Why is the mass of the singlet meson higher than the octet mesons in QCD?

[Malamala]

Hello! I am reading some group theory applied to QCD and they show how by using the lightest 3 quarks in the $l=0$ state we get 9 pseudoscalar mesons and 9 vector mesons. The difference in masses between the 2 classes is explained by the existence of a spin-spin interaction, which seems like a reasonable argument. However they don't say anything about the fact that the mass of the singlet in each case (the 9 mesons are grouped in an octet and a singlet) is significantly higher than the masses of the mesons in the octet. What is the reason for that? Thank you!

 

[Vanadium 50]

How does this connect to the title? (Title has now been changed, removing confusion)

 

[snorkack]

In case of scalar mesons: what is the reason eta prime and eta mesons are at much different masses, rather than close?

 

[Vanadium 50]

mass of the singlet in each case...is significantly higher than the masses of the mesons in the octet

Which particle do you think is the singlet? Why? Please write down the wavefunction of the particle you think is the singlet and also the wavefunction of a singlet.

 

[vanhees71]

https://en.wikipedia.org/wiki/Eta_and_eta_prime_mesons