I have read the following sentence in a section which is explaining why particle accelerators need such high energy:
As we require high precision position measurement, the Heisenberg uncertainty principle tells us that the standard deviation of momentum $\sigma_p$ must be large. The standard deviation of momentum of a particle can never be greater than its momentum $p$. Therefore, high momentum is required.
Could someone explain this relationship (bold sentence)? I know that the Heisenberg uncertainty principle makes a statement about the fundamental knowability of position and momentum of a particle, but I don't know the relationship between its actual momentum and the standard deviation of momentum.