# PhyBench: A Physical Commonsense Benchmark for Evaluating Text-to-Image
Models

Fanqing Meng2,1, Wenqi Shao1†, Lixin Luo6, Yahong Wang3, Yiran Chen1
Quanfeng Lu5,1, Yue Yang2,1, Tianshuo Yang1, Kaipeng Zhang1, Yu Qiao1, Ping
Luo1,4†

1OpenGVLab, Shanghai AI Laboratory 2Shanghai Jiao Tong University 3Tongji
University
4The University of Hong Kong 5Nanjing University 6University of Michigan

###### Abstract

Text-to-image (T2I) models have made substantial progress in generating images
from textual prompts. However, they frequently fail to produce images
consistent with physical commonsense, a vital capability for applications in
world simulation and everyday tasks. Current T2I evaluation benchmarks focus
on metrics such as accuracy, bias, and safety, neglecting the evaluation of
models’ internal knowledge, particularly physical commonsense. To address this
issue, we introduce PhyBench, a comprehensive T2I evaluation dataset
comprising $700$ prompts across four primary categories: mechanics, optics,
thermodynamics, and material properties, encompassing $31$ distinct physical
scenarios. We assess $6$ prominent T2I models, including proprietary models
DALLE3 and Gemini, and demonstrate that incorporating physical principles into
prompts enhances the models’ ability to generate physically accurate images.
Our findings reveal that: (1) even advanced models frequently err in various
physical scenarios, except for optics; (2) GPT-4o, with item-specific scoring
instructions, effectively evaluates the models’ understanding of physical
commonsense, closely aligning with human assessments; and (3) current T2I
models are primarily focused on text-to-image translation, lacking profound
reasoning regarding physical commonsense. We advocate for increased attention
to the inherent knowledge within T2I models, beyond their utility as mere
image generation tools. The code and data are available at
https://github.com/OpenGVLab/PhyBench.

PhyBench: A Physical Commonsense Benchmark for Evaluating Text-to-Image Models

Fanqing Meng2,1, Wenqi Shao1†, Lixin Luo6, Yahong Wang3, Yiran Chen1 Quanfeng
Lu5,1, Yue Yang2,1, Tianshuo Yang1, Kaipeng Zhang1, Yu Qiao1, Ping Luo1,4†
1OpenGVLab, Shanghai AI Laboratory 2Shanghai Jiao Tong University 3Tongji
University 4The University of Hong Kong 5Nanjing University 6University of
Michigan

††footnotetext:  $\dagger$ Corresponding Authors<EMAIL_ADDRESS><EMAIL_ADDRESS>Figure 1: Error images generated by some popular T2I models.

##  1 Introduction

Text-to-image (T2I) models have revolutionized the visualization of abstract
concepts and detailed scenes from text descriptions Saharia et al. (2022);
Schramowski et al. (2023); Gafni et al. (2022); Gal et al. (2022); Rombach et
al. (2022); Betker et al. (2023). Beyond generating images from textual
prompts, it is crucial for T2I models to adhere to physical commonsense. This
adherence ensures the accurate depiction of interactions between objects,
light, and shadows, which is essential for constructing realistic world
simulators Zhu et al. (2024). However, it is known that proprietary T2I models
often fall short in generating realistic images Borji (2023); Farid (2022);
Liu et al. (2023). For example, DALL-E 3 OpenAI (2023) even generates a
balanced seesaw with an elephant and a mouse on either side as shown in Fig.
1, which is physically impossible due to their different masses.

To drive the research in this field, it is crucial to build an evaluation
benchmark to measure how much different T2I models grasp the physical
commonsense. Such evaluation allows practitioners to identify the strengths
and weaknesses of these models, fostering the development of new techniques
that better integrate physical commonsense. Prior T2I evaluation benchmarks
focus on metrics such as accuracy Huang et al. (2023); Lee et al. (2024),
safety Schramowski et al. (2023), and privacy Yang et al. (2024b), as shown in
Tab. 1. These benchmarks primarily address basic text-to-image translation and
do not delve into the physical commonsense behind the image. These benchmarks
primarily address basic text-to-image translation and do not explore the
underlying physical commonsense in the images. While some studies have
highlighted the challenges T2I models face in generating realistic scenes
Borji (2023), a comprehensive quantitative investigation into the physical
commonsense of T2I models remains largely unexplored.

Constructing such a benchmark presents several challenges. First, the prompt
should be implicit without revealing the underlying physical knowledge, to
assess whether T2I models can independently discern physical commonsense.
Second, the scenarios showcasing the physical commonsense should be simple
enough such that the image depicting user prompts can be generated for T2I
models. In this way, the evaluation concentrates on the physical knowledge
behind images rather than the alignment between the image and the prompt.
Lastly, the prompts in the evaluation set should be comprehensive enough to
cover a wide range of physical commonsense to ensure a thorough evaluation of
the models’ grasp of physical commonsense in different contexts.

Figure 2: An overview of the proposed PhyBench. It encompasses $4$ types of
general physical knowledge spanning $31$ detailed physical scenarios, and
$700$ validated prompts, which has been evaluated on $6$ T2I models.

To address these challenges, we introduce PhyBench, focusing on $4$ types of
physical knowledge, including optics, mechanics, thermodynamics, and material
properties. PhyBench encompasses a total of $700$ prompts, spaning $31$
physical scenarios about gravity, light scattering, ice melt, and more, as
shown in Fig. 2. We evaluate $6$ proprietary and open T2I models including
DALLE 2 & 3 OpenAI (2023), SD XL Podell et al. (2023) & 3 Esser et al. (2024),
Midjourney Midjourney (2023), and Gemini Team et al. (2023).

As illustrated in Fig. 4, the prompt collection process adheres to a stringent
pipeline to cover as many physical commonsense as possible. On the one hand,
the physical commonsense is characterized by $4$ types of physical knowledge
as mentioned above. Prompts in optics, mechanics, and thermodynamics evaluate
the model’s comprehension of interactions between objects, while prompts in
materials assess the model’s understanding of the basic attributes of
individual objects. On the other hand, we refine each physical scenario with
fine-grained physical principles with the help of textbooks and GPT4. Finally,
the physical scenarios are specified by various prompts created with GPT4.
When creating prompts, we also ensure that the prompts used for drawing are
implicit, such as "an elephant and a mouse standing on either side of a
seesaw", rather than explicitly stating their positions like explicit prompts.
With such a top-down pipeline, PhyBench is curated to comprise $700$ prompts
with their physical scenarios recorded.

To accurately evaluate the model’s performance on PhyBench, we propose
PhyEvaler which leverages GPT-4o OpenAI (2023) to score the generated images
with an item-specific scoring instruction. We show that PhyEvaler aligns well
with human rating. The evaluation results reveal that T2I models face great
challenges in generating images conforming to physical commonsense. We
summarized several findings as follows.

  * •

Current text-to-image (T2I) models often struggle to generate images that
adhere to physical commonsense, with the exception of optical scenarios.

  * •

Advanced open-source models, such as Stable Diffusion 3 and Stable Diffusion
XL, have a significant gap in understanding physical commonsense compared to
advanced closed-source models like DALLE 3.

  * •

Rewriting implicit prompts by explicitly revealing physical commonsense can
significantly improve the accuracy of generated images. This suggests that
current T2I models can follow text instructions well but fail to reason about
the physical commonsense in image generation.

The contributions of our work are three-fold. i) We build a new evaluation
benchmark for text-to-image generation called PhyBench to measure the
understanding of physical knowledge for T2I models. ii) We evaluate various
publicly available T2I models on PhyBench, revealing that current T2I models
including DALLE 3, Midjourney, and Stable diffusion 3 achieve plain
performance in understanding simple physical commonsense. iii) We present an
automated evaluation framework called PhyEvaler, which aligns closely with
human evaluation results. We hope PhyBench will inspire the community to focus
on physical knowledge in image generation, rather than simply treating them as
text-to-image translation tools, bringing us closer to a real-world simulator.

Table 1: Comparison with previous text-to-image benchmarks. Unlike prior
datasets, PhyBench quantitatively benchmarks the performance of T2I models in
following physical laws.

Benchmark | Prompt Type | Evaluation | Human Rating
---|---|---|---
Stable Bias Seshadri et al. (2023) | Explicit | Gender & Racial | No
Safe Diffusion Schramowski et al. (2023) | Explicit | Violence | No
HEIM Lee et al. (2024) | Explicit | Align & Quality | Yes
T2I-CompBench Huang et al. (2023) | Explicit | Composition | Yes
ImplictBench Yang et al. (2024b) | Implicit | Safety | No
PhyBench (ours) | Implicit | Physics knowledge | Yes

Figure 3: Samples of images induced by our PhyBench in $4$ different aspects
by DALLE 3 and Gemini. The bold text represents the detailed physical
commonsense and the colored bold text indicates the general physical
knowledge.

##  2 Related work

###  2.1 Text-to-image generation

Text-to-image (T2I) generation is an evolving field dedicated to creating
images from textual descriptions. Initially, research in this area
predominantly focused on leveraging Generative Adversarial Networks (GANs)
Goodfellow et al. (2014) and Autoregressive Transformers Vaswani et al. (2017)
to accomplish this task. These early approaches laid the groundwork for
generating coherent images based on textual input. In recent years, diffusion
models have emerged as a powerful alternative for T2I generation. These models
start with random noise and iteratively refine the image through a de-noising
process. Notable examples include the Stable Diffusion series Rombach et al.
(2022), which have set new benchmarks in the field. These models frequently
use a frozen text encoder, such as CLIP Radford et al. (2021), to transform
prompts into embeddings that drive the de-noising process, thereby generating
images closely related to the prompts. Despite these advancements, current
state-of-the-art T2I models like DALL-E 3 and Midjourney still face challenges
in accurately depicting scenes involving extremely simple physical scenarios.
To assess the capabilities of T2I models in generating images that adhere to
physical laws, we select and evaluate four state-of-the-art closed-source
models: DALL-E 2Betker et al. (2023), DALL-E 3 OpenAI (2023), Midjourney
Midjourney (2023), and Gemini Team et al. (2023), along with two open-source
models: Stable Diffusion XL Rombach et al. (2022) and Stable diffusion 3 Esser
et al. (2024), using our proposed PhyBench.

