On the Conditions for Sphaleron Heating of Axion-like Particles in the Presence of Fermions

Core Concepts

While light fermions can suppress the dissipation of axion-like particles through sphaleron heating, this suppression can be alleviated under various realistic conditions, including chirality-changing interactions, coupling to additional gauge fields, external sources of chiral asymmetries, and the cumulative effect of Hubble dilution.

Abstract

• Bibliographic Information: Drewes, M., & Zell, S. (2024). On Sphaleron Heating in the Presence of Fermions. arXiv preprint arXiv:2312.13739v2.
• Research Objective: This paper investigates the conditions under which sphaleron heating can efficiently dissipate the energy of axion-like particles in a hot plasma, particularly focusing on the impact of light fermions.
• Methodology: The authors employ theoretical analysis based on effective field theory and thermal field theory. They derive and analyze equations of motion for the axion field and fermionic chemical potential, considering various scenarios with different types of interactions and energy scales.
• Key Findings: The study demonstrates that the previously identified suppression of sphaleron heating by light fermions is not a universal phenomenon. The presence of chirality-violating interactions, coupling to additional non-Abelian gauge fields, or external sources of chiral asymmetries can restore the efficiency of sphaleron heating. Additionally, the cumulative effect of Hubble dilution on multiple coupled fermion species can also alleviate the suppression.
• Main Conclusions: The paper concludes that sphaleron heating remains a viable mechanism for axion dissipation in realistic cosmological scenarios, even in the presence of light fermions. This finding has significant implications for models of warm inflation, dynamical dark energy, and axionic dark matter production.
• Significance: This research provides a deeper understanding of the dynamics of axion-like particles in the early universe and expands the potential parameter space for models relying on sphaleron heating.
• Limitations and Future Research: The study primarily focuses on theoretical analysis and assumes thermal equilibrium. Further research could explore the detailed phenomenology of specific models and investigate the thermalization process in more detail.

Stats

The sphaleron rate is estimated as Γsph = csph(αNc)^5T^4, where α is the gauge coupling, Nc is the number of colors, and csph is a numerical factor of order 1.
The dissipation coefficient for the axion field due to sphaleron heating is γs ~ (αNc)^5T^3/f^2, where f is the axion decay constant.
The rate of chirality violation due to a fermion mass term is γch = κNcαm^2/T, where m is the fermion mass and κ is a coefficient of order 1.
The rate of chirality violation due to a Yukawa interaction is γch ~ y^2T, where y is the Yukawa coupling constant.

Quotes

Key Insights Distilled From

On Sphaleron Heating in the Presence of Fermions

by Marco Drewes... at arxiv.org 11-12-2024

https://arxiv.org/pdf/2312.13739.pdf

Deeper Inquiries

How would the presence of additional interactions or particle content beyond the simplified models considered in the paper affect the efficiency of sphaleron heating?

The paper primarily focuses on simplified models to illustrate the key mechanisms by which light fermions can suppress or restore sphaleron heating. Introducing additional interactions or particles can significantly impact the efficiency of this non-perturbative process. Here's how:

Modified Thermalization Rates: New interactions can alter the thermalization rates of particles in the plasma. If these rates become comparable to or slower than the Hubble expansion rate, the assumption of local thermal equilibrium, crucial for the paper's analysis, might break down. This could lead to a more intricate interplay between particle production, thermalization, and sphaleron transitions, potentially affecting the efficiency of energy transfer.

New Sources of Chirality Violation: The paper highlights that chirality-violating interactions are essential for restoring sphaleron heating in the presence of light fermions. Introducing new particles with such interactions, even if they only indirectly couple to the fermions participating in the sphaleron process, can open up additional channels for chirality violation. This could enhance the effective dissipation rate and make sphaleron heating more efficient.

Resonances and Threshold Effects: New particles could introduce resonance effects or modify the available phase space for sphaleron transitions, depending on their masses and couplings. For instance, if a new particle has a mass comparable to the energy scale of the sphaleron, resonant production of this particle could become significant, potentially impacting the energy transfer to the thermal bath.

Modification of the Effective Potential: Interactions with new scalar fields could modify the effective potential of the axion-like field driving inflation. This modification could either enhance or suppress the slow-roll conditions required for sustained inflation, indirectly affecting the duration and efficiency of sphaleron heating.

Backreaction Effects: The paper acknowledges the technical challenges in fully accounting for backreaction effects, even in simplified models. Including additional particles and interactions would further complicate the backreaction of the produced gauge fields and fermions on the inflaton field. This could lead to non-linear dynamics that are difficult to analyze analytically but could significantly impact the overall efficiency of sphaleron heating.
In summary, while the paper provides valuable insights into the role of light fermions in sphaleron heating, extending the analysis to more realistic models with additional particles and interactions is crucial for a comprehensive understanding of this mechanism in the early universe. Numerical simulations and non-perturbative methods would likely be necessary to fully capture the complexities arising from these extensions.

Could the suppression of sphaleron heating by light fermions be exploited in alternative cosmological scenarios or for other types of particles?

