Energy Scale of Sphalerons

Sphalerons are unstable, static, finite energy solutions of classical field equations. They are particularly important in the context of electroweak theory and electroweak symmetry breaking as was expected to occur in the very early universe. Sphalerons act as extensions to the Standard Model of particle physics, and could, if they exist, provide a greater explanation and understanding of first order electroweak phase transitions that led to the matter-antimatter asymmetry observed in the universe today. Given that sphalerons provide a solution to the as-of-yet-unsolved question of matter-antimatter asymmetry, it is imperative that their existence be confirmed or ruled out via particle colliders. The verification or rejection of sphalerons via particle experiment and phenomenology would provide an avenue beyond the Standard Model of particle physics. In this research, the energy requirements or energy scales needed for sphaleron detection are discussed, thereby predicting if current colliders such as the Large Hadron Collider can observe sphalerons, or if future ones such as the Future Circular Collider are in the required sensitivity range to validate or invalidate the existence of sphalerons. Thus, this research discusses the theoretical background of sphalerons, their significance, and potential impact on understanding baryon asymmetry in the universe, thereby highlighting the experimental prospects and challenges in detecting hypothetical sphalerons via high-energy colliders.