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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,Sub-Leading 3NFs ECT*Trento 07/11/2011,*,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,Sub-Leading 3NFs ECT*Trento 07/11/2011,*,R.Machleidt,R.Machleidt,University of Idaho,D.R.Entem,University of Salamanca,Sub-Leading Three-Nucleon Forces,in Chiral Perturbation Theory,Outline,Nuclear forces from chiral EFT:,Overview&achievements,Are we done?No!,Sub-leading three-nucleon forces,Outlook,R.Machleidt,2,Sub-Leading 3NFs ECT*Trento 07/11/2021,From QCD to nuclear physics via chiral EFT(in a nutshell),QCD at low energy is strong.,Quarks and gluons are confined into colorless hadrons.,Nuclear forces are residual forces(similar to van der Waals forces),Separation of scales,R.Machleidt,3,Sub-Leading 3NFs ECT*Trento 07/11/2021,Calls for an EFT,soft scale:Q m,hard scale:,m,;pions and nucleon relevant d.o.f.,Low-energy expansion:(Q/,),with bounded from below.,Most general Lagrangian consistent with all symmetries of low-energy QCD.,-and-N perturbatively,NN has bound states:,(i)NN potential perturbatively,(ii)apply nonpert.in LS equation.,(Weinberg),R.Machleidt,4,Sub-Leading 3NFs ECT*Trento 07/11/2021,R.Machleidt,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,Sub-Leading 3NFs ECT*Trento 07/11/2021,R.Machleidt,6,NN phase shifts up to 300 MeV,Red Line:N3LO Potential by Entem&Machleidt,PRC 68,041001(2003).,Green dash-dotted line:NNLO Potential,and,blue dashed line:NLO Potential,by Epelbaum et al.,Eur.Phys.J.A19,401(2004).,LO,NLO,NNLO,N3LO,Sub-Leading 3NFs ECT*Trento 07/11/2021,R.Machleidt,7,N3LO Potential by Entem&Machleidt,PRC 68,041001(2003).,NNLO and,NLO,Potentials by Epelbaum et al.,Eur.Phys.J.A19,401(2004).,Sub-Leading 3NFs ECT*Trento 07/11/2021,R.Machleidt,8,Applications of the,chiral NN potential,at N3LO,Sub-Leading 3NFs ECT*Trento 07/11/2021,R.Machleidt,9,Chiral NN potential at N,3,LO underbinds by 1MeV/nucleon.(Size extensivity at its best.),Nucleus,D,E/A MeV,4,He,1.08,(0.73,FY,),16,O,1.25,40,Ca,0.84,48,Ca,1.27,48,Ni,1.21,Sub-Leading 3NFs ECT*Trento 07/11/2021,R.Machleidt,10,Sub-Leading 3NFs ECT*Trento 07/11/2021,R.Machleidt,11,including the,chiral 3NF,at N2LO,Sub-Leading 3NFs ECT*Trento 07/11/2021,R.Machleidt,12,Sub-Leading 3NFs ECT*Trento 07/11/2021,R.Machleidt,13,Calculating the properties of light nuclei usingchiral 2N and 3N forces,“No-Core Shell Model“Calculations by P.Navratil et al.,LLNL,Sub-Leading 3NFs ECT*Trento 07/11/2021,R.Machleidt,14,2N(N3LO)force only,Calculating the properties of light nuclei usingchiral 2N and 3N forces,“No-Core Shell Model“Calculations by P.Navratil et al.,LLNL,Sub-Leading 3NFs ECT*Trento 07/11/2021,R.Machleidt,15,R.Machleidt,15,2N(N3LO)force only,Calculating the properties of light nuclei usingchiral 2N and 3N forces,2N(N3LO)+3N(N2LO)forces,“No-Core Shell Model“Calculations by P.Navratil et al.,LLNL,Sub-Leading 3NFs ECT*Trento 07/11/2021,R.Machleidt,16,The Ay puzzle is NOT solved,by the 3NF at NNLO.,Analyzing,Power,Ay,p-d,p-,3,He,2NF only,2NF+3NF,Calculations by,the Pisa Group,Sub-Leading 3NFs ECT*Trento 07/11/2021,R.Machleidt,17,Why do we need 3NFs beyond NNLO?,The 2NF is N3LO;,consistency requires that all contributions are at the same order.,There are unresolved problems in 3N,4N scattering and nuclear structure.,Sub-Leading 3NFs ECT*Trento 07/11/2021,So,lets take a close look at the development,of chiral 3NFs.,R.Machleidt,18,Sub-Leading 3NFs ECT*Trento 07/11/2021,R.Machleidt,19,The 3NF,at NNLO;,used so far.,Sub-Leading 3NFs ECT*Trento 07/11/2021,R.Machleidt,20,Ishikawa&Robilotta,PRC 76,014006(2007),Bernard,Epelbaum,Krebs,Meissner,PRC 77,064004,(2008),In,progress,The 3NF at N3LO explicitly,One-loop,leading vertices,Sub-Leading 3NFs ECT*Trento 07/11/2021,R.Machleidt,21,The ring diagrams,From:Bernard,Epelbaum,Krebs,Meissner,PRC 77,064004(2021),R.Machleidt,21,Sub-Leading 3NFs ECT*Trento 07/11/2021,R.Machleidt,22,Proton-deuteron elastic scattering,Black line:2NF only,Red dashed line:2NF+3NF(N2LO+2N3LO)2NF+3NF(N2LO),From:,Ishikawa&,Robilotta,PRC 76,014006,(2007),The 2N3LO 3NF,is negligible.,R.Machleidt,22,Sub-Leading 3NFs ECT*Trento 07/11/2021,R.Machleidt,23,R.Machleidt,Nuclear forces from chiral EFT EFB21,Salamanca,08-31-2021,23,Small?,The 3NF,at NNLO;,used so far.,Sub-Leading 3NFs ECT*Trento 07/11/2021,R.Machleidt,24,R.Machleidt,Nuclear forces from chiral EFT EFB21,Salamanca,08-31-2021,24,R.Machleidt,Nuclear forces from chiral EFT EFB21,Salamanca,08-31-2021,24,Small?,The 3NF,at NNLO;,used so far.,Sub-Leading 3NFs ECT*Trento 07/11/2021,R.Machleidt,25,What to expect from those,N4LO 1-loop diagrams?,Compare to“similar 2NF diagrams.,R.Machleidt,25,Sub-Leading 3NFs ECT*Trento 07/11/2021,R.Machleidt,26,Small,1-loop,lead.vert.,1-loop,One c,i,vert.,Corresponding 2NF contribu
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