borexino E$\nu$ES data on the $B-L$ model, while Refs. [33, 35] focused on
projections for the $L_{\mu}-L_{\tau}$ model at DARWIN. More recently, Ref.
[68] explored general light mediators as well as $B-L$ and $L_{\mu}-L_{\tau}$
gauge symmetries via both CE$\nu$NS and E$\nu$ES at next generation DM DD
experiments. Solar neutrino constraints on light mediators have been set by
looking at CE$\nu$NS data from CDEX-10 in Ref. [69].

Our work adds to these previous studies by means of a detailed analysis of
several motivated $U(1)^{\prime}$ scenarios based on the most recent data from
the XENONnT [6], LZ [9], and PandaX-4T [11] experiments and by providing
sensitivities expected at a future DARWIN-like facility. Moreover, our present
analysis improves upon previous E$\nu$ES-based work on light mediators [39] as
described in the following. First, we use real, recent data from the current
most sensitive experiments. Besides providing separate bounds for each of
them, we also present for the first time a combined analysis. Secondly, we
carry out an improved statistical analysis by treating the background
components of LZ, XENONnT and PandaX-4T separately, together with their own
uncertainty, closely following Ref. [28]. Finally, we perform a comprehensive
exploration of various vector mediators that go beyond the simplest $B-L$
model, as already introduced. Our work is aimed at extending and complementing
the results obtained in Ref. [52], that addresses bounds on several types of
$U(1)^{\prime}$ models using recent COHERENT data.

The remainder of the work is organized as follows: in Section II we discuss
the effect of additional $U(1)^{\prime}$ symmetries on the E$\nu$ES process.
In Section III we detail the analysis procedure for current (III.1) and future
(III.2) DM DD experiments. In Section IV we present the results of our
analyses and compare with other bounds from the literature before closing in
Section V.

##  II Theoretical framework

We are interested in determining the potential of current DM DD experiments,
to probe new light vector bosons through E$\nu$ES induced by solar neutrinos
on atomic electrons in the detectors’ targets. In this section we introduce
the E$\nu$ES process, and provide its cross section both within the SM and in
the framework of BSM extensions with an additional $U(1)^{\prime}$ symmetry.

###  II.1 E$\nu$ES in the Standard Model

In the SM, the differential E$\nu$ES cross section, with respect to the
electron recoil energy $T_{e}$, is given by

$\displaystyle\begin{split}\frac{d\sigma_{\nu_{\alpha}\mathcal{A}}}{dT_{e}}\Big{|}^{\mathrm{SM}}=&Z^{\mathcal{A}}_{\mathrm{eff}}(T_{e})\frac{G_{F}^{2}m_{e}}{2\pi}\left[(g_{V}+g_{A})^{2}+(g_{V}-g_{A})^{2}\left(1-\frac{E_{\mathrm{er}}}{E_{\nu}}\right)^{2}-(g_{V}^{2}-g_{A}^{2})\frac{m_{e}T_{e}}{E_{\nu}^{2}}\right]\,,\end{split}$
(1)

where $G_{F}$, $E_{\nu}$ and $m_{e}$ denote the Fermi constant, the incoming
neutrino energy and the electron mass, respectively. The SM vector and axial-
vector couplings depend on the flavor $\alpha$ of the incoming neutrino
$\nu_{\alpha}$ and read $g_{V}=2\sin^{2}\theta_{W}-1/2+\delta_{{\alpha}e}$,
$g_{A}=-1/2+\delta_{{\alpha}e}$, $\sin^{2}\theta_{W}=0.23857$ being the weak
mixing angle in the low-energy regime. The term $\delta_{{\alpha}e}$ is due to
the fact that in the case of incoming electron neutrinos both neutral and
charged currents are relevant, while for the case of $\nu_{\mu}$ and
$\nu_{\tau}$ E$\nu$ES acquires contributions from neutral currents only.
Assuming that the target electrons are bound in the atomic nuclei
$\mathcal{A}$ of the detector material, the factor
$Z^{\mathcal{A}}_{\text{eff}}(T_{e})$ in Eq. (1) accounts for the effective
number of electrons that can be ionized given an energy dissipation $T_{e}$,
and it is taken from the Hartree-Fock calculations provided in Ref. [70].

###  II.2 E$\nu$ES in models with an extra $U(1)^{\prime}$ symmetry

Within the context of a general $U(1)^{\prime}$ symmetry, with a new vector
mediator $Z^{\prime}$ with mass $m_{Z^{\prime}}$, the Lagrangian describing
neutrino-fermion interactions reads

$\mathcal{L}_{Z^{\prime}}=g_{Z^{\prime}}Ζ^{\prime}_{\mu}\left({Q^{f}_{Z^{\prime}}}\bar{f}\gamma^{\mu}f+\sum_{\alpha}{Q_{Z^{\prime}}^{\nu_{\alpha}}}\bar{\nu}_{\alpha,L}\gamma^{\mu}\nu_{\alpha,L}\right)+\frac{1}{2}{m_{Z^{\prime}}^{2}}{Z^{\prime\mu}Z^{\prime}_{\mu}}\,,$
(2)

where for the case of E$\nu$ES $f=e$, ${g_{Z^{\prime}}}$ is the new coupling
while ${Q^{i}_{Z^{\prime}}}$ denote the individual vector charges (see Tab.
1). Then, for incoming neutrinos of flavor $\alpha$, the new contribution to
E$\nu$ES can be obtained from the SM expression of the cross section given in
Eq. (1) by changing

$g_{V}\to
g_{V}^{\mathrm{SM}}+\frac{({g_{Z^{\prime}}})^{2}Q^{e}_{Z^{\prime}}Q^{\nu_{\alpha}}_{Z^{\prime}}}{\sqrt{2}G_{F}(2m_{e}T_{e}+m_{Z^{\prime}}^{2})}\,.$
(3)

In this paper we consider the following models: $B-L$, $B-3L_{\alpha}$,
$B-2L_{e}-L_{\mu,\tau}$, $L_{\alpha}-L_{\beta}$ and $L_{e}+2L_{\mu}+2L_{\tau}$
with the corresponding charges summarized in Tab. 1. For completeness, let us
stress that unlike the $B-L$ case where all neutrino fluxes contribute equally
to new physics cross sections, in lepton flavor-dependent models the new
physics contributions come only from the corresponding flavor component of the
total solar neutrino flux, weighted through the charges given in Tab. 1.

On the other hand, in the case of the leptophilic model $L_{\mu}-L_{\tau}$,
since there is no direct coupling to electrons, the new contribution arises at
the one-loop level [52]111For the sake of completeness let us stress that for
the case of CE$\nu$NS there is a plus sign before the second term in Eq. (4)
because of the different electric charge of protons versus electrons (see Ref.
[68]).:

$g_{V}\to
g_{V}^{\mathrm{SM}}-\frac{\sqrt{2}\alpha_{\mathrm{em}}g_{Z^{\prime}}^{2}(\delta_{\alpha\mu}-\delta_{\alpha\tau})}{\pi
G_{F}(2m_{e}T_{e}+m_{V}^{2})}\epsilon_{\tau\mu}(|\vec{q}|)\,,$ (4)

where $\alpha_{\mathrm{em}}$ is the fine-structure constant while the
couplings $\epsilon_{\tau\mu}$ can be approximated as

$\epsilon_{\tau\mu}(|\vec{q}|)=\int_{0}^{1}x(1-x)\ln\left(\frac{m_{\tau}^{2}+x(1-x)|\vec{q}|^{2}}{m_{\mu}^{2}+x(1-x)|\vec{q}|^{2}}\right)\,dx\approx\frac{1}{6}\ln\left(\frac{m_{\tau}^{2}}{m_{\mu}^{2}}\right)\,.$
(5)

Similarly, in the framework of the $B-3L_{\mu,\tau}$ models the corresponding
E$\nu$ES contribution also arises at the one-loop level and reads

