# Is the value of the scalar components of the Higgs field known?

As I understand the relevant popular sources (example), since the end of the Electroweak epoch, the Higgs field became fixed in the whole known Universe. Thus, we are somewhere on the deep blue part (which is really a 4-sphere) of the Mexican hat potential, and this is a constant value of the Higgs field everywhere. Of course $$\rm{|\phi|=246GeV}$$.

This should mean that we have 2 complex (or 4 scalar) universal physical constants, from which we know that their square sum is 246GeV.

But, is the induvidual values of these contants known? What is the value of the 4 real (2 complex) components of the Higgs field now?

The expectation values are, by convention, $$\langle \phi^0 \rangle = v = \langle \Re \phi^0 \rangle \qquad \langle \Im \phi^0 \rangle = 0= \langle \phi^+ \rangle.$$ These are at the minimum of the sombrero. Oscillations around the minimum are the h field and the would-be-goldstons, which have been rearranged into pieces of the gauge fields.