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Chapter 33: Q25CQ (page 1211)

The sigma-zero particle decays mostly via the reaction \[{{\rm{\Sigma }}^{\rm{0}}} \to {{\rm{\Lambda }}^{\rm{0}}}{\rm{ + \gamma }}\]. Explain how this decay and the respective quark compositions imply that the \[{{\rm{\Sigma }}^{\rm{0}}}\]is an excited state of the\[{{\rm{\Lambda }}^{\rm{0}}}\].

Short Answer

Expert verified

Baryons that are composed of the same quarks represents different states of the same particle thus having the same quark structure, \[{{\rm{\Sigma }}^{\rm{0}}}\] represents excited state of \[{{\rm{\Delta }}^{\rm{0}}}\]. The \[{{\rm{\Sigma }}^{\rm{0}}}\] decays to \[{{\rm{\Delta }}^{\rm{0}}}\] without violating the conservation of strangeness with \[{{\rm{\Delta }}^{\rm{0}}}\] the only less massive strange quark.

Step by step solution

01

Definition of Concept

The sigma zero decay relation in terms of quarks is given by,

\(uds \to uds + \gamma \)

02

Explain how this decay and the respective quark compositions imply

Sigma is a type of baryon with an unusual quark structure, uds, similar to how \[{{\rm{\Delta }}^{\rm{0}}}\] has the same quark structure, uds. Baryons made up of the same quarks represent different states of the same particle, resulting in the same quark structure; \[{{\rm{\Sigma }}^{\rm{0}}}\] represents the excited state of \[{{\rm{\Delta }}^{\rm{0}}}\]. The \[{{\rm{\Sigma }}^{\rm{0}}}\] decays to \[{{\rm{\Delta }}^{\rm{0}}}\], without breaking the law of conservation of strangeness, with \[{{\rm{\Delta }}^{\rm{0}}}\] being the only less massive strange quark.

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Most popular questions from this chapter

The principal decay mode of the sigma zero is \[{{\rm{\Sigma }}^{\rm{0}}}{\rm{ }} \to {\rm{ }}{{\rm{\Lambda }}^{\rm{0}}}{\rm{ + \gamma }}\]. (a) What energy is released? (b) Considering the quark structure of the two baryons, does it appear that the \[{{\rm{\Sigma }}^{\rm{0}}}\]is an excited state of the \[{{\rm{\Lambda }}^{\rm{0}}}\]? (c) Verify that strangeness, charge, and baryon number are conserved in the decay. (d) Considering the preceding and the short lifetime, can the weak force be responsible? State why or why not.

Consider an ultrahigh-energy cosmic ray entering the Earth’s atmosphere (some have energies approaching a joule). Construct a problem in which you calculate the energy of the particle based on the number of particles in an observed cosmic ray shower. Among the things to consider are the average mass of the shower particles, the average number per square meter, and the extent (number of square meters covered) of the shower. Express the energy in \({\rm{eV}}\) and joules.

Suppose leptons are created in a reaction. Does this imply the weak force is acting? (for example, consider \(\beta \)decay.)

(a) How much energy would be released if the proton did decay via the conjectured reaction \({\rm{p}} \to {\pi ^{\rm{0}}}{\rm{ + }}{{\rm{e}}^{\rm{ + }}}\)?

(b) Given that the \({\pi ^{\rm{0}}}\) decays to two \(\gamma {\rm{ s}}\) and that the \({{\rm{e}}^{\rm{ + }}}\) will find an electron to annihilate, what total energy is ultimately produced in proton decay?

(c) Why is this energy greater than the proton’s total mass (converted to energy)?

If a GUT is proven, and the four forces are unified, it will still be correct to say that the orbit of the moon is determined by the gravitational force. Explain why.
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