TheassociatedproductionsofthenewgaugebosonBHintheLittlestHiggsmodelwithaStandardModel(SM)gaugebosonrepresentanimportantclassofprocessesforprobingtheextendedgaugesectoroftheLittlestHiggsmodel.Inthisframework,theBHbosonemergesasoneoftheadditionalheavygaugebosonspredictedbythemodel,whicharisesduetothecollectivesymmetrybreakingmechanism.Theseassociatedproductionchannels,suchasBHproducedalongsideaSMWorZboson,providedistinctivesignaturesatcollidersandserveascrucialtestsofthemodel'sstructure.Studyingtheseprocesseshelpsconstrainthemodelparameters,particularlythesymmetrybreakingscalefandthemixinganglesbetweenthenewandSMgaugesectors.Theanalysisofsuchproductionmechanismsoffersinsightsintothemodel'sabilitytoaddressthehierarchyproblemwhileremainingconsistentwithprecisionelectroweakmeasurements.
