Chiral Nuclear Effective Field Theory U. van Kolck University of Arizona Supported in part by US DOE and Sloan Foundation Background by S. Hossenfelder

In Memoriam Vijay Pandharipande See talks by Carlson, Sick 1/1/2019 v. Kolck, Pion Renormalization

v. Kolck, Pion Renormalization Outline Effective Field Theories Pionful (Nuclear) EFT Non-Perturbative Renormalization and Power Counting Role of the Delta Isobar Outlook See parallel session R2 1/1/2019 v. Kolck, Pion Renormalization

Wanted f Dead sor s Alive QCD EXPLANATION OF NUCLEAR PHYSICS Reward understanding of gross features: Why is ? How large are few-nucleon forces? Why is isospin a good symmetry? … Beware coupling constants not small 1/1/2019 v. Kolck, Pion Renormalization

Nuclear physics scales “His scales are His pride”, Book of Job perturbative QCD ~1 GeV no small coupling need a more general way to treat multi-scale problems ~100 MeV ~30 MeV Effective Field Theory (EFT) (expansion in ) 1/1/2019 v. Kolck, Pion Renormalization

v. Kolck, Pion Renormalization What is Effective? local underlying symmetries renormalization-group invariance 1/1/2019 v. Kolck, Pion Renormalization

For Q ~ m, truncate consistently with RG invariance normalization non-analytic, from loops “power counting” e.g. # loops L For Q ~ m, truncate consistently with RG invariance so as to allow systematic improvement (perturbation theory): 1/1/2019 v. Kolck, Pion Renormalization

Nuclear physics scales perturbative QCD ~1 GeV sum ? hadronic th with chiral symm this talk ~100 MeV sum ~30 MeV sum halo nuclei See talks by Hammer, Braaten 1/1/2019 v. Kolck, Pion Renormalization

Nuclear EFT pionful EFT degrees of freedom: nucleons, pions, deltas (+ roper?, …) symmetries: Lorentz, P, T, chiral expansion in: non-relativistic multipole pion loop calculated from QCD: lattice, … chiral symmetry fitted to data 1/1/2019 v. Kolck, Pion Renormalization

Form of pion interactions determined by chiral symmetry … … … … … … Form of pion interactions determined by chiral symmetry 1/1/2019 v. Kolck, Pion Renormalization

v. Kolck, Pion Renormalization Role of the RG LO absorbed absorbed NLO Naturalness: absorbed in higher-order coefficients 1/1/2019 v. Kolck, Pion Renormalization

A= 0, 1: chiral perturbation theory Weinberg ’79 Gasser + Leutwyler ’84 … Gasser, Sainio + Svarc ’87 Jenkins + Manohar ’91 A= 0, 1: chiral perturbation theory nucleon dense but short-ranged long-ranged but sparse # loops # vertices of type i 1/1/2019 v. Kolck, Pion Renormalization

v. Kolck, Pion Renormalization 1 2 1 2 LO But… other counterterms? RESUM absorbed Naturalness: absorbed in higher-order coefficients for 1/1/2019 v. Kolck, Pion Renormalization

A > 2: resummed chiral perturbation theory Weinberg ’90, ‘91 Ordonez + v.K. ’92 … A > 2: resummed chiral perturbation theory infrared enhancement! = + + … = + A-nucleon irreducible A-nucleon reducible Schematically, bound state at 1/1/2019 v. Kolck, Pion Renormalization

v. Kolck, Pion Renormalization Ordonez + v.K. ’92 v.K. ’94 … = + + + … + + + … For parity violation + + + … See talk by Maekawa = + + … + + … + + … higher powers of etc. more nucleons 1/1/2019 v. Kolck, Pion Renormalization

Issue: power counting (relative sizes) Etc. 1/1/2019 v. Kolck, Pion Renormalization

similar to phenomenological potential models: at N2LO, Weinberg ’90, ’91, ‘92 Ordonez + v.K. ’92 v.K. ’94 Ordonez, Ray + v.K. ‘96 ... Naïve Dimensional Analysis (NDA) LO: S-wave contacts + OPE (non-perturbative pions) NLO: P-wave contacts + TPE + 3N forces via delta … + (PUNT) subLOs also iterated in Lippman-Schwinger eq. similar to phenomenological potential models: at N2LO, 1/1/2019 v. Kolck, Pion Renormalization

e.g., = + + + + + + … TM’ pot See talk by Robilotta v.K. ’94 Friar, Hueber + v.K. ‘99 Coon + Han ’99 ... e.g., Fujita-Miyazawa pot = + + one unknown parameter two unknown parameters + + + + … Tucson-Melbourne pot with TM’ pot cf. Brazil pot See talk by Robilotta 1/1/2019 v. Kolck, Pion Renormalization

models with s, w, … might be misleading… Note: NOT your usual potential! Ordonez + v.K. ’92 (cf. Stony Brook TPE) e.g., + + + … Rentmeester et al. ’01, ‘03 chiral v.d. Waals force Nijmegen PSA of 1951 pp data Kaiser, Brockmann + Weise ’97 at least as good! parameters found consistent with pN data! models with s, w, … might be misleading… 1/1/2019 v. Kolck, Pion Renormalization

