My understanding for renormalization is that to deal with the divergence appeared in loop integrals, we introduce an artificial regularization parameter to make the integral converge, and when we take certain limit of the parameter (like to 0 or $\infty$),we recover the original expression for the loop integral.After that, we redefine parameters to absorb the divergence of the integral (which we have already quantify as the artificial parameter) and get physical results.
However, for the same loop integral, it seems that there are more than one way to introduce an artificial regularization parameter and make the integral finite, and each one of the way of introducing the artificial regularization parameter might lead to a different way of renormalization.
Does that mean for the same loop integral, we can have more than one way to renormalize the integral?