###  2.2 Benchmarks for text-to-image generation

The rapid development of text-to-image (T2I) generation models has highlighted
the need for comprehensive benchmarks. There are many sophisticated and
challenging benchmarks have been introduced to better assess their
capabilities. Examples include DrawBench Saharia et al. (2022) and HE-T2I
Petsiuk et al. (2022), which use hundreds of prompts to evaluate skills in
counting, shapes, and writing. Additionally, more complex evaluation tasks,
such as those proposed by T2I-CompBench Huang et al. (2023), offer benchmarks
for challenging compositional generation, where prompts combine different
attributes. And some research has also emphasized the societal implications of
T2I models, particularly concerning safety Schramowski et al. (2023) and bias
Seshadri et al. (2023). These previous efforts typically focus on using
explicit prompts that clearly specify the content to be included in the image,
along with precise positioning and other relevant auxiliary information, to
evaluate the model’s performance. In contrast, the position Yang et al.
(2024b) benchmark proposes evaluating models with implicit prompts, which can
better assess whether a model possesses the required knowledge. To this end,
we introduce PhyBench, a benchmark that uses implicit prompts to evaluate a
model’s understanding of physics. By employing implicit prompts, PhyBench aims
to provide a more nuanced evaluation of a model’s capabilities in generating
images based on physical concepts. A detailed comparison of T2I evaluation
benchmarks is presented in Tab. 1

##  3 Our Benchmark: PhyBench

Figure 4: Data collection pipeline of PhyBench. PhyBench comprises $4$
categories of general physical knowledge. For each category, we first consider
the detailed physical laws that can be represented by T2I models. Using
textbooks, the internet, and other sources, we manually construct appropriate
and simple scenarios for each physical law, including the prompt and explicit
scenario. Subsequently, we use GPT-4 to expand the prompt by replacing key
objects. After rigorous quality checks and filtering, PhyBench includes 700
validated samples.

Our PhyBench focuses on $4$ main aspects, encompassing $31$ physical
scenarios, comprising $700$ prompts, as shown in Fig. 2. We present the
details about dataset construction, image generation, and evaluation method in
Sec. 3.1, Sec. 3.2, and Sec. 3.3, respectively.

###  3.1 PhyBench Construction

PhyBench evaluates physical commonsense from four types of physical knowledge
as described in the following.

Mechanics.  As for mechanics, we categorize it into $6$ aspects according to
the type of force: gravity, buoyancy, normal force, elasticity, pressure, and
surface tension. We construct physical scenarios that either directly or
indirectly reflect these types of forces. For example, for pressure, we
designed the implicit prompt "an empty plastic bottle at the bottom of the
sea", because the bottle would be compressed under high pressure.
Subsequently, we leverage GPT-4 to perform object substitutions (e.g.
replacing "plastic bottle") and environment substitutions (e.g. replacing "at
the bottom of the sea") to expand the prompts. Ultimately, we have generated
170 prompts for this aspect.

Optics.  In optics, we categorize $6$ aspects based on the physical phenomena
of light: reflection, refraction, scattering, dispersion, absorption, and
straight-line propagation. Similar to the process in mechanics, we design
scenarios for each phenomenon and expand them using GPT-4. For instance, for
refraction, due to the different indices of refraction between air and water,
we use the prompt "a plastic straw partially immersed in a clear glass filled
with water." This setup visually demonstrates the refraction by showcasing the
apparent discontinuity in the straw. Ultimately, we have generated 170 prompts
for this aspect.

Thermodynamics.  The thermodynamic laws that can be depicted by T2I models are
limited. Therefore, we choose $6$ types of phase changes to design scenarios
and expand prompts. For instance, for sublimation, we design the implicit
prompt as "The state change of dry ice at room temperature", where the correct
physical phenomenon is the sublimation of dry ice. Ultimately, we have
generated 120 prompts for this aspect.

Material Properties.  Physical properties and chemical properties are two
aspects of material properties. For physical properties, we categorize them
into color, hardness, viscosity, solubility, conductivity, and flame reaction.
For hardness, we use implicit prompts involving collisions to reflect the
hardness differences between objects. For example, the prompt "an egg and a
hard rock collide" should produce an image showing that an egg breaks upon
colliding with a stone.

For chemical properties, we consider combustibility, supporting combustion,
acidity, redox potential, dehydrating properties, molecular structure, and
stability. Since chemical properties often involve chemical reactions, we aim
for simplicity and universality in our prompts by avoiding obscure chemical
substances and instead using common everyday scenarios. For instance, for
redox potential, we use "The scene after an iron rod has been exposed to
oxygen for decades", evaluating the correctness of the image by whether it
depicts a rusted iron rod. After expanding the prompts, we have generated 120
prompts for physical properties and 120 prompts for chemical properties.

###  3.2 Image Generation on PhyBench

To investigate the performance of T2I models in response to implicit prompts,
we utilize $6$ T2I models detailed in Tab. 2. Specifically, we produce $4$
images for each implicit prompt using each T2I model to ensure a thorough
evaluation and to mitigate the effects of randomness in image generation.

Table 2: Information of T2I models evaluated on ImplicitBench.

Model | Creator | # Params | Access
---|---|---|---
Stable Diffusion 3 Sauer et al. (2024) | Stability AI | 2B | Open
Stable Diffusion XL Podell et al. (2023) | Stability AI | 3B | Open
Gemini Team et al. (2023) | Google | - | Limited
Midjourney Midjourney (2023) | Midjourney | - | Limited
DALL-E 2 Betker et al. (2023) | OpenAI | 3.5B | Limited
DALL-E 3 OpenAI (2023) | OpenAI | - | Limited

###  3.3 Evaluation Method

Our evaluation method aims to score each image generated by text-to-image
(T2I) models based on its accuracy in representing correct physical scenarios,
ultimately reflecting the rankings and relative differences among different
models. For simplicity, the evaluation is divided into two aspects: scene
scores (0, 1, 2) and physical correctness scores (0, 1, 2, 3). The former
assesses whether the image adheres to the prompt by depicting the correct
scene, while the latter measures the correctness of the depicted physical
principles. For instance, as for the prompt "an elephant and a mouse are
standing on either side of a seesaw", if the image includes an elephant and a
mouse on a seesaw, the scene score would be 2; And if the elephant’s end is on
the ground and the mouse’s end is in the air, the physical correctness score
would be 3.

GPT-4o as Human-Aligned Scorer.  Previous studies have demonstrated that
GPT-4V is an effective human-aligned evaluator Wu et al. (2024). Therefore, we
employ the more advanced GPT-4o and design special prompts to score images. As
illustrated in Fig. 5, thanks to GPT-4o’s excellent capabilities in
understanding pure text and physical laws, we leverage GPT-4o to generate
scene-specific scoring criteria for each prompt in our PhyBench dataset.
Specifically, we design a grading instruction template that includes
descriptions of the current scene and relevant physical laws, along with
detailed grading criteria that need to be adapted for each scene. We then
prompt GPT-4o to complete the template for each scene. When running the
benchmark, we require GPT-4o to score different images according to these
detailed criteria and provide justifications for each score. This method of
scoring through specific evaluation points has been shown to achieve favorable
outcomes in previous work Wu et al. (2024). Our experiments also reveal that
this framework align closely with human evaluation results.

Improving Spatial Relationship Judgment.  Numerous studies show that
multimodal large models are prone to hallucinations Xu et al. (2023); Ying et
al. (2024). Fortunately, the prompts we use are exceptionally simple,
resulting in images that are straightforward and clear with fewer objects.
Hence, in our experiments, we observe that GPT-4o exhibits minimal
hallucinations in most scenarios. Nevertheless, GPT-4o remains prone to
hallucinations in some scenarios involving spatial relationships, such as
those related to gravity or buoyancy. To address this issue, we utilize
GroundingDino Ren et al. (2024) to annotate the bounding boxes of the main
subjects in the images and incorporate these annotations into the final
scoring prompt. Our experimental results demonstrate that this simple approach
is effective in mitigating the erroneous scoring induced by GPT-4o’s
hallucinations.

Figure 5: The evaluation method of PhyBench. We pre-establish template scoring
criteria and require GPT-4 to generate detailed scoring standards for each
scenario. Finally, we use these detailed criteria to score each image.
Additionally, for scenarios involving spatial relationship assessments, we
provide bounding boxes generated by GroundingDino to enhance the accuracy of
machine scoring.

##  4 Experiments

In this section, We quantitatively assess the ability of different T2I models
to understand physical commonsense on our PhyBench.

###  4.1 Experiments Setup

Evaluation Metric.  We provide the average scores for scene and physical
correctness assessments by GPT-4o, alongside the average results of human
scoring. To better measure the alignment between machine scoring and human
scoring, we calculate the Pearson correlation coefficient based on the overall
scores from both machine and human evaluations for each sample and report the
average number. A detailed description is in Sec. A

###  4.2 Quantitative Evaluation

Figure 6: The overall scores of different T2I models toward PhyBench across
different physical knowledge.

Mechanics.  As shown in Tab. 3, we find that in the type of mechanics,
although DALL-E 3’s physics score is only $1.71$, it significantly surpasses
other models. However, the physics scores of other models do not even exceed
$1.5$, indicating that current models struggle to understand physical
scenarios such as gravity and buoyancy accurately.

It is worth noting that in scenarios involving judgment of spatial
relationships followed by scoring, GPT-4o sometimes experiences
hallucinations. By incorporating the bounding box information of objects as
described in Sec. 3.3, we have achieved more accurate machine scoring results.
As shown in Tab. 4, with the inclusion of bounding box information, the
average machine scoring results are closer to human evaluation outcomes, and
the correlation between machine scores and human scores significantly
improves.

