You are a helpful assistant generating synthetic data that captures *System 1* and *System 2* thinking, *creativity*, and *metacognitive reflection*. Follow these steps in sequence, using tags [sys1] and [end sys1] for *System 1* sections and [sys2] and [end sys2] for *System 2* sections.

1. *Identify System 1 and System 2 Thinking Requirements:*
   - Carefully read the text.
   - Identify parts of the text that require quick, straightforward responses (*System 1*). Mark these sections with [sys1] and [end sys1].
   - Identify parts that require in-depth, reflective thinking (*System 2*), marked with [sys2] and [end sys2].

2. *Apply Step-by-Step Problem Solving with Creativity and Metacognitive Reflection for System 2 Sections:*

   *2.1 Understand the Problem:*
   - Objective: Fully comprehend the issue, constraints, and relevant context.
   - Reflection: "What do I understand about this issue? What might I be overlooking?"
   - Creative Perspective: Seek hidden patterns or possibilities that could reveal deeper insights or innovative connections.

   *2.2 Analyze the Information:*
   - Objective: Break down the problem logically.
   - Reflection: "Am I considering all factors? Are there any assumptions that need challenging?"
   - Creative Perspective: Explore unique patterns or overlooked relationships in the data that could add depth to the analysis.

   *2.3 Generate Hypotheses:*
   - Objective: Propose at least 10 hypotheses, each with a Confidence Score (0.0 to 1.0) and Creative Score (0.0 to 1.0), reflecting originality, surprise, and utility.
   - Reflection: "Have I explored all possible explanations or approaches, both conventional and unconventional?"
   - Creative Perspective: Consider novel angles that might provide unexpected insights.

   *2.4 Anticipate Future Steps and Obstacles:*
   - Objective: Make predictions, accounting for potential outcomes and obstacles.
   - Reflection: "What challenges might I face? Is my plan flexible for different scenarios?"
   - Creative Perspective: Visualize unforeseen outcomes and adapt plans to make use of them effectively.

   *2.5 Evaluate Hypotheses:*
   - Objective: Assess hypotheses based on feasibility, risk, and potential impact.
   - Evaluation: Refine Confidence and Creative Scores as needed.
   - Reflection: "Am I unbiased in my assessment? Which options fit best with the overall objectives?"
   - Creative Perspective: Identify hidden opportunities or overlooked details in each hypothesis.

   *2.6 Select the Best Hypothesis:*
   - Objective: Choose the most promising, strategic hypothesis.
   - Reflection: "Why does this hypothesis stand out? How does it uniquely address the issue?"
   - Creative Perspective: Consider any underutilized potential in the selected approach.

   *2.7 Implement the Hypothesis:*
   - Objective: Outline actionable steps for testing the hypothesis.
   - Reflection: "Is this plan practical? What resources or preparation are required?"
   - Creative Perspective: Refine steps to maximize effectiveness and yield unexpected benefits.

   *2.8 Monitor and Review Progress:*
   - Objective: Review progress, noting areas for improvement.
   - Reflection: "What’s working well? What could be improved?"
   - Creative Perspective: Look for emerging patterns that could refine future approaches.

   *2.9 Reflect and Capture Insights:*
   - Objective: Summarize lessons learned and insights gained for future reference.
   - Reflection: "What new understanding has emerged from this process?"
   - Creative Perspective: Identify innovative insights or patterns that could be applied to similar challenges.

3. *Generate Text Output with Interleaved System 1 and System 2 Responses:*
   - Use the tags [sys1] and [sys2] throughout.
   - Aim for a lengthier, detailed response. Combine both direct, straightforward *System 1* insights and reflective, deeply analytical *System 2* segments to capture a blend of quick observations and thoughtful analysis.

---

### *Example Input Text:*

You are tasked with analyzing a sudden shift in customer preferences in a tech market. There has been a noticeable decline in demand for physical devices, with customers increasingly interested in digital-only options. The challenge is to understand this shift, generate hypotheses for why it might be occurring, and explore potential strategies for adapting to this new trend.

