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Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,R.Machleidt,Prog.Theory of Nuclear Forces FB20,Fukuoka,Japan,08/21/12,*,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,Prog.Theory of Nuclear Forces FB20,Fukuoka,Japan,08/21/12,*,R.Machleidt,1,Recent Progress in the Theory of Nuclear Forces,20th International IUPAP Conference on,Few-Body Problems in Physics,August 20-25,2021,Fukuoka,Japan,R.Machleidt,Prog.Theory of Nuclear Forces FB20,Fukuoka,Japan,08/21/12,R.Machleidt,University of Idaho,Outline,The history of the progress,Nuclear forces from chiral EFT:,Basic ideas and current status,The open issues,Proper renormalization of chiral forces,Sub-leading many-body forces,Outlook,R.Machleidt,2,Prog.Theory of Nuclear Forces FB20,Fukuoka,Japan,08/21/12,R.Machleidt,Prog.Theory of Nuclear Forces FB20,Fukuoka,Japan,08/21/12,3,R.Machleidt,4,2N forces,3N forces,4N forces,Leading Order,Next-to-Next-to Leading Order,Next-to-Next-to-Next-to Leading Order,Next-to Leading Order,The Hierarchy of Nuclear Forces,Prog.Theory of Nuclear Forces FB20,Fukuoka,Japan,08/21/12,R.Machleidt,Prog.Theory of Nuclear Forces FB20,Fukuoka,Japan,08/21/12,5,2N forces,3N forces,4N forces,Leading Order,Next-to-Next-to Leading Order,Next-to-Next-to-Next-to Leading Order,Next-to Leading Order,The Hierarchy of Nuclear Forces,R.Machleidt,Prog.Theory of Nuclear Forces FB20,Fukuoka,Japan,08/21/12,6,N3LO Potential by Entem&Machleidt,PRC 68,041001(2003).,NNLO and,NLO,Potentials by Epelbaum et al.,Eur.Phys.J.A19,401(2004).,R.Machleidt,Prog.Theory of Nuclear Forces FB20,Fukuoka,Japan,08/21/12,7,This is,of course,all very nice;,However there is a“hidden issue,here that needs our attention:,Renormalization,R.Machleidt,Prog.Theory of Nuclear Forces FB20,Fukuoka,Japan,08/21/12,8,So,whats this,Renormalization,about,?,See also contributions by,Gegelia,Ando,Harada,Kukulin.,R.Machleidt,Prog.Theory of Nuclear Forces FB20,Fukuoka,Japan,08/21/12,9,The EFT approach is not just another,phenomenology.Its field theory.,The problem in all field theories are,divergent loop integrals.,The method to deal with them in field theories:,1.Regularize the integral(e.g.apply a“cutoff)to make it finite.,2.Remove the cutoff dependence by,Renormalization(“counter terms).,R.Machleidt,Prog.Theory of Nuclear Forces FB20,Fukuoka,Japan,08/21/12,10,For calculating pi-pi and pi-N,reactions no problem.,However,the NN case is tougher,because it involves,two kinds,of(divergent)loop integrals.,R.Machleidt,Prog.Theory of Nuclear Forces FB20,Fukuoka,Japan,08/21/12,11,The first kind:,“NN Potential:,irreducible diagrams calculated perturbatively.,Example:,Counter,terms,perturbative renormalization,(order by order),R.Machleidt,Prog.Theory of Nuclear Forces FB20,Fukuoka,Japan,08/21/12,12,R.Machleidt,12,The first kind:,“NN Potential:,irreducible diagrams calculated perturbatively.,Example:,Counter,terms,perturbative renormalization,(order by order),This is fine.,No problems.,R.Machleidt,Prog.Theory of Nuclear Forces FB20,Fukuoka,Japan,08/21/12,13,The second kind:,Application of the NN Pot.in the Schrodinger or Lippmann-Schwinger(LS)equation:non-,perturbative,summation of ladder diagrams(infinite sum):,13,13,In diagrams:,+,+,+,R.Machleidt,Prog.Theory of Nuclear Forces FB20,Fukuoka,Japan,08/21/12,14,14,The second kind:,Application of the NN Pot.in the Schrodinger or Lippmann-Schwinger(LS)equation:non-perturbative summation of ladder diagrams(infinite sum):,Divergent integral.,Regularize it:,Cutoff dependent results.,Renormalize to get rid of the cutoff dependence:,14,Non-perturbative renormalization,R.Machleidt,Prog.Theory of Nuclear Forces FB20,Fukuoka,Japan,08/21/12,15,R.Machleidt,15,The second kind:,Application of the NN Pot.in the Schrodinger or Lippmann-Schwinger(LS)equation:non-perturbative summation of ladder diagrams(infinite sum):,Divergent integral.,Regularize it:,Cutoff dependent results.,Renormalize to get rid of the cutoff dependence:,15,Non-perturbative renormalization,15,With what to renormalize this time?,Weinbergs silent assumption:,The same counter terms as before.,(“Weinberg counting),There are several options for non-perturbative renormalization.I will discuss two of them:,Infinite cutoff reno,Finite cutoff reno,R.Machleidt,Prog.Theory of Nuclear Forces FB20,Fukuoka,Japan,08/21/12,16,In lower partial waves(,short distances),in general,no order by order convergence;data are not reproduced.,In peripheral partial waves(,long distances),always good convergence and reproduction of the data.,Thus,long-range interaction o.k.,short-range not(should not be a surprise:the EFT is designed for Q ).,At all orders,either one(if pot.attractive)or no(if pot.repulsive)counterterm,per partial wave:What kind of power counting scheme is this?,Not Weinberg Counting!,Where are the systematic order by order improvements?,R.Machleidt,Prog.Theory of Nuclear Forces FB20,Fukuok
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