Author Jonathan David
Author Jonathan David
Lessons

Particle Physics and Cosmology: The Standard Model and Beyond

by |Published |1 comment

Particle Physics and Cosmology: The Standard Model and Beyond

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

Important Formulas

  • Energy-Mass Relation:

        \[E = mc^2\]

  • Gauge Symmetry:

        \[L = -\frac{1}{4} F_{\mu \nu} F^{\mu \nu} + \bar{\psi}(i \gamma^\mu D_\mu - m)\psi\]

  • Higgs Mechanism Mass:

        \[m = \frac{v g}{\sqrt{2}}\]

  • Quark Mixing (CKM Matrix):

        \[\begin{bmatrix} V_{ud} & V_{us} & V_{ub} \\ V_{cd} & V_{cs} & V_{cb} \\ V_{td} & V_{ts} & V_{tb} \end{bmatrix}\]

  • Fine Structure Constant:

        \[\alpha = \frac{e^2}{4 \pi \epsilon_0 \hbar c}\]

  • Dark Matter Density Parameter:

        \[\Omega_{\text{DM}} = \frac{\rho_{\text{DM}}}{\rho_c}\]

Key Terms and Definitions

  • Standard Model: A theory in particle physics that describes the electromagnetic, weak, and strong nuclear interactions using quantum field theory.
  • Gauge Bosons: Force-carrying particles associated with the fundamental interactions, such as photons for electromagnetism and gluons for the strong force.
  • Higgs Boson: A particle responsible for giving mass to other particles through the Higgs mechanism.
  • Beyond Standard Model (BSM): Theoretical extensions to the Standard Model that address phenomena like dark matter, neutrino masses, and the matter-antimatter asymmetry.
  • Dark Matter: A form of matter that does not emit or absorb light but exerts gravitational effects on visible matter and cosmic structure.
  • Supersymmetry: A theoretical framework proposing a symmetry between fermions and bosons to solve several Standard Model limitations.

Example

Calculate the mass of a W boson (W^\pm) if the coupling constant g = 0.65 and the Higgs field vacuum expectation value v = 246 \, \text{GeV}.

Using the Higgs Mechanism formula:

    \[m = \frac{v g}{\sqrt{2}}\]

Substituting values:

    \[m = \frac{246 \cdot 0.65}{\sqrt{2}} \, \text{GeV}\]

Result:

    \[m \approx 113 \, \text{GeV}\]

The mass of the W boson is approximately 113 \, \text{GeV}.

Stay Connected

For more lessons on advanced physics topics, check out my YouTube channel. If you’re a STEM major, explore the Ultimate Crash Course for detailed eBooks and resources!