Problem#1
The weak force may change quark flavor in an interaction. Explain how β+ decay changes quark flavor. If a proton undergoes β+ decay, determine the decay reaction.
Answer:
A proton is made up of uud quarks and a neutron consists of udd quarks.
If a proton decays by β+ decay, we have p → e+ + n + ve. (both charge and lepton number are
conserved).
Since a proton consists of uud quarks and a neutron is udd quarks, it follows that in β+ decay a u quark changes to a d quark.
Problem#2
What is the total kinetic energy of the decay products when an upsilon particle at rest decays to τ+ + τ–1?
Answer:
The decrease in the rest energy of the particles that exist before and after the decay equals the
energy that is released.
The upsilon has rest energy 9460 MeV and each tau has rest energy 1777 MeV.
E = ∆mc2
E = (mϒ – 2mτ)c2
E = 9460 MeV – 2 x 1777 MeV = 5905 MeV
Over half of the rest energy of the upsilon is released in the decay.
Problem#3
Given that each particle contains only combinations of u, d, s, u̅, d̅ and s̅, use the method of Example 44.7 to deduce the quark content of (a) a particle with charge +e baryon number 0, and strangeness +1; (b) a particle with charge +e baryon number –1 and strangeness +1; (c) a particle with charge 0, baryon number +1 and strangeness –2.
Answer:
The charge, baryon number and strangeness of the particles are the sums of these values for their constituent quarks.
The properties of the six quarks are given in Table 1.
(a) S = 1 indicates the presence of one s̅ antiquark and no s quark. To have baryon number 0 there
can be only one other quark, and to have net charge +e that quark must be a u, and the quark content is us̅.
(b) The particle has an s̅ antiquark, and for a baryon number of –1 the particle must consist of three
antiquarks. For a net charge of -e, the quark content must be d̅d̅s̅.
(c) S = -2 means that there are two s quarks, and for baryon number 1 there must be one more quark. For a charge of 0 the third quark must be a u quark and the quark content is uss.
The particles with baryon number zero are mesons and consist of a quark-antiquark pair.
Particles with baryon number 1 consist of three quarks and are baryons. Particles with baryon number -1 consist of three antiquarks and are antibaryons.
Problem#4
The quark content of the neutron is udd. (a) What is the quark content of the antineutron? Explain your reasoning. (b) Is the neutron its own antiparticle? Why or why not? (c) The quark content of the Ψ is cc̅. Is the Ψ its own antiparticle? Explain your reasoning.
Answer:
To obtain the quark content of an antiparticle, replace quarks by antiquarks and antiquarks by quarks in the quark composition of the particle.
(a) The antiparticle must consist of the antiquarks so n̅ = u̅d̅d̅
(b) n = udd is not its own antiparticle, since n and n̅ have different quark content.
(c) Ψ = cc̅ so Ψ̅ = c̅c = Ψ so the Ψ is its own antiparticle.
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