Axion Masses as an Inevitable Consequence of Supersymmetry Breaking

TL;DR

This work shows that soft supersymmetry breaking can be the sole origin of Peccei–Quinn symmetry breaking and axion mass generation, aligning the PQ scale $f_a$ with the gravitino mass via $f_a \sim m_{3/3}/\kappa$ and giving $m_a^2 \sim 4|B_S|$. Consequently, the axion, saxion, and axino masses are all controlled by the SUSY-breaking scale, producing a predictive, correlated axion supermultiplet spectrum that behaves as an axion-like particle with $m_a \gg m_{a,\mathrm{QCD}}$ in much of parameter space. Planck-suppressed PQ-violating operators are suppressed by model-building choices, ensuring the strong CP problem remains effectively controlled by CP alignment rather than QCD instantons. The framework yields rich phenomenology with laboratory, cosmological, and astrophysical constraints providing complementary probes, and it identifies viable regions testable by current and future intensity-frontier experiments such as beam-dump searches and rare-decay probes.

Abstract

We investigate a supersymmetric framework in which soft supersymmetry-breaking effects provide the dominant origin of Peccei--Quinn (PQ) symmetry breaking and axion mass generation. In the supersymmetric limit the theory possesses an exact PQ symmetry and a massless axion, while the inclusion of soft terms proportional to the gravitino mass induces spontaneous PQ breaking, stabilizes the saxion direction, and generates a mass for the axion. As a consequence, the axion, saxion, and axino masses are all controlled by the supersymmetry-breaking scale, leading to a correlated and predictive spectrum of axion-like states. The presence of explicit soft PQ-breaking terms raises the question of vacuum alignment and CP violation. We show that although the axion mass does not originate from QCD instantons, the induced strong CP phase is parametrically suppressed by the hierarchy between the QCD-induced and soft-induced axion masses. As a result, the explicit breaking does not generate an observable CP-violating vacuum angle across the parameter space of interest. We analyze the phenomenological implications of this scenario, including axion lifetimes, axion--photon couplings, and laboratory, astrophysical, and cosmological constraints. Direct confrontations with beam-dump and collider searches, together with Big Bang nucleosynthesis bounds, demonstrate that a substantial region of parameter space remains viable and testable. The framework thus provides a self-consistent and phenomenologically rich realization of axion-like particles whose masses arise predominantly from soft supersymmetry breaking.

Figures (10)

• Figure 1: Axion lifetime $\tau_a$ as a function of the axion mass $m_a$ for a representative scan over the supersymmetry-breaking parameter space. The shaded region corresponds to axion lifetimes exceeding $\mathcal{O}(1\,\mathrm{s})$, which are excluded by Big Bang nucleosynthesis constraints. Axions in the present framework decay well before the onset of BBN for a wide range of parameters, ensuring cosmological viability.
• Figure 2: Axion--photon coupling $g_{a\gamma}$ as a function of the axion mass $m_a$. The scan illustrates the region relevant for heavy axion-like particles. Existing constraints from beam-dump experiments and laboratory searches apply predominantly at lower masses and weaker couplings, while future experiments may probe portions of the parameter space shown here.
• Figure 3: Parameter space in the $(m_a,f_a)$ plane. Points corresponding to axion lifetimes shorter than $\mathcal{O}(1\,\mathrm{s})$ are cosmologically allowed, while longer lifetimes are excluded by Big Bang nucleosynthesis. This plot illustrates the regions consistent with cosmological constraints.
• Figure 4: Scan of the dimensionless soft PQ-breaking parameter $B_S/m_{3/2}^2$ as a function of the supersymmetry-breaking scale $m_{3/2}$. The distribution indicates that the required soft breaking terms arise naturally without fine-tuning.
• Figure 5: Axion lifetime $\tau_a$ as a function of the axion decay constant $f_a$ obtained from a model-consistent parameter scan. The dashed horizontal line indicates the conservative Big Bang nucleosynthesis (BBN) bound $\tau_a \simeq 1\,\mathrm{s}$. Parameter points above the line correspond to long-lived axions excluded by BBN, while points below the line are cosmologically allowed. The absolute normalization assumes an order-one axion--photon anomaly coefficient.