we know baryons like protons and neutrons have 3 quarks ($uud$ & $udd)$ and mesons like pions and kaons have a quark + its respective antiquark, but could there theoretically be a particle with four or more quarks/antiquarks? how long would it stay stable?
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Yes, and not only they could exist, but also they where already observed. Here is one article in the LHC website where they talk about some of the exotic hadrons they observed. These particles are not stable, evidently. One pentaquark measured here, for example, has a mass width of 7 MeV, which amounts roughly to a half-life $10^{-22}$ s, which is extremely fast.
Franklin Luis
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If a quark–gluon plasma (QGP) droplet is regarded as a particle, then the QGP droplet could definitely accommodate quark numbers $>3$.
One might argue that a QGP droplet is not a particle. However, one criteria of a QGP droplet passing as a particle is that it could stay stable long enough to be observed at CERN and at the Brookhaven National Laboratory's Relativistic Heavy Ion Collider (RHIC). See Wiki page here for more details.
An even more interesting question is: Are protons and neutrons just a specific kind of QGP droplet?
MadMax
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