Vacuum expectation value (VEV) of the Higgs scalar is responsible for fermion
masses and also masses of the W+ W- and Z gauge bosons. Does it mean
that the Higgs particle can extract energy out of vacuum and convert it to a
new form in which gauge bosons and fermions are massive ? For quarks
one can also have QCD correction to masses which are
unrelated to Higgs VEV
It is the wrong statement: they are proportional to VEV of Quark condensate in vase of baryons and are comlicated functions of the operators and perturbative terms. (See See B.L.Ioffe, V.S.Fadin and L.N.Lipatov, QCD. Perturbative and Nonperturbative Aspects, Cambr. UNiv. Press.)
I am not at all surprised by your comment.
Fermions are not quarks only. There are also leptons.
That is both quarks and leptons are classified as
fermions.
Forget about quarks now because they are inside nuclei and
may get complicated QCD mass corrections. We follow text
book by T. Muta which discuss in detail what you have said.
What about leptons they don't have any corrections
due to nuclear effects. Their masses are certainly
proportional to VEV of Higgs. I mean that if =0
then mass is also zero.
It is often said that "lepton masses are quite clean".
In my question I said fermions and gauge bosons
masses are proportional to VEV of Higgs. Your objection
holds only for quarks. I have modified the explanation
of my question and added a new line. Thank you.
You say" Does it mean that the Higgs particle can extract energy out of vacuum and convert it to a new form" ?
But what do you mean here? What is "vacuum" in your formulation? It seems that you mean something different from the common understanding of the vacuum as a ground state of a system.
Ask yourself: for example, how something (or somebody) can _extract_ energy from the _ground_ state (i.e from the lowest, by definition, energy state) of the hydrogen atom?
Normally, any ground state is a point which is equivalent to an "origin of a scale" or an "origin of the coordinate system".
Of course, speaking about a bound system, everybody understands that the ground state gives the "origin of the scale" and any excited state of that system has the total energy above the lowest one (i.e. the ground state). But nobody means that any excitation _takes_ energy from the vacuum!
There is another side (face) in your question: why a symmetric system is choosing an asymmetic state (in other words, _why_ a spontaneous breaking of a symmetry occurs?) Is it _due_ to a fluctuations? What are those fluctuations? What is the reason for the luctuations? What causes those fluctuatins? Are those fluctuations _determined_ or not? This is another story.. May be the questions have no meaning at all...
There is a good example: look at the "problem of 4 towns" ( see in Proceedings of the Summer School on Hidden Symmetries and Higgs Phenomena, Zuoz (Engadin), Switzerland, Aug. 16-22 (1998), PSI Proceedings 98-02 (Dec. 1998), Villigen, PSI, 1998.) A system is symmetric, but as soon as a choice is taken, the symmetry is spontaneously broken...
If you are not satisfied, try to answer a question: why a piece of non-magnetized iron has domains which are magnetized: each in its own direction...
Higgs boson is interacting with quarks< not with hadrons. Its contribution with baryon masses is negligble.
Higgs boson has a not trivial potential. The ground state is not
at the zero of the field. I am uploading a picture of the Higgs
potential. The VEV or the vacuum expectation value of the Higgs
field is the amount of shift of the minimum away from the origin.
Consider a simple model of one generation of leptons only.
Before symmetry breaking the electron is mass less. But after
symmetry breaking electron has a mass of .51 MeV. This is
equivalent to 8.17 x 10^-14 Jules. That is if we consider a
normal size collection of electrons we multiply this by
6.23 x 10^23 then we get, 5 x 10^8 Jules. Then from which
source this energy has come ? This is the point of discussion
in this thread. Any idea is welcome.
Hadronic masses d'not arise from Higgs interations< but from vacuum expectation values of chirality violating operatops(especially9 it refers to baryon masses) and perturbative terms.
B.Ioffe
The source of masses of leptons is the interaction of scalars with fermions. What we call mass is proprotional to the Yukawa coupling of scalar and fermion. This is the reason that when you put the vaccuum expecation value to zero you get massless particles.
Vacuum expectation value is a value of the scalar field at
which potential is minimum. This value enters fermion
masses. No other value of the scalar field enters expressions
for fermion masses. Higgs field is not a constant scalar, the
value oscillates around the minimum and it is possible to get
a Higgs mass, which is the mass of the modes oscillating
about the minimum position.
Masses of elementary particles, like leptons and current quarks are
proportional to the VEV of the Higgs field of electroweak interaction. The
masses of the weak gauge bosons are generated via the BEH
mechanism (formerly Higgs mechanism),where the electroweak Goldstone bosons are transformed into the longitudinal field components of these particles. The main part, i.e. 98% of the visible mass, is due
to the masses of constituent quarks. These masses are proportional
to the VEV of the sigma field. (see arXiv:1403.7804 [hep-ph].
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