Surface Integral of Babu Diagram
  We point out that the surface integral of the Babu diagram gives non-trivial main contribution independent of the charged lepton masses and the scale of new physics. It can fit the experimental data on both solar and atmospheric neutrino oscillations. However, then the coupling constants of the new Higgs singlets with the leptons gain values smaller than that in the usual two-loop radiative analyses. This yields distinction between our consideration on ultraviolet-behaviors and the former based on the infrared radiative corrections. 
Phung Van Dong and Hoang Ngoc Long