Massive and massless neutrinos on unbalanced seesaws

  • The observation of neutrino oscillations requires new physics beyond the standard model (SM). A SM-like gauge theory with p lepton families can be extended by introducing q heavy right-handed Majorana neutrinos but preserving its SU(2)L×U(1)Y gauge symmetry. The overall neutrino mass matrix M turns out to be a symmetric (p+q)×(p+q) matrix. Given p>q, the rank of $M$ is in general equal to 2q,corresponding to 2q non-zero mass eigenvalues. The existence of (p-q) massless left-handed Majorana neutrinos is an exact consequence of the model, independent of the usual approximation made in deriving the Type-I seesaw relation between the effective p×p light Majorana neutrino mass matrix Mν and the q×q heavy Majorana neutrino mass matrix MR. In other words, the numbers of massive left- and right-handed neutrinos are fairly matched. A good example to illustrate this "seesaw fair play rule" is the minimal seesaw model with p=3 and q=2, in which one massless neutrino sits on the unbalanced seesaw.
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XING Zhi-Zhong. Massive and massless neutrinos on unbalanced seesaws[J]. Chinese Physics C, 2008, 32(2): 96-99. doi: 10.1088/1674-1137/32/2/004
XING Zhi-Zhong. Massive and massless neutrinos on unbalanced seesaws[J]. Chinese Physics C, 2008, 32(2): 96-99.  doi: 10.1088/1674-1137/32/2/004 shu
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Received: 2007-06-07
Revised: 1900-01-01
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Massive and massless neutrinos on unbalanced seesaws

    Corresponding author: XING Zhi-Zhong,
  • Institute of High Energy Physics, CAS, Beijing 100049, China2 Interdisciplinary Center for Theoretical Study, University of Science and Technology of China, Hefei 230026, China

Abstract: The observation of neutrino oscillations requires new physics beyond the standard model (SM). A SM-like gauge theory with p lepton families can be extended by introducing q heavy right-handed Majorana neutrinos but preserving its SU(2)L×U(1)Y gauge symmetry. The overall neutrino mass matrix M turns out to be a symmetric (p+q)×(p+q) matrix. Given p>q, the rank of $M$ is in general equal to 2q,corresponding to 2q non-zero mass eigenvalues. The existence of (p-q) massless left-handed Majorana neutrinos is an exact consequence of the model, independent of the usual approximation made in deriving the Type-I seesaw relation between the effective p×p light Majorana neutrino mass matrix Mν and the q×q heavy Majorana neutrino mass matrix MR. In other words, the numbers of massive left- and right-handed neutrinos are fairly matched. A good example to illustrate this "seesaw fair play rule" is the minimal seesaw model with p=3 and q=2, in which one massless neutrino sits on the unbalanced seesaw.

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