11.5 The standard model  (Page 4/9)

What is the Standard Model? Express your answer in terms of the four fundamental forces and exchange particles.

Draw a Feynman diagram to represents annihilation of an electron and positron into a photon.

What is the motivation behind grand unification theories?

If a theory is developed that unifies all four forces, will it still be correct to say that the orbit of the Moon is determined by the gravitational force? Explain why.

If the Higgs boson is discovered and found to have mass, will it be considered the ultimate carrier of the weak force? Explain your response.

One of the common decay modes of the ${\text{Λ}}^0\text{is}{\text{Λ}}^0\to {\pi }^{\text{−}}+\text{p}\text{.}$ Even though only hadrons are involved in this decay, it occurs through the weak nuclear force. How do we know that this decay does not occur through the strong nuclear force?

Using the Heisenberg uncertainly principle, determine the range of the weak force if this force is produced by the exchange of a Z boson.

Use the Heisenberg uncertainly principle to estimate the range of a weak nuclear decay involving a graviton.

(a) The following decay is mediated by the electroweak force:

$\text{p}\to \text{n}+{\text{e}}^{+}+{\upsilon }_{\text{e}}.$

Draw the Feynman diagram for the decay.

(b) The following scattering is mediated by the electroweak force:

${\upsilon }_e+{\text{e}}^{\text{−}}\to {\upsilon }_e+{\text{e}}^{\text{−}}.$

Draw the Feynman diagram for the scattering.

Assuming conservation of momentum, what is the energy of each $\gamma$ ray produced in the decay of a neutral pion at rest, in the reaction ${\pi }^0\to \gamma +\gamma$ ?

What is the wavelength of a 50-GeV electron, which is produced at SLAC? This provides an idea of the limit to the detail it can probe.

The primary decay mode for the negative pion is ${\pi }^{\text{−}}\to {\mu }^{\text{−}}+{\stackrel{\text{−}}{\nu }}_{\mu }.$ (a) What is the energy release in MeV in this decay? (b) Using conservation of momentum, how much energy does each of the decay products receive, given the ${\pi }^{\text{−}}$ is at rest when it decays? You may assume the muon antineutrino is massless and has momentum $p=E\text{/}c$ , just like a photon.

Suppose you are designing a proton decay experiment and you can detect 50 percent of the proton decays in a tank of water. (a) How many kilograms of water would you need to see one decay per month, assuming a lifetime of ${10}^{31}\text{y?}$ (b) How many cubic meters of water is this? (c) If the actual lifetime is ${10}^{33}\text{y}$ , how long would you have to wait on an average to see a single proton decay?