The Effect of Majorana Phase in Degenerate Neutrinos

Abstract

There are physical Majorana phases in the lepton flavor mixing matrix when neutrinos are Majorana fermions. In the case of two degenerate neutrinos, the physical Majorana phase plays a crucial role in the stability of the maximal flavor mixing between the second and the third generations with respect to quantum corrections. The physical Majorana phase of π guarantees that the maximal mixing is stable with respect to quantum corrections, while the Majorana phase of zero causes the maximal mixing destroyed by quantum corrections when neutrino masses are of O(1 eV). The continuous change of the Majorana phase from π to 0 makes the maximal mixing destroyed by quantum corrections with O(1 eV) degenerate neutrino masses. On the other hand, when there is a large mass hierarchy among neutrinos, the maximal flavor mixing is not destroyed by quantum corrections independently of the Majorana phase. * )

Cancellations in neutrinoless double beta decay and the neutrino mass matrix

“…Different values of the parameters lead to modifications of the results which are not difficult to do with the help of Eqs. (13,17,18). From the figures, we can easily analyze some specific configurations: For example, form < 0.6 the (− − +) configuration is ruled out and form > 0.6 the (+ − −) and (− + −) cases, making 0.6 a key scale, since it is independent on the solar solution and the value of |U e3 |.…”

“…The only information about the phases or parities can come from neutrinoless double beta decay: All other mass matrix entries are impossible to measure directly, since the respective branching ratios or cross sections they govern are way beyond experimental access [14]. Apart from the obvious aspect that fundamental parameters of a model need to be measured, other interesting application of the phases exist: In [18] it was found that the Majorana phases play a crucial role in the stability of the mixing angles against quantum corrections. Ref.…”

Energy-scale dependence of the lepton flavor-mixing matrix

“…We should stress here that this fact does not necessarily result in the tiny energy dependence of the MNS matrix. We can explicitly see the significant RGE corrections of the MNS matrix in some situations [9,10]. In ref.…”

“…In ref. [10], the drastic change of the MNS matrix by the RGE was obtained when neutrinos of the second and third generations have masses of O(eV) with δm 2 23 3 × 10 −3 (eV 2 ) [3]. This situation corresponds to the case of r 1 ∼ |c 12 | ∼ 0, r 2 ∼ 1, and |c 23 | 1 in eq.…”

Neutrino masses, mixing angles and the unification of couplings in the MSSM

“…Therefore, it is relevant to assume mass textures with the property that the (m diag E ) 33 and (m diag D ) 33 entries are no longer equal after diagonalization at the GUT scale [29]. To understand the effect, we consider a 2 × 2 example, and assume that the off-diagonal terms in the down-quark mass matrix m D are small compared to the (33) element, whereas this is not the case for the charged-lepton mass matrix.…”