$g_{V}\to
g_{V}^{\mathrm{SM}}-\frac{\sqrt{2}\alpha_{\mathrm{em}}g_{Z^{\prime}}^{2}Q^{\alpha}_{Z^{\prime}}\delta_{\alpha(\mu/\tau)}}{\pi
G_{F}(2m_{e}T_{e}+m_{V}^{2})}\tilde{\epsilon}(|\vec{q}|)\,,$ (6)

where this time $\tilde{\epsilon}$ is given by

$\tilde{\epsilon}(|\vec{q}|)\approx\frac{1}{6}\sum_{f}Q^{f}_{Z^{\prime}}e_{f}\ln\left(\frac{m_{f}^{2}}{\Lambda^{2}}\right)\,,$
(7)

where $f$ runs over $\mu/\tau$ and all quarks. The couplings
$Q^{f}_{Z^{\prime}}$ are given in Tab. 1 and $e_{f}$ denotes the electric
charge of fermion $f$. Finally, $\Lambda$ is the renormalization scale. While
an accurate determination would require the full RGE running that is out of
the scope of this work, for the sake of simplicity we fix $\Lambda=m_{\mu}$
($m_{\tau}$) in the case of $B-3L_{\mu}$ ($B-3L_{\tau}$). We have checked that
by choosing a different scale, e.g. $\Lambda=10^{6}$ GeV, $|\tilde{\epsilon}|$
would change by a factor of around 4 thus resulting in a bound a factor of 2
stronger.

Model |  $Q_{Z^{\prime}}^{u}~{}~{}$ |  $Q_{Z^{\prime}}^{d}~{}~{}$ |  $Q_{Z^{\prime}}^{e/\nu_{e}}$ |  $Q_{Z^{\prime}}^{\mu/\nu_{\mu}}$ |  $Q_{Z^{\prime}}^{\tau/\nu_{\tau}}$
---|---|---|---|---|---
$B-L$ | 1/3 | 1/3 | -1 | -1 | -1
$B-3L_{e}$ | 1/3 | 1/3 | -3 | 0 | 0
$B-3L_{\mu}$ | 1/3 | 1/3 | 0 | -3 | 0
$B-3L_{\tau}$ | 1/3 | 1/3 | 0 | 0 | -3
$B-2L_{e}-L_{\mu}$ | 1/3 | 1/3 | -2 | -1 | 0
$B-2L_{e}-L_{\tau}$ | 1/3 | 1/3 | -2 | 0 | -1
$L_{e}-L_{\mu}$ | 0 | 0 | 1 | -1 | 0
$L_{e}-L_{\tau}$ | 0 | 0 | 1 | 0 | -1
$L_{\mu}-L_{\tau}$ | 0 | 0 | 0 | 1 | -1
$L_{e}+2L_{\mu}+2L_{\tau}$ | 0 | 0 | 1 | 2 | 2
Table 1:  Individual charges in the $U(1)^{\prime}$ models considered in this
work.

##  III Data analysis

In this section, we present the analysis details for the experiments under
consideration. Specifically, we discuss the analysis of current experiments
(XENONnT, LZ and PandaX-4T) in subsection III.1 and the sensitivity for a
next-generation detector, that we model following the DARWIN proposal [21], in
subsection III.2. The analysis procedure follows very closely the one
described in Ref. [28].

###  III.1 Current experiments

Regarding current experiments we analyze data from LZ [9], XENONnT [6] and
PandaX-4T [11]. The current energy threshold for E$\nu$ES in these experiments
is set at $E_{\mathrm{thr}}=1$ keV, although due to the detector efficiency
the actual flux becomes sizable at $\sim 3$ keV. For each experiment the
number of events due to elastic scattering of solar neutrinos is obtained
through the following expression

$R^{\mathrm{E\nu
ES}}_{k}=\mathcal{N}~{}\int_{T_{e}^{k}}^{T_{e}^{k+1}}dT_{e}~{}A(T_{e})~{}\int_{0}^{T_{e}^{{}^{\prime}\mathrm{max}}}dT_{e}^{\prime}~{}R(T_{e},T_{e}^{\prime})~{}\sum_{i=pp,^{7}\text{Be}}\int_{E_{\nu}^{\text{min}}}^{E_{\nu,i}^{\text{max}}}dE_{\nu}~{}\sum_{\alpha}~{}\Phi_{\nu_{\alpha}}^{i}(E_{\nu})~{}\frac{d\sigma_{\nu_{\alpha}\mathcal{A}}}{dT_{e}^{\prime}}\,.$
(8)

Here, $T_{e}$ and $T_{e}^{\prime}$ are the reconstructed and true electron
recoil energies, respectively. The minimal neutrino energy necessary to
produce an electron recoil of $T_{e}^{\prime}$ is given by
$E_{\nu}^{\text{min}}=(T_{e}^{\prime}+\sqrt{2m_{e}T_{e}^{\prime}+T_{e}^{\prime
2}})/2$, while the maximal neutrino energy $E_{\nu,i}^{\text{max}}$ is the
energy endpoint of the production process inside the Sun, indicated with the
index $i$ ($i=pp,^{7}$Be). The recoil energy upper limit is given by
kinematics: $T_{e}^{{}^{\prime}\mathrm{max}}=2E_{\nu}^{2}/(2E_{\nu}+m_{e})$.
The E$\nu$ES cross section for a given neutrino flavor $\nu_{\alpha}$ is given
by $d\sigma_{\nu_{\alpha}\mathcal{A}}/dT_{e}^{\prime}$ and has been discussed
in Section II. The fluxes $\Phi_{\nu_{\alpha}}^{i}(E_{\nu})$ are given by

$\Phi_{\nu_{e}}^{i}=\Phi_{\nu_{e}}^{i\,\odot}P_{ee},\quad\Phi_{\nu_{\mu}}^{i}=\Phi_{\nu_{e}}^{i\,\odot}\left(1-P_{ee}\right)\cos^{2}\vartheta_{23},\quad\Phi_{\nu_{\tau}}^{i}=\Phi_{\nu_{e}}^{i\,\odot}\left(1-P_{ee}\right)\sin^{2}\vartheta_{23},$
(9)

where $\Phi_{\nu_{e}}^{i\,\odot}$ are the fluxes of $\nu_{e}$ produced by
thermonuclear reactions in the interior of the Sun, with
$i=pp,\,^{7}\text{Be}$, etc. indicating the production reaction. For those, we
employ the spectra from Refs. [71, 72, 73, 74] with the normalizations for the
high metallicity model taken from Ref. [75]. As anticipated, the main
contributions relevant for the signal at the experiments under consideration
originate from $pp$ and 7Be neutrinos. Moreover, $P_{ee}$ is the
$\nu_{e}$-survival probability at the detector on Earth, accounting for
neutrino oscillations. As can be seen, the fluxes of $\nu_{\mu}$ and
$\nu_{\tau}$ depend on the mixing angle $\vartheta_{23}$, which is close to
maximal mixing ($\vartheta_{23}\sim\pi/4$) [76, 77, 78]. For simplicity, we
consider $\sin^{2}\vartheta_{23}=0.5$, which implies
$\Phi_{\nu_{\mu}}^{i}=\Phi_{\nu_{\tau}}^{i}$.

Next, $R(T_{e},T_{e}^{\prime})$ and $A(T_{e})$ are the detector resolution and
efficiency functions which are different for all experiments. We use the
detector efficiencies given in Refs. [79, 6, 11]. For the energy resolution at
LZ we use the same function that has been used in Refs. [26, 39]. In the case
of XENONnT we use the resolution function of Ref. [80] and for PandaX-4T we
use the one from Ref. [11]. Finally, $\mathcal{N}=\mathcal{E}N_{T}$ is a
normalization constant which takes into account the exposure
$\mathcal{E}=\\{1.16,0.90,0.63\\}~{}\mathrm{ton\times year}$ for XENONnT, LZ
and PandaX-4T, respectively, while $N_{T}=N_{A}/M(\mathrm{Xe})$ denotes the
number of target nuclei per $\mathrm{ton}$ of detector material, $N_{A}$ and
$M(\mathrm{Xe})$ being the Avogadro number and the molar mass of xenon.

