Chiral Dynamics: Taming Strong QCD

Transcription

1 1 Chiral Dynamics: Taming Strong QCD Ulf-G. Meißner, Univ. Bonn & FZ Jülich Supported by DFG, SFB/TR-16 and by DFG, SFB/TR-11 and by CAS, PIFI and by BMBF 5P15PCFN1 and by HGF VIQCD VH-VI-417 Nuclear Astrophysics Virtual Institute Chiral Dynamics - Taming Strong QCD Ulf-G. Meißner WW7 Fest, TUM, April 14, 216 < >

2 2 CONTENTS Short introduction to chiral dynamics The story of the Λ(145) Chiral symmetry and the nucleon-nucleon interaction Strangeness nuclear physics Summary & outlook Chiral Dynamics - Taming Strong QCD Ulf-G. Meißner WW7 Fest, TUM, April 14, 216 < >

3 3 Short Introduction Chiral Dynamics - Taming Strong QCD Ulf-G. Meißner WW7 Fest, TUM, April 14, 216 < >

4 CHIRAL DYNAMICS 4 QCD with three light flavors: A theoretical paradise Leutwyler L QCD = L QCD qmq, q = u d, M = s m u m d m s Exhibits spontaneuous and explicit chiral symmetry breaking Can be analyzed systematically & precisely using EFT = chiral perturbation theory Weinberg (1979) Gasser, Leutwyler (1984,1985) Many intriguing results, but: often convergence problems in the presence of strange quarks limited by the appearance of resonances and bound states Discuss here such cases & methods that overcome these limitations w/ particular emphasis on WW s contribution [baryon spectrum & interactions] Chiral Dynamics - Taming Strong QCD Ulf-G. Meißner WW7 Fest, TUM, April 14, 216 < >

5 5 The story of the Λ(145) Chiral Dynamics - Taming Strong QCD Ulf-G. Meißner WW7 Fest, TUM, April 14, 216 < >

6 BASICS of the Λ(145) 6 Quark model: uds excitation with J P = 1 2, a few hundred MeV above the Λ(1116) m = MeV, Γ = 5.5 ± 2. MeV [PDG 215] πλ πσ Λ(145) ΚΝ ηλ E Prediction as early as 1959 by Dalitz and Tuan: Resonance between the coupled πσ and KN channels Dalitz, Tuan, Phys. Rev. Lett. 2 (1959) 425; J.K. Kim, PRL 14 (1965) 29 π ο Σ ο + π Σ π + Σ Events(Σ + π ) K p K ο n Clearly seen in K p Σ3π reactions at 4.2 GeV at CERN Hemingway, Nucl.Phys. B 253 (1985) 742 An enigma: Too low in mass for the quark model, but well described in models (hadron exchanges, cloudy bags,...) many authors incl. some in the audience Problems: models are uncontrolled (theory like experiment must have errors!) connections to QCD? Chiral Dynamics - Taming Strong QCD Ulf-G. Meißner WW7 Fest, TUM, April 14, 216 < >

7 The MUNICH BREAKTHROUGH 7 Great idea: Combine (leading-order) chiral SU(3) Lagrangian with coupled-channel dynamics N. Kaiser, P. B. Siegel and W. Weise, Chiral dynamics and the low-energy kaon - nucleon interaction, Nucl. Phys. A 594 (1995) citations Dominance of the Weinberg-Tomozawa term, excellent description of K p data and πσ mass distribution, also inclusion of NLO terms with constrained fits Highly cited follow-ups from TUM group plus other groups, esp. Spanish Mafia Oset, Ramos (1997),... But: unpleasant regulator dependence (Yukawa-type, momentum cut-off) gauge invariance in photo-reactions? Chiral Dynamics - Taming Strong QCD Ulf-G. Meißner WW7 Fest, TUM, April 14, 216 < >

8 A NEW TWIST 8 With my excellent post-doc José Oller, we reanalyzed this problem Oller, UGM Phys. Lett. B 5 (21) 263, 537 cites Technical improvements: Subtracted meson-baryon loop with dim reg standard method Coupled-channel approach to the πσ mass distribution Matching formulas to any order in chiral perturbation theory established Most significant finding: Note that the Λ(145) resonance is described by two poles on sheets II and III with rather different imaginary parts indicating a clear departure from the Breit-Wigner situation... [pole 1: ( i 27.6) MeV, pole 2: ( i 11.) MeV on RS II] Scrutinized through further calculations & group theory arguments 2 years later Jido, Oller, Oset, Ramos, UGM, Nucl. Phys. A 725 (23) 181, 447 cites Chiral Dynamics - Taming Strong QCD Ulf-G. Meißner WW7 Fest, TUM, April 14, 216 < >

