I have been involved in many of these discussions. I will say this. There are many misconceptions about penetration and what causes it. I don't want to make this harder than it has to be.

Kinetic energy: 1/2*m*v^2. This as a term used to quantify the energy carried by a mass in motion.

Momentum: m*v this is a vector quantity. In other words a number is not momentum unless it has a direction. Momentum and energy are two different things.

Let's consider a hypothetical situation. Let's first make some simple assumptions. We have a number of arrows that weigh differently. Some are light and some are heavy. Now we use any broadhead but we use the same broadhead on all arrows. Now remember we have different arrows of different weight and diameter. We shoot each of these arrows out of different bows but have them set up to generate the same kinetic energy. If this is the case, the smaller arrows will pentrate deeper. Now I know everyone is pulling their hair out and cursing at there computer and saying I am a complete idiot and have no concept of physics. Let me explain before you argue that the "world is not round".

This is a case of simple fluid dynamics. We can consider a particle moving through a fluid the same as an arrow (particle) moving through tissue (fluid). With this in mind, the only mathematical tool we have in relating velocity ( ultimately Kinetic energy) and penetration would be an energy balance. Without spending the money and time ( chemical engineering degreee ) this energy balance concept is foreign. Just trust me when I say that only 4 things can affect the particles (arrow) penetration. These are Kineetic energy, potential energy, work, and friction. Now we know that the arrow is not doing any work (no pumps, turbines, motors, etc.). Potential energy can also be neglected (potential energy would be energy stored up by a change in height). So that only leaves friction and KE. Now if the Kinetic energy values are all the same, the arrow with the least amount of friction against the tissue will penetrate further. Assuming that the smaller diameter arrow has the least friction with the tissue due to reduced surface area then viola....the smaller arrow will penetrate further.

To explain why momentum and KE are not both related to penetration would take up a small book. They are related much like velocity and accelartion. Both are affected by velocity but do affect physical actions the same.

So, Kinetic energy is the only valid choice to quantify penetration. No it is not the only factor. Arrow placement, broadhead design, KE, all play a role.

I hopes this helps.