The overall predicted number of events in a given energy-bin $k$ for an
experiment $X$ is given by

$R^{X}_{k}=R^{\mathrm{E\nu ES}}_{k}+\sum_{i}R^{i}_{k}\,,$ (10)

where $R^{\mathrm{E\nu ES}}_{k}$ is the E$\nu$ES contribution, Eq. (8), while
$R^{i}_{k}$ are the remaining background components of each experiment,
extracted from Refs. [81, 6, 11] for LZ, XENONnT and PandaX-4T, respectively.
The total number of predicted events has to be compared with the data $D^{X}$
collected in each experiment. In our analyses we use the data from Fig. 6 of
Ref. [9] for LZ and the data from Fig. 3 of Ref. [11] for PandaX-4T. In the
case of XENONnT we use the data from Fig. 4 (5) of Ref. [6], for recoil
energies above (below) 30 keV.

Due to the low statistics in some bins, for LZ and PandaX-4T we use the
Poissonian least-squares function

$\chi^{2}_{X}=\min_{\vec{\alpha},\vec{\beta}}\left\\{2\left(\sum_{k}R^{X}_{k}-D^{X}_{k}+D^{X}_{k}~{}\ln\left(D^{X}_{k}/R^{X}_{k}\right)\right)+\sum_{i}(\alpha_{i}/\sigma_{\alpha_{i}})^{2}+\sum_{i}(\beta_{i}/\sigma_{\beta_{i}})^{2}\right\\}\,,$
(11)

where $\alpha_{i}$ are normalization constants multiplied to each single
background component in Eq. (10), penalized by the uncertainties
$\sigma_{\alpha_{i}}$. These uncertainties are taken from Tab. VI of Ref. [81]
for LZ and Tab. I of Ref. [11] for PandaX-4T. As indicated in the references,
some of these nuisance parameters are left to vary freely in the analysis.
Also included are the uncertainty coefficients $\beta_{i}$ of the solar
neutrino fluxes, with uncertainties $\sigma_{\beta_{i}}$ taken from Ref. [75].

In the case of XENONnT data, we use instead

$\chi^{2}_{\text{XENONnT}}=\min_{\vec{\alpha},\vec{\beta}}\left\\{\sum_{k}\left(\frac{R^{\text{XENONnT}}_{k}-D^{\text{XENONnT}}_{k}}{\sigma_{k}}\right)^{2}+\sum_{i}(\alpha_{i}/\sigma_{\alpha_{i}})^{2}+\sum_{i}(\beta_{i}/\sigma_{\beta_{i}})^{2}\right\\}\,,$
(12)

where the uncertainties in each bin $\sigma_{k}$ are extracted from Ref. [6].
The remaining components are equivalent to the corresponding ones for LZ and
PandaX-4T.

We also perform a combined analysis of all three experiments by correlating
the uncertainties regarding the neutrino flux among the experiments. In
addition, background components which are common to at least two of the three
experiments are also correlated.

###  III.2 DARWIN sensitivity

The calculation of the event rate at a future experiment like DARWIN is
essentially the same as for the current experiments, given in Eqs. (8) and
(10). The only difference is that we also include the contributions from solar
N, O and $pep$ neutrinos. It should be noted, however, that their contribution
is mostly negligible in comparison with some of the background contributions,
as shown in Fig. 1 of Ref. [21]. We include them, nevertheless, since we use
the full spectrum as shown in Ref. [21].

The individual background components relevant for DARWIN are given in Ref.
[21], and need to be normalized to the considered exposure. We use the same
resolution function and detector efficiency as for XENONnT assuming that the
efficiency remains constant for $T_{e}>T_{e,\text{max}}^{\text{XENONnT}}$.
With these assumptions, we are able to reproduce the E$\nu$ES spectra for all
five neutrino species in Fig. 1 of Ref. [21], which justifies the choices of
efficiency and resolution functions. We compute the sensitivity considering an
exposure of $30~{}\mathrm{ton\times years}$ and $300~{}\mathrm{ton\times
years}$.

When generating the mock data, always compatible with the SM expectation, we
use 51 logarithmically-spaced bins between 1 and 1500 keV recoil energy. Note
that the spectrum at higher energies ($\gtrsim 700$ keV) is not sensitive to
any BSM effect considered in this paper, because the E$\nu$ES rate is much
smaller than some of the background rates. Indeed, the main E$\nu$ES rate
contributions from $pp$ and 7Be neutrinos become irrelevant at $T_{e}\sim 250$
keV and $\sim 700$ keV, respectively. We still use the full spectrum up to
1500 keV, since the inclusion of events at high energies can help to control
the effect of background uncertainties.

##  IV Results

In this section we present the bounds obtained for all models discussed in
Section II. In all cases we compare our bounds with previous ones obtained in
the literature, in particular with the ones included in the DarkCast package
[82], the ones obtained from COHERENT data [52, 66] and from neutrino
oscillation experiments [54]. DarkCast implements constraints from several
classes of experiments222Note that even though not all DarkCast bounds are at
the same confidence level, small differences in confidence level are basically
invisible on the scales of our plots.: beam dump (E141 [83], E137 [84], E774
[85], KEK [86], Orsay [87, 88, 89], $\nu$-CAL I [90, 91, 92, 93], CHARM [94,
95], NOMAD [96], and PS191 [97, 98]), fixed target (A1 [99] and APEX [100]),
colliders (BaBar [101], KLOE [102, 103], LHCb [104]), rare-meson decay (NA48/2
[105]) experiments, neutrino scattering experiments (TEXONO, CHARM-II and
BOREXINO [106, 107, 108, 109, 110]), and searches for dark photons in NA64
[111, 112] and BaBar [113].

### The $B-L$ model

Figure 1: $90\%$ C.L. bounds from our analyses of: LZ (magenta solid),
PandaX-4T (magenta dotted) and XENONnT data (magenta dashed-dotted), a
combined analysis of current data (magenta dashed) and expected sensitivity at
DARWIN with an exposure of 30 (blue dashed) or 300 $\mathrm{ton\times years}$
(blue solid) for the $B-L$ model, in comparison with other existing bounds.

The $90\%$ C.L. exclusion limits in the $m_{Z^{\prime}}-g_{Z^{\prime}}$ plane
for the $B-L$ model are shown in Fig. 1. Our present results for XENONnT and
LZ are in excellent agreement with a previous analysis performed in Ref. [39],
though here the analysis is improved following the method of Ref. [28], as
explained previously. The thin magenta lines correspond to the analyses of
PandaX-4T (dotted), LZ (solid) and XENONnT (dashed-dotted) data, while the
thick magenta dashed line is the result from our combined analysis333In order
to not overcrowd the figures we will show only the combined result in
subsequent figures.. At large (small) masses the dominating contribution to
the bound comes from LZ (XENONnT) data. Note that since we correlated common
uncertainties among the experiments, the combined bound is stronger than a
simple sum of $\chi^{2}$ functions. For low mediator masses ($\lesssim 0.1$
MeV), our combined limit saturates at $g_{Z^{\prime}}\sim 1.5\times 10^{-7}$.

