Heavy QCD Axions: Theories & Colliders

• Heavy QCD axions are axion states with masses far above the traditional sub-eV range, generated by UV modifications that alter standard QCD dynamics.
• They emerge from frameworks like extra-dimensional, mirror symmetry, and product group models that enhance axion masses while suppressing PQ-violating operators.
• Their TeV-scale masses and strong gluon couplings open unique collider discovery channels, overcoming traditional astrophysical constraints.

Heavy QCD axions are defined as axion states associated with the solution to the strong CP problem, but with masses significantly larger than those predicted by the traditional “invisible axion” relationship $m_a \sim \Lambda_{\mathrm{QCD}}^2/f_a$. These heavy states arise in frameworks where the axion potential is dominantly modified by ultraviolet (UV) contributions, mirror symmetry, product group and extra-dimensional constructions, or additional confining sectors, allowing axion masses in the 100 MeV–multi‐TeV range even for decay constants at or near the weak or TeV scale. Such scenarios enable phenomenology that circumvents astrophysical limits and opens up collider-based discovery channels, while maintaining (by construction) the solution to both the strong CP and axion quality problems.

1. Theoretical Motivation and Definition

The QCD axion is introduced as a dynamical solution to the strong CP problem, via the Peccei–Quinn (PQ) mechanism, which requires a pseudo–Nambu–Goldstone boson with a nonderivative, anomalous coupling to gluons. The traditional axion mass is set solely by nonperturbative QCD dynamics: $m_a^{(\mathrm{QCD})} \sim f_\pi m_\pi/f_a$, restricting $f_a \gtrsim 10^8$ GeV and yielding sub-eV axions, to evade laboratory, astrophysical, and cosmological bounds. However, high-energy completions with additional non-QCD contributions to the axion potential can raise $m_a$ to the electroweak or TeV scale, even for modest $f_a \sim 100$ GeV–10 TeV. This “heavy QCD axion” regime is explored as a resolution of the axion quality problem, which refers to the sensitivity of the axion’s potential to Planck-suppressed explicit PQ-violating operators. In these UV-improved models, the heavier axion potential suppresses dangerous corrections and broadens the accessible mass and coupling parameter space (Higaki et al., 2015, Gherghetta et al., 2016, Hook et al., 2019, Bedi et al., 12 Sep 2025).

2. Ultraviolet Constructions and Axion Quality

Multiple UV scenarios enable the appearance of TeV-scale axion masses while preserving the PQ solution and suppressing explicit PQ violation:

• Product Group Models: QCD arises from multiple SU(3) factors broken to the diagonal at high scale $M$, with each subgroup carrying its own axion. Small-instanton contributions are enhanced for individual groups, producing a linear axion combination that couples dominantly to $G\tilde G$, and has an enhanced mass $m_a \sim$ 100 GeV–TeV for $f_a$ in the TeV range. The enhanced short-distance contributions dilute the sensitivity to Planck-suppressed operators (Bedi et al., 12 Sep 2025).
• Extra-Dimensional Constructions: In 5D setups where QCD propagates in a flat extra dimension, the axion may emerge as the phase of a bulk complex scalar. The 4D effective decay constant receives a volume enhancement, and KK-instanton effects further boost the axion mass. This allows $f_a \sim$ TeV and $m_a$ up to several TeV (Bedi et al., 12 Sep 2025).
• Mirror Symmetry Models: A discrete $\mathbb{Z}_2$ symmetry relates the SM to a high-scale mirror sector. If the mirror QCD confines at a higher scale $\Lambda_{\mathrm{QCD}}'$, the axion mass becomes $m_a \sim \Lambda_{\mathrm{QCD}}'^2/f_a$, orders of magnitude above the standard QCD value. The shared global PQ symmetry cancels the $\bar\theta$ angle in both sectors, and the large mirror contribution reinforces the axion potential against PQ-violating effects (Hook et al., 2019, Bedi et al., 12 Sep 2025).
• Color Unification Models: The color group is unified into a larger gauge group that breaks at high scale into $SU(3)_c$ and an additional confining group. The axion potential receives a dominant contribution from the additional strong sector, leading to $m_a \gg m_a^{(\mathrm{QCD})}$ for a given $f_a$. Because the only renormalizable CP violation is inherited from the SM Yukawas, the cancellation of the strong CP phase remains robust (Valenti et al., 2022, Bedi et al., 12 Sep 2025).
• Asymptotically Safe QCD: If QCD develops an interacting UV fixed point, small-size instanton effects enhance the axion mass via a breakdown of the usual exponential suppression $\exp(-2\pi/\alpha_s)$. The net result is a parametrically heavier axion mass compared to the asymptotically free scenario (Kobakhidze, 2016).

3. Phenomenology at High-Energy Colliders

Heavy QCD axions with TeV-scale masses are phenomenologically distinguished from generic ALPs by their strong gluon coupling $$\mathcal{L} \supset (c_3 \alpha_s/8\pi f_a) a G\tilde{G}$$.

