The Higgs mass and the scale of SUSY breaking in the NMSSM

In this letter we study the Higgs mass in the NMSSM with supersymmetry breaking at high scales $M_{SS}$. With the Standard Model as the effective low energy theory, the computation of the Higgs mass relies on the matching condition of the quartic coupling $\lambda$ at $M_{SS}$. In the MSSM, the latter is fixed to a semi-positive value and, thus, sets an upper bound on the SUSY-breaking scale near $M_{SS}\simeq 10^{10}\text{GeV}$. In the NMSSM, $\lambda(M_{SS})$ receives an additional contribution induced by the singlet which allows for negative values of $\lambda(M_{SS})$. In turn, for the measured value of the Higgs mass we find that $M_{SS}$ can take any value up to the GUT scale. Furthermore, the choice of universal soft terms favors SUSY-breaking scales close to the GUT scale.