Neutron matter from chiral effective field theory interactions

Transcription

1 Neutron matter from chiral effective field theory interactions Ingo Tews, In collaboration with K. Hebeler, T. Krüger, A. Schwenk, JINA Neutron Stars, May 26, 2016, Athens, OH

2 Chiral effective field theory for nuclear forces Quantum Chromodynamics Chiral Effective Field Theory Nuclear Physics It could take years (hopefully not decades) for QCD calculations to describe nuclear systems (A>2) at low energies. May 26, 2016 Ingo Tews, JINA Neutron Stars 2

3 Outline Ø Chiral effective field theory: Epelbaum et al., PPNP (2006) and RMP (2009) Systematic basis for low-energy nuclear forces, connected to QCD naturally includes many-body forces Very successful in calculations of nuclei and nuclear matter ØAb-initio calculations using chiral EFT can be used to constrain equation of state of neutron matter ØNeutron-matter applications: IT, Kru ger, Hebeler, Schwenk, PRL & PRC (2013) Symmetry energy Neutron-star mass-radius relation Ø Summary May 26, 2016 Ingo Tews, JINA Neutron Stars 3

4 Chiral effective field theory for nuclear forces Basic principle of effective field theory: u d u d d d λ R u d d R Quantum Chromodynamics At low energies (long wavelength) details not resolved! Ø Choose relevant degrees of freedom for low-energy processes Ø Systematic expansion of interactions constrained by symmetries May 26, 2016 Ingo Tews, JINA Neutron Stars 4

5 Chiral effective field theory for nuclear forces Basic principle of effective field theory: u d u d d λ R d u d d R Effective field theory for nuclear forces At low energies (long wavelength) details not resolved! Ø Choose relevant degrees of freedom for low-energy processes Ø Systematic expansion of interactions constrained by symmetries May 26, 2016 Ingo Tews, JINA Neutron Stars 5

6 Chiral effective field theory for nuclear forces Explicit degrees of freedom: Ø Pions and nucleons Write most general Lagrangian consistent with the symmetries of QCD Separation of scales: Ø Low momenta! breakdown scale Λ % Ø Expand in powers of & ) + ' (, ) Power counting: Ø - = 0: leading order (LO), Ø - = 2: next-to-leading order (NLO),... Weinberg, van Kolck, Kaplan, Savage, Wise, Epelbaum, Kaiser, Machleidt, Meißner, Hammer... May 26, 2016 Ingo Tews, JINA Neutron Stars 6

7 Chiral effective field theory for nuclear forces 2 LECs 7 LECs Explicit degrees of freedom: Ø Pions and nucleons Ø Long-range physics explicit Ø Short-range physics expanded in general operator basis Ø High-momentum physics absorbed intoshort-range couplings, fit to experiment ρ const. 15 LECs May 26, 2016 Ingo Tews, JINA Neutron Stars 7

8 Chiral effective field theory for nuclear forces Epelbaum et al., Eur. Phys. J (2015) Systematic expansion of the nuclear forces: Ø Can work to desired accuracy Ø Can obtain systematic error estimates May 26, 2016 Ingo Tews, JINA Neutron Stars 8

9 Chiral effective field theory for nuclear forces Many-body forces: Ø Have been found to be crucial ingredient to describe nuclear physics Natural hierarchy of nuclear forces: Ø Two-body (NN) forces start at first order Ø Three-body (3N) forces start at third order... Fitting: Ø NN forces in NN system (NN phase shifts) Ø 3N forces in 3N/4N system (Binding energies, radii) May 26, 2016 Ingo Tews, JINA Neutron Stars 9

10 Chiral effective field theory for nuclear forces Consistent interactions: Ø Same couplings for two-nucleon and many-body sector Ø In contrast to phenomenological interactions May 26, 2016 Ingo Tews, JINA Neutron Stars 10

11 Chiral effective field theory for nuclear forces Consistent interactions: Ø Same couplings for two-nucleon and many-body sector Ø In contrast to phenomenological interactions May 26, 2016 Ingo Tews, JINA Neutron Stars 11