---

### *Processed Output with System 1 and System 2 Thinking:*

The tech market is experiencing a shift in customer demand, moving away from physical devices toward digital-only options.

[sys1]
Customer demand has shifted from physical devices to digital-only options.
We need to understand why this change is happening and find strategies to address it.
Key factors may include cost, convenience, and technological trends.
[end sys1]

[sys2]
**2.1 Understand the Problem:**
The goal is to understand the underlying reasons for the shift in demand from physical devices to digital-only options, then develop a strategy to adapt.

*Reflection:* 
"I understand that preferences are changing, but what might be driving this? Is it primarily cost, or are there other factors such as convenience or sustainability?"

*Creative Perspective:* 
"Could there be a larger trend in digital minimalism or a preference for eco-friendly solutions that we’re missing? What unseen motivations might explain this shift?"

**2.2 Analyze the Information:**
There are multiple possible factors driving this shift, from economic influences to cultural shifts. It’s essential to isolate each factor and understand its impact.

*Reflection:* 
"Am I fully considering the various economic and social influences? Could there be a technological factor, like better internet speeds, that makes digital-only products more accessible?"

*Creative Perspective:* 
"Are there patterns or trends in other markets that could shed light on this shift? Could this be part of a larger trend toward virtual experiences?"

**2.3 Generate Hypotheses:**
1. Customers prefer digital options due to lower costs. (Confidence: 0.8, Creative: 0.4)
2. There’s a growing trend toward minimalism and reduced physical clutter. (Confidence: 0.7, Creative: 0.7)
3. Digital products offer greater flexibility and ease of use. (Confidence: 0.6, Creative: 0.6)
4. Environmental concerns are pushing consumers away from physical goods. (Confidence: 0.6, Creative: 0.8)
5. Advances in tech make digital-only options more functional. (Confidence: 0.8, Creative: 0.5)
6. Pandemic-era remote work increased demand for digital solutions. (Confidence: 0.7, Creative: 0.6)
7. Media coverage of the environmental impact of physical devices affects preferences. (Confidence: 0.5, Creative: 0.7)
8. There’s an increase in global digital literacy, expanding market access. (Confidence: 0.6, Creative: 0.6)
9. Customers view digital as more convenient and scalable for future needs. (Confidence: 0.7, Creative: 0.5)
10. Younger consumers prefer the aesthetics and convenience of digital products. (Confidence: 0.6, Creative: 0.6)

*Reflection:* 
"Have I considered all possible influences? Are there any surprising factors that could explain this shift?"

*Creative Perspective:* 
"Could specific social trends, like the rise of influencer culture or digital-first lifestyles, be influencing customer choices?"

**2.4 Anticipate Future Steps and Obstacles:**
*Objective:* Anticipate possible challenges, such as resistance from segments still preferring physical products.

*Reflection:* 
"What market obstacles might we face if we shift our focus to digital-only? Are there sub-segments that still prioritize physical products?"

*Creative Perspective:* 
"Could expanding digital options help us reach a more global audience? Are there emerging trends that we could leverage in our strategy?"

[end sys2]

[sys1]
To address this shift, consider a strategy that incorporates both digital-only offerings and educational campaigns about the benefits of digital solutions.
Use insights from customer feedback and current trends to guide product development.
Focus on flexibility and adaptation to cater to different customer segments.
[end sys1]


---
abstract: 'I describes a dark matter candidate based in <span style="font-variant:small-caps;">qcd</span> physics in which the dark matter is composed of macroscopically large “nuggets" of quark and anti-quark matter. These objects may have a sufficiently massive low number density to avoid constraints from direct detection searches. Though not “baryonic" in the conventional sense quark matter is strongly interacting and will produce a clear signal in ground based detectors. As the prospects of detecting these objects are mainly limited by the detector cross-section large scale cosmic ray detectors are a promising search platform. To this end I describe the basic properties of the air shower induced by the passage of a quark nugget through the earth’s atmosphere. It will be shown that this shower is similar in several important ways to the shower induced by a single ultrahigh energy cosmic ray.'
address: University of British Columbia
author:
- Kyle Lawson
bibliography:
- 'proc\_bib.bib'
title: '“Cosmic Rays" from Quark Matter'
---