9 SU(3) SYMMETRY CONSIDERATIONS 9 Group theory: 8 8 = 1 8 s 8 }{{ a } binding at LO Follow the pole movement from the SU(3) limit to the physical masses: 25 2 x= (I=1) Im z R [MeV] x=1. (I=) 1426 (I=) 14 x=1. x=.5 disappear (I=1) x=.5 x=.6 x=.5 15 x=.5 x= (I=) x=1. 17 Singlet Octet Re z R [MeV] Chiral Dynamics - Taming Strong QCD Ulf-G. Meißner WW7 Fest, TUM, April 14, 216 < >

10 MUNICH-TOKYO RELOADED 1 Improved calculation with all NLO terms and constraints from kaonic hydrogen Y. Ikeda, T. Hyodo and W. Weise, Chiral SU(3) theory of antikaon-nucleon interactions with improved threshold constraints, Nucl. Phys. A 881 (212) citations 1.5 [fm] 1.5 dominantly KN Re f(k p K p) +,+&#-.'"(% #('!"#$%& #(% #(" #($!"%#!""#!"$#!"#$%&#'"(%!"## 2.5 [fm] Im f(k p K p) 2 Hyodo, Jido, Prog. Part. Nucl. Phys. 76 (212) &$# &"# &%# &'# #(' #(% #(" #($ )*#$%&#'"(% dominantly πσ Precise proton amplitudes Predictions for neutron amps. M. Bazzi et al. [SIDDHARTA Collaboration], Phys. Lett. B 74 (211) 113 Re f(k p K p) [fm] Im f(k p K p) [fm] s [MeV] Λ(145) s [MeV] s [MeV] s [MeV] Similar developments by the Bonn and Murcia groups Mai, UGM, Nucl. Phys. A 9 (213) 51; Oller, Guo, Phys. Rev. C 87 (213) 3522 Chiral Dynamics - Taming Strong QCD Ulf-G. Meißner WW7 Fest, TUM, April 14, 216 < >

11 YET ANOTHER TWIST 11 With my excellent post-doc Maxim Mai, we found yet another surprise: at least 8 solutions of similar quality w/ different pairs of poles for the Λ(145) Mai and UGM, EPJ A 51 (215) 3 Scattering data Kaonic Threshold hydrogen ratios SIDDHARTA: M. Bazzi et al., Phys. Lett. B 74, 113 (211) Scatt. data: Ciborowski et al., J. Phys. G 8, 13 (1982), Humphrey, Ross, Phys. Rev. 127, 135 (1962) Sakitt et al., Phys. Rev. B 139, 719 (1965), Watson et al., Phys.Rev. 131, 2248 (1963) Chiral Dynamics - Taming Strong QCD Ulf-G. Meißner WW7 Fest, TUM, April 14, 216 < >

12 PHOTOPRODUCTION to the RESCUE 12 Simple model for γp K + Σπ CLAS data CLAS, Phys. Rev. C 87, 3526 (213) CLAS data prefer solution 4 also good description of Σ + π distribution from K p Σ + π π + π (not fitted) Events(Σ + π ) solution 2 also acceptable Chiral Dynamics - Taming Strong QCD Ulf-G. Meißner WW7 Fest, TUM, April 14, 216 < >

13 PRESENT STATUS of the TWO-POLE SCENARIO 13 Two poles from scattering plus CLAS data: PDG 216: POLE STRUCTURE OF THE Λ(145) REGION Written November 215 by Ulf-G. Meißner and Tetsuo Hyodo Chiral Dynamics - Taming Strong QCD Ulf-G. Meißner WW7 Fest, TUM, April 14, 216 < >

14 - - OPEN ENDS - 14 The story is not yet told to the end: Consider various NLO approaches precise location of the lighter pole subthreshold amplitudes not yet well determined Cieply, Mai, UGM, Smejkal, ReF K p ImF K p ReF K n ImF K n 1. (fm) p 2 1 (fm) - p 2 (fm) n.5. (fm) n.5 Re F K Im F K 1 Re F K -.5 Im F K s 1/2 (MeV) s 1/2 (MeV) s 1/2 (MeV) s 1/2 (MeV) Kyoto-Munich Bonn 2 Bonn 4 Murcia 1 Murcia 2 Prague Prague: Cieply, Smejkal, Nucl. Phys. A 881 (212) 115 Conclusion on this section: Sorry Wolfram, no retirement yet! Chiral Dynamics - Taming Strong QCD Ulf-G. Meißner WW7 Fest, TUM, April 14, 216 < >

