Inthescenariowherethedarkmatter(DM)particlesχχˉpairannihilatethrougharesonanceparticleR,theconstraintfromDMrelicdensitymakesthecorrespondingcrosssectionforDM-nucleielasticscatteringextremelysmall,andcanbebelowtheneutrinobackgroundinducedbythecoherentneutrino-nucleiscattering,whichmakestheDMparticlebeyondthereachoftheconventionalDMdirectdetectionexperiments.WepresentanimprovedanalyticalcalculationoftheDMrelicdensityinthecaseofresonantDMannihilationfors-andp-wavecasesandinvesitgatetheconditionfortheDM-nucleiscatteringcrosssectiontobeabovetheneutrinobackground.WeshowthatinHiggs-portaltypemodels,forDMparticleswiths-waveannihilation,thespin-independentDM-nucleusscatteringcrosssectionisproportionaltoΓR/mR,theratioofthedecaywidthandthemassofR.ForatypicalDMparticlemass～50GeV,theconditionleadstoΓR/mR≥O(10-4).Inp-waveannihilationcase,thespin-independentscatteringcrosssectionisinsensitivetoΓR/mR,andisalwaysabovetheneutrinobackground,aslongastheDMparticleislighterthanthetopquark.TherealsingletDMmodelisdiscussedasaconcreteexample.
