Particle Physics and Cosmology: Particles and Interactions

Citation: The content below is based on the most recent edition of University Physics with Modern Physics.

Important Formulas

Energy-Mass Relation:
$E = mc^2$
Electromagnetic Force:
$F = \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r^2}$
Weak Interaction Decay Rate:
$\Gamma = \frac{G_F^2 m^5}{192 \pi^3 \hbar^4}$
Strong Force Potential:
$V(r) = -\frac{4}{3} \frac{\alpha_s \hbar c}{r}$
Gravitational Force:
$F = G \frac{m_1 m_2}{r^2}$
Coupling Constant Strength:
$\alpha = \frac{g^2}{4 \pi}$

Key Terms and Definitions

Elementary Particles: The fundamental constituents of matter, including quarks, leptons, and bosons.
Fundamental Interactions: The four basic forces in nature: gravitational, electromagnetic, strong, and weak forces.
Gauge Bosons: Force carriers for the fundamental interactions, such as photons for electromagnetism and gluons for the strong force.
Fermions: Particles with half-integer spin that make up matter, including quarks and leptons.
Bosons: Particles with integer spin that mediate the fundamental forces, including the Higgs boson and gauge bosons.
Weak Force: A fundamental interaction responsible for processes like beta decay, mediated by $W$ and $Z$ bosons.

Example

A muon ( $\mu^-$ ) decays via the weak interaction with a lifetime of $2.2 \, \mu s$ . Calculate the decay rate ( $\Gamma$ ).

Using the decay rate formula:

$\Gamma = \frac{\hbar}{\tau}$

Substituting values ( $\hbar = 6.58 \times 10^{-22} \, \text{MeV} \cdot \text{s}$ ):

$\Gamma = \frac{6.58 \times 10^{-22}}{2.2 \times 10^{-6}}$

$\Gamma \approx 3.0 \times 10^{-16} \, \text{MeV}$

Result:

The decay rate of the muon is approximately $3.0 \times 10^{-16} \, \text{MeV}$ .

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