# Parton Distribution Functions plot

I was looking at a plot of the parton distribution functions today and had a question. On the y axis, it seems like the value of x f(x) for gluons is greater than one at small x. I was under the impression that parton distribution functions are probability densities and cannot be greater than one. Also, x is a fraction of momentum and can also not be greater than one. Does anyone know why this is?

A probability cannot be greater than 1, but a probability density can be. The parton distribution represents basically the probability per unit momentum fraction, so it can be large over a small region of $x$ without contributing much to the actual probability, $\int f(x)\mathrm{d}x$.
• Actually, I think the integral $\int_0^1 f(x)\mathrm{d}x$ can be interpreted as the average value of the particle number operator, and that average is going to be 1 by definition. (I had to think about it for a while to reconvince myself of this) Commented Aug 17, 2012 at 4:30