• Production Mechanisms: Although the gluon coupling determines the axion’s primary decay, production at $e^+e^-$ or $\mu^+\mu^-$ colliders is dominantly via electroweak processes, such as vector boson fusion (VBF) and associated production, enabled by effective couplings to $B\tilde{B}$ and $W\tilde{W}$ ($c_1$, $c_2$ coefficients). The clean final state environment at a muon collider, with low QCD backgrounds, is particularly advantageous (Bedi et al., 12 Sep 2025).
• Decay Signatures: The dominant decay is to two gluons, yielding a high-mass dijet resonance. At hadron colliders, such a resonance is challenging to resolve against the QCD background, whereas at a muon collider, event selection (e.g., recoil Z tagging, or jet substructure analysis) enables robust discrimination. Secondary channels include $a \to \gamma\gamma$, $ZZ$, and $Z\gamma$, determined by the coefficients $c_1$, $c_2$ (Higaki et al., 2015, Gherghetta et al., 2016).
• Discovery Reach: For $c_1, c_2, c_3 = \mathcal{O}(1)$, a 3 TeV muon collider (with $\mathcal{L} \sim 1$ ab$^{-1}$) can probe $m_a$ up to $\sim$3 TeV, while a 10 TeV collider extends the reach to $m_a \sim 10$ TeV for $f_a$ in the 1–10 TeV range (Bedi et al., 12 Sep 2025). The collider program is sensitive to parameter space wholly inaccessible to astrophysical probes, which lose sensitivity at large $m_a$ and small $f_a$.

Collider	Mass Reach (TeV)	$f_a$ Reach (TeV)
LHC	$\sim 1$	$\sim 10$
$e^+ e^-$	$<$ few	$<$ few
Muon Collider	$\sim 10$	$1$–$10$

4. UV Model Consistency and the Quality Problem

• UV Stability: The suppression of Planck-suppressed PQ-violating operators is strengthened by the UV structure—either via lower $f_a$ (hence lower sensitivity as corrections scale as $(f_a/M_{\mathrm{Pl}})^d$) or by alignment or symmetry mechanisms inherent to the model. In product group scenarios, only collective violation of all the product subgroup PQ symmetries reintroduces a dangerous term, suppressing explicit breaking (Bedi et al., 12 Sep 2025).
• Quality in Extra-Dimensional Models: For axions as phases of bulk scalars, higher-dimensional operators are suppressed both by the smallness of $f_a$ and by the limited number of higher-derivative invariants that connect the PQ current to the UV (Bedi et al., 12 Sep 2025).
• Mirror Models: The shared global PQ symmetry and the presence of a large mirror QCD scale reinforce the PQ solution and make the potential shallow only to the degree that the mirror sector can dominate higher-order corrections (Hook et al., 2019, Bedi et al., 12 Sep 2025).

In all cases, heavy QCD axions can naturally evade the axion quality problem that plagues high-$f_a$ models.

5. Cosmological and Experimental Implications

• Cosmology: The modification of the axion mass and coupling can alleviate axion overproduction, avoid isocurvature constraints (especially when axions are heavy and decay before matter–radiation equality or have late–time dilution (Hook et al., 2019, Co et al., 2022)), and produce cosmological signatures such as stochastic gravitational waves from domain wall collapse (Ferreira et al., 2021, Lee et al., 12 Jul 2024). Heavy QCD axions can participate in baryogenesis scenarios (axiogenesis) through field rotation and transfer of chiral asymmetry (Co et al., 2022).
• Experimental Prospects: While conventional axion models are constrained by cooling of stars and supernovae, heavy QCD axions with $m_a \gtrsim 100$ MeV evade such constraints. High-energy colliders—especially future muon colliders—provide the most promising discovery channel through dijet resonance searches at high invariant mass, with sensitivity up to $m_a \sim 10$ TeV (Bedi et al., 12 Sep 2025). Complementary searches in B and K meson decays, displaced vertex techniques at Belle II, and dedicated dimuon resonance searches at neutrino facilities and beam dump experiments (ArgoNeuT, DUNE, SHiP, FASER 2) can probe lower-mass regions (Bertholet et al., 2021, Collaboration et al., 2022, Co et al., 2022). The relationship between $f_a$, $m_a$, and production/decay rates is discussed in detail across these proposals, especially highlighting trade-offs between production cross-section and decay length.

6. Comparison with Conventional and Other Non-QCD Axion Models

Heavy QCD axions differ from generic ALPs by their required gluon anomaly coupling and by their necessity to solve the strong CP problem in tandem with the axion quality problem. Phenomenologically, heavy QCD axions can be discovered via hadronic signatures, whereas generic ALPs are typically sought via photon or lepton final states. Their parameter space is orthogonal to the traditional QCD axion window probed by haloscopes or helioscopes. UV completions are more constrained by anomaly matching and the need to maintain vacuum alignment (ensuring the physical $\bar\theta$ vanishes), motivating models with product group structure, extra dimensions, mirror sectors, or unified color (Gherghetta et al., 2016, Bedi et al., 12 Sep 2025).

7. Summary and Outlook

Heavy QCD axions represent a theoretically motivated and phenomenologically accessible extension of the standard QCD axion framework. By allowing for TeV-scale masses and decay constants, these constructions evade the axion quality problem and open a new regime for discovery at high-energy colliders. Multiple UV frameworks—product-group models, extra-dimensional constructions, mirror symmetry, and color unification—are viable, all yielding enhanced axion mass via short-distance or exotic strong sector effects while maintaining the dynamical solution to the strong CP problem. These states can be robustly targeted at future muon colliders through hadronic resonance searches, with complementary probes at lower masses from flavor and beam dump experiments. The expanding theoretical landscape and collider sensitivity forecast a comprehensive program to probe the heavy QCD axion parameter space over the coming decade (Bedi et al., 12 Sep 2025).