Type-II neutrino seesaw mechanism extension of NMSSM from SUSY breaking mechanisms

We propose to accommodate economically the type-II neutrino seesaw mechanism in (G)NMSSM from GMSB and AMSB, respectively. The heavy triplets within neutrino seesaw mechanism are identified to be the messengers. Therefore, the $\mu$-problem, the neutrino mass generation, LFV as well the soft SUSY breaking parameters can be economically combined in a non-trivial way. General features of such extensions are discussed. The type-II neutrino seesaw-specific interactions can give additional Yukawa deflection contributions to the soft SUSY breaking parameters of NMSSM, which are indispensable to realize successful EWSB and accommodate the 125 GeV Higgs. Relevant numerical results, including the constraints of dark matter and possible LFV processes $l_i\rightarrow l_j \gamma$ etc, are also given. We find that our economical type-II neutrino seesaw mechanism extension of NMSSM from AMSB or GMSB can lead to realistic low energy NMSSM spectrum, both admitting the 125 GeV Higgs as the lightest CP-even scalar. The possibility of the 125 GeV Higgs being the next-to-lightest CP-even scalar in GMSB-type scenario is ruled out by the constraints from EWSB, collider and precision measurements. The possibility of the 125 GeV Higgs being the next-to-lightest CP-even scalar in AMSB-type scenario is ruled out by dark matter direct detection experiments. Possible constraints from LFV processes $l_i\rightarrow l_j \gamma$ can give an upper bound for the messenger scale.

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