Some implications of lepton flavor violating processes in a supersymmetric Type II seesaw model at TeV scale

Abstract

We have conceived a supersymmetric Type II seesaw model at TeV scale, which has some additional particles consisting of scalar and fermionic triplet Higgs states, whose masses are around a few hundred GeV. In this particular model, we have studied constraints on the masses of triplet states arising from the lepton flavor violating (LFV) processes, such as μ→3e and μ→eγ. We have analyzed the implications of these constraints on other observable quantities such as the muon anomalous magnetic moment and the decay patterns of scalar triplet Higgses. Scalar triplet Higgs states can decay into leptons and into supersymmetric fields. We have found that the constraints from LFV can affect these various decay modes.

Appendices

Appendix A: Scalar potential

The scalar potential of the SUSY Type II seesaw model at TeV scale will have the following form:

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The first term in Eq. (23) is the F-term contribution where the summation over the fields Y run over the superfields of W of Eq. (1). The second and third terms of Eq. (23) are D-term contributions due to SU(2) _L and U(1) _Y gauge groups, respectively. The last two terms of Eq. (23) are soft terms of MSSM and of fields involving triplet scalar fields. The form of $V_{\rm soft}^{\rm MSSM}$ can be found in Refs. [18–23]. The $V_{\rm soft}^{\rm triplet}$ is given in Eq. (5). The triplet representation of SU(2) generators, which are needed in D ^a of Eq. (23), are

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For computing D-terms, the forms of the scalar fields are as follows: $H_{u}=(H^{+}_{u},H^{0}_{u})^{\rm T}$, $H_{d}=(H^{0}_{d},H^{-}_{d})^{\rm T}$, $\varPhi_{1}=(\phi_{1}^{++},\phi^{+}_{1},\phi^{0}_{1})^{\rm T}$, $\varPhi_{2}=(\phi_{2}^{0},\phi^{-}_{2},\phi^{--}_{2})^{\rm T}$. We have described the D-terms of doublet and of triplet Higgses, but the D-terms for other scalar fields of the model can be analogously written.

Appendix B: Conventions of neutralino and chargino mass matrices and their diagonalizing matrices

Our conventions regarding neutralino and chargino mass matrices are the same as in [23]. In the basis $\varPsi^{0}=(\tilde{B},\tilde{W}^{3},\tilde{H}_{d},\tilde{H}_{u})^{\rm T}$, the mixing mass matrix of neutralinos can be written as $\mathcal{L}_{N}= -\frac{1}{2} (\varPsi^{0} )^{\rm T}M_{N}\varPsi^{0}+ \mathrm{h.c.}$ The form of M _N is same as Eq. (8.2.2) of Ref. [23]. The physical neutralino states are defined from $\varPsi^{0}_{j}=\sum_{k=1}^{4}V^{N}_{jk}N_{k}$, where the unitary matrix V ^N diagonalizes M _N as

$$ \bigl(V^N \bigr)^{\rm T}M_NV^N={ \rm diag}(m_{N1},m_{N2},m_{N3},m_{N4}). $$

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In the basis $\varPsi^{-}=(\tilde{W}^{-},\tilde{H}^{-}_{d})^{\rm T}$, $\varPsi^{+}=(\tilde{W}^{+},\tilde{H}^{+}_{u})^{\rm T}$, the mixing mass terms for charginos can be written as $\mathcal{L}_{c}=- (\varPsi^{-} )^{\rm T} M_{C}\varPsi^{+}+{\rm h.c.}$ The matrix M _C is same as Eq. (8.2.14) of Ref. [23]. The physical chargino states are defined from: $\varPsi^{-}_{j} =\sum_{k=1}^{2} U^{\chi}_{jk}~\chi^{-}_{k}$, $\varPsi^{+}_{j}=\sum_{k=1}^{2}V^{\chi}_{jk}~\chi^{+}_{k}$. The unitary matrices U ^χ and V ^χ diagonalize M _C as

$$ \bigl(U^\chi \bigr)^{\rm T}M_CV^\chi ={ \rm diag}(m_{C1},m_{C2}). $$

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