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Studying Higgs mechanism in EW theory and QCD I have a couple of questions that I would like to clarify:

1) The quark mass term in QCD Lagrangian should come from Higgs mechanism in EW sector of SM. I mean that you don't have a contribution to the mass coming from Higgs and other from a Dirac term that only satisfies $SU(3)_c$ symmetry but not $SU(2)_L$. Is this correct?

2) Let's imagine a world with a Higgs such that its vacuum expected value is zero. Then, Higgs mechanism does not break $SU(2)_L$ symmetry and, hence, leptons and quarks keep massless. In this world, with quarks but massless we could have hadrons but their masses would come out from QCD gluonic interactions among themselves and the gluonic and EW interactions of the virtual sea quarks, that of course are massless per se. We'd lose contribution from the mass given by Higgs mechanism (which is massless too) but not the resulting from electromagnetic interactions between valence and virtual quarks.

But if quarks and leptons are massless, due to Special Relativity, they move at the speed of light so, is this a problem for bounding to create hadrons? Moreover, the massless property of quarks would allow proton to decay into neutron, so this world would be lifeless.

Despite all these, there is no way to get a mass for gauge bosons or charged leptons since we keep unchanged the SM symmetry, or am I ignoring some fancy way?

Maybe, since quarks are now energetically equivalent in this world CKM matrix is matrix of ones up to a complex phase to keep the CP violation.

What else do you think could be different from our real world?

Vicky
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2 Answers2

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There is a misconception that Higgs field is the only source that gives mass to elementary particles such as quarks and leptons.

But in reality, quarks get mass from QCD strong interactions even in the absence of the Higgs field! In other words, if you can magically switch off Higgs field, leptons would indeed be massless, but quarks would still have masses.

More specifically, QCD strong interactions can generate masses for quarks via quark-antiquark condensation that breaks the chiral symmetry, $$ \langle \bar{q}q\rangle \sim \int \frac{1}{\not p - m} = \int \frac{m}{p^2 - m^2}, $$ where $\langle \bar{q}q\rangle \neq 0$ is the quark-antiquark condensation, and $m \neq 0$ is the dynamically generated quark mass.

Mesons are the resultant Nambu-Goldstone bosons from this dynamical chiral symmetry breaking. Of course, if non-zero Higgs VEV is present, the chiral symmetry is NOT exact, which renders the mesons Pseudo-Nambu-Goldstone bosons.

A side note: The above dynamical symmetry breaking mechanism bears a resemblance to BCS superconductivity theory, where the quark-antiquark condensation condensation is replaced by the cooper pair of elections.

MadMax
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These questions have been addressed in the Big Bang model, for the time before symmetry breaking and the Higgs field has zero vev.

bbtime

Note that quark confinement into hadrons comes after weak symmetry breaking. Everything is different from our present world, before symmetry breaking time, of $10^{-12}$ sec from the Big Bang.

anna v
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