Optics.  As shown in Tab. 5. In optical scenarios, all models perform well,
with Midjourney excelling in both machine and manual scoring, even surpassing
a score of $2.5$. We find that for some simple laws, such as light travelling
in straight lines and scattering, nearly all models perform well, leading to
high overall scores. We believe this is because optical laws are present in
pre-trained images, resulting in a better understanding of optics.

Thermodynamics.  As shown in Tab. 6, we find that all models struggle with
thermodynamic scenarios. Even the best-performing model, Gemini, achieves only
a $1.31$ score in simulating the physical scenarios of thermodynamics. The
scenarios are typically straightforward, often involving a single object, such
as a cup of water above $100$ degrees Celsius. However, most current models
fail to understand these implicit prompts, either incorrectly depicting the
state of objects under specified temperature conditions or misrepresenting
them entirely.

Material Properties.  Material properties include physical and chemical
properties, similar to thermodynamics, generally involving only one object.
For example, "An image of iron powder" reflects the color of chemicals, and "A
scene of an iron rod after being exposed to oxygen for decades" reflects redox
properties. As shown in Tab. 7 and Tab. 8, current models largely fail to
understand such prompts, with the highest score for physical properties being
only $1.28$ and the top score for chemical properties just $0.84$. We
hypothesize that this may be due to the lack of these specific scenarios in
the training data.

Table 3: Specific scores of different T2I models for mechanical laws.

Model |  Score($\uparrow$) | Corr($\uparrow$)
---|---|---
Sce | Sce(hum.) | Phy | Phy(hum.)
SD 3 | 1.76 | 1.74 | 1.18 | 1.23 | 0.89
SD XL | 1.46 | 1.50 | 0.91 | 0.87 | 0.85
Gemini | 1.83 | 1.81 | 1.37 | 1.39 | 0.78
Midjourney | 1.82 | 1.77 | 1.33 | 1.24 | 0.76
DALL-E 2 | 1.53 | 1.49 | 1.15 | 0.92 | 0.72
DALL-E 3 | 1.88 | 1.87 | 1.64 | 1.71 | 0.77
SD XL(rewrite) | 1.62 | 1.69 | 1.23 | 1.20 | 0.90
DALL-E 3(rewrite) | 1.93 | 1.92 | 2.09 | 2.02 | 0.84

Table 4: The effect of adding spatial relationship information in GPT-4o. We
only show examples of distinguishing by positional relationship, including
some samples in gravity, buoyancy, and object pressure.

Model |  Score($\uparrow$) | Correlation($\uparrow$)
---|---|---
Sce | Sce(ground) | Sce(hum.) | Phy | Phy(ground) | Phy(hum.) | w/o ground | w/ ground
SD 3 | 1.81 | 1.68 | 1.58 | 0.80 | 0.68 | 0.66 | 0.75 | 0.86
SD XL | 1.01 | 1.03 | 1.08 | 0.21 | 0.25 | 0.30 | 0.82 | 0.88
Gemini | 1.77 | 1.71 | 1.66 | 1.05 | 1.14 | 1.14 | 0.67 | 0.78
Midjourney | 1.79 | 1.65 | 1.56 | 0.92 | 0.82 | 0.74 | 0.69 | 0.80
DALL-E 2 | 1.31 | 1.23 | 1.10 | 0.87 | 0.65 | 0.57 | 0.59 | 0.71
DALL-E 3 | 1.97 | 1.97 | 1.87 | 1.36 | 1.56 | 1.56 | 0.70 | 0.81

Table 5: Specific scores of different T2I models for optics laws.

Model |  Score($\uparrow$) | Corr($\uparrow$)
---|---|---
Sce | Sce(hum.) | Phy | Phy(hum.)
SD 3 | 1.72 | 1.74 | 1.77 | 1.75 | 0.90
SD XL | 1.66 | 1.64 | 1.92 | 1.78 | 0.89
Gemini | 1.92 | 1.94 | 2.58 | 2.51 | 0.73
Midjourney | 1.94 | 1.95 | 2.64 | 2.56 | 0.74
DALL-E 2 | 1.84 | 1.81 | 2.21 | 2.21 | 0.74
DALL-E 3 | 1.95 | 1.95 | 2.53 | 2.41 | 0.73
SD XL(rewrite) | 1.79 | 1.77 | 2.09 | 2.13 | 0.88
DALL-E 3(rewrite) | 1.95 | 1.96 | 2.67 | 2.65 | 0.78

Table 6: Specific scores of different T2I models for thermodynamics laws.

Model |  Score($\uparrow$) | Corr($\uparrow$)
---|---|---
Sce | Sce(hum.) | Phy | Phy(hum.)
SD 3 | 1.70 | 1.82 | 0.51 | 0.52 | 0.89
SD XL | 1.50 | 1.56 | 0.59 | 0.54 | 0.88
Gemini | 1.68 | 1.78 | 1.45 | 1.31 | 0.79
Midjourney | 1.58 | 1.73 | 1.28 | 1.15 | 0.82
DALL-E 2 | 1.44 | 1.50 | 1.02 | 0.98 | 0.75
DALL-E 3 | 1.63 | 1.53 | 1.14 | 1.09 | 0.74
SD XL(rewrite) | 1.69 | 1.85 | 1.98 | 2.08 | 0.87
DALL-E 3(rewrite) | 1.88 | 1.94 | 2.40 | 2.46 | 0.80

Table 7: Specific scores of different T2I models for physical properties of
material properties.

Model |  Score($\uparrow$) | Corr($\uparrow$)
---|---|---
Sce | Sce(hum.) | Phy | Phy(hum.)
SD 3 | 1.60 | 1.67 | 1.15 | 1.18 | 0.86
SD XL | 1.34 | 1.31 | 0.97 | 0.93 | 0.87
Gemini | 1.71 | 1.81 | 1.39 | 1.28 | 0.83
Midjourney | 1.63 | 1.80 | 1.13 | 0.99 | 0.81
DALL-E 2 | 1.40 | 1.44 | 1.04 | 0.94 | 0.65
DALL-E 3 | 1.77 | 1.84 | 1.23 | 1.10 | 0.83
SD XL(rewrite) | 1.44 | 1.47 | 1.60 | 1.61 | 0.88
DALL-E 3(rewrite) | 1.89 | 1.88 | 2.42 | 2.45 | 0.84

Table 8: Specific scores of different T2I models for chemical properties of
material properties.

Model |  Score($\uparrow$) | Corr($\uparrow$)
---|---|---
Sce | Sce(hum.) | Phy | Phy(hum.)
SD 3 | 1.29 | 1.37 | 0.32 | 0.41 | 0.88
SD XL | 1.27 | 1.36 | 0.22 | 0.23 | 0.90
Gemini | 1.61 | 1.68 | 0.62 | 0.71 | 0.70
Midjourney | 1.36 | 1.57 | 0.62 | 0.69 | 0.74
DALL-E 2 | 1.30 | 1.38 | 0.45 | 0.36 | 0.70
DALL-E 3 | 1.58 | 1.64 | 0.79 | 0.84 | 0.83
SD XL(rewrite) | 1.43 | 1.58 | 1.06 | 1.11 | 0.89
DALL-E 3(rewrite) | 1.77 | 1.70 | 1.82 | 1.82 | 0.87

###  4.3 Takeway Findings

Thorugh extensive evaluation, we have several observations. 1) The scenes we
design are simple enough that most models are able to depict them based on the
prompts. 2) The machine scoring results show a high correlation with manual
evaluation outcomes under our previous designs, indicating that GPT-4o can
serve as an excellent human-aligned scorer on PhyBench. 3) As shown in Fig. 6,
although the models can render the scenes, their performance on physical
correctness is generally poor, with only optical scenarios showing relatively
better results. 4) Open-source models exhibit a significant gap in
understanding physical commonsense compared to proprietary models. In Fig. 9
in appendix, we present qualitative visual results and compare the performance
of different models.

##  5 Discussion

In this section, we conduct robustness analysis experiments, including prompt
rewriting and the use of different T2I models. The experimental results
indicate that current T2I models primarily possess superficial text-to-image
translation functionalities but lack internal knowledge, such as an
understanding of physical commonsense. In section .B.1, we also do some
detailed case analysis.

###  5.1 Ablation Study

Figure 7: The PhyRewriter framework. We utilize GPT-4’s strong textual
capabilities to generate explicit prompts that accurately depict physical
phenomena.

Rewriting Prompt.  We employ a straightforward strategy to compel models to
generate images that comply with physical commonsense, as shown in Fig. 7.
GPT-4’s powerful textual capabilities enable it to accurately understand
simple physical scenarios. We input the original prompt and the physical laws,
along with several in-context examples, to prompt GPT to generate an explicit
prompt that includes the outcomes resulting from these physical laws. We have
employed explicit prompts corresponding to implicit prompts and selected SDXL
and DALL-E 3 as representatives of open-source and proprietary models,
respectively. Note that we use "My prompt has full detail so there is no need
to add more:" as a prefix for DALL-E 3 to prevent it from rewriting the
prompt.

As shown in Tab. 6, Tab. 7, and Tab. 8, the results demonstrate that this
simple strategy significantly enhances performance for all models. For
instance, in thermodynamic scenarios, SDXL with explicit prompts outperforms
all models using implicit prompts; after employing explicit prompts, DALL-E
3’s score increased from 1.09 to 2.46. This demonstrates that the models can
generate images from PhyBench but fail to accurately render images from
implicit prompts due to a lack of physical commonsense.

Figure 8: Error cases of RPG in PhyBench.

Other Text-to-Image models with Reasoning Capabilities.  We also consider T2I
models with reasoning capabilities. RPG Yang et al. (2024a) is a T2I agent
framework that leverages the reasoning abilities of LLMs to generate images.
We use RPG for experiments in PhyBench. Unfortunately, the success rate of RPG
in generating images is notably low, as also reported in their GitHub
repository. This limitation hinders quantitative comparison, so we perform a
qualitative analysis instead.

