The Chern-Simons number as an order parameter: classical sphaleron transitions for SU(2)-Higgs field theories for mH≈120 GeV

The classical transitions between topologically distinct vacua in a SU(2)–Higgs model, using a Higgs field of mass approximately 120 GeV, is examined to probe the crossover region between the symmetric and broken phase. Assuming the Higgs mass is constant, we find the width of this crossover region is approximately 20% of the average temperature. We suggest that this observable is a better parameter to explore this region of phase space than equal-time correlation functions.