CANTON-{\mu} Proposal: A Next-Generation Muon $g\!-\!2$ Measurement at Sub-0.1 ppm Precision

The CANTON-$\mu$ proposal outlines a next-generation muon $g\!-\!2$ experiment at China's HIAF designed to surpass Fermilab's precision by leveraging intense pulsed muon beams to achieve sub-0.1 ppm accuracy, thereby enabling stringent tests of the Standard Model and significantly improved constraints on CPT symmetry.

The Gist

The Big Picture: A New Race to Measure a Tiny Spin

Imagine the universe is a giant, complex clockwork machine. For decades, physicists have been trying to figure out exactly how this machine ticks. One of the most important "gears" in this machine is the muon, a particle that is basically a heavy, unstable cousin of the electron.

Every muon has a tiny magnetic needle attached to it, like a miniature compass. As the muon spins, this compass wobbles (precesses). The rate of this wobble is called the "g-2" (pronounced "g-minus-two").

According to our current rulebook, the Standard Model of Physics, we can calculate exactly how fast this wobble should happen. But when we measure it in real life, there's a tiny, nagging difference. It's like if you calculated that a car should drive at exactly 60 mph, but every time you tested it, it was actually going 60.0000001 mph.

That tiny difference is the "anomaly." It could mean our rulebook is missing a chapter, or that there are invisible particles (New Physics) pushing on the muon that we can't see yet.

The Current Situation: Fermilab's Record

Right now, the best measurement comes from Fermilab in the US. They are incredibly precise, but they have a limitation: they only measure positive muons (like measuring only the right hand of a person).

There is a theory called CPT symmetry which says that if you flip a particle's charge (make it negative) and reverse time, the laws of physics should stay exactly the same. To test this, we need to measure the negative muon with the same high precision. So far, no one has done this well enough.

The New Proposal: CANTON-𝜇

This paper proposes a new experiment called CANTON-𝜇 (Coherent Anomalous magNetic momenT ObservatioN with muon) to be built at the HIAF facility in China. Think of HIAF as a massive, high-powered particle factory that is just being built.

Here is how they plan to beat the current records:

1. The "Magic" vs. The "Real"

To measure the muon's wobble, scientists usually have to inject them into a giant magnetic ring at a very specific speed called the "magic momentum."

• The Old Way (Fermilab): It's like trying to balance a spinning top on a needle. You have to hit the exact speed, or the electric fields in the machine mess up your measurement. This limits how fast you can go and how many muons you can use.
• The CANTON Way: They propose two new designs (Concept A and Concept B) that act like a wide, smooth highway instead of a needle.
  • Concept A (The Sector Magnet): Imagine a track made of separate curved sections with gaps in between. The muons fly straight through the gaps and only turn inside the magnets. This removes the need for the "magic speed" and gets rid of the electric field interference entirely. It's like driving a car where you don't have to worry about potholes because the road is perfectly segmented.
  • Concept B (The Hybrid): This is a smarter version of the old ring, using both electric and magnetic forces to keep the muons stable, allowing them to run faster and more efficiently.

2. The "Flashlight" vs. The "Laser"

The biggest problem with measuring these tiny wobbles is statistics. You need a lot of muons to get a clear picture.

• Fermilab uses a steady stream of muons, like a flashlight. It's bright, but it's constant.
• HIAF (the Chinese facility) can produce muons in intense, rapid pulses, like a strobe light or a high-speed camera flash. Because HIAF can fire these pulses so quickly and intensely, they can gather data much faster.

The Analogy: Imagine trying to count how many raindrops fall in a bucket.

• Fermilab is like a steady drizzle. You have to wait a long time to get enough drops to be sure of the count.
• HIAF is like a firehose. You get a massive amount of data in a split second.

3. The Two-Phase Plan

The project has two goals, like climbing a mountain in two stages:

• Phase 1 (The Baseline): Match Fermilab's precision (0.13 ppm) but measure negative muons for the first time with this level of accuracy. This will test if the "CPT symmetry" holds up.
• Phase 2 (The Upgrade): Once the facility gets upgraded (HIAF-U), they will crank up the power. They will aim for 0.05 ppm precision. This is three times more precise than Fermilab. At this level, even if the "rulebook" (Standard Model) is slightly off, we will definitely see it.

