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nuclear force is one of the oldest problem in nuclear physics .
however , its theoretical description is still an unsettled issue . here , we first explain a traditional , phenomenological approach to the nuclear force , and a fairly new approach based on nuclear effective field theory ( neft)@xcite . after the explanation ,
we formulate a scenario for a relation between nuclear forces based on the two approaches . the main subject in this report
is to discuss the relation from a viewpoint of the renormalization group ( rg ) .    in the phenomenological nuclear force ( ) ,
the long - range part is described by the one - pion - exchange potential ( opep ) .
the short - range part is poorly known , and therefore a phenomenological model is used ; heavy - meson exchanges or purely phenomenological parameterization .
parameters involved in the model are fixed so as to reproduce low - energy @xmath0 scattering data and the deuteron binding energy . in this way ,
several high - precision @xmath0 potentials have been constructed , such as the cd - bonn and the nijmegen potentials .
although these models are phenomenologically very successful , there are some problems as follows . at first , each model describes the short - range part differently , and is largely model - dependent . secondly , there is no systematic way to construct the short - range mechanism .
thirdly , there is little connection to the underlying theory , qcd .
in contrast , it is claimed that a nuclear force based on neft ( ) is free from the problems inherent in .
the claim is based on the derivation procedure of , which is briefly given as follows .
one starts with an effective chiral lagrangian , taking care of the spontaneously broken chiral symmetry of qcd .
the lagrangian consists of effective degrees of freedom for a system in question , and is the most general as long as assumed symmetries are satisfied .
one identifies a set of irreducible diagrams from the lagrangian with .
the importance of an irreducible diagram is assigned by a counting rule .
however , one may find questions about : ( q1 ) in , short - distance physics is described by contact interactions , which is much simpler compared to the short - range mechanism employed in .
is the contact interaction really appropriate to describe the short - distance physics ? ( q2 )
is  still one of many phase - equivalent potentials , as  is ? ( q3 ) is there any relation between model independent  and model dependent ?
in fact , the answer to ( q3 ) naturally leads us to the answers to ( q1 ) and ( q2 ) .
thus , we formulate a scenario for the relation between  and .
it is noted that the model space ( the state space for the nucleon ) of  is considerably smaller than that of . with this point in mind , we can formulate the following scenario for the relation between  and .
we may construct many  which reproduce @xmath0 scattering data and the deuteron binding energy .
they are different in describing the short - distance physics , and therefore model dependent . starting with such ,
we reduce their model space by integrating out the high momentum states of the nucleon . reducing the model space corresponds to viewing the system in a coarse - grained manner .
as the model space is reduced , information about details of the short - distance physics is gradually lost .
eventually , we obtain a low - momentum effective interaction ( @xmath1 ) defined in a reduced model space .
@xmath1 does not have the model dependence which  have .
a parameterization of @xmath1 constitutes .
this is the scenario for the relation between  and .
obtained in this way is , by construction , does not have a dependence on modelling the short - distance physics .
the short - range part of @xmath1 is expected to be accurately simulated by simple contact interactions because the detailed information has been integrated out .
therefore , if we show that this scenario is realized , then we can answer all of the questions raised in the previous paragraph .
the purpose of this report is to confirm the scenario , thereby proposing the relation between  and @xcite .
furthermore , keeping the relation in mind , we can understand features of neft more deeply , which we will discuss later .
in order to examine the scenario , stated in the previous section , for the relation between  and , an appropriate model - space reduction method is necessary . in effective
filed theory , we use an effective lagrangian in which high - energy degrees of freedom have been integrated out using a path integral : @xmath2 where @xmath3 ( @xmath4 ) is high-(low- ) energy degrees of freedom , and @xmath5 ( @xmath6 ) consists of @xmath3 and @xmath4 ( only @xmath4 ) . an effective ( more fundamental ) lagrangian is @xmath6 ( @xmath5 ) .
the model - space reduction , integrating out high - momentum states of the nucleon , also should be done with the path integral .
although it is difficult in general , in case the lagrangian is composed by only the nucleon field and two nucleons interact through contact interactions , we can perform the path integral .
it is noted that we restrict ourselves to two - nucleon system throughout this report . in the center of mass frame , performing the path integral is equivalent to solving the following wilsonian renormalization group ( wrg ) equation : @xmath7 where @xmath8 is @xmath0 potential for a partial wave @xmath9 , and @xmath10 the nucleon mass . in @xmath11 , @xmath12 ( @xmath13 ) denotes the off - shell relative momentum of the two nucleons before ( after ) the interaction , @xmath14 denotes the on - shell momentum , and @xmath15 is the cutoff value specifying the model space .
