Dirac Neutrinos in the Seesaw Mechanism: Violation of the Number of Dirac Neutrinos
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EMENTARY PARTICLES AND FIELDS Theory
Dirac Neutrinos in the Seesaw Mechanism: Violation of the Number of Dirac Neutrinos I. T. Dyatlov* Petersburg Nuclear Physics Institute, National Research Center Kurchatov Institute, Gatchina, Russia Received November 19, 2019; revised November 19, 2019; accepted November 19, 2019
Abstract—The seesaw mechanism, which explains the smallness of the neutrino masses by the involvement of high Majorana masses, leads to particles of the same Majorana nature and to a direct violation of the lepton number. A seesaw version entailing the appearance of only Dirac neutrinos subjected to the same kind of violation is proposed. Such a situation seems possible for heavy neutrinos coupled nonperturbatively to the Higgs boson H. It is required for mirror neutrinos in a model that explains the structure of the quark and lepton weak-mixing matrices by the existence of very heavy mirror neutrinos analogous to Standard Model fermions. A nonperturbative character of the problem being discussed prevents the construction of an analytic solution to it, but the conditions deduced for this problem are indicative of a preferable appearance of precisely Dirac neutrinos within this mechanism. The phenomenon under discussion may be of importance for leptogenesis processes if all neutrinos are Dirac particles. DOI: 10.1134/S1063778820030059
1. INTRODUCTION Majorana masses, which violate the lepton number, are a substantial element of the seesaw mechanism, which may underlie the extreme smallness of the neutrino masses. The seesaw result is well known and was repeatedly applied and described (for an overview, see [1]). Specifically, there arise two neutrinos of inevitably the Majorana type and having different masses—a heavy and a light one. The Lagrangian of the seesaw mechanism for the neutrino masses (one generation) has the form (ν) ¯ ¯ (1) L = μ ΨR ΨL + ΨL ΨR MR ¯ RC Ψ ¯T , ΨTR CΨR + Ψ + R 2 where ΨR,L are the chiral components of the (R, L) neutrinos, ΨR is a weak isoscalar, and ΨL is an isospinor component. This Lagrangian involves the Dirac, (μ), and Majorana, (MR ), masses. Weak SUL (2) symmetry plays a key role in the choice of Lagrangian in the form (1). The Dirac mass μ appears in the Standard Model upon spontaneous SUL (2) breaking by the vacuum expectation value of the Higgs isodoublet ΦH [2]. The Majorana mass MR may be directly present in the Lagrangian, since ΨR is an isoscalar. It may also appear via a procedure that is similar to that behind the emergence of μ [2], but *
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which involves the vacuum expectation value of a new isoscalar meson. Majorana terms featuring the isodoublet component ΨL are not considered, usually. Their introduction without direct SUL (2)-invariance breaking requires resort to a drastically different, more complicated, procedure [1] where there should exist isovector scalars, with their own vacuum expectation value, or nonrenormalizable terms proportional to ∼ Φ2H . However, new arbitrary constants (ML ) are unable to change the
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