- #1

- 1,728

- 13

## Homework Statement

(a) What are their vertex and propagator factors?

(b) Find the value of R.

(c) Explain the peaks at 3, 10 and 100 GeV.

## Homework Equations

## The Attempt at a Solution

__Part (a)__They have the same propagator factor ##\frac{1}{P \cdot P}##.

Vertex factor for muon production is ##(1)(-1)g_{EM}^2 = -g_{EM}^2##.

Vertex factor for hadron production is ##\sum -q^2##.

__Part (b)__In the rage of 2GeV to 20GeV, types of quarks produced: u,d,s,c,b.

[tex]R = 3 \times \frac{e^2\left( -\frac{4}{9} -\frac{1}{9} - \frac{1}{9} - \frac{4}{9} - \frac{1}{9} \right)}{-e^2} = \frac{11}{3}[/tex]

Factor of 3 comes from the 3 colours, R, G and B.

__Part (c)__Masses of quarks: u, d ~ ##10^{-3} GeV##, s~ ##0.1GeV##, c~##1 GeV##, b~##4eV##, t~##170GeV##.

Peak at 3GeV comes from production of charmed quarks.

Peak at 10GeV comes from production of bottom quarks.

Peak at 100GeV comes from production of top quarks.