# How can we explain that $\Sigma \pm$ have different masses whereas K$\pm$ have the same mass?

I guess it is because of the forces between the quarks inside them but I am not quite sure how to explain it.

• What is the quark content of the $\Sigma^{+}$? What is its antiparticle? Do the $\Sigma^{+}$ and $\Sigma^{-}$ have the same relation to each other as the $K^{+}$ and $K^{-}$? Jan 31, 2017 at 15:08

K$^+$ and K$^-$ are antiparticles - they contain the same quarks, but in a different configuration. K$^+$ is $u \overline{s}$, while K$^-$ is $\overline{u} s$.

$\Sigma^+$ and $\Sigma^-$ are not antiparticles, they contain different sets of quarks. $\Sigma^+$ is $uus$ and $\Sigma^-$ is $dds$. The $\Sigma \pm$ have different masses, as the $u$ and $d$ quarks have different masses. There may be some additional contribution because of the binding energy, but this is likely to be a second-order effect.

Note that the $\overline{\Sigma^+}$ and $\overline{\Sigma^-}$, the antiparticles of these also exist.

The answer by Gremlin is correct, the quark antiparticles are of the same mass as the quark particles .

This is an expansion on that answer:

Let us start with the kaons . K+K- mesons have the same mass,

493.667+/-.013Mev , the K0 497.648 MeV and are composed by valence quarks

Note that the K+ is the untiparticle of K- and must have the same mass by conservation rules.

The K0 is composed of different quarks

Borrowing a plot ( it is made for a proton), this is a snapshot of what a hadron would look if we could look a it

It is the valence quarks though that characterize the particle's quantum numbers , as all the rest are in a soup of quark antiquark pairs and gluons.

The difference in mass between K+/- and K0 is 3.981 MeV and mostly due to the difference between the mass of the d quark= 4.8Mev and the u quark =2.3 MeV, which is 2.5 MeV. These masses are arrived not by the simplified argument given here but using lattice QCD because of the complexity of interactions within the hadron bag, but they explain the difference in masses.

The sigma+ is uus and the sigma- dds, and their mass difference is 8.079, in the same ballpark of the difference of two d quarks to two up quarks.

Please understand that the quark masses in the tables are the invariant masses and it is only at rest that masses can add up. The added numbers are a lower limit as are the differences because of the relativistic kinematics entering such a complicated many body problem that a hadron is.