Does the higgs mechanism explain the observed masses of sub particles?

[Herbascious J]

I was wondering if there are any theories that show how much mass the higgs field gives to each particle and why? I am specifically wondering about the observed masses for each particles rest mass. Does the higgs mechanism give mass in quanta, and if so is there a reason for the amounts?

 

[mfb]

I was wondering if there are any theories that show how much mass the higgs field gives to each particle and why?

For every elementary particle except the Higgs itself*, it gives those particles their rest mass (to a very good approximation).
For composite particles like hadrons, this is not true, but that is a completely different question.

Does the higgs mechanism give mass in quanta

Every particle gets a mass exactly corresponding to its particle type, but there is no smallest "mass unit" (unlike electric charge, where such a unit exists).

and if so is there a reason for the amounts?

There is no known reason why the particle masses are as they are.*edit for clarity: the Higgs mechanism does give a mass to the Higgs boson, but that is not the only relevant contribution to its mass.

 

[ChrisVer]

In the QFT point of view, the Higgs Mechanism is applied to spontaneously break your symmetry, and by this process it gives mass to the excanged bosons, except for photon.
Now if you want to write an SU(2)xU(1) symmetry obeying Lagrangian (that's the one you initially had), there is no reason to exclude the "Yukawa terms", and as a result of non-vanishing Higg's vacuum expectation value you'll get lepton and quarks masses.
The Yukawa terms are just SU(2)xU(1) invariant, lorentz invariant (so they obey your symmetries) and couple the left and right movers through Higg's field- but even the existence of left-right coupling is equivalent to a mass term if you check the Dirac equation lagrangian in Weyl's representation.

Although the Higg's mechanism gives masses to the quarks, you can't easily compute the hadron or mesons' masses because of the extra energy these systems hold within (sea of particles and gluons) which you must already know from the fact that the mass of proton is not even nearly equal to the sum of 2 u and 1 d quarks' masses.

The theory, even for the Higgs particle, cannot yet explain the reason why the particles have these masses. Neither does Higg's mechanism,which in fact explains the "how they get them", and not "why they have those values". What the theory could always do is create limits of the masses, so we knew for Higgs that it was approximately somewhere between 130 to 1000 GeV, It happened to be at 126, so I think they will look through those numbers again :p