Solving the strong CP problem (2501.16427v1)

Abstract: I briefly review solutions to the strong CP problem based on axions, parity invariance, CP-invariance, and present a new idea based on CP as part of a spontaneously broken flavour symmetry such as a U(1) or modular invariance.

• The paper presents three key theoretical strategies—axion models, parity-based adjustments, and modular symmetry—to resolve the strong CP problem by driving the CP-violating term below 10⁻¹¹.
• It evaluates the axion solution’s dual role in addressing CP violation and its potential connection to dark matter, highlighting experimental search prospects.
• The study proposes modular symmetry as an innovative framework linking scalar dynamics with low-energy phenomena, paving the way for future refined models.

Insights into Addressing the Strong CP Problem

In the presented paper, Alessandro Strumia addresses the longstanding strong CP problem within the framework of particle physics, offering a range of potential solutions that engage with both theoretical elegance and empirical applicability. The strong CP problem, fundamentally, concerns the observed smallness of the CP-violating term $\bar{\theta}$ in quantum chromodynamics (QCD). Despite the CKM matrix being well characterized by complex phases, experimental constraints require $\bar{\theta}$ to be extremely small, $\lesssim 10^{-11}$, thereby prompting scrutiny into potential physical explanations.

Framework of Solutions

Strumia reviews traditional solutions to this dilemma, categorizing them principally in relation to their energy scale applications:

1. Axion Solution: This theory involves the introduction of the axion, a hypothetical particle emerging from a spontaneously broken U(1) Peccei-Quinn symmetry, which dynamically drives $\bar{\theta}$ to zero. Axions remain a significant focus for experimental searches, given their implications for dark matter. Experiments probing axion-photon couplings are approaching sensitivity levels suggested by mainstream axion models.
2. Parity and CP-Invariance Solutions: Alternative theoretical interpretations explore broader symmetries, such as parity (P) and CP-invariance. These paradigms require substantial modifications to the Standard Model, including potential new scalar fields to induce symmetry breaking, with goals of conserving $\bar{\theta}$ within acceptable boundaries. The investigation into heavy quarks and CP-conserving scalar frameworks forms the crux of these hypotheses.
3. Spontaneous CP Violation through Scalar Fields: A newer proposition suggests that CP violation could inherently be tied to the vacuum expectation values of complex scalar fields within an augmented flavor symmetry, such as a global U(1) or a modular symmetry. This innovation purports CP as a flavor property that is spontaneously broken, producing small $\bar{\theta}$ values naturally aligned with experimental constraints.

Theoretical Implications and Future Directions

Strumia's approach, particularly regarding modular symmetry, holds promise for establishing a cohesive link between the geometric aspects of flavor spaces in higher dimensions and observable properties in low-energy physics. By framing CP violations in the context of modular invariance, this function offers a modulated approach to exploring scalar field characteristics without predisposing complicated symmetry breakings at all observed scales. More than conceptual elegance, this idea necessitates further refinement via detailed string theoretical models to ascertain practical veracity and anticipate measurable outcomes.

The paper underscores the interplay of gauge principles and anomaly considerations in sculpting fundamental particle interactions. Unlike the axion solution, which may suffer from the "quality problem" due to the non-perturbative nature of gravitational interactions with global symmetries, modular symmetry could provide inherent gauged countermeasures.

Experimentally, searching for modular remnants in conceivable high-energy environments remains speculative. Yet, detailed paper of potential soft supersymmetry-breaking mechanisms, alongside harnessing predictions from string compactifications, could enrich our comprehension of underlying modular structures. Such ventures may offer novel parameter spaces for detecting subtle CP violation signatures impacting both particle and cosmological phenomena.

Conclusion

While Strumia's paper methodically explores existing and novel solutions to the strong CP problem, it simultaneously serves as a catalyst for future research directions, encouraging the pragmatic union of advanced symmetry breaking concepts and empirical exploration. Bridging these gaps necessitates continued collaboration between theoretical physicists and experimentalists to unravel the uncertainties buried within the QCD vacuum and broader particle physics.