Through comparison of numerous images, we find that RPG struggles to
accurately model physical scenarios. As shown in Fig. 8, even with simple
scenes, RPG fails to generate images correctly, whether using the original or
rewritten prompts. We attribute this to two main factors: 1) current T2I
models with reasoning capabilities focus on layout and object details (such as
texture and shape) but lack an understanding of physical laws. 2) Even with
explicit prompts, the models still fail to generate the correct images. We
believe this is due to a lack of training data for these types of images.

##  6 Conclusion

In this paper, we introduce PhyBench, the first comprehensive and quantitative
benchmark for evaluating T2I models’ understanding of physical commonsense.
PhyBench covers $4$ main aspects: mechanics, optics, thermodynamics, and
material properties. It includes $31$ specific physical scenarios and $700$
manually reviewed prompts. Besides, we develop PhyEvaler, using GPT-4o for a
comprehensive evaluation of six popular T2I models, showing a strong
correlation with human evaluation. Our results reveal that current T2I models
struggle to generate images that adhere to physical commonsense, indicating
that while these models excel in text-to-image translation, they lack in-depth
physical knowledge.

##  7 Limitations

Through extensive experiments, we find that current T2I models lack an
understanding of fundamental physical commonsense. However, strategies such as
prompt rewriting or agent frameworks do not address the core issue. We aim to
develop a T2I model capable of autonomously understanding and applying
knowledge, which we leave for future work.

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##  Appendix A Experiments

In this section, we present qualitative visual results and compare the
performance of different models, as shown in Fig. 9. We find that even in the
simplest scenarios, current text-to-image (T2I) models are prone to errors.
For example, for the prompt "A cylindrical block of wood placed in front of a
mirror", DALL-E 3 and Midjourney incorrectly depict objects in a mirror.
Similarly, for "An apple, a piece of wood, and an iron block in a tank filled
with water", DALL-E 3, Gemini, and Midjourney all misrepresent the state of
one or more objects, while DALL-E 2 omits an object entirely.

Figure 9: Visual comparisons of different T2I models toward PhyBench across
$4$ aspects.

###  A.1 Experiments Setup

Prompt format.  To ensure fairness, for Midjourney, Gemini, and DALLE 2, we
use the original prompt directly. For DALL-E 3 and Gemini, we use the prefix
"I NEED to test how the tool works with extremely simple prompts. DO NOT add
any detail, just use it AS-IS:" to prevent them from rewriting the prompt. For
Stable Diffusion models, we employ GPT-4 to reformat the prompt into several
short phrases suitable for the models.

Human Evaluation.  We require all paper authors to score each image according
to the same criteria: 0-2 points for scene accuracy and 0-3 points for
adherence to physical laws. Each image receives scores from 10 different human
evaluators, and the average of these scores is taken as the final human
rating.

##  Appendix B Discussion

###  B.1 Case Analysis

Figure 10: Case analysis of images generated by DALL-E 3. The three examples
in the upper row are successful cases where DALL-E 3 is able to generate
physically correct images. The three examples in the lower row demonstrate
failure cases, with erroneous sections highlighted in red boxes. Following
prompt rewriting, the model generates physically correct images, with
corrected sections marked in green boxes.

As shown in Fig. 10, the three images in the upper row are generated
correctly, all following the physical laws (reflection, scattering of light,
and weightlessness). These physical laws are more widely reflected in natural
images, allowing image generation models to learn and replicate them
effectively.

However, for more challenging scenes in our dataset, these models fail to
accurately represent physical laws in the generated images. Fig. 10 shows
three failure cases. For the scene "an apple and a rock in a water tank filled
with water", based on the law of buoyancy, the apple, being less dense than
water, would float on the surface, and the rock, being denser, would sink to
the bottom. However, the generated image depicts both the apple and the rock
at the bottom of the tank. GPT-4 rewrites the prompt to includes this
information: "A realistic image of an apple floating on the surface of clear
water in a glass water tank. At the bottom of the tank, a rock is clearly
visible resting on the tank floor. The water tank is transparent to clearly
show the apple floating above and the rock sunk below". Using the revised
prompt, DALL-E 3 is able to generate an image showing the apple floating and
the rock at the bottom.

Similarly, the scene "a thin empty plastic bottle in a hyperbaric chamber"
presents another challenge. Given the high atmospheric pressure inside such
chambers, an empty, thin aluminum can will crumple or implode due to the
external pressure being far greater than the internal pressure. When prompted
with the basic prompt, DALL-E generates a smooth, glossy can in a hyperbaric
chamber, which is a simple composition of the elements in the prompt. After
refining the prompt to "A realistic scene inside a hyperbaric chamber showing
a crumpled thin aluminum can due to the high external pressure", the model
successfully depicted the can’s deformation.

For material properties, the scene "a glass of mixture of baking soda and
litmus solution that has been standing for a while" involves the knowledge of
acidity and alkalinity. As an alkaline substance, when mixed with a litmus
solution, it will turn the litmus blue. With the original prompt, DALL-E
generates a glass of liquid with an incorrect milky white and green colors.
When given the revised prompt "A realistic close-up of a clear glass filled
with a blue-colored liquid. …", the model is able to generate the correct blue
color.


††thanks: These authors contributed equally to this work.††thanks: These
authors contributed equally to this work.

# Ultra-Heavy Dark Matter Search with Electron Microscopy of Geological Quartz

Reza Ebadi †<EMAIL_ADDRESS>Department of Physics, University of Maryland,
College Park, Maryland 20742, USA  Quantum Technology Center, University of
Maryland, College Park, Maryland 20742, USA  Anubhav Mathur Department of
Physics and Astronomy, Johns Hopkins University, 3400 N. Charles St.,
Baltimore, Maryland 21218, USA  Erwin H. Tanin Department of Physics and
Astronomy, Johns Hopkins University, 3400 N. Charles St., Baltimore, Maryland
21218, USA  Nicholas D. Tailby  Department of Earth and Planetary Sciences,
American Museum of Natural History, New York, New York 10024, USA  Mason C.
Marshall Quantum Technology Center, University of Maryland, College Park,
Maryland 20742, USA  Department of Electrical and Computer Engineering,
University of Maryland, College Park, Maryland 20742, USA  Harvard-Smithsonian
Center for Astrophysics, Cambridge, Massachusetts 02138, USA  Aakash Ravi
Quantum Technology Center, University of Maryland, College Park, Maryland
20742, USA  Raisa Trubko  Department of Physics, Worcester Polytechnic
Institute, Worcester, Massachusetts 01609 USA  Department of Physics, Harvard
University, Cambridge, Massachusetts 02138, USA  Department of Earth and
Planetary Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
Roger R. Fu  Department of Earth and Planetary Sciences, Harvard University,
Cambridge, Massachusetts 02138, USA  David F. Phillips
<EMAIL_ADDRESS>Harvard-Smithsonian Center for Astrophysics,
Cambridge, Massachusetts 02138, USA  Surjeet Rajendran<EMAIL_ADDRESS>Department of Physics and Astronomy, Johns Hopkins University, 3400 N. Charles
St., Baltimore, Maryland 21218, USA  Ronald L. Walsworth<EMAIL_ADDRESS>Department of Physics, University of Maryland, College Park, Maryland 20742,
USA  Quantum Technology Center, University of Maryland, College Park, Maryland
20742, USA  Department of Electrical and Computer Engineering, University of
Maryland, College Park, Maryland 20742, USA

(August 27, 2024)

###### Abstract

Self-interactions within the dark sector could clump dark matter into heavy
composite states with low number density, leading to a highly suppressed event
rate in existing direct detection experiments. However, the large interaction
cross section between such ultra-heavy dark matter (UHDM) and standard model
matter results in a distinctive and compelling signature: long, straight
damage tracks as they pass through and scatter with matter. In this work, we
propose using geologically old quartz samples as large-exposure detectors for
UHDM. We describe a high-resolution readout method based on electron
microscopy, characterize the most favorable geological samples for this
approach, and study its reach in a simple model of the dark sector. The
advantage of this search strategy is two-fold: the age of geological quartz
compensates for the low number density of UHDMs, and the distinct geometry of
the damage track serves as a high-fidelity background rejection tool.

##  I Introduction

A major outstanding puzzle in modern physics is the nature of dark matter (DM)
[1]. Despite the ever-improving sensitivities of direct detection experiments,
the simplest DM candidates have not been observed, motivating searches for a
wider range of possible dark sectors. Moreover, challenges that simple cold DM
candidates face on sub-galactic scales [2, 3] might be relieved with more
complex dark sectors. For instance, self-interacting DM has been investigated
to address small-scale challenges such as the core-cusp problem [4, 5].

Nearly all current DM detection strategies, ranging from direct-detection
efforts in the laboratory to indirect signals from DM annihilation (or decay),
are based on the assumption that the DM is distributed around the universe as
a gas of free particles with a large number density. This picture naturally
emerges if self-interactions within the dark sector are weak, but is not
strictly prescribed by existing observational constraints. The most stringent
limits arise from observations of the Bullet Cluster, which restrict the self-
interaction cross section per unit mass to be $\sigma_{\chi\chi}/m_{\rm
DM}\lesssim 1\leavevmode\nobreak\ {\rm cm}^{2}/{\rm g}$ [4]. It is apparent
that the limit on $\sigma_{\chi\chi}$ itself is significantly weakened if DM
is clustered into composite states with large masses $m_{\rm DM}$.

If the dark sector has strong self-interactions, it would undergo a
nucleosynthesis process in the early universe much like the nuclei of the
standard model (SM), whereby individual particles coalesce to form large
composite states [6, 7]. SM nucleosynthesis suffers from a number of
theoretical accidents (such as the deuterium bottleneck) that render certain
light elements unstable and thereby inhibit the production pathway of ultra-
heavy elements. Still, the SM manages to produce large composite systems [8].
It is thus not surprising that a completely unconstrained dark sector could
also produce large composite objects. We will refer to these composite states,
which can easily be much heavier than $10^{24}\leavevmode\nobreak\ {\rm GeV}$,
as ultra-heavy dark matter [9, 10].