As can be seen in Fig. 1, current DM DD experiments produce slightly weaker
(stronger) bounds for large (small) masses than other experiments measuring
E$\nu$ES [106, 107, 108, 109, 110], like TEXONO, CHARM-II and BOREXINO (“$\nu$
scattering”, depicted as coral-shaded areas). On the other hand, DM DD bounds
do improve upon CE$\nu$NS constraints444Note that the depicted constraints
actually include CE$\nu$NS+E$\nu$ES events in the analysis of COHERENT-CsI
data (see Refs. [64, 66] for details). from the COHERENT experiment [66]
(green area), by about two orders of magnitude at $m_{Z^{\prime}}\lesssim
0.01$ MeV. It should be noted that current bounds from DM experiments are
never dominating in comparison to other probes for large mediator masses,
i.e., $m_{Z^{\prime}}\gtrsim 10$ MeV. However, DARWIN will provide the
dominating bounds in the region $0.02$ GeV $\lesssim m_{Z^{\prime}}\lesssim
0.4$ GeV, between the blue- and coral-shaded regions corresponding to beam-
dump and accelerator experiments and scattering experiments, respectively. The
purple dotted lines indicate the region of parameter space that could explain
the $(g-2)_{\mu}$ anomaly [114] and that is therefore now excluded by several
experiments. Let us finally note that below the $\sim$ MeV scale strong bounds
from big bang nucleosynthesis [115] (orange dashed-dotted lines) and stellar
cooling [116] effects (yellow area) apply, although their exact estimation
will eventually depend on the specific model and thermal history in the early
Universe. Finally, bounds from SN1987A [117, 118] (light gray) constrain the
region in the plot for small couplings.

### The $B-2L_{e}-L_{\mu/\tau}$ models

Figure 2: $90\%$ C.L. bounds from our combined analysis of LZ, PandaX-4T and
XENONnT data and the sensitivity at DARWIN for the $B-2L_{e}-L_{\mu}$ (upper
panel) and $B-2L_{e}-L_{\tau}$ (lower panel) models. Also shown are bounds
from other experiments for comparison.

The upper (lower) panel of Fig. 2 shows the results for the $B-2L_{e}-L_{\mu}$
($B-2L_{e}-L_{\tau}$) models [51, 52]. Due to our choice of
$\sin^{2}\theta_{23}=0.5$ the bounds from DM DD experiments are the same for
both models. However, the bounds from other experiments can change. Note that
although not analyzed in Ref. [52], COHERENT data could also be used to place
bounds on the $B-2L_{e}-L_{\tau}$ scenario, however the resulting limit would
be slightly weaker than those for $B-2L_{e}-L_{\mu}$ and definitely weaker
than our combined constraint from LZ+PandaX-4T+XENONnT. As in the previous
case of the $B-L$ model, solar E$\nu$ES data at DM DD experiments will be able
to provide the dominating bound in the $0.02$ GeV $\lesssim
m_{Z^{\prime}}\lesssim 0.2$ GeV mass region even after a relatively short
exposure time at DARWIN, while the current limit (magenta dashed) is slightly
weaker than other probes, but nonetheless comparable to other limits from
neutrino scattering at $m_{Z^{\prime}}\gtrsim 1$ MeV. All in all, at small
masses $m_{Z^{\prime}}\lesssim 1$ MeV the bounds from DM DD experiments are
significantly stronger than those from other laboratory probes, while being
surpassed by astrophysical and cosmological observations.

Figure 3: The bounds from our combined analysis of LZ, PandaX-4T and XENONnT
data and the sensitivity at DARWIN at 90% C.L. for $B-3L_{e}$ (first row),
$B-3L_{\mu}$ (second row) and $B-3L_{\tau}$ (third row). Also shown are bounds
from other experiments for comparison.

### The $B-3L_{\alpha}$ models

We next discuss the results obtained for the $B-3L_{\alpha}$ models. Results
are presented in Fig. 3. In the case of $B-3L_{e}$ we find a behavior that
resembles previous models. At large mediator masses current DM DD experiments
are slightly weaker than other probes, while DARWIN has the prospect to
provide the leading bound in the future. At small masses our bounds are the
strongest limits obtained using neutrino fluxes in some parts of the parameter
space. However, the bound from oscillation experiments [54] (light lavender)
starts to dominate for mediator masses below $\sim\mathcal{O}(10)$ keV.

In the second and third row of Fig. 3 we show the results for the $B-3L_{\mu}$
and $B-3L_{\tau}$ models, respectively. We focus on a reduced range of
mediator masses, since for smaller masses a more thorough treatment of the
loop-effects in Eq. (7) might become necessary. As can be seen, our bounds
from current DM DD experiments as well as the projected sensitivity for DARWIN
seem not to be competitive with oscillation experiments. The reason is that
these models affect the E$\nu$ES process only at the loop-level and hence the
overall effect on the cross section is very tiny in comparison with the
$B-3L_{e}$ model, for which the interaction occurs instead at tree level.

### The $L_{\alpha}-L_{\beta}$ models

In the last two subsections we discuss models that only couple to leptons. We
start with the $L_{\alpha}-L_{\beta}$ models. Our results are presented in
Fig. 4. As in previous cases, we find that DARWIN will be able to provide the
dominant bound in some regions of the parameter space, even with relatively
small exposure, for $L_{e}-L_{\mu/\tau}$. For the same symmetry arguments
already mentioned above, our bounds and sensitivities are the same for both
models. Even though DARWIN will provide the strongest bound at large mediator
masses, at small masses the bounds from oscillation experiments remain very
strong as can be seen in Fig. 4.

In the case of the $L_{\mu}-L_{\tau}$ model, current bounds from DM DD
experiments are of similar strength as those from other E$\nu$ES probes
(“$\nu$ scattering”) and are expected to become much stronger once DARWIN
starts taking data. The current combined limit already rules out
$L_{\mu}-L_{\tau}$ as en explanation to the $(g-2)_{\mu}$ anomaly, at
$m_{Z^{\prime}}\lesssim 100$ MeV. We do not show oscillation bounds for this
model, because this scenario was not considered in Ref. [54]. The COHERENT
result, available for the case of $L_{\mu}-L_{\tau}$ only, is taken from Ref.
[66]555For $g_{Z^{\prime}}<10^{-3}$ the COHERENT bound is entirely driven by
E$\nu$ES events.. Let us also mention that bounds for very small mediator
masses have been calculated in Ref. [119]. However, for the mass range of
interest in this work, those bounds are many orders of magnitude weaker than
the ones derived in this work. Finally, a large region of parameter space with
small coupling is excluded due to supernovae data [118, 120].

Figure 4: The bounds from our combined analysis of LZ, PandaX-4T and XENONnT
data and the sensitivity at DARWIN at 90% C.L. for $L_{e}-L_{\mu}$ (first
row), $L_{e}-L_{\tau}$ (second row) and $L_{\mu}-L_{\tau}$ (third row). Also
shown are bounds from other experiments for comparison.

### The $L_{e}+2L_{\mu}+2L_{\tau}$ model

Figure 5: The bounds from our combined analysis of LZ, PandaX-4T and XENONnT
data and the sensitivity at DARWIN at 90% C.L. for $L_{e}+2L_{\mu}+2L_{\tau}$.
Also shown are bounds from other experiments for comparison.

The last model that we consider is $L_{e}+2L_{\mu}+2L_{\tau}$. The results are
shown in Fig. 5. As in the case of previous models we find that DM DD
experiments currently provide limits comparable to other $\nu-e^{-}$
scattering experiments but will improve in some parts of the parameter space
with future facilities like DARWIN. For low mediator masses, however, DM DD
bounds are already much stronger than the ones obtained from other experiments
using E$\nu$ES and will be further improved by DARWIN. As in previous
scenarios, these bounds probe parts of the parameter space in complementarity
to those probed by astrophysical observations or by other terrestrial
experiments like beam dump and colliders.

