The seesaw mechanism in the $\mu \nu$SSM

The $\mu \nu$SSM proposes to use right-handed neutrino supermultiplets in order to generate the $\mu$ term and neutrino masses simultaneously. We discuss neutrino physics and the associated electroweak seesaw mechanism in this model. We show how to obtain, from the neutralino-neutrino mass matrix of the $\mu \nu$SSM, the effective neutrino mass matrix. In particular we discuss certain limits of this matrix that clarify the neutrino-sector behavior of the model. We also show that current data on neutrino masses and mixing angles can easily be reproduced. These constraints can be fulfilled even with a diagonal neutrino Yukawa matrix, since this seesaw does not involve only the right-handed neutrinos but also the MSSM neutralinos. To obtain the correct neutrino angles turns out to be easy due to the following characteristics of this seesaw: R-parity is broken and the relevant scale is the electroweak one.