The status of $SU(3)_C$ symmetry in the Standard Model 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"?
 A: 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.
A: 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.
A: $SU(3)_C$ is unbroken. If it was broken, there might be several mass states corresponding to what is a single type of a particle in our world.
E.g., there is nothing like charged pion made of red quark and anti-red antiquark, charged pion made of red quark and anti-red antiquark and charged pion made of green quark and anti-green antiquark. There is just a charged pion (which, in fact, is a symmetric superposition of all the three states above).