12 Chiral effective field theory for nuclear forces Many-body forces are crucial: Oxygen Otsukaet al., PRL (2010) Calcium Gallant et al., PRL (2012) N NN + 3N forces: Ø Give correct physics of neutron-rich nuclei See also Hebeler et al., ARNPS (2015) May 26, 2016 Ingo Tews, JINA Neutron Stars 12

13 Chiral effective field theory for nuclear forces Many-body forces are crucial: Hebeler et al., PRC (2011) Drischler et al., PRC (2016) N NN + 3N forces: Ø Give correct saturation with theoretical uncertainties in nuclear matter Drischler et al., PRC (2016) May 26, 2016 Ingo Tews, JINA Neutron Stars 13

14 Chiral effective field theory for nuclear forces Recently: Ø First complete neutron matter calculation at fourth order IT, Kru ger, Hebeler, Schwenk, PRL (2013) In neutron matter: Ø Calculation is simpler in neutron matter Ø Only certain parts of the manybody forces contribute Ø Chiral many-body forces completely predicted from NN sector May 26, 2016 Ingo Tews, JINA Neutron Stars 14

15 Neutron matter EM 500 MeV (NN only) EGM 450/500 MeV (NN only) EGM 450/700 MeV (NN only) Bands: Ø Include several sources of uncertainty: Ø Interactions Ø Many-body method E/N [MeV] 10 5 NN interactions: Ø E/N at saturation density: MeV n [fm -3 ] IT, Krüger, Hebeler, Schwenk, PRL (2013) May 26, 2016 Ingo Tews, JINA Neutron Stars 15

16 Neutron matter EM 500 MeV EGM 450/500 MeV EGM 450/700 MeV Bands: Ø Include several sources of uncertainty: Ø Interactions Ø Many-body method E/N [MeV] n [fm -3 ] IT, Krüger, Hebeler, Schwenk, PRL (2013) NN interactions: Ø E/N at saturation density: MeV 3N interactions: Ø Have large impact on energy and uncertainty: MeV May 26, 2016 Ingo Tews, JINA Neutron Stars 16

17 Neutron matter E/N [MeV] EM 500 MeV EGM 450/500 MeV EGM 450/700 MeV NLO lattice (2009) QMC (2010) APR (1998) GCR (2012) Good agreement with other calculations Ø but in those no theoretical uncertainties Akmal et al., PRC (1998) Gandolfi et al., PRC (2012) n [fm -3 ] IT, Krüger, Hebeler, Schwenk, PRL (2013) May 26, 2016 Ingo Tews, JINA Neutron Stars 17

18 Neutron matter E/N [MeV] this work LS 180 LS 220 LS 375 FSU2.1 NL3 TM1 DD2 SFHo SFHx Good agreement with other calculations Ø but in those no theoretical uncertainties Akmal et al., PRC (1998) Gandolfi et al., PRC (2012) Chiral EFT puts constraints on neutron matter EOS n [fm -3 ] Lines from Hempel, Lattimer, G. Shen May 26, 2016 Ingo Tews, JINA Neutron Stars 18

19 Symmetry energy and L parameter Put constraints on symmetry energy and its density dependence L: Ø 1 2 = MeV Ø 9 = MeV Good agreement with experimental constraints Lattimer, Lim, ApJ (2013) May 26, 2016 Ingo Tews, JINA Neutron Stars 19

20 Symmetry energy and L parameter Put constraints on symmetry energy and its density dependence L: Ø 1 2 = MeV Ø 9 = MeV Good agreement with experimental constraints Drischler, Soma, Schwenk, PRC (2014) May 26, 2016 Ingo Tews, JINA Neutron Stars 20

21 Neutron Stars Equation of state for neutron star matter: extend results to small Y e,p Hebeler, Lattimer, Pethick, Schwenk, PRL (2010) and APJ (2013) Agrees with standard crust EOS after inclusion of many-body forces May 26, 2016 Ingo Tews, JINA Neutron Stars 21

22 Neutron Stars Equation of state for neutron star matter: extend results to small Y e,p Hebeler, Lattimer, Pethick, Schwenk, PRL (2010) and APJ (2013) log 10 P [dyne / cm 2 ] crust EOS (BPS) neutron star matter with c i uncertainties crust log 10 [g / cm 3 ] Agrees with standard crust EOS after inclusion of many-body forces Extend to higher densities using polytropic expansion May 26, 2016 Ingo Tews, JINA Neutron Stars 22

