insight - Scientific Computing - # Higgs Inflation and Axion Physics

The Impact of Large Non-Minimal Coupling on Gauge Couplings and Axion Physics

Q: How do the findings of this research impact our understanding of the early universe and the evolution of fundamental forces?

This research significantly challenges our conventional understanding of the early universe and the evolution of fundamental forces, particularly the strong force described by Quantum Chromodynamics (QCD). Here's how: Rethinking the Strength of Fundamental Forces: The Standard Model of particle physics, our best description of fundamental forces, assumes that the strengths of these forces evolve with energy but remain relatively consistent throughout the history of the universe. This research suggests that the presence of a large non-minimal coupling of a scalar field to gravity could lead to dramatic shifts in these couplings, particularly the QCD coupling, during the early universe. This implies that the strong force may have been significantly stronger in the early universe than it is today. Impact on Early Universe Dynamics: A stronger QCD during the early universe would have profound consequences. It could influence the dynamics of the electroweak phase transition, potentially affecting baryogenesis mechanisms and the abundance of light elements. It could also alter the inflationary dynamics, impacting the generation of primordial density perturbations and gravitational waves. New Perspective on Axion Physics: Axions are hypothetical particles proposed to solve the strong CP problem in QCD. This research shows that the presence of a large non-minimal coupling could significantly impact axion physics. It could lead to a heavier axion, affect its abundance in the early universe, and alter the constraints from isocurvature perturbations. In summary, this research compels us to reconsider the seemingly static nature of fundamental forces and explore the possibility of dramatic shifts in their strengths during the early universe. This has profound implications for our understanding of early universe cosmology, particle physics beyond the Standard Model, and the search for new physics.

Q: Could the presence of a large non-minimal coupling and the resulting gauge coupling jump have implications for other beyond-the-Standard-Model physics scenarios, such as grand unification theories?

Yes, the presence of a large non-minimal coupling and the resulting gauge coupling jump could have significant implications for various beyond-the-Standard-Model physics scenarios, including Grand Unified Theories (GUTs): Altered Unification Scale: GUTs propose that at extremely high energies, the strong, weak, and electromagnetic forces unify into a single force. The energy scale at which this unification occurs is crucial for GUT phenomenology. The presence of a large non-minimal coupling and gauge coupling jumps could significantly alter the running of these couplings, potentially shifting the unification scale to higher or lower energies. This could impact the predictions of proton decay, the existence of magnetic monopoles, and other GUT-scale phenomena. New Mechanisms for Symmetry Breaking: GUTs often rely on the Higgs mechanism to break the unified force into the separate forces we observe today. The presence of a large non-minimal coupling could introduce new scalar fields and interactions, potentially leading to alternative mechanisms for symmetry breaking in GUTs. Impact on Cosmological Phase Transitions: GUTs predict a series of cosmological phase transitions in the early universe as the unified force breaks down into its constituent forces. The presence of a large non-minimal coupling and gauge coupling jumps could significantly alter the dynamics of these phase transitions, potentially affecting the generation of baryon asymmetry, cosmic strings, and other cosmological relics. In essence, the findings of this research introduce a new layer of complexity to beyond-the-Standard-Model physics scenarios like GUTs. It highlights the possibility of a more dynamic and evolving landscape of fundamental forces in the early universe, potentially leading to new insights and predictions for these theories.

Core Concepts

Large non-minimal coupling of a scalar field to gravity can induce significant shifts in gauge couplings, leading to enhanced small instanton effects and impacting axion physics, particularly in the context of Higgs inflation.