Direct searches for canonical DM in the form of a gas of small particles
leverage the large influx of these particles in a detector to compensate for
their small cross section with SM particles. For example, about $10^{16}$
weakly interacting massive particles (WIMPs) of mass 100 GeV would pass
through a ${\rm m}^{3}$ detector in a year, allowing for the direct detection
of WIMP-nucleon scattering cross sections as low as $10^{-45}\text{ cm}^{2}$
[11]. UHDMs, on the other hand, would arrive with significantly lower flux and
require a different detection strategy. Thus, an experimental strategy for
UHDM detection should leverage generic signatures of large composite objects
instead of focusing on the specifics of any one composite DM model, as the
rich dynamics of an interacting dark sector can produce a plethora of models.
Accordingly, we focus here on the fact that the many constituent particles of
a UHDM will enhance its cross section with SM matter such that each rare UHDM
incidence could result in a spectacular (and possibly lethal [12]) event with
a distinct signature imitated by no SM effect. The detector sensitivity is
therefore less important in such scenarios and can be traded for greater
exposure that maximizes the probability of a rare UHDM transit. In this paper,
our primary focus is to establish the detectability of such a signal. While we
provide an example of a DM model that yields such a signal, it is
straightforward to construct other examples of ultra-heavy particles that can
cause similar damage (e.g., Q-balls [13], charged primordial black hole relics
[14]).

Damage tracks left by particles passing through the Earth over geological
times could be recorded by ancient rock samples buried underground. For this
reason, such geological samples have been proposed and used as "natural
particle detectors" in the past, including for magnetic monopoles [15, 16, 17,
18, 19, 20, 21, 22], macroscopically large DM [23], WIMPs [24, 25, 26, 27, 28,
29, 30], and neutrinos [31, 32]. The geological exposure times of ancient rock
detectors range from the present back to the time they were last heated
naturally to the point of annealing, which can be up to $\sim 10^{9}$ years
and is thus much longer than typical DM direct detection laboratory
experiments (by factors of up to $10^{9}$). This advantage makes geological DM
detectors ideal probes of sparser, higher-mass composite DM. As we discuss in
Sec. II, searches with $10\leavevmode\nobreak\ {\rm m}^{2}$ of billion-year
old rock would probe DM masses up to $m_{\rm DM}\sim
10^{28}\leavevmode\nobreak\ {\rm GeV}$. A major challenge for such a detection
strategy is the ability to efficiently identify DM signatures in a large
volume of rock and distinguish them from geological, radioactive, and cosmic
ray backgrounds. Such discrimination is significantly simpler in searches for
UHDMs, since the extremely long and continuous cylindrical damage patterns
they generically leave are qualitatively different from the sporadic defects
due to expected backgrounds.

Here, we assess the use of geologically old quartz samples as solid-state
particle detectors to search for damage tracks left by UHDMs. Quartz, a
crystalline polymorph of silica SiO2, is one of the most abundant and well-
studied minerals in the lithosphere [33]. Defects and damage tracks can be
resolved down to the micron scale with SEM-CL: a scanning electron microscope
(SEM) combined with a cathodoluminescence (CL) detector. Imaging provided by
the SEM is supplemented with spectral information from CL, which reveals the
nature of trace elements and point defects in the quartz [34]. This modality
has already proved successful at providing answers to key geological questions
[35, 36, 37, 38, 39, 40, 41]. The technical advantages of SEM-CL mapping, as
well as the considerable literature on its application in quartz, make it an
appropriate choice for our readout method.

Note that a similar search for long damage tracks was performed by Price and
Salamon [22] in ancient mica crystals with null results. While they used this
result to constrain the abundance of magnetic monopoles, the experiment is
also sensitive to UHDMs with masses $m_{\rm DM}\lesssim 10^{26}\,{\rm GeV}$
[42, 43]. Mica is a crystalline mineral with almost perfect basal cleavage,
offering efficient sample preparation. However, the readout method used in
their experiment requires acid etching prior to microscopy in order to enlarge
damage tracks and render them visible in an optical microscope. Such an
etching process also enlarges background signals in the form of naturally-
occurring lattice defects. Hence, the success of the experiment hinges on the
low level of background in the samples and its scalability is limited by the
availability of sufficiently pristine mica crystals. By contrast, the lack of
etching in our proposed SEM-CL readout and the more readily available quartz
mineral that meets our requirements allow us to scan over larger sample areas
and extend the search pioneered by Price and Salamon to higher DM masses.

The rest of the discussion is organized as follows. In Sec. II we present an
experimental realization of the UHDM detection method sketched above, identify
optimal samples, and assess its model-independent sensitivity. We then
demonstrate its ability to probe a simple composite UHDM model, taking into
account various existing constraints, in Sec. III. Finally, we conclude in
Sec. IV.

##  II Detection Feasibility

In this section, we investigate experimental issues for UHDM detection with
quartz. Based on the considerations below, we establish the criteria for UHDM
signatures to be robustly detectable with microscopy of about
$\text{\,}\mathrm{\SIUnitSymbolMicro m}$-resolution. We discuss the discovery
reach of this approach in Sec. II.4 (see equations (2)-(4)).

Figure 1: Schematic of the proposed readout method. (a) A quartz sample of
size $\sim{\rm cm}^{3}$. The black straight line illustrates a damage track as
a result of an ultra-heavy composite dark matter (UHDM) particle passing
through the sample. The sample is sectioned into multiple sections of
thickness $\sim 100\leavevmode\nobreak\ $\text{\,}\mathrm{\SIUnitSymbolMicro
m}$$. We show several sections where the top and bottom surfaces are
highlighted, which would be scanned using SEM-CL. (b) Correlated damage spots
of micron-scale diameter over a macroscopic (mm-scale or longer) distance,
between sections is the unique signature of the ultra-heavy DM particle
interaction with quartz. Note that the probability of background features
coincidently aligning reduces exponentially with the number of correlated
layers. For a realistic feature density of $1000/{\rm cm}^{2}$, simulations
show that correlations of 4 layers efficiently rejects false positive signals.

###  II.1 Damage Tracks

Solid-state systems [44, 45, 46] have been used as particle track detectors
with applications ranging from nuclear science to geophysics, as such tracks
yield information about the history of the sample and properties of the
impinging particles [47]. For example, DM detection using crystal damage
tracks has been proposed as a directional signal in semiconductors such as
diamond, where a WIMP scattering event would give rise to damage tracks of
$\sim\leavevmode\nobreak\ 30-100\leavevmode\nobreak\ {\rm nm}$ in length; the
directional information in these tracks could enable such a detector to probe
below the "neutrino floor" [48, 49]. Paleodetection, which looks for damage
tracks of a similar size in ancient rock samples, has also been investigated
for WIMP detection [28, 29, 30].

We propose using ancient quartz as a detector for ultra-heavy composite dark
matter (UHDMs). As we discuss in Sec. II.4, each UHDM could deposit enough
energy to locally melt nearby quartz along its trajectory. Since quartz
nucleation under ambient conditions is a very slow process [50], the melted
region would solidify into amorphous silica without recrystallizing. Detecting
such amorphous micro-regions within quartz samples is feasible with SEM-CL,
where defects in the tetrahedrally coordinated SiO2 microstructure contribute
to CL emission [51]. Even in the absence of melting, the same SEM-CL method
would in principle be sensitive to linear tracks of lattice distortions left
by UHDMs. However, quantitatively characterizing the sensitivity of this
method to such tracks requires further study of the backgrounds in natural
quartz, which we leave for future work. Thus, in what follows we focus on
detecting UHDMs that can cause melting.

###  II.2 Quartz Samples and Backgrounds

The signature of the proposed UHDM detection method is a long damage track, of
micron-scale cross section, extending through the entire length of the quartz
sample (see Figure 1a). This signature has the distinct advantage that no
known mechanism produces such a track, allowing for strong geometric rejection
of background signals. A variety of effects may induce localized disruption of
the crystal lattice on the micron scale, such as extended growth defects or
radioactive decays, but these localized features cannot pass through the
entire macroscopic crystal. And although particles with low interaction
probability (e.g., neutrinos or relativistic cosmic rays) can pass through an
entire sample, their low nuclear cross sections yield dispersed individual
damage events rather than a continuous, micron-scale-diameter track. The
density of atmospheric neutrino-induced damage tracks falls off exponentially
with the track length, with essentially zero density of tracks longer than a
few mm [32]. Note that the imparted energy per unit length along such tracks
is much lower than the robust detection threshold; however, if detected, they
can be rejected as a UHDM signal due to the lack of correlation throughout the
full $\sim$ cm extent of the sample.

Fractures induced by historical geological stresses could similarly pass
continuously through an entire sample, but would in general be two- or three-
rather than one-dimensional, and would not leave behind amorphous quartz
within the damage track. Geologically-induced single line defects might also
be present in quartz samples, however, at smaller scales, only observable by
transmission electron microscopy (TEM) [52] or atomic force microscopy (AFM).
So these features are not relevant backgrounds for the proposed readout.

To take advantage of the distinctive extended geometry of a UHDM signal, we
propose a multi-phase scanning readout, where we search for correlated feature
positions at multiple depths in the sample (see Figure 1). This allows us to
reject backgrounds, which have an exponentially suppressed likelihood of lying
along a single line (as shown by simulations discussed in Figure 1). An
expected background signal, given the imaging resolution of our method, is
from the presence of radioactive isotopes such as uranium, which lead to
fission tracks and alpha recoil damage within the crystal lattice. These
processes leave behind halos of size $\sim\leavevmode\nobreak\
10\leavevmode\nobreak\ $\text{\,}\mathrm{\SIUnitSymbolMicro m}$$ [53], which
are readily detectable using our proposed SEM-CL protocol (see Figure 2d). In
a single two-dimensional SEM-CL scan, these could mimic a UHDM damage track,
but would be disqualified as UHDM signals by lack of correlated damage in
subsequent slices. The presence of some radioactivity-induced features is
potentially beneficial to our analysis, as their preservation would indicate
that recent annealing events would not have removed older, UHDM-induced
features. As such, if the fission track age can be determined from the host
quartz, the absence of UHDM-induced features implies the lack of UHDM
interaction events since the time of occurrence of the fission track.

