Majorana Neutrinos and Gravitational Oscillation

Majorana particles are natural representations of massive neutrinos since the most general mass term for a four component fermion eld describes two Majorana particles with di erent masses. Majorana neutrinos also appear in many extensions of the minimal Standard Model; this is the case, for example, in SO(10) grand uni ed theories [1]. Neutrinos in general, and in particular Majorana neutrinos, can be used to probe the core of some of the most interesting cosmological objects. Due to their small cross sections these particles can stream out una ected from even the most violent environments such as those present in Active Galactic Nuclei (AGN). The presence of several neutrino avors and spin states modi es this picture: in their trek from their source to the detector the neutrinos can undergo avor and/or spin transitions which can obscure some of the features of the source. Because of this, and due to the recent interest in neutrino astronomy (e.g. AMANDA, Nestor, Baikal, etc. [2]), it becomes important to understand the manner in which these avor-spin transitions can occur, in the hope of disentangling these e ects from the ones produced by the properties of the source. Without such an understanding it will be impossible to determine the properties of the AGN core using solely the neutrino ux received on Earth. In a previous publication [3] we considered the e ects of the AGN environment on the neutrino ux under the assumption that all neutrinos were of the Dirac type. In this complementary publication we will consider the case of Majorana neutrinos and provide a deeper phenomenological study of this system, concentrating on the dependence of the e ects on the magnitude of the neutrino magnetic moment and on the energy dependence of the predicted neutrino uxes. The evolution of Majorana neutrinos in AGN is in uenced both by its gravitational and electromagnetic interactions. The latter are due to the coupling with the magnetic eld through a transition magnetic moment . The combination of these e ects leads to ! e or  transitions. For simplicity we will deal with two neutrino species only, the extensions to three (or more) species is straightforward (though the analysis can become considerably more complicated [5]). The paper is organized as follows. We start with a brief description of neutrino production and gravitational oscillation in AGN environment in section 2. This is followed by a calculation of transition and survival probabilities of oscillating neutrinos and the resulting ux modi cations (sections 3 and 4). In section 5 we give our conclusions.