Relation between Heavy Neutrino Mass and Majorana CP Phase in a Minimal Seesaw Leptogenesis Scenario

Abstract

The recent neutrino oscillation experiments have provided us with robust evidence that neutrinos have tiny masses.1) An attractive idea is given by the seesaw mechanism2) which explains the smallness of the neutrino masses through the existence of right-handed Majorana neutrinos. Among many realistic seesaw models existing in the literature, the minimal seesaw model contains only two right-handed Majorana neutrinos, thus it is the most economical one.3) Also, the seesaw mechanism provides a very natural explanation of the baryon asymmetry in the universe through the baryogenesis via leptogenesis scenarios.4) Baryon asymmetry has been measured using the Wilkinson Microwave Anisotropy Probe (WMAP) as a baryonphoton ratio ηB = (6.1 −0.2)× 10−10.5) In this paper, we study the relation between the heavy-neutrino mass and the Majorana CP phase in a minimal seesaw leptogenesis scenario with tri/bi-maximal mixing. Generally, when we use the so-called reconstruction formula to estimate the baryon-photon ratio, at least one of the elements in the Dirac mass matrix is fixed to zero; we denote it by b2 = 0.6),7) Recently, we have pointed out that we can take not only b2 = 0 but also nonzero b2, e.g., b2 = X where X is any constant, to use the reconstruction formula.8) In the following analysis, we use the reconstruction formula with nonzero b2 to estimate the relation between the heavy-neutrino mass and the Majorana CP phase.