Quartz samples with low impurity levels are essential for reducing background
levels. High-resolution cathodoluminescence (CL) studies reveal both the
microstructure of the samples and trace element inclusions. Titanium (Ti) and
aluminum (Al) are the two of the most abundant impurities in quartz. Ti is the
dominant CL activator while Al is not generally considered an activator [54,
37]. Trace element studies show that quartz samples of different geological
origins have a wide range of Ti and Al concentrations. Low-temperature
hydrothermal vein quartz (HVQ) has the lowest trace element concentrations:
quartz typically has a Ti concentration of a few 100 ppm; but this number
could be as low as 6 ppm for an HVQ sample, which simultaneously has a low Al
concentration [55, 41]. Here, we characterize preliminary measurements to
demonstrate that low-Ti vein quartz samples are a suitable choice for our
proposed experiment (see Figure 2).

Figure 2: Example quartz sample characterization. SEM-CL images of two
samples, (a) magmatic quartz from Bishop Tuff with Ti concentration $51\pm 6$
ppm, and (b) vein quartz from Jack Hills with Ti concentration $5.2\pm 6.5$
ppm, measured on a mass spectrometer. The scan rate is $20\leavevmode\nobreak\
{\rm s}/{\rm mm}^{2}$ with $1.5\leavevmode\nobreak\
$\text{\,}\mathrm{\SIUnitSymbolMicro m}$$ resolution for magmatic quartz and
$5\leavevmode\nobreak\ {\rm s}/{\rm mm}^{2}$ with $3\leavevmode\nobreak\
$\text{\,}\mathrm{\SIUnitSymbolMicro m}$$ resolution for vein quartz (we
forecast the full-scale UHDM experiment time and resources using these
values). In (b) we identify a few high-count pixels in the vein quartz image,
which demonstrates the possibility of high-resolution detection of
concentrated CL emission. The inset shows a zoomed-in image of the region of
interest with high-count pixels. These pixels could be a melting track
intersection, which needs to be investigated by correlating multiple sections
as described in the text. (c) Normalized histogram of the pixel counts in
arbitrary units for each of the two sample SEM-CL images. Vein quartz shows a
lower CL noise level as well as smaller variation, making it a suitable target
for our detection proposal. (d) SEM-CL signal from a uranium halo (measured in
a different quartz sample from those shown in (a) and (b)). Microscopic
uranium inclusions have decayed over time; the fission products from these
inclusions create crystal lattice damage, which emits cathodoluminescence (CL)
upon excitation by the SEM. The CL signal from an ultra-heavy composite dark
matter (UHDM) particle track would also result from crystal lattice defects at
and around the track of melted quartz. Any such uranium halos in a UHDM search
would be disqualified as potential damage tracks by lack of correlated damage
in other slices of the sample.

We note that any mineral deposits with comparable geological history and
suitability for low-background CL scanning could in theory serve as a target
in a UHDM search. However, HVQ is well suited for a high sensitivity search:
it is available in large quantities with high purity and crystal homogeneity
from deposits with well characterized geological history. Hydrothermal fluid
flow is commonly localized along fracture systems, fault systems, and shear
zones that can produce vast arrays of quartz veins. When a fracture or fault
remains open and under hydrothermal pressure for a sufficient period of time,
hydrothermal vein quartz grows as large, euhedral, and high-purity crystals.
These properties will enable us to analyze a large net exposure with the
proposed protocol, using serial sectioning and SEM-CL scanning of large
samples, with background rejection via correlation of damage spots across
layers (see Figure 1b).

HVQ from the Jack Hills of Western Australia is an ideal source of quartz for
the DM search. The siliciclastic units at Jack Hills contain numerous, large
quartz veins that appear as prominent surface features (i.e., clusters of
milky white outcrops that can form very localized topographic highs) observed
throughout the range. The veins are generally either undeformed or very weakly
deformed, and often show an abundance of high-purity, gem-quality quartz
crystals. These HVQ systems can reach impressive sizes at several locations
within the Jack Hills from cm-scale to 50 meters wide [56]. Several of the
vein systems can be followed for several kilometers and appear to be
associated with major episodes of brittle faulting. The combined work of
Rasmussen et al. [57] and Spaggiari [58] provide strong evidence that units
(including the hydrothermal quartz veins) at Jack Hills, particularly in the
vicinity of the "classic" W74 location, have likely remained at temperature
conditions less than 330-420 ∘C for $\sim$ 1.7 Gyr. The fact that the tectonic
environment can be evaluated in detail [59, 60, 61, 58] (including thermometry
and age dating) and consistently demonstrates equilibria at such low
temperature (i.e., at or below greenschist facies), is to the best of our
knowledge unique to Jack Hills, making it an ideal source of HVQ for our
proposed measurements.

###  II.3 Experimental Protocol

The proposed experimental protocol is as follows:

  1. 1.

Identify quartz samples that are (i) old, having last annealed no less than 1
Gyr ago; and (ii) clean, with low CL noise level and less than a few thousand
micron-scale resolved CL features per cm2.

  2. 2.

Prepare about $10^{4}$ samples of size $\sim{\rm cm}^{3}$ that satisfy the
above conditions and prepare each of the samples into sections of thickness
$\sim 100\leavevmode\nobreak\ $\text{\,}\mathrm{\SIUnitSymbolMicro m}$$ (see
Figure 1a). Polish the top and bottom surfaces of each section, then scan them
with SEM-CL.

  3. 3.

Search for correlated damage spots, across the first few sections, that are
aligned, section-to-section, along a straight line (see Figure 1b).

  4. 4.

If such a damage track of interest is identified, perform a dedicated search
in subsequent sections to reject false positives.

  5. 5.

Repeat steps 3 and 4 for all the ${\rm cm}^{3}$ samples.

To prepare HVQ samples for SEM-CL analysis we perform a standard petrographic
polishing preparation. Conventional polishing, using successive SiC powders
ranging from 240-1200 ANSI111American National Standards Institute grit sizes
($\sim$10 minutes per grit) are used to gradually reduce surface topography.
SiC polishing is followed by a series of automated polishing stages on a
MiniMet polishing/grinding unit, proceeding from 3 to 1 to 0.1 micron Al2O3
grits ($\sim$30-60 mins per grit, with $\sim$1 minute of ultrasonic bathing
between grits). As these polishing stages are generally done on automated or
semi-automated systems, large volumes of material can be processed. The
effects of polishing on the quartz surface is negligible for most aspects of a
UHDM search; there may be some localized damage to the near surface
environment, restricted to the first few nm [62], whereas SEM-CL typically
probes about $1\leavevmode\nobreak\ $\text{\,}\mathrm{\SIUnitSymbolMicro m}$$.

Additionally, polishing and SEM scanning should not significantly heat the
sample. Paleomagnetic studies on ancient rock samples show that the
magnetization, which would change under heating by only a few tens of degrees,
remains unchanged after polishing [63]. While SEM interrogation may induce
some heating for macroscopic, microns-thick samples such as we propose here,
such heating should be limited to $\sim 10^{\circ}{\rm C}$ [64, 65]–especially
with appropriately chosen SEM beam parameters. SEM-CL can therefore be
considered a non-destructive readout method.

Alternative methods –including high resolution computed tomography x-ray (CT)
or superresolution optical microscopy– offer sufficiently high resolution to
measure UHDM-induced damage tracks, as well as the prospect of three-
dimensional imaging. However, these methods generally require much longer scan
times than SEM-CL, as well as method-specific constraints such as sample size
restrictions or synchrotron beam availability. If correlated damage spots in
serially-sectioned quartz slabs are identified by the proposed SEM-CL readout,
follow-up experiments on the same sample could be pursued (due to the non-
destructive nature of the SEM technique); e.g., 3D imaging using techniques
such as CT or laser scanning confocal microscopy at different wavelengths.

The scanning rate with SEM-CL depends on sample properties such as the
concentration of CL activators. Given a typical data acquisition time of
$\sim$ 100 min per ${\rm cm}^{2}$ with $\text{\,}\mathrm{\SIUnitSymbolMicro
m}$ resolution (for example see Figure 2), we plan the experiment in three
stages:

  * •

Quartz-$1\,{\rm m}^{2}$: About two years of experiment time with four SEM-CL
apparatuses will be required to scan samples with a total area of about 1 m2.
The total quartz exposure of $\sim 1\,{\rm m}^{2}\,{\rm Gyr}$ for such a
search would probe UHDMs of mass $m_{\rm DM}\lesssim
10^{27}\leavevmode\nobreak\ {\rm GeV}$. This first stage search would probe a
currently unconstrained mass range with a new technique; see Figure 3.

  * •

Quartz-$10\,{\rm m}^{2}$: 20 SEM apparatuses running for about four years
would provide a total quartz exposure to UHDMs of $\sim 10\,{\rm m}^{2}\,{\rm
Gyr}$, yielding sensitivity $m_{\rm DM}\lesssim 10^{28}\leavevmode\nobreak\
{\rm GeV}$.

  * •

Quartz-$100\,{\rm m}^{2}$: 100 SEM apparatuses running for about eight years
would provide a total quartz exposure to UHDMs of $\sim 100\,{\rm m}^{2}\,{\rm
Gyr}$, yielding sensitivity $m_{\rm DM}\lesssim 10^{29}\leavevmode\nobreak\
{\rm GeV}$.

