Bi-Maximal Neutrino Mixing in the MSSM with a Single Right-Handed Neutrino

We discuss neutrino masses in the framework of a minimal extension of the minimal supersymmetric standard model (MSSM) consisting of an additional single righthanded neutrino superfield N with a heavy Majorana mass M , which induces a single light see-saw mass mν3 leaving two neutrinos massless at tree-level. This trivial extension to the MSSM may account for the atomospheric neutrino data via νμ → ντ oscillations by assuming a near maximal mixing angle θ23 ∼ π/4 and taking ∆m23 ∼ m2ν3 ∼ 2.5× 10 eV . In order to account for the solar neutrino data we appeal to one-loop radiative corrections involving internal loops of SUSY particles, which we show can naturally generate an additional light neutrino mass mν2 ∼ 10 eV again with near maximal mixing angle θ12 ∼ π/4. The resulting scheme corresponds to so-called “bi-maximal” neutrino mixing involving “just-so” solar oscillations. CERN-TH/98-256 February 28, 2008 Atmospheric neutrino data from Super-Kamiokande [1] and SOUDAN [2], when combined with the recent CHOOZ data [3], are consistent with νμ → ντ oscillations with near maximal mixing and ∆m23 ∼ 2.5 × 10 eV . 1 A critical appraisal of current neutrino data can be found in [5, 6]. In practice a common standard approach to neutrino masses is to introduce three right-handed neutrinos with a heavy Majorana mass matrix. When the usual Dirac mass matrices of neutrinos and charged leptons are taken into account, the see-saw mechanism then leads to the physical light effective Majorana neutrino masses and mixing angles relevant for experiment. There is a huge literature concerning this and other kinds of approach to neutrino masses which is impossible to do justice to. In ref.[7] we merely list a few recent papers, from which which the full recent literature may be reconstructed. For older work on neutrino masses see for instance [8], where extensive references to earlier work may be found. In a recent paper [9] one of us followed a minimalistic approach and introduced below the GUT scale only a single “right-handed neutrino” 2 N into the standard model (or supersymmetric standard model) with a heavy Majorana mass 1 2 MN̄N c where M < MGUT . With only a single right-handed neutrino the low energy neutrino spectrum consists of a light neutrino ν3 ≈ s23νμ+c23ντ with mass mν3 , plus two massless neutrinos consisting of the orthogonal combination ν0 ≈ c23νμ − s23ντ together with νe which we have here assumed for simplicity has a zero Yukawa coupling λe to N . 3 By contrast the Yukawa couplings λμ and λτ of νμ and ντ to N are non-zero and determine the 23 mixing angle via t23 = λμ/λτ . Maximal mixing corresponds to λμ = λτ , with λe = 0 and ∆m 2 23 = m 2 ν3 may be chosen to be in the correct range to The data are equally consistent if ντ is replaced by a light sterile neutrino, and indeed many authors have considered adding an extra light singlet neutrino state [4], although we shall not do so here. 2 Since CP conjugation converts a right-handed neutrino into a left handed anti-neutrino, it should strictly be called a gauge singlet. We shall use notation such as s23 ≡ sin θ23, c23 ≡ cos θ23, t23 ≡ tan θ23, extensively throughout this paper.