>>12080706you are looking for the renormalization group.
Really basically, with the example of mass in a field theory: when you have a particle in a self-interacting field, that particle is necessarily surrounded by a cloud of virtual force carriers which cause it to interact with itself and the field it is a part of. We can ignore these interactions by changing the effective mass of the particle and then treating it as non-self-interacting.
The problem is that this self-correction varies with distance, and if you look closely enough, or look at self-interactions with a small enough distance, this self-interaction strength tends to infinity, meaning the mass correction term also blows up to infinity. Some physicists then posited an infinite 'bare' mass of opposite sign, such that when the infinite correction was added the result would be finite, but this was not at first justified. Then physicists found a relationship between this scale and the effective mass of the particle in the form of an equation in a group called the renormalization group, which when solved (this has been done in certain simple cases) allows them to focus on particular length-scales without having to deal with messy infinities on different scales. This causes definite predictions of the bare mass to be lost afaik.
