VOLUME 64, NUMBER 10 PHYSICAL REVIEW LETTERS 5 MARcH 1990 Radiative Neutrino Decay in a Medium Juan Carlos O'Olivo Instituto de Ciencias Nucleares, Universidad Nacionai Autonoma de Mexico, Circuito Exterior CU, 04510 Mexico, D. F. Jose F. Nieves Department of Physics, University of Puerto Rico, Rio Piedras, Puerto Rico 0093I Palash B. Pal Institute of Theoretical ScienceU, nt'cersity of Oregon, Eugene, Oregon 97403 (Received 27 October 1989; revised manuscript received 3 January 1990) We calculate the rate of decay of a heavy neutrino into a lighter neutrino and a photon in a back- ground that contain electrons but no p's or r's. Unlike the same decay in the vacuum, the rate of this process is not suppressed by the Glashow-Iliopoulos-Maiani mechanism. Some physical implications of the process are discussed. PACS numbers: 13.35.+s, 13.40. Hq, 14.60.Gh, 98.80.Cq The subject of unusual properties of neutrinos in ma- terial media has attracted a lot of attention recently. Wolfenstein' showed that the masses and mixings of neutrinos may be significantly aff'ected by the presence of a medium. Mikheyev and Smirnov realized that this fact could provide a solution to the solar-neutrino prob- lem. More recently, it has been demonstrated that the electromagnetic properties of neutrinos can even be qual- itatively different within a medium compared to the properties in the vacuum. For example, a Majorana neutrino may have electric and magnetic dipole moments in a medium, whereas in the vacuum these quantities must vanish. As discussed in Ref. 3, the reason behind this qualitative difference lies in the transformation prop- erties of the medium under the discrete symmetries C, P, T, and combinations thereof. In particular, the medium can introduce CP and CPT asymmetries in the effective particle interaction, which would be absent in the vacu- um that is supposed to be CPT symmetric. As a comple- ment to this analysis, the matter-induced electromagnet- ic form factors have been calculated in a recent paper by the present authors. In this Letter, we want to discuss the eff'ects that a background medium inflicts on another interesting pro- cess involving neutrinos, viz. , the radiative decay of a heavier neutrino to a lighter one: v(k) —v'(k') + y(q), ~here in parentheses we have written the four-momenta of the particles. Our motivation is the following. On the one hand, this process has been studied for the possibility of detecting the cosmic neutrino background by observ- ing the photons coming out of the process. Recently, Fukugita has raised the possibility that a suitable life- time for the process in Eq. (1) might be crucial in ex- plaining the deviation of the cosmic micro~ave spec- trum from a pure blackbody distribution. On the other hand, it is known that in the vacuum the rate for this process is suppressed by the Glashow-Iliopoulos-Maiani (GIM) mechanism. However, a medium that contains electrons but not muons or taons is not flavor symmetric. Therefore, in such a medium, the background-dependent part of this amplitude is not GIM suppressed. As a re- sult, the decay rate could be much larger than that in the vacuum. In light of these questions, we calculate below the lifetime of the process in a thermal medium, which is essential for discussing the evolution of neutrinos in the early Universe. Besides, the present calculation will also provide insight into neutrino processes in stellar objects. We begin the calculation by assuming that the disper- sion relations of the particles are not significantly affected by the medium, so that we can use the relations valid in the vacuum. In order to be self-consistent, we should then take the wave-function renormalization fac- tors associated with all external lines to equal unity. In eff'ect, these assumptions imply that we consider only the transverse polarization states of the photon. In addition, we assume that the mass of v' vanishes, or at least is so small compared to m, the mass of v, that it can be neglected. The matrix element of the process in Eq. (1) can now be written as i%'= — iu(k')r.'u(k)e'*(q), (2) where u(k) denotes the Dirac spinor with momentum k and e denotes the polarization vector of the photon. We have used the primes on Af and I, to denote that we will consider the background-dependent part only. Following the notation used in Ref. 4, I ' can be written as I, '=U,*, U„T~py L, (3) ~here U is the lepton mixing matrix and L is the projec- tion operator for left-handed fermions. We assume that the background contains electrons but not muons or 1088 1990 The American Physical Society