Physics case for low-$\sqrt{s}$ QCD studies at FCC-ee

This paper proposes that the FCC-ee can significantly advance precision QCD studies by collecting approximately $10^9$ hadronic events at center-of-mass energies between 20 and 80 GeV through initial- and final-state radiation during Z-pole runs and dedicated low-energy collisions, thereby enabling detailed investigations of jet properties, event shapes, and nonperturbative dynamics.

The Gist

Imagine the Future Circular Collider (FCC-ee) as the ultimate "particle microscope" that scientists are planning to build. Its main job is to smash electrons and positrons (anti-electrons) together at incredibly high speeds to study the fundamental building blocks of the universe.

Usually, this machine is designed to operate at a very specific, high-energy setting called the "Z-pole" (about 91 GeV). Think of this like a camera set to a specific zoom level to take the perfect portrait of a famous celebrity (the Z boson). Scientists know they will get millions of these perfect portraits.

But here's the problem:
While the "Z-pole" is great for studying heavy particles, it leaves a huge gap in our understanding of how particles behave at medium energies. It's like having a camera that can only take photos of giants (high energy) or tiny ants (low energy), but completely misses the people walking in between.

This paper argues that the FCC-ee shouldn't just stick to its main setting. It suggests two clever ways to fill in that "medium energy" gap to better understand QCD (Quantum Chromodynamics), which is the physics of how particles stick together to form matter.

The Two Strategies

The authors propose two "hacks" to get these missing medium-energy photos:

1. The "Flashlight" Trick (ISR/FSR Events)

Imagine you are taking a photo of a bright light bulb (the collision). Sometimes, the light bulb flickers or emits a stray beam of light (a photon) that shoots off to the side before the main explosion happens.

• The Physics: When an electron emits a hard photon (a flash of light) before colliding, it loses some energy. The collision that actually happens is therefore weaker and happens at a lower energy than the machine was set to.
• The Analogy: It's like two boxers stepping into the ring ready to fight at full strength, but one boxer suddenly gets distracted by a fly and throws a punch with only half their strength. The resulting fight is "medium intensity."
• The Plan: The FCC-ee will produce so many collisions (trillions!) that even if only a tiny fraction of them have this "flashlight" effect, we will still end up with billions of these medium-energy events. The paper shows that by filtering these out, we can study how particles behave at energies between 20 and 80 GeV.

2. The "Dedicated Detour" (Special Runs)

The second idea is simpler but requires a schedule change. Instead of running the machine at its maximum speed, they could intentionally slow it down for a short period.

• The Physics: The machine is capable of running at lower energies (around 40 GeV and 60 GeV).
• The Analogy: Imagine a high-speed train that usually runs at 200 mph. For one month, the engineers decide to slow it down to 60 mph to study how the tracks behave at that specific speed.
• The Plan: The paper estimates that because the machine is so powerful, they only need to run at these lower speeds for about one month at each energy level to collect enough data to rival decades of past experiments.

Why Does This Matter? (The "Why Bother?")

Why do we care about these medium-energy collisions?

1. The "Glue" Mystery: QCD is the theory of the "strong force," the glue that holds atomic nuclei together. At very high energies, we can calculate this glue using math. At very low energies, the glue gets messy and hard to calculate. The "medium" zone is the tricky middle ground where we need to understand how the "glue" turns into actual particles (like protons and pions).
2. Calibrating the Machine: To understand the heavy particles (like the Higgs boson) that the FCC-ee will study later, we need to perfectly understand the "background noise" of how particles break apart. These medium-energy runs act as a calibration tool. It's like tuning a musical instrument before a concert; if you don't tune it at the medium notes, the high notes will sound off.
3. Filling the History Books: Previous experiments (like LEP in the 90s) mostly focused on the high-energy "Z-pole." They didn't have enough data in this medium range. This new plan would give us 1,000 times more data than any previous experiment in this energy range, allowing us to see details we've never seen before.

The Bottom Line

This paper is a proposal saying: "Don't just look at the big picture. Let's also zoom in on the middle ground."

By using a clever trick with stray photons or by taking a short, dedicated detour to lower speeds, the FCC-ee can collect billions of new data points. This will help physicists finally solve the puzzle of how the "glue" of the universe works, making our understanding of the entire Standard Model of physics much sharper and more precise.

Technical Summary

1. Problem Statement

While the Future Circular Collider (FCC-ee) is designed to operate at high center-of-mass (CM) energies ($\sqrt{s} \approx 91, 160, 240, 365$ GeV), there is a significant gap in precision Quantum Chromodynamics (QCD) data for hadronic final states in the intermediate energy range of $\sqrt{s} \approx 20–80$ GeV.

• Historical Context: Previous experiments at B-factories ($\sim 10$ GeV) and older colliders like PETRA, PEP, and TRISTAN ($12–64$ GeV) provided limited statistics and suffered from large systematic uncertainties due to outdated detector technologies.
• Theoretical Need: To fully understand nonperturbative QCD phenomena (hadronization, color reconnection) and heavy-quark mass effects (e.g., the "dead cone"), data is required across a wide range of energy scales. Measurements at a single energy (like the Z-pole) cannot effectively disentangle perturbative corrections from nonperturbative hadronization effects, which scale differently with energy ($\Lambda_{\text{QCD}}/\sqrt{s}_{\text{had}}$).
• Gap: The energy range between B-factories and the Z-pole is currently poorly explored, limiting the precision of Standard Model tests and the tuning of Monte Carlo (MC) event generators.