##  V Conclusions

The large exposures achieved at recent dark matter direct detection
experiments, combined with the very low threshold operation capabilities of
recent LXe and future LAr detectors, mark a turning point in solar neutrino
detection. Motivated by this unique opportunity, we have performed a thorough
analysis of compelling $U(1)^{\prime}$ models, by analyzing current (XENONnT,
LZ and PandaX-4T) and future (DARWIN) DM DD experiments via the E$\nu$ES
channel. In particular, we have focused on spectral distortions expected in
the E$\nu$ES rates that arise in the presence of novel interactions within the
anomaly-free $B-L$, $L_{\alpha}-L_{\beta}$, $B-2L_{e}-L_{\mu,\tau}$,
$B-3L_{\alpha}$, and $L_{e}+2L_{\mu}+2L_{\tau}$ models. By means of an
improved statistical analysis, in which the various experimental uncertainties
are treated separately, we have obtained stringent constraints on the relevant
parameter space of the new vector mediator, $(m_{Z^{\prime}},g_{Z^{\prime}})$.
We have presented a combined analysis of ongoing experiments: XENONnT, LZ and
PandaX-4T showing that it leads to slightly improved sensitivities compared to
those obtained by analyzing each experiment individually. Specifically, we
have shown that for $m_{Z^{\prime}}\gtrsim 100~{}\mathrm{MeV}$ current DM DD
experiments place competitive constraints, complementing other experimental
probes including neutrino oscillation data, beam dump and collider searches.
On the other hand, in the low mass regime i.e. for $m_{Z^{\prime}}\lesssim
1~{}\mathrm{MeV}$ we have illustrated that the E$\nu$ES channel dominates the
constraints among terrestrial experiments. We have further shown that
sensitivities achievable at future DM DD experiments like DARWIN —in view of
their large size— will offer further improvements. We have finally discussed
complementarities of our present results with constraints coming from
astrophysical observations, especially those obtained from BBN and stellar
cooling data.

## Acknowledgments

We thank Martin K. Hirsch for enlightening discussions. V.D.R. acknowledges
financial support by the CIDEXG/2022/20 grant (project “D’AMAGAT”) funded by
Generalitat Valenciana and by the Spanish grant PID2020-113775GB-I00
(MCIN/AEI/10.13039/501100011033). The work of DKP was supported by the
Hellenic Foundation for Research and Innovation (H.F.R.I.) under the “3rd Call
for H.F.R.I. Research Projects to support Post-Doctoral Researchers” (Project
Number: 7036).

