The hadrons can be divided into two parts: mesons (bosons of two quarks) and baryons (fermions of three quarks). Why we not found a particle made from more than three quarks?
Dear Vikas,
in fact we have. Earlier this year, the experimental discovery of the pentaquark had been announced: http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.115.072001
Furthermore, I am not sure what you are referring to by "stable". All hadrons decay, except for (maybe) the proton. Thus we have also not found a stable state with two quarks, and at most one with three.
Best regards,
Alexander
Concerning the first part of the question.
Quarks have some quantum number called color. In order to be stable they need to be colourless. You can build coluorless combinations with 3 quarks of 3 different colors, or with a quark and anti-quark with the same color. Concerning Pentaquark, its discovery was announced many times. But it is possible to build colourless particles with 5 quarks, so they can, and should, effectively exist. The difficulty in finding them comes from the difficulty to disentangle penta-quarks from baryon-meson molecula.
Cheers,
Biagio
@Biagio
Good answer.
But also an understanding of quark masses helps.
Article Harmonic quintessence and the derivation of the charge and m...
Three quark states have a label, called baryon number, that is conserved and the Standard Model describes this. Therefore, only the lightest baryon is stable and that's the proton. Baryon number isn't conserved, if quarks and leptons belong in the same representation, as in ``grand unified theories'', which predict proton decay and how to obtain a rate compatible with current data is a challenge in constructing them, that isn't fully resolved.
Two quark states, mesons, don't have such a (conserved) label, meson number isn't conserved, so all mesons decay into leptons, through electromagnetic or weak interactions.
Less than two means one, since quarks are counted. As mentioned, quarks are charged under the strong interactions, their charge is color. There doesn't exist a quark, that's neutral under the strong interactions, but the only observable particles are neutral combinations; this is called ``color confinement''. It can be described by studying the strong interactions by numerical simulations, it hasn't been proven mathematically, however.
States with more than three quarks are possible and, as mentioned, have been observed; but, since there isn't any property, any conserved quantity, that prevents their transformation to baryons and mesons, they will transform, decay, to states of baryons and mesons.
So the short answer is color confinement for why one quark states aren't observed and the absence of any other conserved quantity higher than baryon number, for why states with more than three quarks aren't stable. These statements are independent of quark masses-these enter the picture when recognizing that the down quark is heavier than the up quark, therefore the proton, rather than the neutron, is the lightest baryon, which describes the fact that the neutron decays to proton, electron and electron-anti-neutrino and not the proton to neutron, positron and electron-neutrino, through β-decay; therefore hydrogen is stable.
Curiously, for the other two families the ``up'' quark (charm, top) is heavier than the ``down'' quark (strange, beauty) .
two quark states are q qbar type --> baryon number zero
three quark states q q q type --> baryon number 1
Because baryon number is a symmetry of the subatomic world, these states must decay conserving baryon number. Proton is stable because there is no decay channel (consisting of lighter baryons) available for it to decay to. Neutron decays because it is heavier than proton (lifetime approx 880 sec). All mesons decay very fast (in less than a sec).
For exact numbers for lifetimes of baryons and mesons see PDG (particle data group) tables,
http://pdg.lbl.gov
Note that if baryon number is strictly conserved then it will not allow baryogenesis. Therefore GUT theories are interesting which allow for baryon number violation. Proton decay is being searched in experiments.
Ref: http://www.symmetrymagazine.org/article/do-protons-decay
Less than two quarks is 1 quark states. One quark state is not possible in the low energy world, because color is confined. Low energy states are colorless. To understand why baryons are mesons are colorless, one has to do some nontrivial QCD algebra involving SU(3) group theory and its representations.
I hope this helps.
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