2. Methodology

The authors propose two complementary strategies to access low-energy hadronic data at the FCC-ee:

Strategy A: ISR/FSR Events at the Z-Pole

• Concept: Utilize the enormous dataset expected at the Z-pole ($\sqrt{s} \approx 91.2$ GeV, $L_{\text{int}} \approx 205 \text{ ab}^{-1}$). Events where Initial-State Radiation (ISR) or Final-State Radiation (FSR) emits a hard photon reduce the effective CM energy of the hadronic system ($\sqrt{s}'$).
• Simulation & Selection:
  • Used PYTHIA 8 for generator-level simulations and SHERPA 3.0.1 for background processes.
  • Applied DELPHES fast simulation with the IDEA detector card to model detector effects.
  • Defined three selection criteria based on LEP experience (L3, OPAL, DELPHI):
    1. Wide-angle photon: Isolated high-energy photon + two jets satisfying kinematic triangle conditions.
    2. Collinear photon: Missing longitudinal momentum indicating a beam-collinear photon.
    3. Negligible radiation: Standard Z-decay events for calibration.
  • Analyzed the geometric acceptance (down to $\theta \approx 100$ mrad) to reconstruct hadronic invariant masses ($m_{\text{HFS}}$) down to 20 GeV.

Strategy B: Dedicated Low-Energy Runs

• Concept: Perform short, dedicated runs at specific CM energies below the Z-pole, specifically $\sqrt{s} \approx 40$ GeV and $60$ GeV.
• Feasibility Study:
  • Estimated running time based on the assumption that instantaneous luminosity scales with beam energy ($L \propto \sqrt{s}$).
  • Consulted parametric accelerator simulations (provided by K. Oide) starting from Z-pole beam settings without machine modifications to verify luminosity potential at lower energies.

3. Key Contributions

• Quantification of Data Potential: The paper provides the first realistic estimates for collecting $\mathcal{O}(10^9)$ hadronic events in the 20–80 GeV range at FCC-ee, a dataset size orders of magnitude larger than previous experiments (LEP, PETRA, TRISTAN).
• Dual-Strategy Validation: It demonstrates that both ISR/FSR exploitation and dedicated low-energy runs are viable, offering a trade-off between statistical volume (ISR/FSR) and purity/precision (dedicated runs).
• Detector Impact Analysis: It highlights that the FCC-ee's extended geometric acceptance (down to 100 mrad vs. 200 mrad at LEP) is crucial for reconstructing low-mass hadronic systems that were previously lost in the beam pipe.

4. Results

A. ISR/FSR Event Samples (Z-Pole)

• Yield: Approximately $1.8 \times 10^9$ to $4.2 \times 10^9$ selected hadronic events can be collected in 5 GeV bins across the $\sqrt{s}' = 30–86$ GeV range.
• Purity:
  • Selections for events with collinear or wide-angle photons achieve purities of $\approx 90\%$ for $20 < m_{\text{HFS}} < 70$ GeV.
  • Backgrounds from $\tau^+\tau^-$ and $\gamma\gamma$ processes are manageable but require careful selection.
• Resolution: The reconstructed invariant mass resolution is sufficient for general studies, but fluctuations from escaping neutrinos limit precision for high-precision $\alpha_S$ extractions compared to dedicated runs.

B. Dedicated Low-Energy Runs

• Luminosity & Time: Assuming $L \propto \sqrt{s}$, the authors estimate that collecting $10^9$ hadronic events requires:
  • $\sqrt{s} = 40$ GeV: ~23 days (approx. 1 month including setup).
  • $\sqrt{s} = 60$ GeV: ~20 days.
  • $\sqrt{s} = 80$ GeV: ~6 days.
• Feasibility: Accelerator simulations confirm that luminosities of $\sim 65 \times 10^{34} \text{ cm}^{-2}\text{s}^{-1}$ (at 40 GeV) are achievable, supporting the feasibility of these short runs.

C. Physics Reach

• The proposed datasets will enable precision measurements of:
  • Light, heavy-quark, and gluon jet properties.
  • Event shapes and fragmentation functions (FFs).
  • Nonperturbative dynamics and hadronization models.
  • Heavy-quark mass effects (dead cone) and alternative $\alpha_S$ extractions.

5. Significance

This paper establishes a robust physics case for expanding the FCC-ee program beyond its nominal high-energy runs.

• Complementarity: The low-energy data will fill the critical gap between B-factory and Z-pole measurements, allowing for the separation of perturbative and nonperturbative QCD effects that cannot be resolved at a single energy scale.
• Precision Improvement: The sheer volume of data ($\sim 10^9$ events) will reduce statistical uncertainties by orders of magnitude compared to historical data, enabling stringent tests of QCD predictions and improved tuning of MC generators (essential for future Higgs and top-quark physics).
• Strategic Value: It demonstrates that the FCC-ee can act as a "precision QCD factory" across a broad energy spectrum, maximizing the scientific return on the collider investment with minimal additional operational time (via ISR/FSR) or short, targeted dedicated runs.

In conclusion, the authors argue that leveraging both ISR/FSR events at the Z-pole and dedicated low-energy runs is essential for a comprehensive understanding of strong interaction physics at the FCC-ee.