Ambiguities in the gravitational correction of quantum electrodynamics
  We verify that quadratic divergences stemming from gravitational corrections to QED which have been conjectured to lead to asymptotic freedom near Planck scale are arbitrary (regularization dependent) and compatible with zero. Moreover we explicitly show that such arbitrary term contributes to the beta function of QED in a gauge dependent way in the gravitational sector. 
J. C. C. Felipe, L. A. Cabral, L. C. T. Brito, Marcos Sampaio and M.   C. Nemes
hep-th