15 15 Chiral symmetry and the nucleon-nucleon interaction Chiral Dynamics - Taming Strong QCD Ulf-G. Meißner WW7 Fest, TUM, April 14, 216 < >

16 NUCLEAR CHIRAL EFFECTIVE FIELD THEORY 16 The silver jubilee of Weinberg s work extending chiral EFTs to nuclear physics S. Weinberg, Nuclear forces from chiral Lagrangians, Phys. Lett. B 251 (199) 288 [submitted 14 August 199]. 969 citations counted in INSPIRE as of 26 March 216 S. Weinberg, Effective chiral Lagrangians for nucleon - pion interactions and nuclear forces, Nucl. Phys. B 363 (1991) 3 [submitted 2 April 1991]. 936 citations counted in INSPIRE as of 26 March 216 after 25 years, a mature field? Epelbaum, Hammer, UGM, Rev. Mod. Phys. 81 (29) cites yes and no let s discuss some recent developments but first things first: The Munich work! Chiral Dynamics - Taming Strong QCD Ulf-G. Meißner WW7 Fest, TUM, April 14, 216 < >

17 THE MUNICH BUILDING BLOCK 17 First field-theory calculation of OPE and TPE basis of all precision studies thereafter! N. Kaiser, R. Brockmann and W. Weise, Peripheral nucleon-nucleon phase shifts and chiral symmetry, Nucl. Phys. A 625 (1997) citations Established the TPE in the peripheral waves Introduced spectral function representation coordinate space representation PHASE SHIFT [deg] H T lab [MeV] PHASE SHIFT [deg] H T lab [MeV] V C (r) [MeV] Isoscalar Central Potential 2π σ + ω σ r [fm] (m π r) 3 W T (r) [MeV] π+2π 1π Isovector Tensor Potential r [fm] PHASE SHIFT [deg] T lab [MeV] 3 H5 3.4 H T lab [MeV] PHASE SHIFT [deg].5 1π + 2π SAID 1π 3 ε 5 2 Chiral Dynamics - Taming Strong QCD Ulf-G. Meißner WW7 Fest, TUM, April 14, 216 < > ING ANGLE [deg] 1

18 NUCLEAR FORCES in CHIRAL NUCLEAR EFT expansion of the potential in powers of Q [small parameter] explains observed hierarchy of the nuclear forces most higher-order Chiral NNexpansion contributionsof calculated nuclear by forces Norbert Kaiser [based on NDA] Two-nucleon Zwei-Nukleon-Kraft force Three-nucleon Drei-Nukleon-Kraft force Four-nucleon Vier-Nukleon-Kraft force 18 Weinberg, van Kolck render LO Beitrag (Q ) tur 1. NLO Ordnung (Q 2 ) tur 2. NOrdnung 2 LO (Q 3 ) tur 3. NOrdnung 3 LO (Q 4 ) N 4 LO (Q 5 ) have been worked out and employed (recently, also parts of the N 5 LO NN force have been worked out ) worked out and applied worked out and to be applied calculations in progress have been worked out but not employed yet [LENPIC, work in progress] have not been completely worked out yet Chiral Dynamics - Taming Strong QCD Ulf-G. Meißner WW7 Fest, TUM, April 14, 216 < >

19 NN FORCES to FOURTH ORDER 19 Epelbaum, Krebs, UGM, Eur. Phys. J. A 51: 53 (215) new regularization of long-range physics [coordinate space cut-off]: ( ) r [ )] 6 V reg long range ( r ) = V long range( r )f reg, f reg = 1 exp ( r2 R R 2 = No distortion of the long-range potential better at higher energies = No additional spectral function regularization in the TPEP required = Study of the chiral expansion of multi-pion exchanges: R = fm Baru et al., EPJ A 48 (212) 69 new way of estimation the theoretical uncertainty [before: only cut-off variations] ( ) Mπ p = Expansion parameter depending on the region: Q = max, Λ b = Breakdown scale Λ b = 6 MeV for R =.8 1. fm Λ b Chiral Dynamics - Taming Strong QCD Ulf-G. Meißner WW7 Fest, TUM, April 14, 216 < >

20 CONVERGENCE of the CHIRAL SERIES 2 phase shifts show expected convergence [large N2LO corrections understood] [deg] [deg] S 1 LO NLO N 2 LO N 3 LO 1 S 2 3 P P 1 3 D 1 3 P D [deg] D P D E lab [MeV] E lab [MeV] E lab [MeV] E lab [MeV] = clear improvement comp. to earlier N3LO potentials [momentum space reg.] Entem, Machleidt (23); Epelbaum, Glöckle, UGM (25) Chiral Dynamics - Taming Strong QCD Ulf-G. Meißner WW7 Fest, TUM, April 14, 216 < >

