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In the Standard Model of Particle physics the $SU(2)_{EW}$ symmetry and the $SU(2)$ isospin symmetry are broken. What about $SU(3)_C$? Is it broken too?

if YES, what breaks the symmetry?

If NO, what are the consequences? Anything like "all baryons have almost the same mass"?

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@Qmechanic The last edit done by moderator changes the scope of the question. Since OP mentions baryon masses, it could happen that s/he wonders about $SU(3)_F$ as well. – firtree May 13 '13 at 8:28
@firtree: I was also thinking about $SU(3)_F$, but concluded that OP was likely mostly thinking about $SU(3)_C$. I think your answer is still very relevant. If you think you can improve the question, please edit it. – Qmechanic May 13 '13 at 8:36
@Qmechanic I would like to edit the question but I cannot find the good wording for the vague idea. Probably you, with your editor/moderator experience, are better fit to do that. – firtree May 13 '13 at 9:52
up vote 2 down vote accepted

There are two SU(3) symmetries you can come across. Basically, SU(N) emerges everywhere when you have N quantum states and some physics does not distinguish these states - then all quantum superpositions of these states make a fundamental representation of SU(N) significant to that physics (but maybe insignificant to some other).

Thus in particle physics there are two SU(3) discussed often. The SU(3) of colors represents the exact, unbroken symmetry. Then there is the SU(3) of flavours, which mixes $u$, $d$, $s$ quarks in strong interactions. It is very rough and it is broken by the masses of quarks ($m_s$ is about 150 MeV, that is dozen percent of the QCD scale of about 1 GeV). After breaking it leaves the flavour SU(2) of only $u$, $d$ quarks, and that is much more accurate ($m_d-m_u$ in the order of unities of MeV), though still approximate. Nevertheless, these symmetries are used to classify hadron states, and to descibe physics on the hadron level (which is the effective theory with respect to SM). It may be credited for the close masses of hadron multiplets, but this is (almost) another way to say "hadrons have close masses because quarks inside them have close masses".

Also, $SU(3)_C$ is a gauge (local) symmetry, while $SU(3)_F$ is a global symmetry.

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No, the colorful $SU(3)$ of QCD is not broken. However, it is confining which means that all physical objects that may exist in isolation have to be neutral (singlets, invariant) under the whole $SU(3)$. Objects that are charged (not neutral), like the quarks themselves, behave as "individual end points of a rope" and they always try to produce a flux tube that leads to other charged objects that neutralize the total charge.

Confinement is why mesons (quark-antiquark pairs) and baryons (three quarks of complementary colors, e.g. reg-green-blue) are the only simple composite particles that may be created out of the colorful quarks.

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