Search for Dark Photons between 16.96--19.52 $μ$eV with the HAYSTAC Experiment

The HAYSTAC experiment used Phase II data to exclude dark photon kinetic couplings above $4.90 \times 10^{-15}$ in the 19.46–19.52 $\mu$eV range and $2.90 \times 10^{-15}$ in the 16.96–19.46 $\mu$eV range, thereby ruling out a previously reported signal at 19.5 $\mu$eV.

The Gist

Imagine the universe is filled with a vast, invisible ocean of "dark matter." For decades, scientists have been trying to catch a glimpse of this ocean using two main theories: one suggests it's made of tiny, ghostly particles called axions, and the other suggests it might be made of dark photons.

Think of dark photons as the "shadow siblings" of the light we see every day. They are heavy cousins of regular photons (light particles) that don't interact with our normal world easily. The only way they might talk to us is through a very faint "kinetic mixing"—like a whisper that occasionally leaks from one room into another.

The Experiment: A Giant Radio Tuner

The HAYSTAC experiment is like a super-sensitive, tunable radio receiver designed to listen for these whispers.

• The Setup: They built a giant, hollow copper box (a cavity) and placed it inside a massive magnet.
• The Goal: If dark photons exist, they should occasionally turn into regular radio waves inside this box. The researchers tune the box to different frequencies, hoping to "catch" the signal at just the right pitch.
• The Upgrade: In their latest phase (Phase II), they upgraded their "ears" using a special quantum trick called "squeezed states," which made their receiver twice as sensitive as before.

The Plot Twist: A Claimed Signal

Recently, another team of scientists (TASEH) re-examined their own old data and claimed to have heard a faint "ping" at a specific frequency (around 19.5 micro-electron volts). They said, "We think we found a dark photon here!"

However, there was a catch. In the TASEH experiment, this "ping" happened even when their magnet was turned off.

• For Axions: If you hear a sound without the magnet, it's usually a fake signal (noise), so you ignore it.
• For Dark Photons: These particles don't need the magnet to turn into light. So, a signal without a magnet is actually a good sign for dark photons!

The Investigation: HAYSTAC Steps In

Because the HAYSTAC experiment is much more sensitive than TASEH, the HAYSTAC team decided to check that specific frequency range (19.46–19.52 µeV) to see if they could hear the same "ping."

They looked at a dataset they had collected in the summer of 2022. This run was a bit messy:

• The Glitch: During the experiment, a metal rod inside their detector slipped and hit the bottom of the box. This made the detector "stutter" (its quality dropped by half).
• The Fix: They usually throw away messy data, but because the TASEH claim was so exciting, they decided to carefully re-analyze this specific "stuttering" data, making sure to account for the glitch.

The Result: Silence

The team crunched the numbers and asked: "If the TASEH signal were real, would HAYSTAC have heard it?"

• The Prediction: If that TASEH signal were real, HAYSTAC's super-sensitive ears should have heard a massive, deafening roar—about 17 times louder than the background static noise.
• The Reality: HAYSTAC heard nothing. The "radio" was perfectly quiet.

The Conclusion

Because HAYSTAC didn't hear the signal, they can confidently say:

1. The TASEH "ping" is likely not a dark photon. If it were, HAYSTAC would have definitely seen it.
2. New Limits: They have now drawn a new "exclusion zone." They can say with 90% confidence that dark photons in this specific frequency range do not exist with the strength that TASEH claimed.

In short, HAYSTAC acted like a high-tech lie detector. The TASEH team claimed to hear a whisper; HAYSTAC listened with a super-ear and found the room was completely silent. This suggests the original "whisper" was likely just background noise, and the search for dark photons in this specific frequency range must continue elsewhere.

Technical Summary

Technical Summary: Search for Dark Photons between 16.96–19.52 µeV with the HAYSTAC Experiment

Problem and Motivation
The dark photon is a hypothetical massive vector boson and a viable dark matter candidate, arising from a "dark sector" model that introduces an additional U(1) symmetry to the Standard Model. Its interaction with standard model particles occurs via kinetic mixing with photons, characterized by a mixing strength $\chi$. Unlike axion-photon conversion, which requires a magnetic field, dark photon conversion can occur with or without one.

A recent reanalysis of data from the TASEH collaboration reported a tentative dark photon signal at 19.479 727 µeV (4.710 178 GHz) with a kinetic mixing strength of $|\chi_{rand}| \simeq 6.5 \times 10^{-15}$. This signal was initially excluded in the original TASEH axion search because it persisted in the absence of a magnetic field—a valid veto for axions but not for dark photons. The HAYSTAC experiment, having previously collected data in the overlapping frequency range of 19.46–19.52 µeV (a run later aborted due to degraded cavity performance), sought to re-examine this region to test the validity of the TASEH candidate. Additionally, the authors aimed to extend dark photon exclusion limits across the full mass range covered by HAYSTAC's Phase II data (16.96–19.46 µeV).

