At finite isospin chemical potential μI, the tension between measured decays and partial branching ratios of neutral and charged bosons as functions of dimuon mass squared and the SM isospin asymmetry shall be analyzed in the nonperturbative QCD-effective model, the Polyakov linear sigma-model. With the derivation of the explicit symmetry-breaking term h3, the QCD phase structure could be mapped out to finite μB and μI. We conclude the critical temperatures Tχ decrease with increasing μB and μI and the (Tχ-μI) boundary could be extended to the (Tχ-μB) plane.