Why Does This Matter? (The "New Physics" Hunt)

If CANTON-𝜇 finds a difference between the positive and negative muons, or if the measurement doesn't match the theory, it's a huge deal.

• The Energy Scale: The paper explains that this experiment is sensitive enough to "see" particles that are so heavy, even the world's biggest particle colliders (like the Large Hadron Collider) can't create them. It's like trying to find a hidden island. The LHC is a boat that can sail up to the edge of the visible ocean. CANTON-𝜇 is a satellite that can see the island from space, even if the island is too heavy for the boat to reach.
• The CPT Test: By comparing positive and negative muons, they are testing the fundamental symmetry of the universe. If they find a difference, it means the universe treats matter and antimatter slightly differently, which would rewrite our understanding of reality.

Summary

CANTON-𝜇 is a proposal to build a next-generation muon measuring machine in China. By using a new type of "track" design and a super-powerful particle factory, they plan to measure the muon's magnetic wobble with unprecedented precision. They want to check if positive and negative muons behave exactly the same (testing the laws of symmetry) and hunt for invisible new particles that are too heavy for current colliders to find.

It's not just about getting a better number; it's about opening a window to a deeper layer of reality that we haven't seen yet.

Technical Summary

1. Problem Statement

The anomalous magnetic moment of the muon ($a_\mu \equiv (g-2)/2$) is a critical "golden observable" for testing the Standard Model (SM) and probing physics beyond it.

• Theoretical Uncertainty: The SM prediction for $a_\mu$ is currently unsettled due to discrepancies between two calculation methods for Hadronic Vacuum Polarization (HVP): the data-driven dispersive method (which shows internal inconsistencies, e.g., CMD-3 vs. BaBar/KLOE) and Lattice QCD. The 2025 Theory Initiative (WP25) favors Lattice QCD, reducing the tension with experimental data, but further clarification is needed.
• Experimental Limitations: Current precision is dominated by the Fermilab E989 experiment (0.127 ppm), which measured only positive muons ($\mu^+$).
  • The negative muon ($\mu^-$) measurement has not been updated since Brookhaven E821 (2001, 0.7 ppm), leaving a gap in testing CPT symmetry.
  • Conventional experiments rely on the "magic momentum" ($\approx 3.1$ GeV/$c$) to cancel electric field effects, restricting kinematic flexibility and limiting statistical gains from higher energies.
  • Existing facilities struggle to produce high-intensity, high-purity $\mu^-$ beams comparable to $\mu^+$ beams.

2. Methodology and Experimental Design

The proposal outlines the CANTON-𝜇 project, to be conducted at the High Intensity Heavy-Ion Accelerator Facility (HIAF) in Huizhou, China. The project leverages HIAF's unique capability to produce intense, pulsed, GeV-scale muon beams of both polarities.

A. Beam Source and Production

• Facility: HIAF uses a 9 GeV proton beam (upgradable to 25 GeV) striking a target to produce pions, which decay into muons.
• Beamline: The High-energy FRagment Separator (HFRS) provides high-resolution separation, achieving nearly 100% muon purity by removing $\pi, p, e$ backgrounds.
• Intensity:
  • Phase 1 (HIAF baseline): $\sim 4 \times 10^5$ $\mu^\pm$/s at 2–4 GeV/$c$.
  • Phase 2 (HIAF-U upgrade): Proton intensity increases to $4 \times 10^{14}$/s with 25 GeV energy, boosting muon flux to $\mathcal{O}(10^7)$–$10^8$ $\mu$/s at 10–20 GeV/$c$.
• Key Advantage: Unlike surface muon sources where $\mu^+$ dominates, HIAF produces $\mu^-$ and $\mu^+$ with comparable intensities, enabling high-precision $\mu^-$ measurements.

