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I have seen many papers about measurements related to $b$ quarks, for example the forward-backward asymmetry of the $b$ quark or the decay width of $Z$ to $b \bar b$ pairs, but not so many for the lighter quarks. Is there any reason for this? Is it related with its mass? Why is there more interest in the $b$ quark than in the others?

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@AXensen has given lots of good reasons. Let me add and enlarge a few...

  1. It is possible to identify a b quark, from its lifetime and/or from its decay products. This is also true for charm quarks, which are also studied. However it's effectively very hard to tell a u quark from a d quark or even an s quark, they all just give light quark jets.
  2. The B mesons have lots of possible decays so many measurements can be done, tying down the elements of the CKM matrix (which includes CP violation measurements) and ensurung its consistency.
  3. The lifetime is long enough, compared to the oscillation time for neutral mesons, for interesting mixing measurements.
  4. Because (like Everest) it's there and we can do all these measurements.
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I don't really have a complete answer... would be excellent if someone who works on LHCb (the LHC detector that focuses on studying b-quarks) could give a better answer. But I have some ideas:

  1. b-quark mesons have lifetimes around $10^{-12}\text{ s}$. So if they are going a reasonable fraction of the speed of light, they can get a few hundred microns away from the beam pipe before decaying. LHCb can detect this distance by having silicon detectors very close to the beam pipe. It's a bit beyond the capabilities of ATLAS or CMS. This is in contrast to the top quark, which has a lifetime around $10^{-25}\text{ s}$, so it will never be observed as decaying anywhere other than the collision point. This distance from the beampipe gives valuable information about the event - like if you can reconstruct the energy of the particle with calorimeters you know exactly how long it took for your B-hadron to decay in its rest frame.

  2. QCD simplifies a bit when one of the quarks is much more massive than the QCD scale ($4\text{ GeV}>\sim \Lambda_{\text{QCD}}=1\text{ GeV}$). So in B-hadrons, the B quark isn't very relativistic and can be approximated as the center of mass. This makes B hadrons (masses and lifetimes) a bit easier to compare to QCD predictions. The top quark, being more massive, doesn't quite work for this because it doesn't even live long enough for hadronization to occur ($\hbar/1\text{ GeV}<\sim 1/\Gamma_{\text{top}}$)

  3. It's standard practice, once you've discovered a particle in one collider, to try to precisely measure properties of that particle in another collider which is better equipped to make a lot of that particle. Every collider in the world for many years has been able to study the strange and charm quarks. So now it's b and t's turn.

  4. The Higgs' most common decay is to two b quarks. (which then hadronize)

  5. (5. and 6. are really speculative and I invite commentary debating this) CP violation is one of the foremost interests of particle physicists, and in order to observe it, you need a process which involves all three quark generations. So it may help to study a decay that starts off with the heaviest generation of quarks. Otherwise you need a loop that includes a B or T, and the propagator will suppress that process.

  6. If there is a fourth generation of quarks, it is likely to couple most strongly to the top and the bottom (see the general structure of the CKM matrix). This is also called "checking that the CKM matrix is unitary." So it may be that precisely measuring processes involving the B or T quarks is our best bet for finding CKM matrix non-unitarity.

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