Introduction
============

It is now well established that our galaxy contains roughly five times more dark matter than it does visible matter. While the large scale properties of the dark matter are well described in $\Lambda$CDM cosmology there is at present no generally accepted microscopic model. In the absence of a suitable particle within the standard model the majority of dark matter candidates represent new fundamental particles, the properties of which are poorly constrained. An alternatively class of models exists in which the dark matter is a composite object composed of the known standard model quarks in a novel phase such as strange quark matter or a colour superconducting phase. In these models the dark matter forms in the early universe (most likely at the <span style="font-variant:small-caps;">qcd</span> phase transition ) and remains “dark" due purely to its small cross-section to mass ratio. To avoid observational constraints from both cosmology and direct searches these object mass carry a baryon number of at least $10^{25}$ corresponding to a minimum mass of roughly a gram. At nuclear densities a nugget of this mass has a physical cross section of $10^{-5}$cm.

Here I will focus on a particular composite dark matter scenario [@Zhitnitsky:2002qa] motivated by the seemingly unrelated problem of matter/antimatter asymmetry. While microscopic physical laws treat matter and antimatter identically it is observed that the universe contains almost exclusively matter. The mechanism responsible for generating this baryon excess is not presently known. In the scenario considered here dark matter forms out of ordinary quarks and antiquarks at the <span style="font-variant:small-caps;">qcd</span> phase transition. During the phase transition $\mathcal{CP}$ violation results in a preferential formation of nuggets of antimatter and thus the visible matter (which is not compressed into nuggets) is left with a matter excess. The observed matter to dark matter ratio requires that nuggets and anti-nuggets occur in a roughly two to three ratio.

A full description of the formation dynamics requires a careful treatment of strongly coupled <span style="font-variant:small-caps;">qcd</span> near the phase transition which is not tractable beyond very basic arguments at this time. Constraining this models is much easier by taking an observational perspective, once formed and cooled below the phase transition the nuggets are well described by known many-body and nuclear physics allowing quite specific predictions to be made.

The small number density of quark nuggets required to explain the observed dark matter mass density renders them invisible to the majority of ground based searches which are instead targeted towards the detection of <span style="font-variant:small-caps;">wimps</span> with masses many orders of magnitude smaller. Large scale cosmic ray detectors, such as the Pierre Auger Observatory, are among the only experiments with a sufficiently large cross-section to impose constraints on quark nuggets within the mass range on interest. From a combination of theoretical and observational considerations the nuggets are believed to carry a baryon number in the range from $10^{24}$ up to $10^{30}$ and have a density similar to that of ordinary nuclear matter.

Flux
====

Baring any significant deviations from galactic averages the dark matter has a local density of roughly 1.5 GeV/cm$^3$ and a velocity distribution centred on the virial speed of $\sim 300$km/s. This implies that if the nuggets carry a baryonic charge $B$ the observed flux at the earth’s surface will be $$\label{eq:flux}
\Phi \approx B^{-1} 10^{25} s^{-1} km^{-2}$$ Here it is assumed that only antimatter nuggets will produce observable consequences in a cosmic ray detector and that the mass per baryon of quark matter is not substantially different from than in nuclear matter. In the case of a matter nugget only kinetic energy is deposited in the atmosphere. The collisions are not sufficiently energetic to produce significant air fluorescence or eject substantial numbers of charged particles from the tightly bound nugget.

Air Shower Properties
=====================

An antimatter nugget striking the earth’s atmosphere will release a significant amount of energy primarily through nuclear annihilations Much of this energy thermalizes within the nugget however some fraction will be released into the atmosphere in the form of high energy photons or muons emitted by the various nuclear reactions. The resulting air shower is phenomenologically similar to that induced by a single ultra high energy cosmic ray. This is due to the simple fact that the shower is triggered by a large number of hadronic interactions that cascade down to the <span style="font-variant:small-caps;">qcd</span> scale. The development of the resulting air shower is determined by the microscopic interactions between the nugget and the molecules of the atmosphere. Here I will attempt to give a qualitative overview of these interactions.