B. Novel Storage Ring Concepts

To overcome the "magic momentum" constraint and improve precision, two experimental concepts are proposed:

• Concept A: Sector Magnet with Polarized Proton Co-Magnetometer

  • Design: A discrete-sector storage ring where muons travel in straight lines between magnetic dipoles.
  • Innovation: Eliminates electric quadrupoles (EQs), removing the need for magic momentum and suppressing electric-field systematic errors.
  • Field Calibration: Uses a polarized proton co-magnetometer injected into the same orbit. The proton spin precession frequency directly measures the average magnetic field, averaging over the entire orbit and avoiding water-shielding corrections required in NMR probes.
  • Flexibility: Allows operation at a wide range of momenta, enabling momentum scans to map and cancel residual electric field effects.

• Concept B: Hybrid Weak Focusing (Fermilab Upgrade)

  • Design: A continuous ring using a hybrid lattice of electric and magnetic quadrupoles.
  • Innovation: By tuning the ratio of magnetic ($n_B$) to electric ($n_E$) focusing, the "effective magic" condition can be achieved at non-magic momenta, allowing higher-energy operation while suppressing electric field corrections.

3. Key Contributions

1. First Proposal to Surpass Fermilab Precision: CANTON-𝜇 is the first proposed experiment explicitly aiming to exceed the current 0.127 ppm precision record.
2. Dual-Polarity Capability: It is the first modern proposal to prioritize high-precision $\mu^-$ measurements, crucial for CPT symmetry tests.
3. Novel Calibration Technique: The introduction of the in-situ polarized proton co-magnetometer offers a fundamentally different approach to magnetic field calibration, potentially reducing systematic uncertainties associated with NMR probe placement and diamagnetic shielding.
4. Scalable Precision Roadmap: The proposal defines a clear path from Phase 1 (matching Fermilab) to Phase 2 (sub-0.1 ppm) via the HIAF-U upgrade.

4. Projected Results and Sensitivity

• Phase 1 (Current HIAF):

  • Precision Goal: 0.13 ppm (matching Fermilab).
  • Systematics: Target total systematic uncertainty of 50 ppb (improved from Fermilab's ~76 ppb) by eliminating electric field corrections (Concept A) or using hybrid focusing (Concept B).
  • Physics Reach: A result consistent with the Brookhaven $\mu^-$ central value would yield a 5$\sigma$ discrepancy with the SM2025 prediction, providing a discovery-level test.

• Phase 2 (HIAF-U Upgrade):

  • Precision Goal: 0.05 ppm (approx. 2.6x better than Fermilab).
  • Statistical Gain: The higher muon energy ($\gamma \approx 142$) increases the dilated muon lifetime by 5x, drastically improving statistical sensitivity.
  • Systematics: Further reduction via low-emittance beam operation and alternating $\mu^+/\mu^-$ runs to cancel charge-symmetric systematics.

• New Physics Reach:

  • Energy Scale: At 0.05 ppm, the experiment can probe new physics mass scales up to 100 TeV (in chirally enhanced scenarios), exceeding the direct reach of the LHC.
  • CPT Symmetry: By comparing $\mu^+$ and $\mu^-$ at HIAF (latitude 23.1°N) with data from Fermilab/BNL, the experiment can constrain CPT-violating SME coefficients ($b_Z$) at the $10^{-24}$ GeV level, improving current limits by an order of magnitude.

5. Significance

The CANTON-𝜇 proposal represents a paradigm shift in muon $g-2$ research:

• Resolving the Theory-Experiment Tension: By achieving sub-0.1 ppm precision, it will provide a definitive benchmark to validate whether the SM2025 (Lattice-based) or SM2020 (Data-driven) predictions are correct, or if new physics is required.
• CPT Symmetry Test: It offers the most sensitive test of CPT symmetry in the muon sector to date, a fundamental symmetry test that has been stagnant for two decades.
• Complementarity: The unique ability to measure both charge states with high precision, combined with novel storage ring geometries, provides essential cross-checks against the Fermilab results, strengthening the global confidence in any observed anomaly.
• Technological Leadership: The project leverages China's HIAF infrastructure to establish a world-leading muon source, positioning it as a primary facility for future precision muon physics.

In conclusion, CANTON-𝜇 proposes a feasible, high-impact path to the next generation of muon $g-2$ measurements, capable of either discovering new physics beyond the Standard Model or setting stringent constraints on it, while simultaneously performing a landmark test of CPT symmetry.