The quark theory assigns certain quark combinations to the different particles, par example:
Proton p = (uud)
Neutron n = (udd)
ngative delta Δ– = (ddd)
ngative omega Ω– = (sss)
Provided that the quark theory is right, why shold be quark combinations like (ud), (us) or (ds) not possible?
Quarks carry the strong nuclear force. The strong force comes in 3 charges red, green, and blue (and 3 anti charges anti-red, anti-green, and anti-blue). In the same way the EM force has positive charge and anti-positive (ie negative) charge. Free particles have an overall colour charge of white (Think how Sunlight is white but made up of different colours) . This means quarks can come together only in groups where the colour charge cancels out over long distances. So you can have quark anti-quark pairs (charge anti-charge), or add the charges together (red+blue+green = white). This also holds for theorectical particles made of 4 quarks (2 quarks 2 anti-quarks) and 5 quarks (four quarks and 1 anti-quark or the reverse). In your example ud only has two quarks so only two colour charges so cannot exist. If you want a more indepth answer start reading about colour charge.
Quarks transform as 3 of SU(3). One can take products of these representations as
3 x 3 = 3bar + 6
3 x 3 x 3 = (3bar +6) x 3= (1+8)+(8+10)
We see that 3 x 3 does not contain a singlet but 3 x 3 x 3 does contain a singlet. Because all terms in the Lagrangian density should be Lorentz invariant and gauge invariant, one cannot have a term like, ud, us or ds.
Thanks for your answers!
Dear D. J. Auty!
In case of the combination color - anti-color the resulting colur should also be white.(?) There are existing in theory also combinations of two quarks like (u; anti-u), (d; anti-d). Furthermore the EM force is one force between two opposite charges. In case of the color charge should act between the six different colors 15 different colour forces.
I would remind that quarks are not proven, the color charge is not observed and the the mathematical descriptions are mathematical formalisms. Quark-theory is at least only a theoretical model.
My Regards!
Hans
Hi Hans-G
"There are existing in theory also combinations of two quarks like (u; anti-u), (d; anti-d)". Also in expriment these are called, among other things, pions. Here the u will have the colour charge and the anti-u will have the anti-colour. So cancel out to equal white (while in the baryons you have all colours that combine to white). The EM force only has 1 charge and a anti-charge (+ and - charge) and 1 force carrier. The Strong force has 3 charges and 3 anti-charges (red and anti-red, blue and anti-blue, and green and anti-green) and has 8 force carriers for the different combinations. You say quarks are't proven, yet expriments show that the proton and neutron are made of small particles and there are particles that have been discovered which have the characteristics of pentaquarks.
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