Parton density function

1 minute read


There is a similar concept in particle physics. It is the parton distribution function.

These are defined for a quantity called Bjorken-x. IF you imagine a projectile moving i.e. a nucleon, if you think about its constituents, its building bricks, each of them carries part of its momentum.

If you are wondering what this is, think about something that moves with a certain speed. Then you take its weight - heart attack, its mass - and multiply it by its speed. You have the momentum.

Take the average fit man. People would appreciate me if I thought of an average fit man as a 180 cm tall man, weighing approximately 80 kg on Earth (if you weigh yourself on the Moon you are cheating). He goes out for a walk during the Covid pandemic and travels at a speed of 5.4 km/hour. These are translated to a speed of 5.41000/3600 m/s = 1.5 m/s (please, do notify me if there are mistakes). Hence, we can say that its momentum is then 120 kgm/s…

Its constituents can be considered carrying a momentum of 1.5 m/s times their own mass. So if you sum all the bricks together, you can then consider the sum of momenta as 1.5 m/s times the sum of the masses of the single bricks.

This is basically what happens in particle physics, although a bit more complicated than that… But just slightly so.

You can imagine that the momenta of the single bricks are then limited by two edges: nothing and all.

If you then consider the quantity Bjorken-x as the ratio between the momenta of the brick and the whole, x is then limited by zero and one.

Welcome to UPC physics! Our ultimate goal is studying pdf close to zero… Next time.