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Duality in Left-Right Symmetric Seesaw Mechanism

E. Kh. Akhmedov·M. Frigerio
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Abstract

We consider type I+II seesaw mechanism, where the exchanges of both right-handed neutrinos and isotriplet Higgs bosons contribute to the neutrino mass. Working in the left-right symmetric framework and assuming the mass matrix of light neutrinos $m_ν$ and the Dirac-type Yukawa couplings to be known, we find the triplet Yukawa coupling matrix $f$, which carries the information about the masses and mixing of the right-handed neutrinos. We show that in this case there exists a duality: for any solution $f$, there is a dual solution $\hat{f}=m_ν/v_L-f$, where $v_L$ is the VEV of the triplet Higgs. Thus, unlike in pure type I (II) seesaw, there is no unique allowed structure for the matrix $f$. For $n$ lepton generations the number of solutions is $2^n$. We develop an exact analytic method of solving the seesaw non-linear matrix equation for $f$.

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E. Kh. Akhmedov, M. Frigerio. 2006-03-07. Duality in Left-Right Symmetric Seesaw Mechanism. https://doi.org/10.1103/physrevlett.96.061802

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