21 UNCERTAINTIES 21 uncertainties show expected pattern [deg] [deg] [deg] S 1 3 D 2 1 S 2 3 P P P 1 3 D D 2 3 D 3 3 P E lab [MeV] E lab [MeV] E lab [MeV] E lab [MeV] NLO N2LO N3LO Chiral Dynamics - Taming Strong QCD Ulf-G. Meißner WW7 Fest, TUM, April 14, 216 < >

22 NN FORCES to FIFTH ORDER 22 Epelbaum, Krebs, UGM, Phys. Rev. Lett. 115 (215) Entem, Kaiser, Machleidt, Nosyk, Phys. Rev. C 91 (215) 142 No contact interactions at this order - odd in Q New contributions fixed from πn scattering, LECs c i, d i, e i : Büttiker, Fettes, UGM, Steininger (1998-2); Krebs, Gasparian, Epelbaum (212), Hoferichter, Ruiz de Elvira, Kubis, UGM (215) L πn = L (1) πn + L(2) πn (c i) + L (3) πn (d i) + L (4) πn (e i) Three-pion exchange can be neglected explicit calculation of the dominant NLO contribution Kaiser (21) no influence on phase shifts or deuteron properties Chiral Dynamics - Taming Strong QCD Ulf-G. Meißner WW7 Fest, TUM, April 14, 216 < >

23 PHASE SHIFTS at N4LO 23 Precision phase shifts with small uncertainties up to E lab = 3 MeV [deg] [deg] [deg] S 1 3 D 2 1 S 2 3 P P P 1 3 D D 2 3 D 3 3 P E lab [MeV] E lab [MeV] E lab [MeV] E lab [MeV] NLO N2LO N3LO N4LO Chiral Dynamics - Taming Strong QCD Ulf-G. Meißner WW7 Fest, TUM, April 14, 216 < >

24 FRONTIERS 24 Three-nucleon forces LENPIC collaboration see also Hammer, Nogga, Schwenk, Rev. Mod. Phys. 85 (213) 197 Applications in nuclei: conventional many-body approaches/nuclear lattice simulations Achim Schwenk s talk [if I only had more time...] Nuclear matter and the EoS, neutron stars again pioneering TUM work N. Kaiser, S. Fritsch and W. Weise, Chiral dynamics and nuclear matter, Nucl. Phys. A 697 (22) citations nuclear matter/neutron matter asymmetry energy E [MeV] chiral OPE+TPE Friedman, Phandharipande (1981) many interesting follow-ups ρ [fm 3 ] Chiral Dynamics - Taming Strong QCD Ulf-G. Meißner WW7 Fest, TUM, April 14, 216 < >

25 25 Strangeness nuclear physics Chiral Dynamics - Taming Strong QCD Ulf-G. Meißner WW7 Fest, TUM, April 14, 216 < >

26 PUZZLES in HYPER-NUCLEAR PHYSICS 26 The hyperon puzzle: EoS does not support 2 solar mass neutron stars e.g. Li, Schulze (28),..., Bombaci, need repulsion in the YN and YY interactions (Y = Λ, Σ) and/or repulsive YNN,..., forces Very small spin-orbit splitting in Λ single particle states e.g. Ajimura et al., PRL 86 (21) 4255 Λ-nucleus interaction is attractive but Σ-nucleus interaction is repulsive e.g. Friedman, Gal, Phys. Rep. 452 (27) 89 M/M sun Av18+TNI Av18+TNI+ESC8b PSR J M max = 2.28 M sun M max = 1.38 M sun R [km] central density [fm -3 ] VOLUME 86, NUMBER 19 PHYSICAL REVIEW LETTER E γ (MeV) E(1/2 )-E(3/2 ) = kev FIG. 3. Peak positions obtained by fitting the g ray spectra are shown as a function of R. Chiral Dynamics - Taming Strong QCD Ulf-G. Meißner WW7 Fest, TUM, April 14, 216 < > we change the absolute cross section keeping the angular distribution which is theoretically robust [18] to reproduce R M/M sun of Chemistry De in our enriched K. Imai for the Discussions wit are greatly appr supported in pa Research in Prio and and i ergy under Co No. DE-FG2-87 [1] R. Chrien an 113 (1989), a [2] P. H. Pile et a [3] T. Hasegawa T. Hasegawa [4] W. Brückner [5] M. May et al

