Studies on the Weak Charges of Particles

In order to include massive neutrino theoretically, a new concept of the weak charges of the particles, fundamental fermions, intermediate bosons and hadrons, is introduced. A new conservation law of the weak charge is first reported. According to the chirality of the weak charge the origin of parity nonconservation in the weak interactions is reasonably explained. According to the symmetry of the weak charge, an extension of the standard model is proposed. In this scenario, all the three generations of neutrinos are massive Dirac particles; both the right-handed neutrinos and the right-handed neutral baryons have zero weak charge, and so they do not take part in the weak interactions. PACS numbers: 12.60.Cn, 11.30.Er, 14.60.St, 13.30.-j In spite of its tremendous successes when confronted with experiment, the standard model (SM) has some shortcomings and leaves unanswered many fundamental questions. Perhaps one of the important outstanding problems amongst them is the neutrino mass, which would have a significant impact on astrophysics, cosmology and particle physics. In the SM neutrinos are exactly massless. However, theoretically here is no compelling reason for massless neutrinos, and there exists already a vast literature on the model of massive neutrinos [1]. Many extensions of the SM contain neutrinos with Majorana or Dirac masses. Experimentally there is now a host of evidence for neutrino oscillation [2], and that is most naturally explained if neutrinos are massive and mix with one another. Especially, the recent result of Super-Kamiokande collaboration [3] gave the mass squared difference ∆m = 5×10−6×10 eV and the mixing angle sin2θ > 0.82. Therefore, some physicists believe that neutrinos might indeed have a very small mass [4]. If neutrinos have non-zero mass, it will radically alter our understanding of the violation of parity conservation law in the weak interactions and implies physics beyond the SM of particle physics [5]. The massless neutrinos are inevitable outcome of the parity nonconservation in the weak interactions. Therefor, in order to include massive neutrino theoretically, a possible suggestion is studying the root cause of the parity violation in the weak interactions. In fact, as early as 1982 Professor Yang emphasized again that a more fundamental origin of the violation of discrete symmetry should be investigated [6]. ∗Present address: Residence 10-2-7, Shaanxi Normal University, Xi’an 710062, P. R. China. E-mail address: [email protected] In this paper we will be forced to propose the concept of the weak charges of the particles in order to study the above issues. The weak charges of the fundamental fermions are introduced by analogy between the interaction Lagrangian for neutral weak currents and the electromagnetic currents, the weak charges of the intermediate bosons by analogy between the Lagrangian terms describing the self-interaction of gauge fields. The weak charges of some baryons and mesons are calculated. The question of parity nonconservation in the weak interactions is explained by the chirality of the weak charge. The conservation law of the total weak charge is tested in all interactions and the conservation law of the chiral weak charge, in the weak interactions. In the last section the SM is extended to include the right-handed neutrinos. I The weak charges of particles I.1 The weak charges of the fundamental fermions The existence of the three generations of the fundamental fermions, leptons and quarks, has been established in the SM. We shall confine ourselves to considering only one of them, e.g., first generation because they are absolutely alike. According to the SM we choose the group SU(2)×U(1) as the gauge group, and the left-handed (LH) fermions as the SU(2)-doublets and the right-handed (RH) fermions as the SU(2)-singlets,