Sphalerons and their phenomenology

Electroweak baryon number violation is one of the most striking, and least directly tested, predictions of the Standard Model. It arises from the chiral anomaly, which links changes in baryon and lepton number to topological transitions of the $SU(2)_L$ gauge fields. At zero temperature, these transitions proceed via tunnelling (instanton processes) and are argued to be exponentially suppressed, whereas at high temperatures they can occur via thermal activation. The unstable static field configuration sitting at the top of the barrier is the 'sphaleron'; it provides a concrete, semiclassical handle on B+L violation and on the conditions needed for electroweak baryogenesis. This talk provides a pedagogical introduction to sphalerons, targeting experimenters and phenomenology practitioners, starting from the vacuum structure and the Chern–Simons number, then moving to the sphaleron solution, its energy scale, and the selection rules. I will then connect these ideas to phenomenology, focusing on what a sphaleron-like transition would look like in a high-energy experiment: many fermions with characteristic baryon and lepton number violation, accompanied by a very busy electroweak boson shower. Finally, I will review recent progress on modelling the decay dynamics and on developing search strategies, including modern classification techniques, and I will discuss where present and future facilities (pp collisions, heavy ions, and ultra-high-energy cosmic rays) might have realistic sensitivity to such spectacular non-perturbative events.