Velocities of different quark types inside nuclei

Question

Using the uncertainty relation \begin{equation} \Delta x \Delta p \geq \frac{\hbar}{2} \end{equation} we can calculate the momentum uncertainty on a length scale of a nuclei. Assuming $r_{nucleus} \sim 1 fm$ we get a momentum uncertainty of $\Delta p = 98.66 MeV \cdot c \sim 100 MeV \cdot c$.

What is the impact of this uncertainty on the kinematics of different quark types? I've read that the velocities of up and down quarks inside protons and neutrons are nearly equal to the speed of light. Now, when we get to the heavier quark types like charm or bottom, they already have rest energies of more than $1\frac{GeV}{c^2}$. Here, I would assume that they move at extremely low velocities in order to fulfill the uncertainty principle (on lenght scales of a nucleus). Are my thoughts corrrect or is there something special about quark kinematics that I have to consider here?

Sorry I'm new to this topic and it's probably a pretty simple question for you.

Answer 1

Heavy quarks are not constituent particles of nucleons. They are mostly made of $u,d,s$ quarks. Actually, we find a net zero strangeness number in the nucleons. Following uncertainty principle one can show pair production and annihilation may occur for a short time. But as you go for heavier quarks the probability of their production is much less. Thus I don't think we worry much about heavy quark dynamics within nucleons.

However heavy quark dynamics play important role in the heavy ion collisions, where quark-gluon plasma (QGP) is produced and quarks roam freely in the QGP system. There heavy quarks are good candidate for understanding the early time dynamics of the QGP system as well as its thermodynamics. The motion of the heavy quarks in this QGP system is treated non-relativistically in most of the literature. Thus I would argue that, although your intuition about the velocity of heavy quarks is correct but it is not applicable to nucleons as there are hardly any heavy quarks created inside nucleons.

This is probably just one aspect of your question (Heavy quark). I hope there are other members in this community who can answer your other questions better.