33.5 Quarks: is that all there is?  (Page 8/20)

The reaction ${\pi }^{+}+p\to {\text{Δ}}^{\text{++}}$ (described in the preceding problem) takes place via the strong force. (a) What is the baryon number of the ${\text{Δ}}^{\text{++}}$ particle?

(b) Draw a Feynman diagram of the reaction showing the individual quarks involved.

One of the decay modes of the omega minus is ${\Omega }^{-}\to {\text{Ξ}}^0+{\pi }^{-}$ .

(a) What is the change in strangeness?

(b) Verify that baryon number and charge are conserved, while lepton numbers are unaffected.

(c) Write the equation in terms of the constituent quarks, indicating that the weak force is responsible.

Repeat the previous problem for the decay mode ${\Omega }^{-}\to {\text{Λ}}^0+K^{-}.$

One decay mode for the eta-zero meson is ${\eta }^0\to \gamma +\mathrm{\gamma .}$

(a) Find the energy released.

(b) What is the uncertainty in the energy due to the short lifetime?

(c) Write the decay in terms of the constituent quarks.

(d) Verify that baryon number, lepton numbers, and charge are conserved.

One decay mode for the eta-zero meson is ${\eta }^0\to {\pi }^0+{\pi }^0$ .

(a) Write the decay in terms of the quark constituents.

(b) How much energy is released?

(c) What is the ultimate release of energy, given the decay mode for the pi zero is ${\pi }^0\to \gamma +\gamma$ ?

Is the decay $n\to e^{+}+e^{-}$ possible considering the appropriate conservation laws? State why or why not.

Is the decay ${\mu }^{-}\to e^{-}+{\nu }_e+{\nu }_{\mu }$ possible considering the appropriate conservation laws? State why or why not.

(a) Is the decay ${\text{Λ}}^0\to n+{\pi }^0$ possible considering the appropriate conservation laws? State why or why not.

(b) Write the decay in terms of the quark constituents of the particles.

(a) Is the decay ${\text{Σ}}^{-}\to n+{\pi }^{-}$ possible considering the appropriate conservation laws? State why or why not. (b) Write the decay in terms of the quark constituents of the particles.

The only combination of quark colors that produces a white baryon is RGB . Identify all the color 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.

(a) Show that the conjectured decay of the proton, $p\to {\pi }^0+e^{+}$ , violates conservation of baryon number and conservation of lepton number.

(b) What is the analogous decay process for the antiproton?

Verify the quantum numbers given for the ${\Omega }^{+}$ in [link] by adding the quantum numbers for its quark constituents as inferred from [link] .

Verify the quantum numbers given for the proton and neutron in [link] by adding the quantum numbers for their quark constituents as given in [link] .

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

(b) Given that the ${\pi }^0$ decays to two $\gamma$ s and that the $e^{+}$ 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)?

(a) Find the charge, baryon number, strangeness, charm, and bottomness of the $J/\Psi$ particle from its quark composition.

(b) Do the same for the $\Upsilon$ particle.

There are particles called D -mesons. One of them is the $D^{+}$ meson, which has a single positive charge and a baryon number of zero, also the value of its strangeness, topness, and bottomness. It has a charm of $+1.$ What is its quark configuration?

There are particles called bottom mesons or B -mesons. One of them is the $B^{-}$ meson, which has a single negative charge; its baryon number is zero, as are its strangeness, charm, and topness. It has a bottomness of $-1$ . What is its quark configuration?

(a) What particle has the quark composition $\stackrel{-}{u}\stackrel{-}{u}\stackrel{-}{d}$ ?

(b) What should its decay mode be?

(a) Show that all combinations of three quarks produce integral charges. Thus baryons must have integral charge.

(b) Show that all combinations of a quark and an antiquark produce only integral charges. Thus mesons must have integral charge.