ar X iv : h ep - p h / 06 08 23 3 v 2 6 O ct 2 00 6 preprint SHEP - 06 - 21 February 2 , 2008 Another step towards a no - lose theorem

We show how the LHC potential to detect a rather light CP-even Higgs boson of the NMSSM, H1 or H2, decaying into CP-odd Higgs states, A1A1, can be improved if Higgs-strahlung off W bosons and (more marginally) off top-antitop pairs are employed alongside vector boson fusion as production modes. Our results should help extracting at least one Higgs boson signal over the NMSSM parameter space. The Minimal Supersymmetric Standard Model (MSSM) is affected by the so-called ‘μproblem’. Its Superpotential contains a dimensionful parameter, μ, that, upon Electro-Weak Symmetry Breaking (EWSB), provides a contribution to the masses of both Higgs bosons and Higgsino fermions. Furthermore, the associated soft Supersymmetry (SUSY) breaking term mixes the two Higgs doublets. Now, the presence of μ in the Superpotential before EWSB indicates that its natural value would be either 0 or the Planck mass MP . On the one hand, μ = 0 would mean that no mixing is actually generated between Higgs doublets at any scale and the minimum of the Higgs potential occurs for < Hd >= 0, so that one would have in turn massless down-type fermions and leptons after SU(2) symmetry breaking. On the other hand, μ ≈ MP would reintroduce a ‘fine-tuning problem’ in the MSSM since the Higgs scalars would acquire a huge contribution ∼ μ to their squared masses (thus spoiling the effects of SUSY, which effectively removes otherwise quadratically divergent contributions to the Higgs mass from SM particles). Therefore, the values of this (arbitrary) parameter μ are phenomenologically constrained to be close to MSUSY or MW . The most elegant solution to the μ-problem is to introduce a new singlet scalar field S into the theory and replace the μ-term in the MSSM Superpotential by an interaction term Hereafter, hatted variables describe Superfields while un-hatted ones stand for the corresponding scalar components.