33.5 Quarks: Is That All There Is?

How many pointlike particles would an experiment scattering high energy electrons from any meson discover within the meson?

1. 1
2. 2
3. 3
4. 4

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

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

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

Repeat the previous problem for the decay mode $\Omega^{- } \rightarrow \Lambda^{0} + K^{- } .$

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

(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 $\pi^{0} \rightarrow \gamma + \gamma$?

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

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

(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.

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

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

(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)?

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?

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

(b) What should its decay mode be?