23 Neutron Stars Hebeler, Lattimer, Pethick, Schwenk, PRL (2010) and APJ (2013) May 26, 2016 Ingo Tews, JINA Neutron Stars 23

24 Neutron Stars Constrain resulting EOS: causality and observed 1.97 M neutron star Hebeler, Lattimer, Pethick, Schwenk, PRL (2010) and APJ (2013) May 26, 2016 Ingo Tews, JINA Neutron Stars 24

25 Neutron Stars 3 this work RG evolved Mass [M.] causality Radius for 1.4 M neutron star: Ø ; = km Maximum mass neutron star: Ø >?@A 3.05> (14 km) Uncertainties from many-body forces and polytropic expansion Radius [km] IT, Krüger, Hebeler, Schwenk, PRL (2013) May 26, 2016 Ingo Tews, JINA Neutron Stars 25

26 Neutron Stars If a 2.4 M neutron star was observed: Hebeler et al., PRL (2010) and APJ (2013) May 26, 2016 Ingo Tews, JINA Neutron Stars 26

27 Neutron Stars Radius for 1.4 M neutron star: Ø ; = km Maximum mass neutron star: Ø >?@A 3.05> (14 km) Uncertainties from many-body forces and polytropic expansion IT, Krüger, Gezerlis, Hebeler, Schwenk (2013) May 26, 2016 Ingo Tews, JINA Neutron Stars 27

28 Improving neutron-matter band E/N [MeV] this work LS 180 LS 220 LS 375 FSU2.1 NL3 TM1 DD2 SFHo SFHx QMC n [fm -3 ] IT, Krüger, Hebeler, Schwenk (2013) Fourth order in chiral EFT, Perturbation theory Credit: Stefano Gandolfi Phenomenological forces, Quantum Monte Carlo May 26, 2016 Ingo Tews, JINA Neutron Stars 28

29 Improving neutron-matter band Chiral EFT forces in Quantum Monte Carlo: Ø Energies agree well within uncertainty bands Ø uncertainties comparable but QMC band at lower order Gezerlis, IT, Epelbaum, Gandolfi, Hebeler, Nogga, Schwenk, PRL (2013) & PRC (2014) IT, Gandolfi, Gezerlis, Schwenk, PRC (2016) Lynn, IT, Carlson, Gandolfi, Gezerlis, Schmidt, Schwenk, PRL (2016) May 26, 2016 Ingo Tews, JINA Neutron Stars 29

30 Summary Chiral effective field theory: ØProvides strong constraints on symmetry energy, neutron star EOS ØImprovement of neutron-matter EOS work in progress ØUsing QMC methods at higher order expected to reduce theoretical uncertainties by a factor of two Gezerlis, IT, Epelbaum, Gandolfi, Hebeler, Nogga, Schwenk, PRL (2013) & PRC (2014) IT, Gandolfi, Gezerlis, Schwenk, PRC (2016) Lynn, IT, Carlson, Gandolfi, Gezerlis, Schmidt, Schwenk, PRL (2016) Constraints on symmetry energy and neutron stars: Ø 1 2 = MeV Ø 9 = MeV Ø Radius for 1.4 M neutron star: km IT, Krüger, Hebeler, Schwenk, PRL & PRC (2013) Mass [M.] causality this work RG evolved Radius [km] May 26, 2016 Ingo Tews, JINA Neutron Stars 30

31 Thanks Thanks to my collaborators: Ø Technische Universitaẗ Darmstadt: K. Hebeler, J. Lynn, A. Schwenk Ø Ohio State University: A. Dyhdalo, D. Furnstahl Ø Universitaẗ Bochum: E. Epelbaum Ø Los Alamos National Laboratory: J. Carlson, S. Gandolfi Ø University of Guelph: A. Gezerlis Ø Forschungszentrum Ju lich: A. Nogga Thanks to FZ Jülich for computing time and NIC excellence project. Thank you! May 26, 2016 Ingo Tews, JINA Neutron Stars 31