On the amelioration of quadratic divergences
  Once massless quadratically divergent tadpole diagrams are discarded, because they contain no intrinsic scale, it is possible to convert other divergences into logarithmic form, using partial fraction identities; this includes the case of quadratic divergences, as has been applied to the linear sigma model. However the procedure must be carried out with due care, paying great attention to correct numerator factors. 
R. Delbourgo and M.D. Scadron