27 (contd.) HYPERON NUCLEON INTERACTIONS 27 Author's personal LO chiral EFT for YN interaction pioneered at Bonn/Jülich For NLO, teamed up with the TUM group J. Haidenbauer, S. Petschauer, N. Kaiser, U.-G. Meißner, A. Nogga, W. W. Nucl. J. Haidenbauer Phys. A 915 (213) et al. 24 / Nuclear Physics Polinder, Haidenbauer, UGM, Nucl. Phys. A 779 (26) 244 phase shift J. Haidenbauer, S. Petschauer, LON. Kaiser, UGM, A. Nogga and W. Weise, Hyperon-nucleon interaction at next-to-leading order NLO in chiral effective field theory, Nucl. Phys. A 915 (213) citations Λp 1 S NLO LO U! (MeV) good description of all scatt. data + 3 Λ H BE much needed repulsion found error bands need to be refined 22 repulsion -6.6 Fig. 6. The Λp 1 S and 1 WW, Hyperfine Interact. 233 (215) 131 P 1 phase shifts δ as a function of p lab.t NLO for variations of the cutoff in the range Λ = 5,...,65 MeV, Figure 2: The Λ s.p. potenti Λ = 55,...,7 MeV. The dashed curve is the result of the Jülich band shows the chiral EFT re LO for Λ = 55,...,7 MeV Chiral Dynamics - Taming Strong QCD Ulf-G. Meißner WW7 Fest, TUM, April 14, 216 < > -45

28 HYPERONS in NUCLEAR MATTER 3 28 Consider hyperons in the medium Brueckner G-matrix gap choice (only Re parts) Haidenbauer, UGM, Nucl. Phys. A 936 (215) 29 continuous choice [also thesis S. Petschauer] Re UΛ(k) [MeV] χeft NLO χeft LO Jülich 4 NSC97f 4 J. Haidenbauer, S. Petschauer, N. Kaiser, UGM, and W. Weise, Hyperons in nuclear matter from SU(3) chiral effective field theory, Eur. Phys. J. A 52 (216) 15 reproduce small Λ s.o. force predict sizeable Σ s.o. force (S Σ 5S Λ ) attractive U Λ (k = ) & becoming repulsive repulsive U Σ (k = ) & staying repulsive Re UΣ(k) [MeV] k [fm 1 ] χeft NLO χeft LO Jülich 4 NSC97f k [fm 1 ] Chiral Dynamics - Taming Strong QCD Ulf-G. Meißner WW7 Fest, TUM, April 14, 216 < >

29 THREE BODY FORCES PNM 2.4 Lonardoni et al., Phys. Rev. Lett. 114 (215) 9231 Hell, Weise, Phys. Rev. C 9 (214) 4581 Need a more systematic approach to these elusive forces M MO. M [M] Phenomenological ΛNN forces can do the job n matter QMC PSR J ΛN RN + RNN ΛNN(2) (II)+ PSR J ChEFT ΛN + ΛNN(1) RN + RNN (I).8 ΛN.4 RN. A powerful team [also thesis S. Petschauer] S. Petschauer, N. Kaiser, J. Haidenbauer, UGM, and W. Weise, Leading three-baryon forces from SU(3) chiral effective field theory, Phys. Rev. C 93 (216) R [km] R [km] WW, Hyperfine Interact. 233 (215) 131 Figure 2. (Color online) Mass-radius relations. The key is the same of Fig. 1. Full dots represent the predicted maximum masses. Horizontal bands at 2M are the observed masses of the heavy pulsars PSR J [18] and PSR J [19]. The grey shaded region is the excluded part of the plot due to causality. The repulsion introduced by the three-body force plays a crucial role, substantially increasing the value of the Λ threshold density. In particular, when model (II) for the ΛN N force is used, the energy balance never favors the onset of hyperons within the the density domain that has been studied in the present work (ρ.56 fm 3 ). It is interesting to observe that the mass-radius relation for PNM up to ρ = 3.5ρ already predicts a NS mass of 2.9(1)M (black dot-dashed curve in Fig. 2). Even if Λ particles would appear at higher baryon densities, the predicted maximum mass is consistent with present completely worked out & LECs to be estimated from decuplet excitations, let us see what these will give in hyper-nuclei and dense nuclear systems Chiral Dynamics - Taming Strong QCD Ulf-G. Meißner WW7 Fest, TUM, April 14, 216 C < O > B

30 SUMMARY 3 Thank you Wolfram for all the insight We owe you a lot! Chiral Dynamics - Taming Strong QCD Ulf-G. Meißner WW7 Fest, TUM, April 14, 216 < >

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