33.5 Quarks: is that all there is?  (Page 7/20)

Beta decay is caused by the weak force, as are all reactions in which strangeness changes. Does this imply that the weak force can change quark flavor? Explain.

Why is it easier to see the properties of the c , b , and t quarks in mesons having composition $W^{-}$ or $t\stackrel{-}{t}$ rather than in baryons having a mixture of quarks, such as udb ?

How can quarks, which are fermions, combine to form bosons? Why must an even number combine to form a boson? Give one example by stating the quark substructure of a boson.

What evidence is cited to support the contention that the gluon force between quarks is greater than the strong nuclear force between hadrons? How is this related to color? Is it also related to quark confinement?

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

An antibaryon has three antiquarks with colors $\stackrel{-}{R}\stackrel{-}{G}\stackrel{-}{B}$ . What is its color?

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

How can the lifetime of a particle indicate that its decay is caused by the strong nuclear force? How can a change in strangeness imply which force is responsible for a reaction? What does a change in quark flavor imply about the force that is responsible?

(a) Do all particles having strangeness also have at least one strange quark in them?

(b) Do all hadrons with a strange quark also have nonzero strangeness?

The sigma-zero particle decays mostly via the reaction ${\text{Σ}}^0\to {\text{Λ}}^0+\gamma$ . Explain how this decay and the respective quark compositions imply that the ${\text{Σ}}^0$ is an excited state of the ${\text{Λ}}^0$ .

What do the quark compositions and other quantum numbers imply about the relationships between the ${\text{Δ}}^{+}$ and the proton? The ${\text{Δ}}^0$ and the neutron?

Discuss the similarities and differences between the photon and the $Z^0$ in terms of particle properties, including forces felt.

Identify evidence for electroweak unification.

The quarks in a particle are confined, meaning individual quarks cannot be directly observed. Are gluons confined as well? Explain

(a) Verify from its quark composition that the ${\text{Δ}}^{+}$ particle could be an excited state of the proton.

(b) There is a spread of about 100 MeV in the decay energy of the ${\text{Δ}}^{+}$ , interpreted as uncertainty due to its short lifetime. What is its approximate lifetime?

(c) Does its decay proceed via the strong or weak force?

Accelerators such as the Triangle Universities Meson Facility (TRIUMF) in British Columbia produce secondary beams of pions by having an intense primary proton beam strike a target. Such “meson factories” have been used for many years to study the interaction of pions with nuclei and, hence, the strong nuclear force. One reaction that occurs is ${\pi }^{+}+p\to {\text{Δ}}^{\text{++}}\to {\pi }^{+}+p$ , where the ${\text{Δ}}^{\text{++}}$ is a very short-lived particle. The graph in [link] shows the probability of this reaction as a function of energy. The width of the bump is the uncertainty in energy due to the short lifetime of the ${\text{Δ}}^{\text{++}}$ .

(a) Find this lifetime.

(b) Verify from the quark composition of the particles that this reaction annihilates and then re-creates a d quark and a $\stackrel{-}{d}$ antiquark by writing the reaction and decay in terms of quarks.

(c) Draw a Feynman diagram of the production and decay of the ${\text{Δ}}^{\text{++}}$ showing the individual quarks involved.