Abstract

Bibliographic Information: Wada, J., & Yin, W. (2024). Gauge coupling jump and small instantons from a large non-minimal coupling. arXiv preprint arXiv:2411.00768.
Research Objective: This paper investigates the threshold effects of a large non-minimal coupling between a scalar field and the Ricci scalar on gauge couplings, focusing on the implications for small instanton contributions and axion physics.
Methodology: The authors employ theoretical calculations within the framework of both Metric and Palatini formulations of gravity. They analyze the impact of loop corrections from quark Yukawa interactions on the QCD gauge coupling. The study also utilizes the Wilsonian effective action approach to investigate small instanton effects.
Key Findings: The research reveals that a large non-minimal coupling can lead to a jump in the gauge coupling at an intermediate energy scale. This jump, attributed to non-renormalizability and the presence of "higher dimensional terms," can enhance small instanton contributions. The study specifically highlights that the QCD axion's properties, including its mass, abundance, and isocurvature perturbations, are significantly affected by this phenomenon.
Main Conclusions: The authors conclude that the presence of a large non-minimal coupling for any scalar field can substantially alter axion physics. They emphasize the need to consider these effects when studying axion models, particularly in the context of Higgs inflation.
Significance: This research provides valuable insights into the interplay between gravity, scalar fields, and gauge theories. It highlights the potential impact of non-minimal couplings on fundamental particle physics phenomena, particularly in the early universe.
Limitations and Future Research: The study primarily focuses on theoretical calculations and relies on certain assumptions, such as the specific form of the threshold effects. Further investigations, potentially involving numerical simulations or exploration of specific UV completions, could provide a more comprehensive understanding of these phenomena.

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Stats

The QCD scale during inflation is estimated as ΛQCD,inf ∼Mpl/√ξ e^(−8π^2/11g^2).
The axion mass during inflation is estimated as ma,inf ∼Λ^2QCD,inf/fa.
The small instanton contribution is estimated as Vinst(θ) ∼10^−3(8π^2/g^2)^6 M^4plξ^2 e^(−8π^2/g^2) cos[θ]×(1/4π)^7.
The small instanton contribution in the presence of nf quarks is estimated as δΛV (θ) ∼10^−3(8π^2/g^2)^6 M^4plξ^2 e^(−8π^2/g^2) cosθ^(-7−nf/3)Πiyi.
The heavy QCD axion mass is estimated as ma ≃4 GeVg^−6e^(−4π^2/g^2) (10^10/ξ) 10^16 GeV/fa.

Quotes

"If a scalar field couples to the Ricci scalar with a large non-minimal coupling, the Standard Model coupling parameters can differ above and below an intermediate field range of the scalar due to the non-renormalizability."
"In this paper, we point out that in the presence of a large non-minimal coupling to a scalar, there is a threshold effect, naturally causing the shift of the coupling when the scalar field value is around the intermediate scale..."
"We show that the small instanton contribution can be enhanced if the gauge coupling becomes strong in the UV regime due to this effect."

Key Insights Distilled From

Gauge coupling jump and small instantons from a large non-minimal coupling

by Juntaro Wada... at arxiv.org 11-04-2024

https://arxiv.org/pdf/2411.00768.pdf

Gauge coupling jump and small instantons from a large non-minimal coupling

Deeper Inquiries

How do the findings of this research impact our understanding of the early universe and the evolution of fundamental forces?

This research significantly challenges our conventional understanding of the early universe and the evolution of fundamental forces, particularly the strong force described by Quantum Chromodynamics (QCD). Here's how:

Rethinking the Strength of Fundamental Forces: The Standard Model of particle physics, our best description of fundamental forces, assumes that the strengths of these forces evolve with energy but remain relatively consistent throughout the history of the universe. This research suggests that the presence of a large non-minimal coupling of a scalar field to gravity could lead to dramatic shifts in these couplings, particularly the QCD coupling, during the early universe. This implies that the strong force may have been significantly stronger in the early universe than it is today.

Impact on Early Universe Dynamics: A stronger QCD during the early universe would have profound consequences. It could influence the dynamics of the electroweak phase transition, potentially affecting baryogenesis mechanisms and the abundance of light elements. It could also alter the inflationary dynamics, impacting the generation of primordial density perturbations and gravitational waves.