Many successes of Weinberg’s counting, e.g., See talks by Machleidt, Meissner Many successes of Weinberg’s counting, e.g., At N3LO, fit to NN phase shifts comparable to those of “realistic” phenomenological potentials With N3LO NN and N2LO 3N potentials, good description of 3N observables and 4N binding energy levels of p-shell nuclei Entem + Machleidt ’03 Epelbaum, Gloeckle + Meissner ’04 Epelbaum et al. ’02 Gueorguiev, Navratil, Ormand + Vary ’05 Binding Energy (MeV) Exp: -64.7507(3) Thy: -64.03* *Convergence study not completed 1/1/2019 v. Kolck, Pion Renormalization No-Core Shell Model

No! Is Weinberg’s power counting consistent? BUT Is Weinberg’s power counting consistent? No! attractive in some channels singular potential not enough contact interactions for RG invariance even at LO! 1/1/2019 v. Kolck, Pion Renormalization

v. Kolck, Pion Renormalization 1/1/2019 v. Kolck, Pion Renormalization

Renormalization of the potential OPE: s wave matching so that 1/1/2019 v. Kolck, Pion Renormalization

approaches fixed point Beane, Bedaque, Savage + v.K. ’02 integer determined by low-energy data exact solution, fit to scatt length analytical form, fit to scatt length neglecting term approaches fixed point 1/1/2019 v. Kolck, Pion Renormalization

expand around the chiral limit (perturbative pions) or promote including fitted to eff range Nijmegen PSA expand around the chiral limit (perturbative pions) or promote to leading order (due to infrared enhancement) First breach of W pc 1/1/2019 v. Kolck, Pion Renormalization

exact vs perturbation th Beane, Bedaque, Childress, Kryjevski, McGuire + v.K. ’02 determined by low-energy data 3rd 4 exact 1st 2nd exact vs perturbation th 1/1/2019 v. Kolck, Pion Renormalization limit-cycle-like behavior

analogous, but for coupled channels… Frederico, Timoteo + Tomio ’99 Beane, Bedaque, Savage + v.K. ’02 Ruiz-Arriola + Valderrama ‘05 analogous, but for coupled channels… Nijmegen PSA in MeV EFT – Nijm PSA slope ~2 sufficient in leading order !? 1/1/2019 v. Kolck, Pion Renormalization

Pion-mass dependence Triplet scattering length Deuteron binding energy Lattice QCD: quenched Fukugita et al. ‘95 Deuteron binding energy EFT: (incomplete) NLO Beane, Bedaque, Savage + v.K. ’02 Beane + Savage ’03 Epelbaum, Gloeckle + Meissner ‘03 1/1/2019 v. Kolck, Pion Renormalization

Problems! But what about higher partial waves? Nogga, Timmermans + v.K. ’05 But what about higher partial waves? Attractive-tensor channels: Problems! cutoff dependence incorrect renormalization… 1/1/2019 v. Kolck, Pion Renormalization

one undetermined phase in each channel promote counterterms limit-cycle-like behavior cutoff independence e.g., LO EFT Nijmegen PSA 1/1/2019 v. Kolck, Pion Renormalization

v. Kolck, Pion Renormalization LO EFT W pc Nijmegen PSA Promising… 1/1/2019 v. Kolck, Pion Renormalization

triton short-range interactions stronger than in Nogga, Timmermans + v.K. ’05 short-range interactions stronger than in Weinberg’s pc for attractive tensor channels where centrifugal barrier c.f. Birse ’05 + subLOs in perturbation theory Second breach of W pc on the other hand: triton correct renormalization… LO EFT indeed 1/1/2019 v. Kolck, Pion Renormalization … but leading-order value not so great because of kinetic-potential energy cancellation!?

No! Can one integrate out the delta with small error? + … Pandharipande, Phillips + v.K. ’05 EFT folklore: in nuclei, can integrate out delta with small error + … But 30% error 1/1/2019 v. Kolck, Pion Renormalization

relatively large error from the pN scattering fit leaks into 3N force + + … at threshold while relatively large error from the pN scattering fit leaks into 3N force extrapolation involved best strategy is not to integrate out delta (cf. Ordonez, Ray + v.K. ’96 Gerstendoerfer, Kaiser + Weise ’98) 1/1/2019 v. Kolck, Pion Renormalization

Conclusions and Outlook EFT allows a systematic, model-independent, unified description of strong interactions at low energies Power counting complicated by nonperturbative nature of nuclei Weinberg’s power counting not entirely correct due to failure of NDA in attractive-tensor channels where pions have to be iterated New power counting has been formulated: more counterterms at each order relative to Weinberg’s; expect even better description of observables Consistency and convergence of new power counting yet to be checked: two-nucleon NLO calculation of systems other few-nucleon Finally a consistent and efficient power counting in the pionful EFT?! 1/1/2019 v. Kolck, Pion Renormalization