Particle Physics and Cosmology: Quarks and Gluons

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

Important Formulas

Energy-Mass Relation:
$E = mc^2$
Strong Force Potential:
$V(r) = -\frac{4}{3} \frac{\alpha_s \hbar c}{r} + kr$
Quark Confinement Energy:
$E \propto \sigma r$
where $\sigma$ is the string tension.
Color Charge Conservation:
$\sum Q_{\text{color}} = 0$
QCD Beta Function:
$\beta(\alpha_s) = -\beta_0 \alpha_s^2$
Gluon Exchange Force:
$F = \frac{g_s^2}{4 \pi r^2}$

Key Terms and Definitions

Quarks: Elementary particles that combine to form protons, neutrons, and other hadrons. They come in six flavors: up, down, charm, strange, top, and bottom.
Gluons: Massless particles that act as the exchange particles for the strong force, binding quarks together inside protons and neutrons.
Strong Force: The fundamental force that holds quarks together in hadrons, mediated by gluons.
Color Charge: A property of quarks and gluons in quantum chromodynamics (QCD) analogous to electric charge in electromagnetism, but with three types: red, green, and blue.
Quark Confinement: The phenomenon where quarks are never found in isolation but only within composite particles like protons and neutrons.
Asymptotic Freedom: A property of QCD where quarks interact more weakly as they come closer together at high energies.

Example

Determine the potential energy of two quarks separated by $r = 1 \, \text{fm}$ , where $\alpha_s = 0.118$ and $k = 0.9 \, \text{GeV/fm}$ .

Using the strong force potential formula:

$V(r) = -\frac{4}{3} \frac{\alpha_s \hbar c}{r} + kr$

Substituting values ( $\hbar c = 197 \, \text{MeV fm}$ ):

$V(r) = -\frac{4}{3} \frac{0.118 \cdot 197}{1} + 0.9 \cdot 1$

$V(r) = -30.96 + 0.9$

$V(r) = -30.06 \, \text{MeV}$

Result:

The potential energy of the quark pair is approximately $-30.06 \, \text{MeV}$ .

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