###  II.4 Model-Independent Sensitivity

The proposed experiment would be sensitive to a wide range of ultra-heavy dark
matter (UHDM) candidates, independent of the underlying dark sector
microphysics, that (1) pass through the quartz sample with sufficiently high
probability while (2) depositing enough energy in a sufficiently concentrated
way to melt a micron-size lateral region.

Given a DM candidate of mass $m_{\rm DM}$, we can estimate the expected number
of DM transits in a sample of area $L\times L$ over a duration $T$ to be

$N\sim 1\left(\frac{10^{29}\text{ GeV}}{m_{\rm
DM}}\right)\left(\frac{L}{10\,{\rm m}}\right)^{2}\left(\frac{T}{10^{9}\text{
year}}\right)$ (1)

based on the local DM density, $\rho_{\rm DM}\approx 0.3\,{\rm
GeV}/\text{cm}^{3}$. As described in the previous sections, the quartz samples
under consideration are roughly $T\sim 10^{9}\text{ year}$ old, and a 100
${\rm m}^{2}$ sample area can be scanned in stage three. The requirement that
$N\gtrsim 1$ imposes an upper bound on the UHDM mass, $m_{\rm DM}\lesssim
10^{29}\text{ GeV}\sim 100\text{ kg}$. The advantage afforded by the large
exposure of such a long-lived sample is manifest.

An UHDM moving through the Earth will collide with and deposit energy to SM
particles along its path. The energy $E_{1}$ imparted to each SM nucleus can
go as high as the kinematical limit of $10\leavevmode\nobreak\ {\rm keV}$
(corresponding to nuclei acquiring twice the velocity of the UHDM in a
collision) depending on how elastic these collisions are, while the stopping
power $dE/dx$ depends on $E_{1}$ as well as the UHDM radius. For simplicity,
we assume in our estimates that the UHDM travels at least a few kilometers
deep into the Earth’s surface while maintaining its Milky Way virial velocity
of $v_{\rm DM}\sim 10^{-3}c$. This amounts to an upper bound on the energy
deposition rate

$\frac{dE}{dx}\lesssim 10^{13}\frac{{\rm
MeV}}{$\text{\,}\mathrm{\SIUnitSymbolAngstrom}$}\left(\frac{m_{\rm
DM}}{10^{29}\text{ GeV}}\right).$ (2)

Most of the deposited energy will likely go to SM nuclei. Only a tiny portion
will go directly to electrons, whose low mass limits their kinetic energy gain
(for kinematics reasons) and whose coupling to DM is severely limited by
astrophysical and cosmological constraints [66]. The nuclei and electrons will
then thermalize, leading to a loosening of molecular bonds as the electrons
acquire more energy, and eventually cause melting. Due to thermal diffusion,
the melted region will enlarge and cool. What ultimately remains, in the case
of quartz, is a long cylindrical trail of amorphous silica, precisely the kind
of damage that is detectable with the method outlined above.

In order to leave a robustly detectable damage trail, the UHDM must deposit
sufficient energy per unit length $dE/dx$ exceeding the required latent heat
to melt each unit-length segment of a micron-radius cylinder. This amounts to
a $dE/dx$ threshold for robust detection of

$\frac{dE}{dx}\gtrsim\frac{{\rm
MeV}}{$\text{\,}\mathrm{\SIUnitSymbolAngstrom}$}\,.$ (3)

See Figure 3a for model-independent sensitivity projections. Further, since
quartz has a melting point of $10^{4}\leavevmode\nobreak\ \rm K\sim
1\leavevmode\nobreak\ {\rm eV}$ and energy tends to spread outward, the energy
deposition must be sufficiently localized that the energy $E_{1}$ gained by
each nucleus is greater than the melting temperature, i.e. it must lie in the
range

$1\,{\rm eV}\lesssim E_{1}\lesssim 10\,{\rm keV}$ (4)

where the upper bound is the kinematical limit for energy transfer per nucleus
(with mass number $A\sim 10$).

Figure 3: Sensitivity projections for the proposed ultra heavy dark matter
(UHDM) search. (a) Model-independent reach of the geological-quartz detector
proposal expressed as stopping power $dE/dx$ vs mass $m_{\rm DM}$ of a passing
UHDM particle, together with the existing constraints from MACRO for energy
deposition per nucleus $E_{1}\sim 1\leavevmode\nobreak\ {\rm eV}$ [67, 68] as
well as from damage track searches in ancient mica [22]. The vertical and
slanted boundaries of the quartz-detectable parameter space (for different
effective detector areas) stem from the requirements of an $O(1)$ probability
of transit, Eq. (1), and a negligible slowing of the UHDM up to a $1\text{
km}$ depth, Eq. (2), respectively. The black horizontal line indicates the
melting threshold for a micron-sized lateral region, Eq. (3), above which
robust detection is possible. (b) Parameter space of the UHDM model considered
in Sec. III. Left: reach on coupling $g_{\rm n}$ vs DM mass $m_{\rm DM}$.
Right: reach on coupling $g_{\rm n}$ vs mediator mass $m_{\phi}$. Also shown
are existing constraints from ancient mica [22], fifth force experiments [66],
and stellar cooling of SN1987A [66] and horizontal branch (HB) stars [66]
(note that the stellar cooling bounds are model-dependent [69]). In these
$g_{\rm n}$ plots, we set $g_{\chi}$ to its upper bound
$m_{\phi}/\Lambda_{\chi}$ from Eq. (14).

##  III Example UHDM Model

In this section, we consider an example of a simple, ultra-heavy composite
dark matter (UHDM) state [10] that can give rise to the desired damage tracks
while being consistent with existing experimental and observational
constraints. These composite objects consist of $N_{\chi}$ dark fermions
$\chi$ whose mass, inverse size, and binding energy to form the UHDM are
determined by a single scale $\Lambda_{\chi}$. It follows that they have mass
$m_{\rm DM}\sim N_{\chi}\Lambda_{\chi}$ and size $R\sim
N_{\chi}^{1/3}\Lambda_{\chi}^{-1}$. We assume that the fermions $\chi$
interact with standard model nucleons $\psi_{\rm n}$ through a
repulsive222Attractive DM-nucleon interactions are just as compelling as the
repulsive interaction considered here. We note that the attractive
interactions might have more complicated dynamics as nuclei may get trapped
and accumulate inside the UHDM. See e.g. [70]. Yukawa interaction mediated by
a scalar $\phi$ of mass $m_{\phi}$:

$-\mathcal{L}\supset\frac{1}{2}m_{\phi}^{2}\phi^{2}+g_{\rm
n}\phi\bar{\psi}_{\rm n}\psi_{\rm n}-g_{\chi}\phi\bar{\chi}\chi\,.$ (5)

We show that UHDMs with the following properties satisfy the robust
detectability criteria detailed in Sec. II.4 without running afoul of any
existing constraints:333Due to various constraints, this parameter space has a
complicated geometry. Here we simply identified the lower and upper limits for
each parameter.

$\displaystyle 10^{26}\,{\rm GeV}\lesssim$ $\displaystyle m_{\rm DM}\lesssim
10^{29}\,{\rm GeV}$ (6) $\displaystyle 10\text{ nm}\lesssim$ $\displaystyle
R\lesssim 1\text{ cm}$ (7) $\displaystyle 0.1\,{\rm eV}\lesssim$
$\displaystyle m_{\phi}\lesssim{\rm MeV}\,\leftrightarrow\,\,10^{2}\text{
fm}\lesssim m_{\phi}^{-1}\lesssim 1\,$\text{\,}\mathrm{\SIUnitSymbolMicro m}$$
(8) $\displaystyle 100\,{\rm keV}\lesssim$
$\displaystyle\Lambda_{\chi}\lesssim 10\,{\rm GeV}\,.$ (9)

This allows us to probe wide ranges of the couplings $g_{\rm n}$ and
$g_{\chi}$. Two slices of this parameter space are shown in Figure 3b. Eq. (6)
follows from Eq. (1) and ancient mica constraints; Eq. (7) follows from (3),
(4), (13), and the quartz sample size of 1 cm; Eq. (8) follows from fifth
force constraints and the requirement that the UHDM-nucleus interaction be
treated classically; Eq. (9) follows from Eqs. (6) and (7).

###  III.1 Detectability with Quartz

The optimal UHDM detection signature is expected for mediators with a range
$m_{\phi}^{-1}$ satisfying $\Lambda_{\chi}^{-1}\ll
m_{\phi}^{-1}\lesssim$\text{\,}\mathrm{\SIUnitSymbolMicro m}$$, since this is
the intermediate regime where the UHDM-nucleon coupling is enhanced by the
number of constituents $\chi$ of the UHDM within the range of the mediator
$(m_{\phi}^{-1}/\Lambda_{\chi}^{-1})^{3}$ while simultaneously evading
existing fifth force constraints. For simplicity of analysis we only consider
part of the parameter space where $m_{\phi}^{-1}\ll R$. In doing so, we limit
the UHDM’s cross section to be at most geometrical.

An SM nucleus located inside the UHDM only sees the composite DM particle’s
constituents $\chi$ within the range of the mediator $m_{\phi}^{-1}\ll R$.
Hence, to the SM nucleus each point in the bulk of the UHDM is just like any
other, yielding a potential energy $V(r)$ as a function of the distance $r$
from the center of the UHDM with the following profile:

$V(r)=\begin{cases}+V_{0},&r<R\\\ 0,&r>R\end{cases}$ (10)

where at the boundary $r\approx R$ the potential drops to zero exponentially
over a length scale of order $m_{\phi}^{-1}$, and

$\displaystyle
V_{0}\sim\left(\frac{\Lambda_{\chi}}{m_{\phi}}\right)^{3}\frac{g_{\chi}(10g_{\rm
n})}{m_{\phi}^{-1}}$ (11)

for SM nuclei with mass number $A\sim 10$. As a result, from the perspective
of a nucleus the UHDM is just a constant potential hill moving at a velocity
$v_{\rm DM}\sim 10^{-3}c$.