Methodology
The HAYSTAC experiment utilizes a tunable copper-plated stainless steel cavity (1.545 L volume) placed within an 8 T superconducting magnet. The search relies on detecting excess noise in the cavity's $TM_{010}$ mode. The experiment operates in two primary phases: Phase I (2016–2017) and Phase II (2019–2024), the latter utilizing a squeezed state receiver to enhance scan rates.

The analysis focuses on two datasets:

1. Phase II (a)-(d): Previously published axion search data covering 16.96–19.46 µeV.
2. Phase II (e): A previously unpublished dataset collected in July 2022, covering 19.46–19.52 µeV. This run was aborted after the tuning rod slipped, contacting the cavity end cap and reducing the unloaded quality factor ($Q_0$) from a nominal ~40,000 to ~20,000.

To address the degraded performance in Phase II (e), the authors performed COMSOL simulations to quantify the impact on the form factor ($C_{010}$). They determined that the form factor is highly insensitive to the rod's vertical position (varying <1%). However, out of prudence, they assumed a baseline form factor 2x lower than predicted to match the observed $Q_0$ reduction.

Data processing followed standard HAYSTAC procedures:

• Spectra were generated with 100 Hz frequency resolution.
• Power spectral densities (PSD) were filtered to remove structures wider than the expected axion line shape (~5 kHz).
• Spectra were scaled by signal-to-noise ratio, aligned, and summed to form a "grand spectrum."
• Candidates were identified as power excesses exceeding $3.468\sigma$ (corresponding to a 10% false negative rate for a $5.1\sigma$ target significance).
• Known Radio Frequency Interference (RFI) candidates, identified by correlation with ambient RF receivers, were excised with 10 kHz cuts.

The axion exclusion limits ($g_{a\gamma\gamma}$) were recast into dark photon kinetic mixing limits ($\chi$) using the relation $\chi = g_{a\gamma\gamma} \frac{B_0}{m_\chi} \sqrt{\langle \cos^2 \theta \rangle}$. Two polarization scenarios were considered:

1. Random Polarization: The field changes every coherence time ($\tau_{coh} \sim 200 \mu s$), yielding $\langle \cos^2 \theta \rangle = 1/3$.
2. Fixed Polarization: The field has a single orientation. The authors adopted a conservative effective value of $\langle \cos^2 \theta \rangle \approx 0.004$ based on their specific frequentist analysis framework, rather than the $0.019$ used in broader comparisons.

Key Contributions and Results

• Rejection of TASEH Candidate: In the 19.46–19.52 µeV region (Phase II e), HAYSTAC found no evidence of the signal reported by TASEH. Given HAYSTAC's sensitivity, a signal with $|\chi_{rand}| \simeq 6.5 \times 10^{-15}$ would have appeared as a $17.1\sigma$ excess above the noise. No such excess was observed.
• New Exclusion Limits (Phase II e): Due to the conservative assumption regarding the degraded form factor in Phase II (e), the experiment excludes kinetic mixing couplings of $|\chi_{rand}| \ge 4.90 \times 10^{-15}$ at the 90% confidence level in the 19.46–19.52 µeV range.
• Extended Exclusion Limits (Phase II a-d): Using previously reported axion data, the collaboration excludes couplings of $|\chi_{rand}| \ge 2.90 \times 10^{-15}$ at the 90% confidence level across the 16.96–19.46 µeV range.
• Fixed Polarization Limits: Under the fixed polarization scenario, the 90% confidence level exclusions are $|\chi_{fix}| \ge 4.47 \times 10^{-14}$ for Phase II (e) and $|\chi_{fix}| \ge 2.64 \times 10^{-14}$ for Phases II (a)-(d).
• Candidate Handling: Three candidates were identified in Phase II (e) at 4.719 720, 4.719 816, and 4.719 925 GHz. The highest was identified as a synthetic axion signal injection used for calibration. The other two were small excesses ($<4.5\sigma$) not correlated with external sources; their presence was accounted for in the Bayesian framework, slightly degrading the overall exclusion limits.

Significance
The paper establishes that the tentative dark photon signal reported by the TASEH collaboration at 19.5 µeV is not supported by HAYSTAC data. Despite the HAYSTAC experiment's Phase II (e) run being aborted due to technical issues, the reanalysis of this specific dataset, combined with conservative assumptions about cavity performance, provides a robust exclusion that rules out the TASEH candidate under the assumption of a randomly polarized dark photon field. Furthermore, the work extends the global exclusion limits for dark photon kinetic mixing in the 16.96–19.52 µeV mass range, utilizing the full scope of HAYSTAC's Phase II data.