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

4

00V(k,k) (MeV 2) × 10 4V(k,k) (MeV 2) × 10 5

0 50 100

k (MeV) 150 200-1-0.5-2-1-3-1.5-4 0 50 100k (MeV) 150 200

Figure1.NN-potential 1S0|V|1S0 ;the

upper,theReid93,theNijmegenIandthe

CD-Bonnpotentials,respectively.The

solidanddash-dottedcurvesareVM(Λ=

200MeV),thesolidoneresultsfromthe

NijmegenIandtheCD-Bonnpotentials,

whilethedash-dottedfromtheReid93.Figure2.NN-potential 3D1|V|3S1 .ThesolidcurveisVM(Λ=200MeV)result-ingfromtheCD-Bonnpotential.Thedashed(dotted)curveisasimulationofVMusingtheOPEPplusone(two)contactinteraction(s).Thedash-dottedcurveistheOPEP.

claimed.However,theclaimisbasedontheprocedureofderivingthenuclearoperators,whichisnotaquantitativeargument.Inthiswork,wequantitativelyshowedthatVEFTdoesnothavethedependenceonmodellingthedetailsofshort-distancephysics.Thisisaconsequenceofviewingthesystemroughly,therebyignoringthedetailedstructureoftheshort-distancephysics.Itisnoted,therefore,adescriptionofasystembasedonNEFTisnotalwaysbetterthanthosebasedonphenomenologicalmodels.Inmanycases,theygiveessentiallythesamelow-energyobservablesbecausetheyareequivalentthroughtheRG.NEFTmayhavesuperiorityincaseswheredetailedinformationaboutmulti-pionexchangemechanismplayanimportantrole.

Finally,withNEFT,onecandescribeasystemmoree cientlyandsimply,comparedtothephenomenologicalmodels.Thee ciencyisduetotheperturbativecalculation,andthesimplicityisduetotheignoranceofthedetailsoftheshort-distancephysics.Tosummarize,weconsideredthenuclearforcefromtheviewpointoftheRG,andshowedthatthereexiststheequivalencerelationbetweenVEFTandVph.Wesimultane-ouslyshowedthatVEFTdoesnothavethemodeldependenceduetothedetailsoftheshort-distancephysics,andthatthesimplecontactinteractionsinVEFTaccuratelyde-scribetheshort-distancephysicsinacertainsmallmodelspace.Basedontheresult,wediscussedthenewfeaturesinNEFT.

REFERENCES

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3.M.C.Birse,J.A.McGovernandK.G.Richardson,Phys.Lett.B464,(1999)169.