Yes, the suppression of sphaleron heating by light fermions, a phenomenon explored in the paper, could potentially be exploited in various cosmological scenarios beyond warm inflation or for particles other than axion-like fields. Here are a few intriguing possibilities:

Early Universe Phase Transitions: The dynamics of phase transitions in the early universe, such as the electroweak phase transition, are sensitive to the particle content and their interactions. The suppression of sphaleron processes by light fermions could influence the dynamics of these transitions, potentially altering their order (first-order vs. second-order) and affecting the generation of baryon asymmetry or other cosmological relics.

Dark Matter Production Mechanisms: If dark matter particles couple to a hidden sector with sphaleron-like processes, the presence of light fermions in that sector could suppress their production rate. This suppression mechanism could be relevant for models where dark matter is produced thermally through interactions with a hidden sector plasma. By tuning the couplings and masses of the particles involved, one might achieve the observed dark matter relic abundance while avoiding potential overproduction issues.

Lepton Asymmetry Generation: The paper discusses the role of sphaleron processes in generating fermionic asymmetries. In scenarios where lepton number violation occurs at high energies, the suppression of sphaleron-induced washout by light fermions could play a role in preserving a primordial lepton asymmetry. This asymmetry could then be converted into the observed baryon asymmetry through sphaleron processes at lower temperatures, offering an alternative or complementary mechanism to traditional baryogenesis models.

Constraints on Hidden Sector Models: The sensitivity of sphaleron heating to the presence of light fermions could be used to constrain hidden sector models. For instance, if cosmological observations disfavor warm inflation driven by sphaleron heating in a particular energy range, it could imply constraints on the mass and couplings of light fermions in hidden sectors that interact with the inflaton field.

Gravitational Wave Signals: The dynamics of sphaleron processes, including their potential suppression by light fermions, can source gravitational waves. Depending on the energy scale and efficiency of these processes, the resulting gravitational wave signals could be detectable by future experiments, providing a unique probe of particle physics beyond the Standard Model and the dynamics of the early universe.
In conclusion, the suppression of sphaleron heating by light fermions is not limited to warm axion inflation but has broader implications for our understanding of cosmology and particle physics. Exploring these alternative scenarios and their potential observational signatures could offer valuable insights into the fundamental laws of nature and the evolution of the cosmos.

What are the broader implications of understanding energy dissipation mechanisms in the early universe for our understanding of fundamental physics and the evolution of the cosmos?

Understanding energy dissipation mechanisms in the early universe is crucial for unraveling the intricate interplay between particle physics and cosmology. It holds profound implications for our understanding of fundamental physics and the evolution of the cosmos in several key ways:

Testing Physics Beyond the Standard Model: The energy scales prevalent in the early universe, far exceeding those achievable in terrestrial experiments, provide a unique testing ground for physics beyond the Standard Model. Energy dissipation mechanisms, often involving hypothetical particles and interactions, can leave distinctive imprints on cosmological observables like the cosmic microwave background radiation or the abundance of light elements. By studying these observables, we can constrain or potentially discover new physics beyond the realm of current experimental reach.

Unveiling the Inflaton's Identity: Inflation, a period of rapid expansion in the very early universe, is a cornerstone of modern cosmology. However, the nature of the inflaton, the field driving inflation, remains elusive. Energy dissipation mechanisms during inflation, such as those involving couplings between the inflaton and other fields, can significantly impact the inflationary dynamics and the generation of primordial density perturbations. These perturbations, in turn, seed the formation of large-scale structures in the universe. By scrutinizing the detailed properties of these structures, we can gain insights into the inflaton's potential and its interactions, shedding light on the fundamental physics driving inflation.

Probing the Thermal History of the Universe: The thermal history of the universe, from the extremely hot and dense state shortly after the Big Bang to the cooler and more dilute universe we observe today, is shaped by the interplay between expansion and energy dissipation. Understanding these mechanisms is crucial for reconstructing this thermal history and addressing fundamental questions like the origin of matter-antimatter asymmetry or the formation of dark matter.

Connecting Particle Physics to Cosmology: Energy dissipation mechanisms often involve non-perturbative effects in quantum field theory, such as sphaleron processes, which are challenging to study in other contexts. The early universe provides a natural laboratory for exploring these non-perturbative phenomena and their interplay with gravity. This interplay can have profound implications for our understanding of quantum field theory in curved spacetime and the unification of fundamental forces.

Predicting Gravitational Wave Signals: As mentioned earlier, energy dissipation processes in the early universe can generate gravitational waves. Detecting these primordial gravitational waves would provide a unique window into the very early universe, allowing us to probe energy scales and epochs inaccessible by electromagnetic observations. This would open up a new avenue for testing cosmological models and exploring the fundamental nature of gravity.
In conclusion, unraveling the complexities of energy dissipation mechanisms in the early universe is not merely an academic exercise but a crucial endeavor with far-reaching implications. It holds the key to unlocking some of the deepest mysteries in fundamental physics and cosmology, potentially revolutionizing our understanding of the universe's origin, evolution, and the fundamental laws governing its behavior.