L5.5 QCD: Asymptotic Freedom

TL;DR

Asymptotic freedom is a property of the strong force where the coupling strength between color-charged particles decreases at high momentum transfers, allowing for perturbative calculations. However, at low momentum transfers, quarks and gluons are confined and cannot exist as free particles.

Transcript

MARKUS KLUTE: Welcome back to 8.701. So in this lecture, we want to talk about asymptotic freedom, about confinement, and also the running of the strength of the strong force. In the recitation, we already talked about vacuum polarization, QED, and how it relates to QCD. So here we're just going to remind ourselves again about what has been discuss... Read More

Key Insights

• 📶 Loop contributions in QED cause the coupling strength to increase with larger momentum transfers, while gluon self-coupling in QCD leads to a decrease in the coupling strength at high momentum transfers.
• 👻 Asymptotic freedom in QCD is the property where the coupling becomes zero at very high momentum transfers, allowing for perturbative calculations.
• 😘 At low momentum transfers, quarks and gluons are confined and cannot exist as free particles.
• 💪 The running of the strong coupling parameter is defined using a lambda parameter or lambda QCD, which eliminates the dependence on the scale involved.
• 💪 Experimental measurements have confirmed the running of alpha s, the strength of the strong interaction, and are in reasonable agreement with each other.
• 👻 Asymptotic freedom allows for calculations in QCD using perturbation theory at high energies.

Questions & Answers

Q: How does loop contributions in QED affect the effective charge?

Loop contributions in QED make the effective charge a function of momentum transferred, causing the coupling strength to increase with larger values of momentum squared. This leads to an increase in the effective charge at higher momentum transfers.

Q: What is the effect of gluon self-coupling in QCD?

In QCD, gluon self-coupling leads to an opposite effect compared to loop contributions in QED. The self-coupling produces anti-screening or camouflaging of the color charge, resulting in a decrease in the coupling strength at high momentum transfers.

Q: What is asymptotic freedom and how does it relate to QCD?

Asymptotic freedom is a property of the strong force in QCD where the coupling becomes zero at very high momentum transfers. This allows for perturbative calculations using the Feynman calculus. However, at low momentum transfers, quarks and gluons are confined, meaning they cannot exist as free particles.

Q: How is the running of the strong coupling parameter (alpha s) defined?

The running of the strong coupling parameter is defined by the dependence of the coupling strength on the momentum transfer. It is commonly represented as alpha s over a function of momentum squared. This dependence is influenced by factors such as the number of colors and flavors involved.

Summary & Key Takeaways

• In QED, loop contributions make the effective charge a function of momentum transferred, causing the coupling strength to increase with larger values of momentum squared.

• In QCD, gluon self-coupling leads to an opposite effect, resulting in a decrease in the coupling strength at high momentum transfers.

• Asymptotic freedom is the property of the strong force where the coupling becomes zero at very high momentum transfers, allowing for perturbative calculations. However, at low momentum transfers, quarks and gluons are confined.