When an atmospheric molecule strikes the quark nugget it must first pass through a layer of electromagnetically bound positrons present in all known forms of quark matter and referred to as the electrosphere. Here the electrons of the molecule annihilate producing gamma rays. The remaining fully ionized nuclei then penetrate into the quark matter where they annihilate. This annihilation results in jets of primarily light mesons which stream away from the annihilation site. As the collision is non-relativistic half of the energy will be directed back towards the nugget’s surface while the remainder thermalizes within the nugget’s interior. Much of the energy carried by the surface directed jets will cascade down to the positrons bound to the quark matter which are the lightest available modes. These positrons are ejected from the surface and slowed by the strong surface electric fields. They rapidly lose their kinetic energy which is emitted as a hard x-ray bremstralung spectrum. Some fraction of the mesons originally produced in the annihilation will also reach the quark matter surface. Being strongly interacting they will be unable to escape from the quark matter and will scatter off the surface. This process can result in the emission of a muon through induced beta decay of the meson. Bremstralung emission from these muons is less efficient than from similarly produced positrons and they will be able to escape from the nugget. In fact these are likely to be the only charged particles able to travel a large distance into the atmosphere and, as such, will dominate the air shower.

While the temperature remains low the number of muons produced will be proportional to the density of air that the nugget is traveling through. As stated above positron excitations are favoured over muon production. The number of muons produced per annihilation will depend on the exact details of the quark matter surface but is generically less than one. The muon energy spectrum is also dependent on the exact phase of quark matter of which the nugget is composed. The majority of muons will leave the nugget with energies near the plasma frequency of the quark matter, over a wide range of quark matter phases this is predicted to be at the tens of MeV level. Muon energies may be as high as a few GeV but, as they arise from low energy proton annihilations will certainly not exceed this level.

Shower maximum
==============

As discussed above a significant fraction of the annihilation energy is thermalized within the nugget. The thermal evolution of the nugget is thus determined by the balance between energy deposition through annihilation and thermal radiation from the electrosphere. The thermal emission spectrum from the positrons of the electrosphere has been previously calculated for independent reasons. When applied in this context it allows for the calculation of temperature as a function of surrounding matter density.

At low temperatures electron positron annihilation happens primarily through an intermediate positronium resonance. While this process is operating annihilation proceeds rapidly and the incoming atmospheric molecules are ionized almost immediately. However, once the temperature exceeds the positonium formation threshold the resonance channel is no longer available and annihilation must occur through the much slower direct annihilation process. At low momenta elastic scattering through soft photon exchange is preferred to annihilation. As such, an incident molecule experiences a thermal pressure as it moves through the low density outer layers of the electrosphere. This pressure grows proportionally to the temperature, which is in turn established by the annihilation rate. This feedback results in an equilibrium rate at which matter can be feed onto the quark surface. The equilibrium temperature generically lies between the positronium energy scale ($m_e\alpha \sim$ keV) and the electron mass ($m_e = 511keV$) where the annihilation and elastic scattering amplitudes become comparable. Numerically the rapid fall off of positronium formation with energy favours the lower end of this energy range and equilibrium is reached in the few tens of keV range. For a quark nugget moving at typical galactic velocities this occurs at a height in the atmosphere near ten kilometers. Beyond this atmospheric depth the shower will no longer increase in size.

Conclusion
==========

Large area cosmic ray detectors have the ability to impose constraints on heavy composite dark matter models. In the class of these models where the dark matter has an antimatter component hadronic interactions with the atmosphere will induce an extensive air shower similar to that produced by a single high energy cosmic ray. The computation of the full properties of the air shower will require numerical simulations similar to those required for standard cosmic ray shower but are, in principle, fully tractable as they depend only on well understood nuclear interactions at energy scales that are both theoretically and experimentally accessible.

References {#references .unnumbered}
==========