## References

  * [1] M. Schumann, “Direct Detection of WIMP Dark Matter: Concepts and Status,” J. Phys. G 46 no. 10, (2019) 103003, arXiv:1903.03026 [astro-ph.CO].
  * [2] D. Baxter et al., “Recommended conventions for reporting results from direct dark matter searches,” Eur. Phys. J. C 81 no. 10, (2021) 907, arXiv:2105.00599 [hep-ex].
  * [3] J. Billard et al., “Direct detection of dark matter—APPEC committee report*,” Rept. Prog. Phys. 85 no. 5, (2022) 056201, arXiv:2104.07634 [hep-ex].
  * [4] XENON Collaboration, E. Aprile et al., “The XENON1T Dark Matter Experiment,” Eur. Phys. J. C 77 no. 12, (2017) 881, arXiv:1708.07051 [astro-ph.IM].
  * [5] XENON Collaboration, E. Aprile et al., “Dark Matter Search Results from a One Ton-Year Exposure of XENON1T,” Phys. Rev. Lett. 121 no. 11, (2018) 111302, arXiv:1805.12562 [astro-ph.CO].
  * [6] XENON Collaboration, E. Aprile et al., “Search for New Physics in Electronic Recoil Data from XENONnT,” Phys. Rev. Lett. 129 no. 16, (2022) 161805, arXiv:2207.11330 [hep-ex].
  * [7] LZ Collaboration, D. S. Akerib et al., “LUX-ZEPLIN (LZ) Conceptual Design Report,” arXiv:1509.02910 [physics.ins-det].
  * [8] LZ Collaboration, D. S. Akerib et al., “The LUX-ZEPLIN (LZ) Experiment,” Nucl. Instrum. Meth. A 953 (2020) 163047, arXiv:1910.09124 [physics.ins-det].
  * [9] LZ Collaboration, J. Aalbers et al., “First Dark Matter Search Results from the LUX-ZEPLIN (LZ) Experiment,” Phys. Rev. Lett. 131 no. 4, (2023) 041002, arXiv:2207.03764 [hep-ex].
  * [10] PandaX Collaboration, X. Cao et al., “PandaX: A Liquid Xenon Dark Matter Experiment at CJPL,” Sci. China Phys. Mech. Astron. 57 (2014) 1476–1494, arXiv:1405.2882 [physics.ins-det].
  * [11] PandaX Collaboration, D. Zhang et al., “Search for Light Fermionic Dark Matter Absorption on Electrons in PandaX-4T,” Phys. Rev. Lett. 129 no. 16, (2022) 161804, arXiv:2206.02339 [hep-ex].
  * [12] PandaX Collaboration, A. Abdukerim et al., “PandaX-xT: a Multi-ten-tonne Liquid Xenon Observatory at the China Jinping Underground Laboratory,” arXiv:2402.03596 [hep-ex].
  * [13] T. Bringmann and M. Pospelov, “Novel direct detection constraints on light dark matter,” Phys. Rev. Lett. 122 no. 17, (2019) 171801, arXiv:1810.10543 [hep-ph].
  * [14] V. De Romeri, A. Majumdar, D. K. Papoulias, and R. Srivastava, “XENONnT and LUX-ZEPLIN constraints on DSNB-boosted dark matter,” arXiv:2309.04117 [hep-ph].
  * [15] I. M. Bloch, A. Caputo, R. Essig, D. Redigolo, M. Sholapurkar, and T. Volansky, “Exploring new physics with O(keV) electron recoils in direct detection experiments,” JHEP 01 (2021) 178, arXiv:2006.14521 [hep-ph].
  * [16] R. Z. Ferreira, M. C. D. Marsh, and E. Müller, “Do Direct Detection Experiments Constrain Axionlike Particles Coupled to Electrons?,” Phys. Rev. Lett. 128 no. 22, (2022) 221302, arXiv:2202.08858 [hep-ph].
  * [17] H. An, M. Pospelov, J. Pradler, and A. Ritz, “Direct Detection Constraints on Dark Photon Dark Matter,” Phys. Lett. B 747 (2015) 331–338, arXiv:1412.8378 [hep-ph].
  * [18] (XENON Collaboration)§, XENON Collaboration, E. Aprile et al., “Search for events in XENON1T associated with gravitational waves,” Phys. Rev. D 108 no. 7, (2023) 072015, arXiv:2306.11871 [hep-ex].
  * [19] R. Essig et al., “Snowmass2021 Cosmic Frontier: The landscape of low-threshold dark matter direct detection in the next decade,” in Snowmass 2021.  3, 2022.  arXiv:2203.08297 [hep-ph].
  * [20] D. S. Akerib et al., “Snowmass2021 Cosmic Frontier Dark Matter Direct Detection to the Neutrino Fog,” in Snowmass 2021.  3, 2022.  arXiv:2203.08084 [hep-ex].
  * [21] DARWIN Collaboration, J. Aalbers et al., “Solar neutrino detection sensitivity in DARWIN via electron scattering,” Eur. Phys. J. C 80 no. 12, (2020) 1133, arXiv:2006.03114 [physics.ins-det].
  * [22] J. Aalbers et al., “A next-generation liquid xenon observatory for dark matter and neutrino physics,” J. Phys. G 50 no. 1, (2023) 013001, arXiv:2203.02309 [physics.ins-det].
  * [23] DarkSide-20k Collaboration, V. Pesudo, “Measurement of the underground argon radiopurity for Dark Matter direct searches,” J. Phys. Conf. Ser. 2156 no. 1, (2021) 012043.
  * [24] J. Billard, L. Strigari, and E. Figueroa-Feliciano, “Implication of neutrino backgrounds on the reach of next generation dark matter direct detection experiments,” Phys. Rev. D 89 no. 2, (2014) 023524, arXiv:1307.5458 [hep-ph].
  * [25] C. A. J. O’Hare, “New Definition of the Neutrino Floor for Direct Dark Matter Searches,” Phys. Rev. Lett. 127 no. 25, (2021) 251802, arXiv:2109.03116 [hep-ph].
  * [26] M. Atzori Corona, W. M. Bonivento, M. Cadeddu, N. Cargioli, and F. Dordei, “New constraint on neutrino magnetic moment and neutrino millicharge from LUX-ZEPLIN dark matter search results,” Phys. Rev. D 107 no. 5, (2023) 053001, arXiv:2207.05036 [hep-ph].
  * [27] A. de Gouvêa, E. McGinness, I. Martinez-Soler, and Y. F. Perez-Gonzalez, “pp solar neutrinos at DARWIN,” Phys. Rev. D 106 no. 9, (2022) 096017, arXiv:2111.02421 [hep-ph].
  * [28] C. Giunti and C. A. Ternes, “Testing neutrino electromagnetic properties at current and future dark matter experiments,” arXiv:2309.17380 [hep-ph].
  * [29] D. G. Cerdeño, M. Fairbairn, T. Jubb, P. A. N. Machado, A. C. Vincent, and C. Bœhm, “Physics from solar neutrinos in dark matter direct detection experiments,” JHEP 05 (2016) 118, arXiv:1604.01025 [hep-ph]. [Erratum: JHEP 09, 048 (2016)].
  * [30] B. Dutta, S. Liao, L. E. Strigari, and J. W. Walker, “Non-standard interactions of solar neutrinos in dark matter experiments,” Phys. Lett. B 773 (2017) 242–246, arXiv:1705.00661 [hep-ph].
  * [31] G. B. Gelmini, V. Takhistov, and S. J. Witte, “Geoneutrinos in Large Direct Detection Experiments,” Phys. Rev. D 99 no. 9, (2019) 093009, arXiv:1812.05550 [hep-ph].
  * [32] R. Essig, M. Sholapurkar, and T.-T. Yu, “Solar Neutrinos as a Signal and Background in Direct-Detection Experiments Searching for Sub-GeV Dark Matter With Electron Recoils,” Phys. Rev. D 97 no. 9, (2018) 095029, arXiv:1801.10159 [hep-ph].
  * [33] D. W. P. d. Amaral, D. G. Cerdeno, P. Foldenauer, and E. Reid, “Solar neutrino probes of the muon anomalous magnetic moment in the gauged $\mathrm{U}{(1)}_{L_{\mu}-{L}_{\tau}}$,” JHEP 12 (2020) 155, arXiv:2006.11225 [hep-ph].
  * [34] B. Dutta, R. F. Lang, S. Liao, S. Sinha, L. Strigari, and A. Thompson, “A global analysis strategy to resolve neutrino NSI degeneracies with scattering and oscillation data,” JHEP 09 (2020) 106, arXiv:2002.03066 [hep-ph].
  * [35] D. W. P. Amaral, D. G. Cerdeno, A. Cheek, and P. Foldenauer, “Confirming $U(1)_{L_{\mu}-L_{\tau}}$ as a solution for $(g-2)_{\mu}$ with neutrinos,” Eur. Phys. J. C 81 no. 10, (2021) 861, arXiv:2104.03297 [hep-ph].
  * [36] V. Munoz, V. Takhistov, S. J. Witte, and G. M. Fuller, “Exploring the origin of supermassive black holes with coherent neutrino scattering,” JCAP 11 no. 11, (2021) 020, arXiv:2102.00885 [astro-ph.HE].
  * [37] J. Wyenberg and I. M. Shoemaker, “Mapping the neutrino floor for direct detection experiments based on dark matter-electron scattering,” Phys. Rev. D 97 no. 11, (2018) 115026, arXiv:1803.08146 [hep-ph].
  * [38] D. Aristizabal Sierra, V. De Romeri, L. J. Flores, and D. K. Papoulias, “Impact of COHERENT measurements, cross section uncertainties and new interactions on the neutrino floor,” JCAP 01 no. 01, (2022) 055, arXiv:2109.03247 [hep-ph].
