One Propagator, Three RegimesTesting High-Energy Physics Across Scales
This is a pilot. You are the first cohort to attempt this capstone. That means the material has not been tested by prior students, the timing has not been calibrated by experience, and some exercises may turn out to be harder — or easier — than intended. The organisers and tutors face the same uncertainty you do.
What we can promise is that every question you raise will be taken seriously, every problem you uncover will improve the course for those who follow, and your critical feedback is not merely welcome but essential. Your lab notes, your confusion, your objections — these are the raw data from which a better capstone will be built.
The physics itself is real: a single propagator structure connects a tabletop gravity experiment, an atomic spectroscopy measurement, and a collider dataset spanning twelve orders of magnitude in energy. Whether that connection is deep or merely convenient is one of the questions you will answer. We do not know what you will find. That is the point.
Purpose
This capstone integrates three laboratory experiments into a single conceptual arc: How do heavy mediators in quantum field theory manifest in low-energy precision experiments and long-range force measurements?
Students move from isolated techniques to a unified research logic: propagator → effective operator → observable constraint. The organising principle is the tree-level exchange amplitude for a massive mediator,
evaluated in three kinematic limits that produce three distinct experimental signatures.
| Kinematic Limit | Physical Regime | Observable | Lab |
|---|---|---|---|
| Static, |q| ≪ mϕ | Long-range potential | Yukawa tail in torque signal | Lab 1 |
| Bound state, |q| ~ αme | Contact interaction | HFS shift ΔE ∝ |ψ(0)|² | Lab 2 |
| On-shell, q² → mϕ² | Resonance pole | Cross-section peak + Γinv | Lab 3 |
The denominator structure (q² − m²) and the emergence of Yukawa screening are generic to any massive mediator; spin changes numerators and selection rules. Labs 1–2 use a scalar as the minimal long-range-force benchmark. Lab 3 uses the Z⁰ as the canonical pole-and-width case study. Lab 4 confronts students with the question of what can — and what cannot — be unified onto a common parameter plane.
Structure
Learning Phase
Formative feedback only — no direct grade impact.
Each lab follows the standard FP three-step protocol:
| Step | Format | What happens |
|---|---|---|
| 1. Entrance Session | 15-min presentation + 30-min discussion | Present key physics; demonstrate understanding of what, why, and how. Tutors participate as discussants, not examiners. |
| 2. Active Lab + Lab Notes | Throughout experiment | Engaged measurement and in-lab analysis. Estimate results as you go. Plot data during acquisition. Problems caught during measurement can be fixed; problems discovered during report writing cannot. |
| 3. Findings Session | ~30-min presentation + 15-min discussion | Present findings with uncertainties, comparison to expectations, and unresolved questions. |
Your lab notes from each session must allow verification and reconstruction of your work. They form the raw material for the report and the evidentiary basis for your seminar presentation.
More than 2 failed steps (entrance or findings sessions, across all experiments) results in course failure. A third failed step — whether Step 1, 2, or 3, in the same or different experiments — results in immediate course termination.
Exam Phase
Assessed against pre-published criteria. No changes after submission.
This capstone is a standalone special lab class. The final grade is composed of:
| Component | Weight | Deadline |
|---|---|---|
| Full Report | 30% | 7 calendar days before seminar |
| Seminar Presentation | 70% | Scheduled date |
Full Report
The report follows the standard full scientific report format. It must cover all four labs and the synthesis. Structure:
- Title. Descriptive, concise, accurately reflecting the content.
- Abstract (fewer than 200 words). Motivations, goals, methods, and main results including uncertainties.
- Introduction. Topic, motivations, relevant background, aim and hypothesis. The propagator-unification concept should be introduced here as the organising principle.
- Methods. Experimental setup, materials, and equipment in the context of the underlying theory, including the relevant formulae. Cover all four labs.
- Analysis and Results. Findings in detail with graphical representations and uncertainties. Discuss the data analysis process, including how you quantified and distinguished statistical and systematic uncertainties. The unified exclusion plot and gap analysis must appear as key results.
- Discussion. Summarise findings and relate them to the introduction. State whether measurements were limited by statistical or systematic effects. Include the critical evaluation: does the propagator-unification concept reflect genuine physical unity, or is it a pedagogical convenience? Suggest improvements.
- Conclusions. Summarise the main points and state your conclusion clearly.
- References. All sources cited using a consistent style. Credible and verifiable.
- Appendices. Raw data, lab notes (all four labs, required), and analysis code.
Submit as a single file via ILIAS, 7 calendar days before the scheduled seminar.
Seminar Presentation (60 minutes)
| Phase | Duration |
|---|---|
| Uninterrupted presentation | ~30 min |
| Open discussion | ~15 min |
| Exam questions (organisers/tutors) | ~15 min |
Requirements: coherent logical thread | claims follow from evidence | uncertainties acknowledged | results traceable to submitted full report.
The seminar develops the full report into a complete scientific narrative. Address your talk to your peers — it must be understandable to students who have not conducted your experiment. Cover all four labs and the synthesis. The unified exclusion plot must appear with full explanation. Include a section on the gap analysis and critical evaluation of the propagator-unification concept.
For general FP conduct rules, safety requirements, and escalation procedures, see the FP Rulebook.
Repository
All materials, notebooks, and data live in a public GitHub repository. Fork the repo, work in your lab directories, and push final results.
one-propagator/
├── framework/
│ ├── propagator_derivations.py
│ └── likelihood_utils.py
├── lab1-gravity/
│ ├── README.md
│ ├── notebook_template.ipynb
│ └── data/
├── lab2-positronium/
│ ├── README.md
│ ├── notebook_template.ipynb
│ └── data/
├── lab3-z0/
│ ├── README.md
│ ├── notebook_template.ipynb
│ └── data/
├── lab4-synthesis/
│ ├── README.md
│ ├── notebook_template.ipynb
│ └── results/
└── archive/
└── README.md
Prerequisites
- Classical mechanics including Lagrangian formulation (Theo I)
- Quantum mechanics including perturbation theory (Theo II/III)
- Exposure to QFT concepts: propagators, Feynman rules, cross sections (Theo III/IV)
- Fourier transforms in scattering context (Born approximation)
- Basic statistical methods: χ² fitting, uncertainty propagation
- Python with NumPy/SciPy
- Laser and radiation safety training completed before first entry
Essential Reading
Primary Sources
- Adelberger et al., “Tests of the Gravitational Inverse-Square Law,” Ann. Rev. Nucl. Part. Sci. 53, 77 (2003).
- Arkani-Hamed, Dimopoulos, Dvali, “The Hierarchy Problem and New Dimensions at a Millimeter,” Phys. Lett. B 429, 263 (1998).
- LEP Collaborations, “Precision Electroweak Measurements on the Z Resonance,” Phys. Rep. 427, 257 (2006).
- Karshenboim, “Precision Physics of Simple Atoms and Constraints on a Light Boson,” Phys. Rev. Lett. 104, 220406 (2010).
Statistical Methods
- Feldman and Cousins, “Unified Approach to the Classical Statistical Analysis of Small Signals,” Phys. Rev. D 57, 3873 (1998).
- Cowan et al., “Asymptotic Formulae for Likelihood-Based Tests of New Physics,” Eur. Phys. J. C 71, 1554 (2011).