Since the de Broglie wavelengths $(10\,{\rm MeV})^{-1}$ of the SM nuclei are
smaller than the mediator ranges $m_{\phi}^{-1}$ of interest, we can treat the
UHDM-nucleus interactions classically. When $V_{0}\gtrsim 10\,{\rm keV}$, the
potential $V_{0}$ prevents any nucleus from entering the UHDM. The UHDM-
nucleus collisions are thus elastic, and the energy $E_{1}$ transferred to a
nucleus saturates the kinematical limit $E_{1}\sim 10\,{\rm keV}$. If
$V_{0}\lesssim 10\,{\rm keV}$, on the other hand, the nuclei can easily climb
the potential hill, and the collisions between a nucleus and the UHDM’s
surface will be inelastic. When a nucleus encounters the surface of the UHDM,
it receives a force $F\sim V_{0}/m_{\phi}^{-1}$ due to the gradient of the
Yukawa potential. This force is exerted throughout the duration $\tau\sim
m_{\phi}^{-1}/v_{\rm DM}$ of the collision, resulting in a nearly-
instantaneous momentum kick $p_{1}\sim F\tau$ which translates to the kinetic
energy $E_{1}\sim 10\,{\rm keV}\left(V_{0}/10\,{\rm keV}\right)^{2}$ per
nucleus. To sum up, the energy imparted to a nucleus after the passage of a
UHDM is

$E_{1}\sim 10\,{\rm keV}\times\text{min}\left[1,\left(\frac{V_{0}}{10\,{\rm
keV}}\right)^{2}\right].$ (12)

Using a lattice spacing of about $5$\text{\,}\mathrm{\SIUnitSymbolAngstrom}$$
for quartz, the energy deposition rate then follows:

$\frac{dE}{dx}\sim\frac{E_{1}}{5$\text{\,}\mathrm{\SIUnitSymbolAngstrom}$}\left(\frac{R}{5$\text{\,}\mathrm{\SIUnitSymbolAngstrom}$}\right)^{2}.$
(13)

Having linked the model parameters with the quantities characterizing quartz
damage tracks, the detectable parameter space can be evaluated based on the
considerations in Sec. II.4 (see Figure 3b).

###  III.2 Existing Constraints

####  III.2.1 The mediator

Past experiments and observations have placed limits on the coupling $g_{\rm
n}$ of the mediator $\phi$ to standard model nucleons with varying severity
for different masses $m_{\phi}$ of the mediator. These include: collider
constraints on the meson decay rate, laboratory fifth-force searches, and
stellar cooling bounds from observations of the SN1987A event and horizontal
branch (HB) stars. Note, however, that the stellar cooling bounds are model-
dependent [69]. The following parameter space is thus ruled out [66]:

  * •

Meson decay: $g_{\rm n}\gtrsim 10^{-6}$, $m_{\phi}\lesssim 100\,{\rm MeV}$.

  * •

Fifth force: $g_{\rm n}\gtrsim 10^{-12}(m_{\phi}/{\rm eV})^{3}$,
$m_{\phi}\lesssim 100\,{\rm eV}$.

  * •

SN1987A: $3\times 10^{-10}\lesssim g_{\rm n}\lesssim 3\times 10^{-7}$,
$m_{\phi}\lesssim 30\,{\rm MeV}$.

  * •

HB stars: $g_{\rm n}\gtrsim 10^{-13}$, $m_{\phi}\lesssim 100\,{\rm keV}$.

Furthermore, the couplings of UHDM constituents $\chi$ to the mediator $\phi$
add extra self-interactions among $\chi$ that may destabilize the UHDM. In
order for the UHDM to be stable the mediated self-interaction potential
$g_{\chi}^{2}\Lambda_{\chi}^{3}m_{\phi}^{-2}$ of a single $\chi$ must not
exceed the binding energy $\Lambda_{\chi}$. This puts an upper bound on the
coupling $g_{\chi}$ of $\chi$ to the mediator $\phi$:

$g_{\chi}\lesssim\frac{m_{\phi}}{\Lambda_{\chi}}.$ (14)

####  III.2.2 Direct detection

Of the currently and previously running direct-detection DM experiments, MACRO
puts a strong constraint on our scenario due to its large volume. MACRO is a
scintillator experiment with exposure of about $10^{3}\text{ m}^{2}\times
10\text{ years}$ corresponding to $m_{\rm DM}\lesssim 10^{22}\,{\rm GeV}$ for
1 event over its decade-long lifespan. It is sensitive to energy depositions
$\gtrsim 10\,{\rm MeV}/{\rm cm}$ to electrons [67]. When a nucleus receives
energy $E_{1}$ from interaction with a UHDM, only some fraction $Q(E_{1})$,
called the quenching factor, of that energy effectively goes to the electrons
tied to the nucleus. It is this relatively small fraction of energy that is
responsible for the processes of scintillation and ionization that may occur
subsequently. We can translate MACRO’s $10\,{\rm MeV}/{\rm cm}$ detection
threshold to a sensitivity to nuclear energy depositions via effecting an
increase by the quenching factor $Q(E_{1})$ [68].

An even more stringent bound on our model arises from direct searches for long
damage tracks in muscovite mica crystals [22]. The non-observation of tracks
extending beyond naturally occurring defects and radioactivity damage was
originally used to constrain the abundance of magnetic monopoles, but also
limits the UHDM parameter space. This past mica search involved total sample
area $\sim 1200\leavevmode\nobreak\ {\rm cm}^{2}$ with sample ages $\simeq
5\times 10^{8}\,{\rm yr}$, corresponding to a DM reach of $m_{\rm DM}\lesssim
10^{26}\leavevmode\nobreak\ {\rm GeV}$. The energy deposition threshold for
detection in this experiment via etching and optical microscopy was identified
as $dE/dx\gtrsim 6\leavevmode\nobreak\ {\rm GeV}/{\rm cm}$.

####  III.2.3 Astrophysical and Cosmological limits

Indirect limits can also be placed on the couplings $g_{\rm n}$ and $g_{\chi}$
from the limits on DM-baryon and DM-DM cross sections. DM-baryon interactions
in the early universe can affect baryon acoustic oscillations and is therefore
constrained by CMB and LSS observations. This puts an upper bound on the DM-
baryon momentum-transfer cross section that would be observed today:
$\sigma_{\chi\rm b}/m_{\rm DM}\lesssim 10^{-3}\text{ cm}^{2}/\text{g}$ [71].
Astronomical observations of the Bullet Cluster also place a limit on the DM-
DM momentum-transfer cross section: $\sigma_{\chi\chi}/m_{\rm DM}\lesssim
1\text{ cm}^{2}/\text{g}$ [4]. Since we are mainly interested in UHDMs with
geometrical cross sections of order $$\text{\,}\mathrm{\SIUnitSymbolMicro
m}$^{2}$ and masses up to $10^{29}\leavevmode\nobreak\ {\rm
GeV}(100\leavevmode\nobreak\ {\rm kg})$, these astrophysical and cosmological
observations only impose significant constraints on the low mass side of our
parameter space. Moreover, these constraints are alleviated if UHDMs
constitute less than $10\%$ of the total DM mass, in which case the maximum
detectable mass would also be lowered by an order of magnitude.

##  IV Conclusion and Outlook

Given the diverse range of theoretically well-motivated dark sectors, it is
critical to perform searches with techniques that are sensitive to a broad
class of dark-sector phenomena. In this paper, we propose a detection method
for ultra-heavy composite dark matter particles (UHDMs). Our proposed
experiment is based on mapping damage tracks in ancient quartz samples with
SEM-CL scanning. This method has two significant advantages: (1) the billion-
year exposure time of such samples enables us to probe DM candidates with
masses as high as $10^{29}\leavevmode\nobreak\ {\rm
GeV}(100\leavevmode\nobreak\ {\rm kg})$, surpassing the reach of existing
direct-detection experiments, and (2) the distinctly-long cylindrical damage
trails left by such UHDMs are easily distinguished from other features at the
relevant scales.

In this work, we focus on detecting long tracks of amorphous silica in quartz
samples expected from passing UHDMs that impart enough energy to cause
melting. In future work, we will consider the feasibility of extending the
experimental sensitivity to energy deposition rates below the melting
threshold. For that purpose, we intend to carry out a number of studies
including: (i) signal calibration by artificially creating damage tracks in
synthetic quartz samples with a high-power pulsed laser of variable intensity
and comparing it with the resulting CL signal levels; and (ii) noise
calibration by preparing a set of quartz samples, natural and synthetic, with
different concentrations of CL activators and analysing their CL emission
rates. These studies will provide us a better understanding of the signal-to-
noise ratio as seen in SEM-CL imaging, which will allow us to better estimate
the detection threshold.

We focus here on quartz as a promising target mineral for UHDM detection
because of the availability of abundant high-quality, old samples and the
suitability of SEM-CL as a high-resolution, fast readout method. However, any
mineral satisfying these two criteria is a potential target material;
identifying such targets is valuable in verifying putative UHDM signals in a
complementary search, possessing different systematics.

Our proposed experiment is largely agnostic to the detailed microphysics of
the dark sector, as long as it results in long damage tracks in geological
quartz. To demonstrate the projected reach of the proposed approach, we
considered a QCD-like dark sector that interacts with the standard model
repulsively via a light mediator. The particle spectrum of this theory
includes heavy bound states, composed of a large number of elementary dark
fermions, which could create interesting targets for detection. We identified
experimentally-detectable regions of the parameter space that satisfy various
limits derived from phenomenological considerations as well as past
observations. In future work, it would be interesting to delineate a broader
range of DM models than can lead to similar damage patterns in ancient rock.

###### Acknowledgements.

This work was supported by the DOE QuANTISED program under Award No. DE-
SC0019396; the Army Research Laboratory MAQP program under Contract No.
W911NF-19-2-0181; and the University of Maryland Quantum Technology Center. SR
is supported by the NSF under grant PHY-1818899, the SQMS Quantum Center and
DOE support for MAGIS.

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