this equation controls the evolution of @xmath8 with respect to a change of @xmath15 .
this equation was firstly derived by birse _
_ in a different manner@xcite .
starting with several phenomenological @xmath0 potentials , we reduce their model spaces using the wrg equation , and examine the evolution .
then , we simulate the obtained effective model - space interaction ( @xmath1 ) with  by adjusting parameters in it .
if the simulation is accurate , then the relation between  and  through rg is realized .    in the simulation , for simplicity , we include only the opep in  as a mechanism explicitly including the pion .
this is not fully consistent with weinberg s counting .
because we consider contact interactions with zero , two , and four derivatives , we should include more irreducible graphs , such as a two - pion exchange potential ( tpep ) .
however , we employ a rather small model space where the details of the tpep play essentially no role ; the tpep is accurately simulated by contact interactions .
therefore , our simplification does not deteriorate the accuracy of the simulation .    in fig .
[ fig1 ] , shown are diagonal components of @xmath16 in the momentum space .
there is the clear model dependence among , which almost disappears after the model - space reduction down to @xmath15 = 200 mev .
the obtained @xmath1 is accurately simulated by the opep and a few contact interactions , which we do not show here . in fig .
[ fig2 ] , diagonal components of @xmath17 ( @xmath15=200mev ) obtained from the cd - bonn potential is simulated using the opep and one or two contact interactions .
we see that the simulation is very accurate .
obtained in this way also accurately simulates the off - diagonal components of @xmath1 .
@xmath0-potential @xmath18 .
the solid curve is @xmath1(@xmath15=200mev ) resulting from the cd - bonn potential .
the dashed ( dotted ) curve is a simulation of @xmath1 using the opep plus one ( two ) contact interaction(s ) .
the dash - dotted curve is the opep .
, width=283 ]     @xmath0-potential @xmath18 .
the solid curve is @xmath1(@xmath15=200mev ) resulting from the cd - bonn potential .
the dashed ( dotted ) curve is a simulation of @xmath1 using the opep plus one ( two ) contact interaction(s ) .
the dash - dotted curve is the opep .
, width=283 ]
we have seen in the previous section that the scenario for the relation between  and  is realized . although we have shown the relation employing a rather small model space , if the tpep and higher order opep are properly included in , then the relation should hold true for a larger model space as well ; probably safe up to @xmath19 400 mev . in a certain large model space where the very details of the tpep is considerable , _
i.e. _ , a phenomenological model can not mimic the tpep any more , the relation may not hold true .
we have been concerned with only the strong nucleon - nucleon interaction . however , this kind of relation probably exists also in other nuclear operators , such as electroweak currents and pion production operators .
now , based on our result , we discuss in the following some features of neft which the traditional approach does not have ; the discussion is not always restricted to the nuclear force .
one is that nuclear operators based on neft are constructed perturbatively .
therefore , one can systematically improve the accuracy , and can discuss theoretical uncertainty .
we note that , for a convergent perturbation , it is necessary to define an operator in a suitably small model space .
we also note that the convergence of the neft - based perturbative expansion is not always good for some processes .
another is that neft - based operators are model independent , which has been often claimed .
however , the claim is based on the procedure of deriving the nuclear operators , which is not a quantitative argument . in this work
, we quantitatively showed that  does not have the dependence on modelling the details of short - distance physics .
this is a consequence of viewing the system roughly , thereby ignoring the detailed structure of the short - distance physics .
it is noted , therefore , a description of a system based on neft is not always better than those based on phenomenological models . in many cases , they give essentially the same low - energy observables because they are equivalent through the rg .
neft may have superiority in cases where detailed information about multi - pion exchange mechanism play an important role .
finally , with neft , one can describe a system more efficiently and simply , compared to the phenomenological models .
the efficiency is due to the perturbative calculation , and the simplicity is due to the ignorance of the details of the short - distance physics .    to summarize , we considered the nuclear force from the viewpoint of the rg , and showed that there exists the equivalence relation between and .
we simultaneously showed that  does not have the model dependence due to the details of the short - distance physics , and that the simple contact interactions in  accurately describe the short - distance physics in a certain small model space .
based on the result , we discussed the new features in neft .
we study a relation between nuclear forces based on phenomenological approach ( ) and nuclear effective field theory ( ) from a viewpoint of renormalization group . 
 we find the relation between these two types of nuclear force using wilsonian renormalization group equation . 
 considering the fact that  is defined in a certain small model space , we show that a simple contact interaction accurately simulates short - distance physics , and that  is free from dependence on modelling the details of the short - distance physics . based on our result , 
 we discuss some features of nuclear effective field theory .