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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

Discuss how we know that \[{\rm{\pi }}\]-mesons\[\left( {{{\rm{\pi }}^{\rm{ + }}}{\rm{,\pi ,}}{{\rm{\pi }}^{\rm{0}}}} \right)\]) are not fundamental particles and are not the basic carriers of the strong force.

Verify the quantum numbers given for the proton and neutron in Table \[33.2\] by adding the quantum numbers for their quark constituents as given in Table \[33.4\].

In supernovas, neutrinos are produced in huge amounts. They were detected from the \({\rm{1987 A}}\) supernova in the Magellanic Cloud, which is about \({\rm{120,000}}\) light years away from the Earth (relatively close to our Milky Way galaxy). If neutrinos have a mass, they cannot travel at the speed of light, but if their mass is small, they can get close.

(a) Suppose a neutrino with a \({\rm{7 - eV/}}{{\rm{c}}^{\rm{2}}}\) mass has a kinetic energy of \({\rm{700 KeV}}\). Find the relativistic quantity \(\gamma {\rm{ = }}\frac{{\rm{1}}}{{\sqrt {{\rm{1 - }}{{{{\rm{\nu }}^{\rm{2}}}} \mathord{\left/ {\vphantom {{{{\rm{\nu }}^{\rm{2}}}} {{{\rm{c}}^{\rm{2}}}}}} \right. \\} {{{\rm{c}}^{\rm{2}}}}}} }}\) for it.

(b) If the neutrino leaves the \({\rm{1987 A}}\) supernova at the same time as a photon and both travel to Earth, how much sooner does the photon arrive? This is not a large time difference, given that it is impossible to know which neutrino left with which photon and the poor efficiency of the neutrino detectors. Thus, the fact that neutrinos were observed within hours of the brightening of the supernova only places an upper limit on the neutrino’s mass. (Hint: You may need to use a series expansion to find \({\rm{v}}\) for the neutrino, since it \(\gamma \) is so large.)

The only combination of quark colours that produces a white baryon is RGB. Identify all the colour combinations that can produce a white meson.

(a) Three quarks form a baryon. How many combinations of the six known quarks are there if all combinations are possible?

(b) This number is less than the number of known baryons. Explain why.
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