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Chapter 39: Problem 28

The \(\Sigma^{+}\) and \(\Sigma^{-}\) have quark compositions uus and \(d d s,\) respectively. Are the \(\Sigma^{+}\) and \(\Sigma^{-}\) each other's antiparticles? If not, give the quark compositions of their antiparticles.

Short Answer

Expert verified
No, the particles \(\Sigma^{+}\) and \(\Sigma^{-}\) are not each other's antiparticles. The \(\Sigma^{+}\) antiparticle's, \(\Sigma^{-}\), quark composition is \(\overline{u}\)\(\overline{u}\)\(\overline{s}\) and the \(\Sigma^{-}\) antiparticle's, \(\Sigma^{+}\), quark composition is \(\overline{d}\)\(\overline{d}\)\(\overline{s}\).

Step by step solution

01

Compare Quark Compositions

Initially, look at the quark compositions of both \(\Sigma^{+}\) and \(\Sigma^{-}\) . \(\Sigma^{+}\) is made up of uus while \(\Sigma^{-}\) is composed of dds. Note that these two particles do not consist of each other's antiparticles. In the case of antiparticles, each quark in the particle will be replaced by its respective antiquark.
02

Determine Antiparticle Quark Compositions

As the particles are not each other's antiparticles, need to find the quark compositions for the antiparticles of \(\Sigma^{+}\) and \(\Sigma^{-}\). The quarks u, d, and s (up, down, strange) have respective antiquarks \(\overline{u}\), \(\overline{d}\), and \(\overline{s}\). Therefore, the antiparticle of \(\Sigma^{+}\), denoted as \(\Sigma^{-}\), is composed of \(\overline{u}\)\(\overline{u}\)\(\overline{s}\), and the antiparticle of \(\Sigma^{-}\), denoted as \(\Sigma^{+}\), is composed of \(\overline{d}\)\(\overline{d}\)\(\overline{s}\).

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