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As I propose in this post, About the mass of the particles, imagine a universe with massless quarks due to Higgs' VEV is exactly zero.

In our universe, where quarks are massive, we have consider that mesons are the result of the spontaneously chiral symmetry breaking (SCSB, shortened). Since chiral symmetry in our world is an apporximate symmetry the Goldstone bosons, i.e., the mesons aren't massless.

But now, in the universe I propose (with Higgs' VEV equals to zero)chiral symmetry is exact. An SCSB would produce real Goldstone bosons which are truly massless since chiral symmetry is not approximate. Nevertheless, mesons that are made of pairs quark-antiquarks that could bind due to QCD interactions, quarks still have colour charge, and these one are the most relevant part of the mass of an hadron.

Besides, we know that there are mesons such as $\eta'$ that do not arise from the SCSB an have mass, so what would happen with this 'special' ones in my proposed universe?

Therefore, I have 2 ideas to understand this universe but give 2 different solutions, so are mesons massless or massive in a universe with Higgs' VEV $= 0$? In one of the comments given by @MadMax in the post I link, he suggests that dynamical chiral symmetry breaking would induce mass to fermions, but I don't even know what 'dynamical' symmetry breaking is.

Vicky
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I'm sorry, but I won't get involved in extended tails in other questions. Let me summarize the consensus (utilized in lattice gauge theory, best suited for nonperturbative QCD estimates) for this chiral limit (exact chiral symmetry).

Without the Higgs mechanism, in your hypothetical world, the current quark masses are zero. Confinement and dynamical breaking of the chiral symmetry are still meant to occur: they are properties of gluons coupling strongly to each other. The consensus/presumption is that the confinement radius and the χSB order parameter $\langle \bar{q} q\rangle\sim \Lambda _{_{QCD}}$ are still comparable to our own world's.

So constituent quarks are still about a third of a GeV, baryons are still about a GeV, and non-pseudoscalar mesons, such as the ρ, are still about half a GeV. Let's not fuss the exact values, since there is subtle debate about the contribution of current quark masses in the present, physical picture.

As I hinted at the top, lattice estimates are routinely taken as the practically vanishing current quark mass limit: the scale of QCD is so much larger than the masses of light current quarks, that Dashen's formula for pseudogoldston masses squared, $m_\pi^2\sim m_q \Lambda_{_{QCD}}/f_\pi^2$, is thought to hold superbly. So, in your notional world, pseudoscalar mesons are massless, qua goldstons, with the possible exception of the η', which gets a QCD topological susceptibility contribution$^1$. A notional world with massless scalars, including charged such, would be a very odd place indeed, and its formal consistency might not be easy to assess given the formal tools we have developed so far.

$^1$ I am a bit shaky on this, but apparently the mass would still be nontrivial, cf DeGrand & Heller (MILC Collab) PhysRev D65 (2002) 114501. There is lots of head scratching about the "ideal" value of the pseudo scalars' decay constant in the absence of current quark masses.

Cosmas Zachos
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  • You state that "constituent quarks are still about a third of a GeV". That is not what I read here: https://www.sciencenews.org/article/proton-mass-quarks-calculation. Can you elaborate? – my2cts May 06 '19 at 23:40
  • No, not really... Science News is aggressively misleading in abusing the term "constituent quarks" for current quarks, and victimizing the confusable. If you read the actual paper, you see that the authors are talking about current quarks, the ones taken to be massless here. Constituent quarks are a peculiar entity carrying 1/3 of the baryon's mass each, and living in the odd shell between the χSB shell and the confinement wall. Their only partners are pions, even though there is some counting relic of colors--but no gluons! It is the model soundly predicting magnetic moments. – Cosmas Zachos May 07 '19 at 00:07
  • Related. The paper garbled in Science news is monitoring the small contribution of the current quark mass term to the proton energy. It is the other terms, the bulk of the contribution that would morph to the constituent masses, in the chiral limit, if only the lattice work could get there. – Cosmas Zachos May 07 '19 at 00:28
  • @CosmasZachos I've read not only in your answer (thanks for it, of course) but also in other posts the term 'dynamical breaking of the chiral symmetry'. Is there any difference between $\chi$SB and 'dynamical'-$\chi$SB? – Vicky May 07 '19 at 07:26
  • Explanation found for dynamical-SB which link I let here in case of someone else needs it: https://physics.stackexchange.com/questions/432246/what-is-dynamical-symmetry-breaking-exactly – Vicky May 07 '19 at 08:23
  • Νο difference! Dynamical indicates SSB without the benefit of scalars, but of course, the same phenomenon can be modeled through scalars in the σ-model, if only interested in group theory instead of gluon dynamics..... – Cosmas Zachos May 07 '19 at 10:11