I am new in Particle Physics and try to understand "Quark-Antiquark States:Meson article in Quarks & Leptons by Halzen and Martin(p=46) Why do this meson states are are acceptable by nature $$A=\frac{(u\bar{u} - d\bar{d})}{\sqrt{2}};B=\frac{(u\bar{u} + d\bar{d}-2s\bar{s})}{\sqrt{2}}; $$ alongwith $$u\bar{u},u\bar{s},d\bar{u},d\bar{s},s\bar{u},s\bar{d},\frac{(u\bar{u} + d\bar{d}+s\bar{s})}{\sqrt{2}}$$.where it is also a $q\bar{q}$ state.How can I find the acceptable (Which also experimentally observable either now or in future?
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1$\begingroup$ I'm afraid the question is founded on a misunderstanding. There is a meson with valence content $(u\bar{u} + d\bar{d})/\sqrt{2}$: the $\omega^0$ (not to be confused with the $\Omega^-$) has that content. $\endgroup$– dmckee --- ex-moderator kittenNov 18, 2019 at 6:56
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$\begingroup$ Okay !Then how many Mason state possible ? $\endgroup$– baponkarNov 18, 2019 at 8:34
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1$\begingroup$ @baponkar Depends on what you mean by "possible". If you count superpositions of different quark-content eigenstates, then there are uncountably infinitely many. If you only want to count the number of quark-content eigenstates, then start here: en.wikipedia.org/wiki/List_of_mesons $\endgroup$– probably_someoneNov 18, 2019 at 13:40
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$\begingroup$ Thank you for the link @probably_someone $\endgroup$– baponkarNov 18, 2019 at 17:30
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The standard model of particle physics, which has the quarks and leptons in group structures of $SU(3) \times SU(2) \times U(1)$ was developed BECAUSE most of the data of particle physics can be fitted with this model, and because it is successful in predicting new data.
That is why you can write a number of possible quark states and quark antiquark states, and if energy and quantum numbers are OK one starts looking for those states. See this for example.
In general we find that the standard model states are acceptable to nature, and that is the success of the model.
