The Origin of Matter

Abstract

“If we accept the view of complete symmetry between positive and negative electric charge so far as concerns the fundamental laws of Nature, we must regard it rather as an accident that the Earth (and presumably whole solar system), contains a preponderance of negative electrons and positive protons. . ..” This is a sentence in the Nobel Lecture given by Paul A. M. Dirac in 1933. 1) This is the first proposal for baryon-anti-baryon symmetric universe. However, astrophysical observations have ruled out the presence of antimatter in the present universe up to the scale of clusters of galaxies. If our universe indeed began baryon symmetric, those imbalances in numbers of baryons and anti-baryons must be generated by some physical processes in the early universe. I show, in this talk, that decays of the heavy (right-handed) Majorana neutrinos in the early universe generate the imbalances between baryon and anti-baryon numbers. The presence of super heavy (right-handed) Majorana neutrinos is an important prediction of unified theories beyond the standard model. An integration of the heavy Majorana neutrinos induces very small masses for neutrinos via the seesaw mechanism. 2) Thus, small neutrino masses is a reflection of unification at very high energy scale. It is quite natural to consider that the heavy Majorana neutrinos are produced thermally in the early universe. When the temperature of the universe cools down to the masses of the heavy Majorana neutrinos, the heavy neutrinos begin to decay into Higgs boson and lepton or Higgs boson and anti-lepton. The decay may produce the lepton-number asymmetry if CP invariance is violated in the decay processes. The CP invariance can be easily violated by phases in new complex Yukawa coupling of Higgs boson to the right-handed neutrinos and left-handed leptons. The decay processes can easily be out of thermal equilibrium. Thus, the decay processes of heavy Majorana neutrinos can satisfy three Sakharov conditions 3) for baryogenesis. This produced lepton-number asymmetry is converted into the baryon-number asymmetry in the present universe through non-perturbation effects of the electroweak gauge theory. 5) This is called “leptogenesis”. 4) I show that the neutrino masses observed in various neutrino-oscillation experiments are just in the range predicted by the thermal leptogenesis. 6)