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In this Letter we consider very light Higgs fields in BMSSM(Beyond MSSM). Thespectrum below TeV scale is the same as the MSSM but the Higgs potential ismodified and is well described in terms of effective dimension five and sixoperators. A correction from the BMSSM operators allows us to consider newparameter space of Higgs sector which is not allowed in the MSSM. It can beregarded as a constrained version of general 2 Higgs doublet model (2HDM) aslong as Higgs sector is concerned. We focus on the possibility that CP oddHiggs (A) mass is about 7 or 8 GeV and charged Higgs mass is comparable to Wmass. At the same time one of the CP even Higgs (h) is light enough such that hand A production at the Z pole is kinematically allowed. The tension betweenforward backward asymmetry of bottom quark Ab_FB measured at LEP and theStandard Model prediction can be ameliorated if bottom quark pair produced fromlight CP even Higgs is taken into account.

Light Higgs Scenario in BMSSM and LEP Precision Data