In most of the books on QFT, the author talks about various methods of regularization but in the end chooses the dimensional regularization and MS-bar scheme when discussing the final renormalization, I have not seen any review, books or lecture notes where the author actually takes momentum cut-off as regularization and proceeds towards renormalizing the theory. I totally understand and appreciate the elegance and usefulness of dimensional method, but in certain situations we may need to take hard momentum cut-off ($ Lambda $) route and do the renormalization, but in doing that we face the problem of exactly how to handle the polynomial divergence ($ Lambda^n $ kind, if any ) and the logarythmic one !
Suppose I have a one-loop calculation of an amplitude:
begin{align}
A = A_{finite} + a_n (frac{Lambda}{m})^n + b logfrac{Lambda^2}{m^2}
end{align}
Where $ m $ is any mass. How exactly should we proceed to derive various renormalized parameters of our theory. What subtraction schemes exist in this regularization ?
