2-LOOP NEUTRINO MASSES AND THE SOLAR-NEUTRINO PROBLEM

The addition of m singlet right-handed neutrinos to the standard model leads to radiatively generated mass corrections for the SU(2)(L) doub let neutrinos. For those neutrinos which are massless at the tree leve l after this addition, this implies a small mass generated at the two- loop level via W-+/- exchange. We calculate these mass corrections exa ctly by obtaining an analytic form for the general case of n doublets and m singlets. As a phenomenological application, we study the m = 1, n = 3 case in detail, for which there are two massive and two massles s neutrinos at the tree level. After calculating the loop-induced mass es, the full mass spectrum is examined in the light of experimental da ta from the four solar neutrino experiments and the COBE satellite. Re quiring compatibility with these experiments enables us to constrain t he parameter space and to obtain a handle on the scale of new physics, as typified by the mass of the heavy singlet. We also obtain the inte resting result that the final mass eigenvalues, corrected for loop eff ects, may all be significantly different from the seesaw value of the lighter of the two neutrinos which have tree level masses, thus demons trating the importance of the loop effects considered here.