New Perspective on Axion Physics:  Axions are hypothetical particles proposed to solve the strong CP problem in QCD. This research shows that the presence of a large non-minimal coupling could significantly impact axion physics. It could lead to a heavier axion, affect its abundance in the early universe, and alter the constraints from isocurvature perturbations.
In summary, this research compels us to reconsider the seemingly static nature of fundamental forces and explore the possibility of dramatic shifts in their strengths during the early universe. This has profound implications for our understanding of early universe cosmology, particle physics beyond the Standard Model, and the search for new physics.

Could the presence of a large non-minimal coupling and the resulting gauge coupling jump have implications for other beyond-the-Standard-Model physics scenarios, such as grand unification theories?

Yes, the presence of a large non-minimal coupling and the resulting gauge coupling jump could have significant implications for various beyond-the-Standard-Model physics scenarios, including Grand Unified Theories (GUTs):

Altered Unification Scale: GUTs propose that at extremely high energies, the strong, weak, and electromagnetic forces unify into a single force. The energy scale at which this unification occurs is crucial for GUT phenomenology. The presence of a large non-minimal coupling and gauge coupling jumps could significantly alter the running of these couplings, potentially shifting the unification scale to higher or lower energies. This could impact the predictions of proton decay, the existence of magnetic monopoles, and other GUT-scale phenomena.

New Mechanisms for Symmetry Breaking: GUTs often rely on the Higgs mechanism to break the unified force into the separate forces we observe today. The presence of a large non-minimal coupling could introduce new scalar fields and interactions, potentially leading to alternative mechanisms for symmetry breaking in GUTs.

Impact on Cosmological Phase Transitions: GUTs predict a series of cosmological phase transitions in the early universe as the unified force breaks down into its constituent forces. The presence of a large non-minimal coupling and gauge coupling jumps could significantly alter the dynamics of these phase transitions, potentially affecting the generation of baryon asymmetry, cosmic strings, and other cosmological relics.
In essence, the findings of this research introduce a new layer of complexity to beyond-the-Standard-Model physics scenarios like GUTs. It highlights the possibility of a more dynamic and evolving landscape of fundamental forces in the early universe, potentially leading to new insights and predictions for these theories.

If the universe indeed experienced a phase of stronger QCD in its early history, what observable signatures could we look for in cosmological data to confirm or refute this hypothesis?

Confirming or refuting the hypothesis of a stronger QCD phase in the early universe requires searching for subtle signatures imprinted on cosmological observables. Here are some potential avenues:

Big Bang Nucleosynthesis (BBN):  BBN describes the production of light elements like helium, deuterium, and lithium in the first few minutes after the Big Bang. The abundance of these elements is sensitive to the cosmological expansion rate and the strength of the strong force. A stronger QCD during BBN could alter these abundances, potentially leaving observable signatures in the primordial element ratios.

Cosmic Microwave Background (CMB): The CMB provides a snapshot of the universe at the time of recombination, around 380,000 years after the Big Bang. While the primary CMB anisotropies are primarily determined by gravity, a stronger QCD could leave subtle imprints on the CMB polarization pattern, particularly the B-mode polarization, through its influence on the primordial plasma.

Stochastic Gravitational Wave Background: Inflationary models predict the generation of a stochastic background of gravitational waves. The amplitude and spectral shape of this background depend on the inflationary dynamics, which could be sensitive to a stronger QCD. Detecting and characterizing this gravitational wave background could provide indirect evidence for a stronger QCD phase.

Axion Searches: If the QCD axion exists and was affected by a stronger QCD in the early universe, it could have different properties than conventionally assumed. This could impact axion dark matter searches, potentially shifting the target mass range or altering the expected signals in experiments.

Rare Decays and Collider Searches:  While a stronger QCD in the early universe might not directly impact present-day collider experiments, it could motivate specific models and parameter spaces in beyond-the-Standard-Model physics. These models might predict new particles or rare decays that could be probed in future collider experiments.
It's important to note that these signatures are likely to be subtle and challenging to disentangle from other cosmological effects. However, with increasingly precise cosmological observations and advancements in theoretical modeling, we can hope to probe the history of the strong force and potentially uncover evidence for a stronger QCD phase in the early universe.