Sphalerons in the NMSSM
  We study sphaleron solutions in the next-to-minimal supersymmetric standard model. We find that the boundary condition on the singlet field at the origin of the radial coordinate is of Neumann type, while the other boundary conditions are of Dirichlet type. The sphaleron energy takes almost the same value as in the MSSM for wide range of parameters, in spite of the negative contribution from the cubic term in the Higgs potential. 
Koichi Funakubo, Akira Kakuto, Shuichiro Tao and Fumihiko Toyoda