It's been known for quite some time now that the electroweak "transition" in the early universe is first-order for a Higgs mass of less than about 75 GeV, but for a larger Higgs mass (including the 125 GeV mass that appears to describe our universe), the transition goes away entirely and becomes a crossover at which no physical quantities change non-analytically. (E.g. see here and here.) If understand the first reference correctly, in the $m_H < 75$ GeV regime, the simplest quantity that jumps discontinuously across the transition is the magnetic screening length, or equivalent its inverse, the "magnetic screening mass" (although the mass remains strictly positive both above and below the transition).
But I've never heard anyone actually identify which two physical quantities cross over at the electroweak "crossover" for $m_h > 75$ GeV. What are they? Put another way, if everything changes analytically as a function of temperature in the heavy-Higgs regime, then on what physical basis can we identifying one particular temperature as the "crossover temperature"?