Axions and Other Hypothetical Particles

1. Axions: The Invisible, Lightweight Particle Hypothesized to Explain Dark Matter

Axions are hypothetical particles proposed in the 1970s to solve a problem known as the strong CP problem in quantum chromodynamics (QCD). The term CP refers to the combination of charge (C) and parity (P) symmetries, which dictate how particles behave if their charges and spatial orientations are reversed. According to theoretical predictions, certain reactions involving quarks (the particles that make up protons and neutrons) should violate CP symmetry. However, experimentally, CP violation does not occur in strong interactions, suggesting an unknown mechanism behind this symmetry preservation. Physicists Roberto Peccei and Helen Quinn introduced the axion concept to explain this mystery.

Properties of Axions:

• Mass: Axions are expected to have extremely low masses, ranging from micro-electronvolts (µeV) to milli-electronvolts (meV).
• Charge and Spin: They are electrically neutral and are considered to have no intrinsic spin, making them scalar particles.
• Weak Interactions: Axions interact only very weakly with other particles, meaning they are nearly invisible and hard to detect.

Mathematical Representation of Axions

The interaction of axions with electromagnetic fields can be represented by the axion-photon coupling term in the Lagrangian (the function describing a system's dynamics). This term is often written as:

$$\mathcal{L}_{a\gamma} = -\frac{g_{a\gamma}}{4} a F_{\mu\nu} \tilde{F}^{\mu\nu}$$

where:

• $g_{a\gamma}$ is the axion-photon coupling constant,
• $a$ is the axion field,
• $F_{\mu\nu}$ is the electromagnetic field tensor, and
• $\tilde{F}^{\mu\nu}$ is the dual of the electromagnetic field tensor.

This coupling term implies that axions could convert into photons (and vice versa) in the presence of a strong magnetic field, a feature that scientists attempt to exploit in detection experiments.

Axion Experiments

Several ongoing experiments aim to detect axions:

• Axion Dark Matter Experiment (ADMX): This experiment looks for axions converting into microwave photons within a resonant cavity under a magnetic field.
• Haloscope Searches: These experiments use microwave cavities in high magnetic fields to detect potential axion-photon conversions.
• Helioscope Searches: For example, the CERN Axion Solar Telescope (CAST) looks for axions coming from the Sun, which would convert into photons when they pass through a magnetic field.

Axions and Dark Matter

One of the most exciting aspects of axions is that they could make up dark matter, the mysterious, unseen matter that appears to constitute around 27% of the universe’s mass-energy content. Since axions are very stable, nearly invisible, and weakly interacting, they fit the profile of a good dark matter candidate.

2. Supersymmetric Particles: Theoretical Partners of Known Particles

Supersymmetry (SUSY) is a proposed extension of the Standard Model that postulates each particle has a “superpartner” with different spin properties. This theory attempts to solve some critical issues in particle physics, such as:

• Hierarchy Problem: Why the Higgs boson has a much lower mass than expected based on quantum corrections.
• Dark Matter Candidate: Some supersymmetric particles could account for dark matter.

In SUSY, each fermion (particles like quarks and electrons that make up matter) has a bosonic partner (particles that mediate forces), and each boson has a fermionic partner. For example:

• Electron (fermion) ↔ Selectron (bosonic superpartner)
• Quark ↔ Squark
• Photon (boson) ↔ Photino (fermionic superpartner)

Supersymmetric Particles and the Minimal Supersymmetric Standard Model (MSSM)

The MSSM is the simplest version of SUSY, extending the Standard Model by introducing superpartners for all Standard Model particles. It also introduces a symmetry-breaking mechanism, adding a Higgs sector to give mass to these particles.

Theoretical Equations and Predictions in SUSY

Supersymmetry involves complex algebraic structures and fields. The Wess-Zumino model is one example, which introduces a Lagrangian for a simple supersymmetric system. Mathematically, SUSY transformations involve anticommuting spinor fields and are represented by the equation:

$$\delta \phi = \bar{\epsilon} \psi, \quad \delta \psi = \partial_\mu \phi \gamma^\mu \epsilon$$

where $\phi$ is a scalar field, $\psi$ is a fermion, and $\epsilon$ is a small spinor parameter.

Experimental Searches for Supersymmetric Particles

To date, no supersymmetric particles have been observed. However, experiments at Large Hadron Collider (LHC) at CERN continue to search for these particles, especially looking for signs of particles like the neutralino—a stable, neutral SUSY particle that could be a dark matter candidate.

3. Other Theoretical Particles: Gravitons, Sterile Neutrinos, and WIMPs

Beyond axions and SUSY particles, other hypothetical particles are considered in various theories aiming to unify forces or explain dark matter.

Gravitons: Hypothetical Particles for Quantum Gravity

In quantum field theory, each fundamental force has a corresponding particle:

• The photon mediates electromagnetism,
• Gluons mediate the strong force, and
• W and Z bosons mediate the weak force.

By analogy, a particle known as the graviton is proposed to mediate gravity, though no gravitons have been detected. A potential graviton's field could be described in theoretical frameworks like string theory, but it is challenging to reconcile with general relativity due to issues like renormalization (handling infinities in calculations).

Sterile Neutrinos and Dark Matter

Sterile neutrinos are a proposed type of neutrino that does not interact via the weak force, unlike known neutrino types. Sterile neutrinos could explain dark matter or contribute to phenomena observed in neutrino oscillations.

WIMPs (Weakly Interacting Massive Particles)

WIMPs are another popular candidate for dark matter. These particles, which have higher masses and weak interactions, have been the target of numerous direct-detection experiments like XENON1T and LUX-ZEPLIN, which look for signs of WIMPs scattering off nuclei.

4. Baryon Asymmetry Problem: Why Is There More Matter Than Antimatter?

One of the unsolved mysteries in cosmology is the Baryon Asymmetry Problem, which asks why the universe appears to be made mostly of matter, with very little antimatter. According to the Standard Model, matter and antimatter should have been created in equal amounts at the Big Bang, leading to their mutual annihilation.

Possible Explanations for Baryon Asymmetry

Some hypotheses attempt to explain this imbalance:

1. CP Violation in the Early Universe: Small CP violations, particularly in quark interactions, may have led to a slight excess of matter over antimatter.
2. Leptogenesis: Proposed by researchers such as M. Fukugita and T. Yanagida, this theory suggests that CP-violating decays of heavy neutrinos in the early universe created an excess of leptons over antileptons, which later transferred to baryons.
3. Electroweak Baryogenesis: This theory proposes that interactions involving the Higgs field at high temperatures in the early universe may have broken baryon symmetry.

References for Further Exploration

For further reading and current research updates:

1. Peccei, R. D., & Quinn, H. R. (1977). CP Conservation in the Presence of Instantons. Physical Review Letters, 38(25), 1440–1443.
2. Arkani-Hamed, N., Dimopoulos, S., & Dvali, G. (1998). The Hierarchy Problem and New Dimensions at a Millimeter. Physics Letters B, 429(3–4), 263–272.
3. Ellis, J. R., & Gaillard, M. K. (1979). Higgs Bosons in GUTs. Nuclear Physics B, 150(1), 141–162.
4. Aghanim, N., et al. (2020). Planck 2018 Results. VI. Cosmological Parameters. Astronomy & Astrophysics, 641, A6.

The discovery of any of these particles would represent a paradigm shift in physics, potentially leading to new laws and a deeper understanding of the universe.