M. Adeel Ajaib

Physicist | Data Scientist | Researcher

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Representation Freedom: Implications for Electroweak Baryogenesis and Neutrinoless Double Beta Decay

November 8, 2024

Note: This article was generated by the AI model Claude based on research findings.

Introduction

Two of the most profound mysteries in particle physics concern the origin of matter in the universe and the nature of neutrino mass. Electroweak baryogenesis attempts to explain why the universe contains matter rather than antimatter, while neutrinoless double beta decay could reveal whether neutrinos are their own antiparticles. The discovery of representation-dependent scattering phenomena in the Dirac equation offers new perspectives on both puzzles, suggesting that representation freedom might play a crucial role in CP violation, lepton number violation, and the generation of the matter-antimatter asymmetry.

The Matter-Antimatter Asymmetry

The universe we observe is composed almost entirely of matter, with very little antimatter. This asymmetry requires explanation, as the Big Bang should have produced equal amounts of matter and antimatter. Sakharov identified three necessary conditions for baryogenesis:

Electroweak Baryogenesis

Electroweak baryogenesis proposes that the matter-antimatter asymmetry was generated during the electroweak phase transition in the early universe, when the Higgs field acquired its vacuum expectation value. The Standard Model provides the necessary ingredients: baryon number violation through sphaleron processes, CP violation through the CKM matrix, and a potential first-order phase transition. However, Standard Model CP violation is far too weak to explain the observed asymmetry.

Representation-Dependent CP Violation

The recent discovery that quantum interference can be representation-dependent suggests a new source of CP violation. If different representations lead to different relative phases between scattering amplitudes, this could contribute additional CP-violating effects beyond those in the CKM matrix. Specifically:

Quantitative Implications

For successful electroweak baryogenesis, the baryon-to-photon ratio must be approximately 6 × 10-10. The Standard Model produces a ratio orders of magnitude too small. Representation-dependent effects could bridge this gap if:

Neutrinoless Double Beta Decay

Neutrinoless double beta decay (0νββ) is a hypothetical nuclear process where two neutrons simultaneously convert to protons, emitting two electrons but no neutrinos. This process violates lepton number by two units and can only occur if neutrinos are Majorana particles (identical to their own antiparticles). Observation of 0νββ would be revolutionary, establishing that lepton number is not conserved and potentially explaining the matter-antimatter asymmetry through leptogenesis.

Standard Theory of 0νββ

The rate of 0νββ depends on the effective Majorana mass:

mββ = |Σi Uei2 mi|

where Uei are elements of the PMNS mixing matrix and mi are neutrino mass eigenvalues. Current experiments constrain mββ < 0.1-0.3 eV, with next-generation experiments aiming for sensitivities down to ~10 meV.

Representation Dependence in 0νββ

Representation freedom could affect neutrinoless double beta decay in several ways:

1. Nuclear Matrix Elements

The 0νββ rate depends on nuclear matrix elements that describe how two neutrons in a nucleus can simultaneously undergo beta decay. These matrix elements involve virtual neutrino propagation between the two decay vertices. If representation affects how neutrinos couple to nucleons, the matrix elements would be representation-dependent.

2. Effective Majorana Mass

The effective Majorana mass mββ involves a coherent sum over neutrino mass eigenstates. Representation-dependent phases could affect this sum:

3. Beyond Light Neutrino Exchange

While standard 0νββ assumes light Majorana neutrino exchange, other mechanisms exist:

Connection Between Baryogenesis and 0νββ

Leptogenesis provides an alternative to electroweak baryogenesis, generating a lepton asymmetry through heavy neutrino decays that is later converted to a baryon asymmetry via sphaleron processes. Representation freedom connects these seemingly disparate phenomena:

Unified Framework

Experimental Signatures and Tests

For Electroweak Baryogenesis

For 0νββ

Theoretical Challenges and Open Questions

Consistency Requirements

Model Building

Phenomenological Predictions

Testable Scenarios

If representation freedom significantly affects baryogenesis and 0νββ, specific predictions emerge:

Connection to Other Beyond Standard Model Physics

Supersymmetry

SUSY models naturally provide additional sources of CP violation for baryogenesis and new contributions to 0νββ. Representation freedom in the SUSY sector could:

String Theory

String compactifications can generate both Majorana neutrino masses and sources of CP violation. Representation freedom might:

Conclusion

The implications of representation freedom for electroweak baryogenesis and neutrinoless double beta decay are profound. These two phenomena—explaining the existence of matter in the universe and probing the nature of neutrino mass—are among the most important unsolved problems in particle physics. The discovery that quantum mechanical scattering can be representation-dependent suggests new mechanisms for both:

Near-term experiments will test these ideas. Next-generation 0νββ searches will reach the sensitivity needed to see representation-dependent modifications, while precision measurements of CP violation at colliders and in low-energy systems will constrain new sources of CP violation. If representation freedom plays a role in these fundamental processes, we may be on the verge of understanding not just what the laws of nature are, but why they take the particular mathematical form they do.

References

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