Mass Neutrino Oscillations In The Gravitational Field

Neutrino is one of the important and characteristic particles in elementary particle family, and the one only participating in the weak interaction. It plays an important role in theoretical physics and astrophysics.After Pauli put forward the neutrino hypothesis, a series of experiments were done for catching for the neutrino. Now, these experiments have proved that the neutrino is the elementary particle that existing externally, which makes people do deeply research on it in many ways. And the mass of the neutrino and mass neutrino oscillations have become hot topics. In the Fermi weak interaction theory and even in the electro-weak unification theory, the neutrino is looked as the massless particle. On the basis of these theories, the results calculated in all kinds of physical process are in good agreement with the experiments. On the other hand, if the mass of the neutrino is nonzero, we can naturally explain some phenomenon such as the hot dark matter in cosmos, the missing of the solar neutrino, etc. So in some theoretical models the neutrino is trying to be endowed with the mass. At the same time, different methods are used to measure and calculate the mass of the neutrino. With the quick development of the experiment technique, the upper limit of the mass of the neutrino measured in experiments is declining perpetually, but at present any experiment doesn't give a definite and exact value to the mass of the neutrino.On the other hand, in 1958, Pontecorvo pointed out that if the mass of neutrino is nonzero, the different kind of neutrinos will transform commuta-tively, that is mass neutrino oscillations happens. From the quantum mechanics of neutrino oscillations we known that at the detector point the oscillation probability of one kind of neutrino transforming into another is relative to the mixing angle, the average energy of the neutrino beam, the source-detector distance and the mass-squared difference between two kinds of neutrinos. In the basis of this, our paper mainly discussed the interference phase factor and the CP violation in mass neutrino oscillations. So we organize our paper as follows:In chapter I , we introduce the discovery , the mass, the mixing and the oscillation of the neutrino, in the basis of which, we present the quantum mechanics of neutrino oscillations.In chapter II , we discuss the neutrino oscillations in flat space-time, and present the interference phase factor. From the result we point out that the phase factor is relative to the average energy of the neutrino, mass-squared difference between two kinds of neutrinos and the source-detector distance.In chapter III, resorting to the geodesic, we discuss the mass neutrino oscillations in Einstein's gravitational theory. With the standard method, we firstly discussed the interference phase factor of neutrino oscillation in Schwarz-schild space-time. Then with the same method we present the phase factor in Reissner-Nordstrom space-time and Kerr space-time, respectively. Prom the result, we known that, though the existence of the charge of the Reissner-Nordstrom field source and the angle momentum of the Kerr field source will have contribution to the phase factor, but comparing to the result in Schwarz-schild field, the contribution is very little. At last, we calculate the interference phase factor in Robertson-Walker space-time.In chapter IV and V, we calculate the interference phase factor of neutrino oscillation in static spherically symmetric space-time in Brans-Dicke (B-D)gravitational theory and torsion gravity, respectively. The contribution obtained in B-D gravitational theory to the quantum mechanical phase of neutrino are very significant and could be considered as a test for establishing the validity of B-D theory. Prom the result in torsion gravity we find that the modification to the vacuum phase factor of mass neutrino by torsion, although bigger than that by general relativity in some conditions, is very small. Therefore, the mass neutrino oscillation experiment cannot provide a criterion to adjudge which gravitational theory is preferred, general relativity, or other gravitational theories.In chapter VI, we introduce the violation of the symmetry under the united operation between the charged conjugate and the parity, or the CP violation. Then we present the theoretical study and the experimental detect ofthe direct CP violation, the new sources and mechanism of CP violation. In the basis of the above, we discuss the CP violation effect in neutrino oscillations, in which we point out that in the two flavor neutrino oscillations, since the mixing matrix is real, there is no CP violation, but in the three flavor neutrino oscillations, the mixing matrix is complex, so there exists CP violation.