  * [39] S. K. A., A. Majumdar, D. K. Papoulias, H. Prajapati, and R. Srivastava, “Implications of first LZ and XENONnT results: A comparative study of neutrino properties and light mediators,” Phys. Lett. B 839 (2023) 137742, arXiv:2208.06415 [hep-ph].
  * [40] N. Mishra and L. E. Strigari, “Solar neutrinos with CE$\nu$NS and flavor-dependent radiative corrections,” Phys. Rev. D 108 no. 6, (2023) 063023, arXiv:2305.17827 [hep-ph].
  * [41] D. W. P. Amaral, D. Cerdeno, A. Cheek, and P. Foldenauer, “A direct detection view of the neutrino NSI landscape,” JHEP 07 (2023) 071, arXiv:2302.12846 [hep-ph].
  * [42] P. Langacker, “The Physics of Heavy $Z^{\prime}$ Gauge Bosons,” Rev. Mod. Phys. 81 (2009) 1199–1228, arXiv:0801.1345 [hep-ph].
  * [43] C. Boehm, D. G. Cerdeno, M. Fairbairn, P. A. N. Machado, and A. C. Vincent, “Light new physics in XENON1T,” Phys. Rev. D 102 (2020) 115013, arXiv:2006.11250 [hep-ph].
  * [44] D. Aristizabal Sierra, V. De Romeri, L. J. Flores, and D. K. Papoulias, “Light vector mediators facing XENON1T data,” Phys. Lett. B 809 (2020) 135681, arXiv:2006.12457 [hep-ph].
  * [45] R. N. Mohapatra, “From Old Symmetries to New Symmetries: Quarks, Leptons and B-L,” Int. J. Mod. Phys. A 29 no. 29, (2014) 1430066, arXiv:1409.7557 [hep-ph].
  * [46] S. Okada, “$Z^{\prime}$ Portal Dark Matter in the Minimal $B-L$ Model,” Adv. High Energy Phys. 2018 (2018) 5340935, arXiv:1803.06793 [hep-ph].
  * [47] R. Foot, “New Physics From Electric Charge Quantization?,” Mod. Phys. Lett. A 6 (1991) 527–530.
  * [48] R. Foot, G. C. Joshi, H. Lew, and R. R. Volkas, “Charge quantization in the standard model and some of its extensions,” Mod. Phys. Lett. A 5 (1990) 2721–2732.
  * [49] R. Foot, H. Lew, and R. R. Volkas, “Electric charge quantization,” J. Phys. G 19 (1993) 361–372, arXiv:hep-ph/9209259. [Erratum: J.Phys.G 19, 1067 (1993)].
  * [50] X. G. He, G. C. Joshi, H. Lew, and R. R. Volkas, “NEW Z-prime PHENOMENOLOGY,” Phys. Rev. D 43 (1991) 22–24.
  * [51] L. M. G. de la Vega, L. J. Flores, N. Nath, and E. Peinado, “Complementarity between dark matter direct searches and CE$\nu$NS experiments in U(1)’ models,” JHEP 09 (2021) 146, arXiv:2107.04037 [hep-ph].
  * [52] M. Atzori Corona, M. Cadeddu, N. Cargioli, F. Dordei, C. Giunti, Y. F. Li, E. Picciau, C. A. Ternes, and Y. Y. Zhang, “Probing light mediators and (g $-$ 2)μ through detection of coherent elastic neutrino nucleus scattering at COHERENT,” JHEP 05 (2022) 109, arXiv:2202.11002 [hep-ph].
  * [53] T. Han, J. Liao, H. Liu, and D. Marfatia, “Nonstandard neutrino interactions at COHERENT, DUNE, T2HK and LHC,” JHEP 11 (2019) 028, arXiv:1910.03272 [hep-ph].
  * [54] P. Coloma, M. C. Gonzalez-Garcia, and M. Maltoni, “Neutrino oscillation constraints on U(1)’ models: from non-standard interactions to long-range forces,” JHEP 01 (2021) 114, arXiv:2009.14220 [hep-ph]. [Erratum: JHEP 11, 115 (2022)].
  * [55] J. Heeck, M. Lindner, W. Rodejohann, and S. Vogl, “Non-Standard Neutrino Interactions and Neutral Gauge Bosons,” SciPost Phys. 6 no. 3, (2019) 038, arXiv:1812.04067 [hep-ph].
  * [56] E. Ma, “Gauged B - 3L(tau) and radiative neutrino masses,” Phys. Lett. B 433 (1998) 74–81, arXiv:hep-ph/9709474.
  * [57] E. Ma and D. P. Roy, “Phenomenology of the $B$ \- 3L($\tau$) gauge boson,” Phys. Rev. D 58 (1998) 095005, arXiv:hep-ph/9806210.
  * [58] E. Ma and U. Sarkar, “Gauged B - 3L(tau) and baryogenesis,” Phys. Lett. B 439 (1998) 95–102, arXiv:hep-ph/9807307.
  * [59] E. Ma, D. P. Roy, and U. Sarkar, “A Seesaw model for atmospheric and solar neutrino oscillations,” Phys. Lett. B 444 (1998) 391–396, arXiv:hep-ph/9810309.
  * [60] L. N. Chang, O. Lebedev, W. Loinaz, and T. Takeuchi, “Constraints on gauged B \- 3 L(tau) and related theories,” Phys. Rev. D 63 (2001) 074013, arXiv:hep-ph/0010118.
  * [61] A. N. Khan, “Constraints on general light mediators from PandaX-II electron recoil data,” Phys. Lett. B 819 (2021) 136415, arXiv:2008.10279 [hep-ph].
  * [62] PandaX-II Collaboration, X. Zhou et al., “A Search for Solar Axions and Anomalous Neutrino Magnetic Moment with the Complete PandaX-II Data,” Chin. Phys. Lett. 38 no. 1, (2021) 011301, arXiv:2008.06485 [hep-ex]. [Erratum: Chin.Phys.Lett. 38, 109902 (2021)].
  * [63] T. Schwemberger and T.-T. Yu, “Detecting beyond the standard model interactions of solar neutrinos in low-threshold dark matter detectors,” Phys. Rev. D 106 no. 1, (2022) 015002, arXiv:2202.01254 [hep-ph].
  * [64] V. De Romeri, O. G. Miranda, D. K. Papoulias, G. Sanchez Garcia, M. Tórtola, and J. W. F. Valle, “Physics implications of a combined analysis of COHERENT CsI and LAr data,” JHEP 04 (2023) 035, arXiv:2211.11905 [hep-ph].
  * [65] P. Coloma, M. C. Gonzalez-Garcia, M. Maltoni, J. a. P. Pinheiro, and S. Urrea, “Constraining new physics with Borexino Phase-II spectral data,” JHEP 07 (2022) 138, arXiv:2204.03011 [hep-ph]. [Erratum: JHEP 11, 138 (2022)].
  * [66] P. Melas, D. K. Papoulias, and N. Saoulidou, “Probing generalized neutrino interactions with the DUNE Near Detector,” JHEP 07 (2023) 190, arXiv:2303.07094 [hep-ph].
  * [67] J.-C. Park and G. Tomar, “Probing non-standard neutrino interactions with interference: insights from dark matter and neutrino experiments,” JCAP 08 (2023) 025, arXiv:2305.10836 [hep-ph].
  * [68] A. Majumdar, D. K. Papoulias, and R. Srivastava, “Dark matter detectors as a novel probe for light new physics,” Phys. Rev. D 106 no. 1, (2022) 013001, arXiv:2112.03309 [hep-ph].
  * [69] M. Demirci and M. F. Mustamin, “Solar neutrino constraints on light mediators through coherent elastic neutrino-nucleus scattering,” arXiv:2312.17502 [hep-ph].
  * [70] J.-W. Chen, H.-C. Chi, C. P. Liu, and C.-P. Wu, “Low-energy electronic recoil in xenon detectors by solar neutrinos,” Phys. Lett. B 774 (2017) 656–661, arXiv:1610.04177 [hep-ex].
  * [71] J. Bahcall. http://www.sns.ias.edu/~jnb/SNdata/sndata.html.
  * [72] J. N. Bahcall and R. K. Ulrich, “Solar Models, Neutrino Experiments and Helioseismology,” Rev. Mod. Phys. 60 (1988) 297–372.
  * [73] J. N. Bahcall, “The Be-7 solar neutrino line: A Reflection of the central temperature distribution of the sun,” Phys. Rev. D 49 (1994) 3923–3945, arXiv:astro-ph/9401024.
  * [74] J. N. Bahcall, E. Lisi, D. E. Alburger, L. De Braeckeleer, S. J. Freedman, and J. Napolitano, “Standard neutrino spectrum from B-8 decay,” Phys. Rev. C 54 (1996) 411–422, arXiv:nucl-th/9601044.
  * [75] F. L. Villante and A. Serenelli, “The relevance of nuclear reactions for Standard Solar Models construction,” Front. Astron. Space Sci. 7 (2021) 112, arXiv:2101.03077 [astro-ph.SR].
  * [76] P. F. de Salas, D. V. Forero, S. Gariazzo, P. Martinez-Mirave, O. Mena, C. A. Ternes, M. Tortola, and J. W. F. Valle, “2020 Global reassessment of the neutrino oscillation picture,” JHEP 2021 (2020) 071, arXiv:2006.11237 [hep-ph].
  * [77] I. Esteban, M. C. Gonzalez-Garcia, M. Maltoni, T. Schwetz, and A. Zhou, “The fate of hints: updated global analysis of three-flavor neutrino oscillations,” JHEP 09 (2020) 178, arXiv:2007.14792 [hep-ph].
  * [78] F. Capozzi, E. Di Valentino, E. Lisi, A. Marrone, A. Melchiorri, and A. Palazzo, “The unfinished fabric of the three neutrino paradigm,” Phys.Rev.D 104 (7, 2021) 083031, arXiv:2107.00532 [hep-ph].
  * [79] LZ Collaboration, J. Aalbers et al., “A search for new physics in low-energy electron recoils from the first LZ exposure,” arXiv:2307.15753 [hep-ex].
