trying to understand Higgs field ?

[Widdekind]

I understand, from perusing Riccardo Barbieri's book Lectures on the ElectroWeak Interactions, that the Higgs hypothesis, for the manifestation of "mass", assigns, to every point in space, a complex-valued scalar field [math]\phi(\vec{x})[/math], whose vacuum expectation value is [math]v \approx 200 \; GeV[/math]. But, particles interact with that field. And, if that field is "perturbed", from its equilibrium value; then a potential energy is generated:

 

[math]\phi(\vec{x}) \sim v \left(1 + h(\vec{x}) \right)[/math]

 

[math]V(\vec{x}) \sim -1 + 4 h^2 + 4 h^3 + h^4 = \left(1 + h\right)^2 \left( \left(1 + h\right)^2 - 2\right)[/math]

By some means, the hypothesized Higgs potential well manifests the "mass" of particles.

 

Can particles be considered to "oscillate" in the quartic Higgs potential, vaguely resembling quadratic potentials, of classical QM, with the eigenstates associated with the various fermions, and their three 'generations' ??

 

Trying to "force fit" some semblance of structure, to the masses, of the standard particles, I observe the following crude correspondences (masses in MeV subscripted, "bare" masses for u,d quarks employed):

 

[math]u_{1.5} \begin{array}{c} \times 1000 \\ \longrightarrow \end{array} c_{1500} \begin{array}{c} \times 100 \\ \longrightarrow \end{array} t_{170,000}[/math]

 

[math]d_{4.5} \begin{array}{c} \times 100 \\ \longrightarrow \end{array} s_{500} \begin{array}{c} \times 10 \\ \longrightarrow \end{array} b_{4500}[/math]

 

 

[math]\nu_1 \begin{array}{c} \times 20? \\ \longrightarrow \end{array} \nu_2 \begin{array}{c} \times 2? \\ \longrightarrow \end{array} \nu_3[/math]

 

[math]e_{0.5} \begin{array}{c} \times 200 \\ \longrightarrow \end{array} \mu_{100} \begin{array}{c} \times 20 \\ \longrightarrow \end{array} \tau_{1800}[/math]

I observe that "extrapolating the trends", implies hypothetical "higher generation" particle states:

 

[math]u_{1.5} \begin{array}{c} \times 1000 \\ \longrightarrow \end{array} c_{1500} \begin{array}{c} \times 100 \\ \longrightarrow \end{array} t_{170,000} \begin{array}{c} \times 10?? \\ \longrightarrow \end{array} superT_{1,700,000} \begin{array}{c} \times 1?? \\ \longrightarrow \end{array} hyperT_{2,000,000}[/math]

 

[math]d_{4.5} \begin{array}{c} \times 100 \\ \longrightarrow \end{array} s_{500} \begin{array}{c} \times 10 \\ \longrightarrow \end{array} b_{4500} \begin{array}{c} \times 1?? \\ \longrightarrow \end{array} superB_{5,000}[/math]

 

 

[math]\nu_1 \begin{array}{c} \times 20? \\ \longrightarrow \end{array} \nu_2 \begin{array}{c} \times 2? \\ \longrightarrow \end{array} \nu_3[/math]

 

[math]e_{0.5} \begin{array}{c} \times 200 \\ \longrightarrow \end{array} \mu_{100} \begin{array}{c} \times 20 \\ \longrightarrow \end{array} \tau_{1800} \begin{array}{c} \times 2?? \\ \longrightarrow \end{array} super \tau_{4,000}[/math]

First, "down-type" fermions (d,e, isospin T₃=-1/2) seem to "max out" near 5 GeV, with leptons (e) "dropping down" in mass ~2x more per generation. Second, "up-type" fermions (t) seem to "max out" near 2 TeV. And, 2 TeV is the energy scale, at which "a theory without a Higgs boson leads to a saturation of unitarity; or, more precisely, to a loss of perturbativity, at an energy [math]E \approx 4 \pi v \left[\approx 2 \; GeV \right][/math]" (Barbieri, p.26).

 

Are the energy scales ~5 GeV (T₃=-1/2) or ~2 TeV (T₃=+1/2) significant? How do they relate to the hypothetical Higgs field ?