How invisible can QCD axions be? From Supernova emission to Cherenkov signals

Technical Summary: "How invisible can QCD axions be? From Supernova emission to Cherenkov signals"

Problem Statement
The Standard Model (SM) of particle physics faces the strong CP problem, requiring the QCD vacuum angle $\bar{\theta}$ to be unnaturally small ($|\bar{\theta}| \lesssim 10^{-10}$). The Peccei-Quinn (PQ) mechanism resolves this by introducing the QCD axion, a pseudo-Nambu-Goldstone boson. While the axion's coupling to gluons is mandatory to solve the strong CP problem, its couplings to photons and SM fermions (electrons, nucleons) are model-dependent and can be suppressed in specific ultraviolet (UV) completions.

This paper investigates the "maximally invisible" axion scenario: a QCD axion where all model-dependent couplings (to photons, electrons, and derivative nucleon couplings) are suppressed, leaving only the irreducible interactions mandated by the gluon coupling. The central question is whether such axions can be detected via their residual, model-independent interactions with ordinary matter, thereby establishing the ultimate lower bound on the detectability of QCD axions.

Methodology
The authors employ a two-pronged approach combining astrophysical production calculations with terrestrial detection estimates:

1. Supernova (SN) Production Analysis:

   • The study focuses on core-collapse supernovae (specifically the GARCHING SFHo-s18.8 model) as the primary source of axions.
   • The authors calculate the axion emissivity arising from two dominant channels induced by the irreducible gluon coupling:
     • Nucleon-nucleon (NN) bremsstrahlung: $N + N \to N + N + a$.
     • Pion conversion: $N + \pi \to N + a$.
   • Crucially, the authors revisit the tree-level matrix elements for these processes. They identify that the axion-nucleon interaction in the maximally invisible scenario arises from a shift-symmetry-breaking operator ($\hat{c}_5$) in Heavy Baryon Chiral Perturbation Theory (HBChPT), rather than the derivative couplings used in standard benchmark models (like KSVZ).
   • They derive the axion emission spectra and integrate over the SN cooling phase to determine the axion luminosity ($L_a$).
   • The axion decay constant ($f_a$) is constrained by the SN 1987A cooling bound, requiring $L_a \lesssim L_\nu$ (where $L_\nu \approx 3 \times 10^{52}$ erg s$^{-1}$ is the observed neutrino luminosity).

2. Detection Strategy:

   • The authors evaluate the prospects for detecting these axions in large-volume water Cherenkov detectors, specifically using Hyper-Kamiokande (HK) as a benchmark.
   • The detection channel is the inverse pion-conversion process: $a + N \to N + \pi^0$.
   • The subsequent decay $\pi^0 \to \gamma\gamma$ produces a distinctive double-ring Cherenkov topology, which can be distinguished from the single-ring signals of neutrino interactions.
   • The expected event rate is calculated by convolving the SN emission spectrum (derived in step 1) with the interaction cross-section for $a + N \to N + \pi^0$, assuming a nearby Galactic supernova (Betelgeuse at $d = 0.2$ kpc).

Key Contributions and Results

• Revised SN Emission Spectra: The authors present the first explicit calculation of the emission spectrum for maximally invisible axions. They find that the spectral shape differs significantly from standard models (e.g., KSVZ). In the maximally invisible case, the high-energy spectral component is suppressed because the $\hat{c}_5$-induced amplitude is independent of the axion energy ($\omega_a$), whereas derivative couplings scale with $\omega_a$. Consequently, nucleon bremsstrahlung remains the dominant production channel even above the pion mass threshold.
• SN 1987A Cooling Bound: Using the revised emissivity, the authors derive a new lower bound on the axion decay constant for the maximally invisible scenario:
  $$f_a \gtrsim 7.17 \times 10^7 \text{ GeV}$$
  This bound is approximately two orders of magnitude weaker (allowing for lower $f_a$) than bounds derived from models with derivative couplings, reflecting the reduced production efficiency.
• Detection Prospects: The authors calculate the expected number of events in Hyper-Kamiokande for a supernova at 0.2 kpc, assuming $f_a$ saturates the SN 1987A bound.
  • Even under optimistic assumptions (axions scattering incoherently on all nucleons in water, a very nearby source, and a detector at full design sensitivity), the predicted signal is less than one event ($N_{events} \approx 0.086$ to $0.773$ depending on target assumptions).
  • The result holds for both extreme assumptions regarding the number of nucleon targets (protons only vs. all nucleons).

Significance and Claims
The paper concludes that "maximally invisible" QCD axions represent a theoretically consistent but experimentally elusive class of particles.

• The "Sobering" Conclusion: The authors state that while the irreducible $\hat{c}_5$ coupling provides a guaranteed detection channel in principle, the interaction rate is too low to yield an observable signal in current or foreseeable water Cherenkov detectors, even for the most favorable astrophysical scenarios.
• Implications for Axion Searches: This result delineates the ultimate reach of direct detection via SM couplings. If maximally invisible axions exist, they may permanently evade direct detection through standard SM interactions. The authors argue that exploring this parameter space will require complementary approaches, such as cosmological probes, gravitational signatures, or flavor-violating signals, rather than direct conversion experiments.
• Caveats: The authors emphasize that their negative result is quantitative and subject to astrophysical uncertainties, particularly the thermal pion abundance in the SN core and the modeling of the SN environment. A hotter or denser core than the benchmark model could potentially raise the signal, but under standard assumptions, the signal remains unobservable.

In summary, the paper establishes that the "floor" of axion interactions with matter, dictated solely by the solution to the strong CP problem, is likely too low to be probed by next-generation Cherenkov detectors, suggesting that a significant portion of the QCD axion parameter space may remain "invisible" to direct experimental scrutiny.