  * [80] XENON Collaboration, E. Aprile et al., “Excess electronic recoil events in XENON1T,” Phys. Rev. D 102 no. 7, (2020) 072004, arXiv:2006.09721 [hep-ex].
  * [81] LZ Collaboration, J. Aalbers et al., “Background determination for the LUX-ZEPLIN dark matter experiment,” Phys. Rev. D 108 no. 1, (2023) 012010, arXiv:2211.17120 [hep-ex].
  * [82] P. Ilten, Y. Soreq, M. Williams, and W. Xue, “Serendipity in dark photon searches,” JHEP 06 (2018) 004, arXiv:1801.04847 [hep-ph].
  * [83] E. M. Riordan et al., “A Search for Short Lived Axions in an Electron Beam Dump Experiment,” Phys. Rev. Lett. 59 (1987) 755.
  * [84] J. D. Bjorken, S. Ecklund, W. R. Nelson, A. Abashian, C. Church, B. Lu, L. W. Mo, T. A. Nunamaker, and P. Rassmann, “Search for Neutral Metastable Penetrating Particles Produced in the SLAC Beam Dump,” Phys. Rev. D 38 (1988) 3375.
  * [85] A. Bross, M. Crisler, S. H. Pordes, J. Volk, S. Errede, and J. Wrbanek, “A Search for Shortlived Particles Produced in an Electron Beam Dump,” Phys. Rev. Lett. 67 (1991) 2942–2945.
  * [86] A. Konaka et al., “Search for Neutral Particles in Electron Beam Dump Experiment,” Phys. Rev. Lett. 57 (1986) 659.
  * [87] M. Davier and H. Nguyen Ngoc, “An Unambiguous Search for a Light Higgs Boson,” Phys. Lett. B 229 (1989) 150–155.
  * [88] J. D. Bjorken, R. Essig, P. Schuster, and N. Toro, “New Fixed-Target Experiments to Search for Dark Gauge Forces,” Phys. Rev. D 80 (2009) 075018, arXiv:0906.0580 [hep-ph].
  * [89] S. Andreas, C. Niebuhr, and A. Ringwald, “New Limits on Hidden Photons from Past Electron Beam Dumps,” Phys. Rev. D 86 (2012) 095019, arXiv:1209.6083 [hep-ph].
  * [90] J. Blumlein et al., “Limits on neutral light scalar and pseudoscalar particles in a proton beam dump experiment,” Z. Phys. C 51 (1991) 341–350.
  * [91] J. Blumlein et al., “Limits on the mass of light (pseudo)scalar particles from Bethe-Heitler e+ e- and mu+ mu- pair production in a proton - iron beam dump experiment,” Int. J. Mod. Phys. A 7 (1992) 3835–3850.
  * [92] J. Blumlein and J. Brunner, “New Exclusion Limits for Dark Gauge Forces from Beam-Dump Data,” Phys. Lett. B 701 (2011) 155–159, arXiv:1104.2747 [hep-ex].
  * [93] J. Blümlein and J. Brunner, “New Exclusion Limits on Dark Gauge Forces from Proton Bremsstrahlung in Beam-Dump Data,” Phys. Lett. B 731 (2014) 320–326, arXiv:1311.3870 [hep-ph].
  * [94] CHARM Collaboration, F. Bergsma et al., “Search for Axion Like Particle Production in 400-GeV Proton - Copper Interactions,” Phys. Lett. B 157 (1985) 458–462.
  * [95] S. N. Gninenko, “Constraints on sub-GeV hidden sector gauge bosons from a search for heavy neutrino decays,” Phys. Lett. B 713 (2012) 244–248, arXiv:1204.3583 [hep-ph].
  * [96] NOMAD Collaboration, P. Astier et al., “Search for heavy neutrinos mixing with tau neutrinos,” Phys. Lett. B 506 (2001) 27–38, arXiv:hep-ex/0101041.
  * [97] G. Bernardi et al., “Search for Neutrino Decay,” Phys. Lett. B 166 (1986) 479–483.
  * [98] S. N. Gninenko, “Stringent limits on the $\pi^{0}\to\gamma X,X\to e+e-$ decay from neutrino experiments and constraints on new light gauge bosons,” Phys. Rev. D 85 (2012) 055027, arXiv:1112.5438 [hep-ph].
  * [99] H. Merkel et al., “Search at the Mainz Microtron for Light Massive Gauge Bosons Relevant for the Muon g-2 Anomaly,” Phys. Rev. Lett. 112 no. 22, (2014) 221802, arXiv:1404.5502 [hep-ex].
  * [100] APEX Collaboration, S. Abrahamyan et al., “Search for a New Gauge Boson in Electron-Nucleus Fixed-Target Scattering by the APEX Experiment,” Phys. Rev. Lett. 107 (2011) 191804, arXiv:1108.2750 [hep-ex].
  * [101] BaBar Collaboration, J. P. Lees et al., “Search for a Dark Photon in $e^{+}e^{-}$ Collisions at BaBar,” Phys. Rev. Lett. 113 no. 20, (2014) 201801, arXiv:1406.2980 [hep-ex].
  * [102] KLOE-2 Collaboration, F. Archilli et al., “Search for a vector gauge boson in $\phi$ meson decays with the KLOE detector,” Phys. Lett. B 706 (2012) 251–255, arXiv:1110.0411 [hep-ex].
  * [103] KLOE-2 Collaboration, A. Anastasi et al., “Limit on the production of a new vector boson in $\mathrm{e^{+}e^{-}}\rightarrow{\rm U}\gamma$, U$\rightarrow\pi^{+}\pi^{-}$ with the KLOE experiment,” Phys. Lett. B 757 (2016) 356–361, arXiv:1603.06086 [hep-ex].
  * [104] LHCb Collaboration, R. Aaij et al., “Search for Dark Photons Produced in 13 TeV $pp$ Collisions,” Phys. Rev. Lett. 120 no. 6, (2018) 061801, arXiv:1710.02867 [hep-ex].
  * [105] NA48/2 Collaboration, J. R. Batley et al., “Search for the dark photon in $\pi^{0}$ decays,” Phys. Lett. B 746 (2015) 178–185, arXiv:1504.00607 [hep-ex].
  * [106] M. Bauer, P. Foldenauer, and J. Jaeckel, “Hunting All the Hidden Photons,” JHEP 07 (2018) 094, arXiv:1803.05466 [hep-ph].
  * [107] TEXONO Collaboration, M. Deniz et al., “Measurement of Nu(e)-bar -Electron Scattering Cross-Section with a CsI(Tl) Scintillating Crystal Array at the Kuo-Sheng Nuclear Power Reactor,” Phys. Rev. D 81 (2010) 072001, arXiv:0911.1597 [hep-ex].
  * [108] R. Harnik, J. Kopp, and P. A. N. Machado, “Exploring nu Signals in Dark Matter Detectors,” JCAP 07 (2012) 026, arXiv:1202.6073 [hep-ph].
  * [109] G. Bellini et al., “Precision measurement of the 7Be solar neutrino interaction rate in Borexino,” Phys. Rev. Lett. 107 (2011) 141302, arXiv:1104.1816 [hep-ex].
  * [110] CHARM-II Collaboration, P. Vilain et al., “Measurement of differential cross-sections for muon-neutrino electron scattering,” Phys. Lett. B 302 (1993) 351–355.
  * [111] NA64 Collaboration, D. Banerjee et al., “Improved limits on a hypothetical X(16.7) boson and a dark photon decaying into $e^{+}e^{-}$ pairs,” Phys. Rev. D 101 no. 7, (2020) 071101, arXiv:1912.11389 [hep-ex].
  * [112] NA64 Collaboration, Y. M. Andreev et al., “Search for Light Dark Matter with NA64 at CERN,” Phys. Rev. Lett. 131 no. 16, (2023) 161801, arXiv:2307.02404 [hep-ex].
  * [113] BaBar Collaboration, J. P. Lees et al., “Search for Invisible Decays of a Dark Photon Produced in ${e}^{+}{e}^{-}$ Collisions at BaBar,” Phys. Rev. Lett. 119 no. 13, (2017) 131804, arXiv:1702.03327 [hep-ex].
  * [114] T. Aoyama et al., “The anomalous magnetic moment of the muon in the Standard Model,” Phys. Rept. 887 (2020) 1–166, arXiv:2006.04822 [hep-ph].
  * [115] G.-y. Huang, T. Ohlsson, and S. Zhou, “Observational Constraints on Secret Neutrino Interactions from Big Bang Nucleosynthesis,” Phys. Rev. D 97 no. 7, (2018) 075009, arXiv:1712.04792 [hep-ph].
  * [116] S.-P. Li and X.-J. Xu, “Production rates of dark photons and Z’ in the Sun and stellar cooling bounds,” JCAP 09 (2023) 009, arXiv:2304.12907 [hep-ph].
  * [117] J. H. Chang, R. Essig, and S. D. McDermott, “Revisiting Supernova 1987A Constraints on Dark Photons,” JHEP 01 (2017) 107, arXiv:1611.03864 [hep-ph].
  * [118] D. Croon, G. Elor, R. K. Leane, and S. D. McDermott, “Supernova Muons: New Constraints on $Z$’ Bosons, Axions and ALPs,” JHEP 01 (2021) 107, arXiv:2006.13942 [hep-ph].
  * [119] G. Alonso-Álvarez, K. Bleau, and J. M. Cline, “Distortion of neutrino oscillations by dark photon dark matter,” Phys. Rev. D 107 no. 5, (2023) 055045, arXiv:2301.04152 [hep-ph].
  * [120] K. Akita, S. H. Im, M. Masud, and S. Yun, “Limits on heavy neutral leptons, $Z^{\prime}$ bosons and majorons from high-energy supernova neutrinos,” arXiv:2312.13627 [hep-ph].