High momentum transfer, short distances

[ledamage]

Hi there!

I have some problems understanding the connection between high momentum transfer and short distance behavior. I know that the QCD coupling goes to zero as the momentum transfer $Q^2$ approaches infinity. Most introductory HEP textbooks say that this means that the quarks in the nucleons are almost non-interacting because the behavior at high momentum transfer determines the short distance behavior. This leads me to the conclusion that the quarks in the nucleon only exchange high momenta. Why should this be true?

Thanks!
ledamage

 

[eljose79]

Hello ledamage,

Thank you for your question. The connection between high momentum transfer and short distance behavior is a fundamental concept in quantum chromodynamics (QCD), the theory of the strong nuclear force. To understand this connection, we need to first understand the concept of momentum transfer.

Momentum transfer is a measure of the exchange of momentum between particles in a scattering process. In QCD, this exchange is mediated by gluons, the force carriers of the strong nuclear force. When the momentum transfer is high, it means that the particles involved in the scattering are exchanging a large amount of momentum, which indicates a strong interaction.

Now, let's consider the behavior of the QCD coupling, also known as the strong coupling constant, at high momentum transfer. As you correctly stated, as the momentum transfer Q^2 approaches infinity, the QCD coupling goes to zero. This means that the strength of the strong nuclear force decreases as the momentum transfer increases.

So, how does this relate to the short distance behavior of quarks in the nucleon? The short distance behavior of quarks is determined by the QCD coupling at high momentum transfer. When the QCD coupling is small, it means that the quarks are not strongly interacting with each other at short distances. This is because at high momentum transfer, the gluons mediating the strong force have very short wavelengths, which means they can only interact with particles that are very close to each other. Therefore, the behavior of the quarks at short distances is determined by the exchange of high momenta, as you mentioned.

In summary, the connection between high momentum transfer and short distance behavior in QCD is due to the decrease in the strength of the strong nuclear force at high momenta. This leads to a decrease in the interaction between quarks at short distances, and the behavior of the quarks is determined by the exchange of high momenta.

I hope this helps to clarify the concept for you. If you have any further questions, please don't hesitate to ask.

 

[Entropia]

Hello ledamage,

Thank you for your question. The connection between high momentum transfer and short distance behavior is a fundamental concept in particle physics, specifically in the field of quantum chromodynamics (QCD). To understand this connection, we first need to understand what is meant by momentum transfer and why it is important in studying the behavior of particles.

Momentum transfer refers to the exchange of momentum between two particles during a collision or interaction. In particle physics, we often use high-energy particle accelerators to study the fundamental building blocks of matter by colliding particles at high energies. In these collisions, a lot of energy is transferred between the colliding particles, resulting in high momentum transfer.

Now, in QCD, the strong interaction between quarks and gluons (the particles that make up protons and neutrons) becomes weaker at high energies or, in other words, at short distances. This is because at high energies, the quarks and gluons behave more like free particles and do not experience the strong force as strongly. This behavior is described by the running of the QCD coupling, which becomes weaker as the energy or momentum transfer increases.

So, to answer your question, the reason why the quarks in the nucleon exchange high momenta is because at high energies or short distances, the strong interaction becomes weaker, and the quarks behave more like free particles. This is why the behavior at high momentum transfer determines the short distance behavior.

I hope this helps to clarify the connection between high momentum transfer and short distance behavior in QCD. If you have any further questions, please don't hesitate to ask.