Baryon Washout, Electroweak Phase Transition, and Perturbation Theory (1101.4665v2)

Abstract: We analyze the conventional perturbative treatment of sphaleron-induced baryon number washout relevant for electroweak baryogenesis and show that it is not gauge-independent due to the failure of consistently implementing the Nielsen identities order-by-order in perturbation theory. We provide a gauge-independent criterion for baryon number preservation in place of the conventional (gauge-dependent) criterion needed for successful electroweak baryogenesis. We also review the arguments leading to the preservation criterion and analyze several sources of theoretical uncertainties in obtaining a numerical bound. In various beyond the standard model scenarios, a realistic perturbative treatment will likely require knowledge of the complete two-loop finite temperature effective potential and the one-loop sphaleron rate.

• The paper demonstrates that conventional baryon preservation criteria based on the gauge-dependent effective potential can lead to unreliable predictions.
• It introduces a gauge-independent framework leveraging Nielsen identities and a dimensionally reduced effective theory to reformulate the baryon washout criterion.
• The study integrates higher-order corrections and non-perturbative insights to refine predictions for the electroweak phase transition, impacting beyond Standard Model scenarios.

Essay on "Baryon Washout, Electroweak Phase Transition, and Perturbation Theory"

The paper "Baryon Washout, Electroweak Phase Transition, and Perturbation Theory," authored by Hiren H. Patel and Michael J. Ramsey-Musolf, presents a critical examination of the conventional perturbative approaches used to address baryon number washout in the context of electroweak baryogenesis (EWB). The paper identifies significant theoretical limitations within standard perturbative methodologies, particularly concerning the gauge dependence of the criteria typically employed to determine baryon number preservation. The authors propose a more robust, gauge-independent approach which may have significant implications for the paper of phase transitions in beyond Standard Model (BSM) scenarios.

Overview and Objectives

Electroweak baryogenesis is a compelling theoretical framework for explaining the baryon asymmetry of the universe. Successful EWB demands a first-order electroweak phase transition (EWPT) to suppress sphaleron-induced washout of the baryon asymmetry generated during this phase. Central to this analysis are two quantities: the critical temperature ($T_C$) at which the phase transition occurs, and the sphaleron rate that determines the dynamics of baryon number washout in the broken phase. Typically, the ratio of the Higgs field expectation value to the critical temperature, $\phi_{\text{min}}(T_C) / T_C$, is used as a criterion for baryon number preservation.

Key Findings and Contributions

One of the pivotal findings of the paper is that the traditional criterion for baryon number preservation—derived from the effective potential in perturbation theory—is inherently gauge dependent. This conclusion arises from the observation that the finite-temperature effective potential's minima, used to define $\phi_{\text{min}}(T_C)$, vary with the gauge-fixing parameter.

The authors develop an improved theoretical framework that utilizes the Nielsen identities to maintain gauge independence in the perturbative expansion. This approach involves:

1. Gauge-Independent Effective Potential: Application of the Nielsen identities ensures that physical quantities are derived from gauge-independent expressions of the effective potential, evaluated at points where the potential is stationary.
2. Reformulated Baryon Number Preservation Criterion: Instead of relying on the gauge-dependent $\phi_{\text{min}}(T_C) / T_C$, the authors propose using the gauge-independent sphaleron energy scale $\bar{v}(T_C) / T_C$ derived from a dimensionally reduced effective theory at high temperatures. This alternative respects gauge independence and allows for more accurate theoretical predictions.
3. Impact of Higher-Order Corrections: The paper also explores the implications of including higher-order corrections and proper treatment of one-loop determinants in estimating the sphaleron rate, emphasizing latent uncertainties in typical perturbative analyses.

Implications and Speculations

The paper implies that many results concerning the viability of EWB in various BSM scenarios might need reevaluation under the new framework. Accurate determination of the EWPT dynamics relies on correctly addressing the gauge-dependent aspects of earlier analyses. Moreover, this work suggests that a more stringent criterion for baryon number preservation might emerge when properly incorporating higher-order effects and non-perturbative contributions such as lattice simulations.

As we advance in the design and understanding of new physics models, particularly supersymmetric and other BSM frameworks, the methodology provided could yield crucial insights into the specific parameter spaces conducive to a viable baryogenesis mechanism. The integration of experimental results from collider searches with such refined theoretical tools might pave the way for a more comprehensive understanding of the early universe's thermal history.

Conclusion

By addressing gauge dependence and refining the techniques for examining the electroweak phase transition, the authors of this paper significantly enhance the theoretical foundation of electroweak baryogenesis. These developments not only provide more accurate predictions for baryon asymmetry preservation but also set the stage for confirming or ruling out EWB as a feasible mechanism for baryogenesis via both perturbative and non-perturbative methods. This work marks a crucial step towards reconciling the discrepancies attributed to gauge artifacts, thus opening new avenues for future research in the field of particle cosmology.