Singlet superfield extension of the minimal supersymmetric standard model with Peccei-Quinn symmetry and a light pseudoscalar Higgs boson at the LHC

Motivated by the mu-problem and the axion solution to the strong CP-problem, we extend the MSSM with one more chiral singlet field $X_e$. The underlying PQ-symmetry allows only one more term $X_e H_u H_d$ in the superpotential. The spectrum of the Higgs system includes a light pseudoscalar $a_X$ (in addition to the standard CP-even Higgs boson), predominantly decaying to two photons: $a_X \to \gamma \gamma$. Both Higgs bosons might be in the range accessible to current LHC experiments.