Counting axions with IAXO

Technical Summary: Counting Axions with IAXO

Problem Statement
Theoretical extensions of the Standard Model, including string theory and solutions to the strong CP problem, generically predict the existence of multiple axion-like particles (axions) rather than a single species. While current and next-generation helioscope experiments (such as CAST and IAXO) are designed to detect solar axions, they are typically interpreted within a single-axion paradigm. A critical gap exists in understanding whether a detected signal could originate from multiple axion species. Specifically, if multiple axions couple to photons, their combined signal might mimic a single axion with different parameters. The central question addressed is: If a next-generation helioscope like IAXO detects a signal, can we disentangle whether it originates from one or multiple axions?

Methodology
The authors employ a multi-step approach combining theoretical derivation, statistical analysis, and phenomenological projection:

1. Theoretical Framework: The paper generalizes the axion-photon conversion probability for a two-axion system. Unlike the single-axion case where conversion depends on the axion mass $m_a$, the two-axion probability involves interference between two mass eigenstates ($a_1, a_2$). The conversion probability $P_{a\gamma \to \gamma}$ includes terms dependent on the individual masses (via $\text{sinc}^2$ functions related to the magnet length $L$) and an interference term dependent on the squared mass difference $\Delta m^2_{21}$ (via a cosine function related to the Earth-Sun distance $L_{ES}$).
2. Spectral Regimes: The analysis focuses on two limiting regimes:
   • Quasi-degenerate regime ($\Delta m^2_{21} \ll m^2_{1,2}$): The spectral signature is dominated by the cosine modulation arising from flavor oscillations over the Earth-Sun distance.
   • Hierarchical regime ($m_1 \ll m_2 \simeq \sqrt{\Delta m^2_{21}}$): The signature is dominated by the $\text{sinc}^2$ modulation from the heavier axion's mass, controlled by the magnet length.
3. Statistical Analysis: The authors utilize a likelihood-based test statistic under the assumption of "Asimov data" (where observed data perfectly matches the theoretical expectation without Poisson fluctuations). They define a null hypothesis ($H_0$: single axion) and an alternative hypothesis ($H_1$: two axions). The discrimination power is quantified by the test statistic $q_0$, allowing the calculation of the minimal coupling $g^{\text{dis}}_{a\gamma}$ required to reject the single-axion hypothesis at a given significance (e.g., $3\sigma$).
4. Experimental Parameters: The study incorporates the projected capabilities of IAXO and IAXO+, including magnetic field strength, magnet length, aperture area, and crucially, the energy resolution of X-ray detectors ($\omega_{\text{res}}$). It also considers a potential supernova (SN) axion signal as a complementary probe.

Key Contributions and Results

• Discrimination Regions: The authors map out regions in the two-axion parameter space (coupling $g_{a\gamma}$ vs. mass splitting $\sqrt{\Delta m^2_{21}}$) where IAXO can distinguish a two-axion signal from a single-axion hypothesis.
  • In the quasi-degenerate regime, discrimination relies on resolving the cosine oscillations in the photon energy spectrum. The reach is highly sensitive to the detector's energy resolution. The maximum accessible mass splitting scales as $\sqrt{\Delta m^2_{21}}^{\text{max}} \propto \omega_{\text{res}}^{-1/2}$. For optimal resolution ($\sim 10$ eV), IAXO can probe mass splittings up to $\sim 10^{-6}$ eV.
  • In the hierarchical regime, discrimination relies on the overall shape distortion and peak shift of the spectrum caused by the $\text{sinc}^2$ envelope. Here, the discrimination reach is largely independent of the detector's energy resolution.
• Exclusion Limits: The paper recasts current CAST exclusion limits and derives projections for IAXO/IAXO+ in the two-axion parameter space, identifying regions where a signal could be observed.
• Supernova Axions: The study explores the potential of detecting axions from a nearby supernova (e.g., Spica). While the larger distance ($L_{SN} \gg L_{ES}$) and higher energies allow probing smaller mass splittings ($\sim 10^{-9}$ eV), the authors note that discrimination is currently limited by large astrophysical uncertainties in the SN axion flux (specifically the pion-nucleon scattering contribution) and the rarity of such events.
• Generalization to N Axions: The authors demonstrate that for practical helioscope purposes, an $N$-axion system often reduces to an effective two-axion problem. If axion masses are clustered, they behave as a single degenerate group; if splittings are large, they wash out. Thus, the discrimination reach derived for the two-axion case applies broadly to complex multi-axion landscapes (e.g., the "axiverse") provided the mass spectrum contains features near the critical scales $m_{c, \text{magnet}}$ or $m_{c, \text{Sun}}$.

Significance and Claims
The paper claims that next-generation helioscopes like IAXO possess the capability to not only detect axions but also determine the multiplicity of the species responsible for the signal.

• Fundamental Physics: Establishing the presence of multiple axions would provide a direct handle on the mass scale of the underlying axion system, offering insights into the structure of the "axiverse" and potentially diagnosing whether the system solves the strong CP problem (via the QCD axion sum rule).
• Dark Matter: Identifying the mass splitting and couplings would guide targeted haloscope searches to determine if the detected particles constitute dark matter.
• Experimental Design: The results highlight the critical importance of X-ray detector energy resolution for probing the quasi-degenerate regime, motivating the development of high-resolution detectors for IAXO+.
• Complementarity: The work suggests a synergy between helioscopes (which measure mass splittings) and haloscopes (which measure absolute masses), providing a comprehensive strategy to unravel the multi-axion landscape beyond the Standard Model.

The authors maintain a modest tone, noting that while discrimination is possible in specific regions of the parameter space, it depends heavily on the specific mass hierarchy and mixing angles, and that supernova-based discrimination remains challenging due to theoretical uncertainties in the source flux.