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Soft leptogenesis in the NMSSM with a singlet right-handed neutrino superfield

In this work, we explore soft leptogenesis in the NMSSM framework extended by a right-handed neutrino superfield. We calculate the CP asymmetry, $\varepsilon$, and find it to be non-zero at tree-level without using thermal effects for the final state particles. This is in contrast to soft leptogenesis in the MSSM extended by a right-handed neutrino superfield where thermal effects are essential. The difference arises due to the presence of a 3-body decay of the sneutrino in the NMSSM that violates lepton number at tree-level. Apart from this, we also find that $\varepsilon\neq 0$ if the additional singlet scalar has a complex vacuum expectation value while all the other NMSSM parameters including the soft SUSY breaking ones relevant for CP asymmetry remain real. We estimate the order of magnitudes of these parameters to produce sufficient baryon asymmetry of the Universe.