We study a relation between nuclear forces based on phenomenological approach (V_ph) and nuclear effective field theory (V_EFT) from a viewpoint of renormalization group. We find the relation between these two types of nuclear force using Wilsonian renorma

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arXiv:nucl-th/0610034v1 10 Oct 2006RenormalizationgroupanalysisofnuclearforceS.X.NakamuraaaTheoryGroup,TRIUMF,4004WesbrookMall,Vancouver,BCV6T2A3,CanadaWestudyarelationbetweennuclearforcesbasedonphenomenologicalapproach(Vph)andnucleare ective eldtheory(VEFT)fromaviewpointofrenormalizationgroup.We ndtherelationbetweenthesetwotypesofnuclearforceusingWilsonianrenormalizationgroupequation.ConsideringthefactthatVEFTisde nedinacertainsmallmodelspace,weshowthatasimplecontactinteractionaccuratelysimulatesshort-distancephysics,andthatVEFTisfreefromdependenceonmodellingthedetailsoftheshort-distancephysics.Basedonourresult,wediscusssomefeaturesofnucleare ective eldtheory.1.IntroductionNuclearforceisoneoftheoldestprobleminnuclearphysics.However,itstheoreticaldescriptionisstillanunsettledissue.Here,we rstexplainatraditional,phenomenolog-icalapproachtothenuclearforce,andafairlynewapproachbasedonnucleare ective eldtheory(NEFT)[Aftertheexplanation,weformulateascenarioforarelationbetweennuclearforcesbasedonthetwoapproaches.Themainsubjectinthisreportistodiscusstherelationfromaviewpointoftherenormalizationgroup(RG).Inthephenomenologicalnuclearforce(Vph),thelong-rangepartisdescribedbythe

one-pion-exchangepotential(OPEP).Theshort-rangepartispoorlyknown,andthereforeaphenomenologicalmodelisused;heavy-mesonexchangesorpurelyphenomenologicalparameterization.Parametersinvolvedinthemodelare xedsoastoreproducelow-energyNNscatteringdataandthedeuteronbindingenergy.Inthisway,severalhigh-precisionNNpotentialshavebeenconstructed,suchastheCD-BonnandtheNijmegenpotentials.Althoughthesemodelsarephenomenologicallyverysuccessful,therearesomeproblemsasfollows.At rst,eachmodeldescribestheshort-rangepartdi erently,andislargelymodel-dependent.Secondly,thereisnosystematicwaytoconstructtheshort-rangemechanism.Thirdly,thereislittleconnectiontotheunderlyingtheory,QCD.Incontrast,itisclaimedthatanuclearforcebasedonNEFT(VEFT)isfreefromtheproblemsinherentinVph.TheclaimisbasedonthederivationprocedureofVEFT,whichisbrie ygivenasfollows.Onestartswithane ectivechiralLagrangian,takingcareofthespontaneouslybrokenchiralsymmetryofQCD.TheLagrangianconsistsofe ectivedegreesoffreedomforasysteminquestion,andisthemostgeneralaslongasassumedsymmetriesaresatis ed.Oneidenti esasetofirreduciblediagramsfromtheLagrangianwithVEFT.Theimportanceofanirreduciblediagramisassignedbyacountingrule.However,onemay ndquestionsaboutVEFT:(Q1)InVEFT,short-distancephysicsisdescribedbycontactinteractions,whichismuchsimplercomparedtotheshort-range