The wave functions in the diquark-quark model for baryons are modified to take into account the effect of the different masses of the quarks in diquark formation. A spatial wave function is introduced multiplying each flavour-spin configuration in the quar

1.Introduction

Theconceptofdiquarkwasintroduced,inthebeginningsofthequarkmodeltodescribebaryonicproperties.Diquarksmaybeconceivedassubstructuresorclustersofpairsofquarksinsidebaryonwavefunction[1,2].Diquark-quarkmodelshavebeenintensivelydevelopedinmanyworksonbaryonstructureandmassspectroscopy,baryondecayandhighenergybaryonscattering[3].Somediquark-quarkwavefunctionswereconstructedtodescribethestructureofbaryons.Thosewavefunctionshavethedisad-vantageofnotbeingcompletelyantisymmetricunderexchangeofanytwoquarks.Infact,theyarenotantisymmetricundertheexchangeofaquarkofthediquarkandthethirdquark.Thisdi cultyiscompensatedbythesimplicityofthemodel.However,theabsenceofantisimmetryisconsistentwiththediquarkinterpretationasanquasielemen-taryobject.Futhermoreinthebaryonwavefunctionconstruction[4]mentionedabove,itwasnottakenintoaccountthee ectofthedi erenceinthemassesofquarks.

Theinteractionsamongthequarksinsidethebaryonsareindependentofthe avours,butthediquarkdimensiondependsonthemassesoftheconstituentquarks.Thehigherthequarkmassesthesmallerthedimensionofthediquark.

Givenabaryonwiththreequarksofdi erentmasses,therearethreedi erentcon gurationsofdiquark-quarkthatcancontributetoitswavefunction.Thediquarksineachcon gurationarenotequallyprobable.Anotherseriousdistinctioninthethreepossiblecon gurationsofthediquark-quarkmodelisthattheirmassesaredi erent.Thisresultconstitutesanambiguityinthediquark-quarkmodelforbaryon.

Inthispaperwegiveaprescriptiontoconstructthebaryonwavefunction,inwhichthecontributionofeachdiquark-quarkcon gurationisadequatelytakenintoaccount.TheexpectationvalueoftheHamiltoniancalculatedwiththewavefunctionobtainedbythisprescriptiongivesthebaryonmass.Themassofthebaryonis,then,theweighedmeanvalueofthemassesofthediquark-quarkcon gurations.Thismeanvalueeliminatestheambiguityinthecomputationofthebaryonmass.TheprescriptionisappliedtotheconstructionofthewavefunctionofthelowestenergybaryonicstatesinSwavewithspin1/2.Inthesewavefunctionsthereexiststwospinstates,S=0eS=1,foreachSwavediquark.Theneach avourcon gurationhasascalarandavectorialdiquark.

2.KinematicsandDiquarkapproximation

Thecoordinatesusedinthedescriptionofthemotionofthethreequarksinthe