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Usually, PDG has the lifetimes/decay widths of all kinds of particles.
However, for quarks, they don't seem to be there, not even in this 2014 PDG Quarks Review (except for the top quark $t$).
But I read that e. g. the bottom quark has a lifetime of $\tau_{b}\approx 1.2 \cdot 10^{-12}$ s.
My question is therefore where we can find the lifetimes of quarks?
There is no such thing as the lifetime of a quark.
We can talk about the lifetime of a neutron, because a neutron can exist as a free particle. Its half-life is about 15 minutes. But it would obviously be wrong to imagine that therefore a 12C nucleus will decay in a matter of minutes because its neutrons are going to decay. 12C is absolutely stable. Other nuclei are unstable but have lifetimes much longer than 15 minutes.
Since quarks don't exist as free particles, it's not meaningful to talk about their half-lives. This would be why the PDG doesn't list them.
In general, if you're going to post and say, "I've read that...," please post a reference to where you read it.
An inverse GeV width corresponds to a lifetime of $0.7 \cdot 10^{-24} s$. This then amounts to the enormous width of the t quark, heavier than a W boson, so it is the only quark that decays semi-weakly, i.e., into a real W boson and a b quark. Therefore, by dint of its freakishly short lifetime it decays before hadronization can occur. This is why it is so much wider than hadrons, and why one may talk about its monster width, in the same breath as the Higgs width.
All five other quarks weak-mutate/"decay" inside hadrons, and then the hadronization process, products, phase space, crucially contribute to their notional "decay" -- you really mean a contribution to an amplitude there, suppressed by a W-propagator.
So it would be problematic, beyond being useless, to even define a non-t quark lifetime.
In my opinion, there is an analogy between quarks and atomic "subclouds", which are not observed as "free" particles either. These subclouds have fractional charges and are stable if the atom is in the ground state. If the atom is in an excited state, the corresponding subclouds become instable, just like t-quark.
