Quantum Monte Ca Carlo calculations s of neutron ma matter er wi - PowerPoint PPT Presentation

Quantum Monte Ca Carlo calculations s of neutron ma matter er wi with Ch Chiral E Effective F Field Th Theory in interac actio ions Ingo Tews, In collaboration with J. Carlson, S. Gandolfi, A. Gezerlis, K. Hebeler, T. Krüger, J. Lynn, A. Schwenk, … Talk, YITP program: "Nuclear Physics, Compact Stars, and Compact Star Mergers”, Oct.20, 2016, Kyoto

Mo Motivation Ø The neutron-matter equation Equation of state of state at T=0 connects of neutron matter several physical systems over a wide density range. Ø An accurate description of the neutron-matter equation of state is therefore crucial. Zwierlein et al., Nature (2005) Credit: B.A. Brown Antoniadis et al., Science (2013) Credit: S. Rosswog Gravitational waves from Ultracold atoms Neutron-rich nuclei Neutron stars neutron star mergers Oct. 20, 2016 Ingo Tews, NPCSM workshop 2

Motivation Mo Ø The neutron-matter equation Equation of state of state at T=0 connects of neutron matter several physical systems over a wide density range. Ø An accurate description of the neutron-matter equation of state is therefore crucial. 44 Tamii et al., PRL (2011) EDFs 40 J (MeV) 36 32 exp ( 68 Ni) From α D exp ( 120 Sn) From α D 28 exp ( 208 Pb) From α D 20 40 60 80 100 120 L (MeV) Ø Neutron matter at saturation density constrains Roca-Maza et al., PRC (2013) Credit: B.A. Brown neutron-skin thickness of neutron-rich nuclei Neutron-rich nuclei Ø Experiments at RCNP, GSI, … Oct. 20, 2016 Ingo Tews, NPCSM workshop 3

Motivation Mo Ø The neutron-matter equation Equation of state of state at T=0 connects of neutron matter several physical systems over a wide density range. Ø An accurate description of the neutron-matter equation of state is therefore crucial. Ø Neutron matter equation of state 4.5 at saturation density and above 4 determines mass-radius relation of 3.5 P [MeV fm () ] neutron stars and gravitational- f peak [kHz] 3 wave signal of neutron-star mergers 2.5 2 Lattimer, Lim Ø EOS properties at saturation 1.5 density are correlated with 10 11 12 13 14 15 16 R 1.6 [km] R ,../ ⊙ [km] neutron-star radii and gravitational Bauswein et al., PRD (2012) wave peak frequency Lattimer, Lim, ApJ (2013). Oct. 20, 2016 Ingo Tews, NPCSM workshop 4

Motivation Mo How to obtain the EOS in an ab initio approach? Quantum Chromodynamics Phenomenological forces Nuclear Forces Chiral effective field theory (e.g. AV18 + UIX) Many-body Quantum Monte Carlo: Broad range of methods methods Very reliable Equation of state of neutron matter Oct. 20, 2016 Ingo Tews, NPCSM workshop 5

Ou Outlin tline 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 Ø Ab-initio calculations using chiral EFT can be used to constrain equation of state of neutron matter Ø Neutron-matter applications: IT, Krüger, Hebeler, Schwenk, PRL & PRC & PLB (2013) • Symmetry energy • Neutron-star mass-radius relation Ø Improving neutron-matter results using Quantum Monte Carlo methods Gezerlis, IT, et al., PRL & PRC (2013, 2014, 2016) Ø Summary Oct. 20, 2016 Ingo Tews, NPCSM workshop 6

Chiral effecti tive field th theory for nuclear fo nuc forces Basic principle of effective field theory: u d d u d d u d λ≫R 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 Oct. 20, 2016 Ingo Tews, NPCSM workshop 7

Chiral effecti tive field th theory for nuc nuclear fo 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 1 ≪ breakdown scale Λ 4 8 8 5 , Ø Expand in powers of ∼ 6 7 ) 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 ... Oct. 20, 2016 Ingo Tews, NPCSM workshop 8

Chiral effecti tive field th theory for nuc nuclear fo forces Explicit degrees of freedom: Ø Pions and nucleons Ø Long-range physics explicit 2 LECs Ø Short-range physics expanded in general operator basis Ø High-momentum physics absorbed 7 LECs into short-range couplings, fit to experiment (phase shifts) ∼const. ρ 15 LECs Second scale: cutoff Λ (resolution): Ø Interactions Λ -dependent Oct. 20, 2016 Ingo Tews, NPCSM workshop 8

Chiral effecti tive field th theory for nuc nuclear fo 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 Oct. 20, 2016 Ingo Tews, NPCSM workshop 9

Chiral effecti tive field th theory for nuclear fo nuc 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 (2 LECs) Fitting: Ø NN forces in NN system (NN phase shifts, …) Ø 3N forces in 3N/4N system (Binding energies, radii, …) Oct. 20, 2016 Ingo Tews, NPCSM workshop 10

Chiral effecti tive field th theory for nuc nuclear fo forces Consistent interactions: Ø Same couplings for two-nucleon and many-body sector Ø In contrast to phenomenological interactions Oct. 20, 2016 Ingo Tews, NPCSM workshop 10

Chiral effecti tive field th theory for nuc nuclear fo forces Many-body forces are crucial: Oxygen Otsuka et 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) Oct. 20, 2016 Ingo Tews, NPCSM workshop 11

Chiral effecti tive field th theory for nuclear fo nuc forces Many-body forces are crucial: Coraggio, Holt, Itaco, Machleidt, Marcucci, Sammarruca, PRC (2014) Drischler et al., PRC (2016) N NN + 3N forces: Ø Give correct saturation with theoretical uncertainties in nuclear matter Drischler et al., PRC (2016) Oct. 20, 2016 Ingo Tews, NPCSM workshop 12

Chiral effecti tive field th theory for nuclear fo nuc forces Neutron matter: Ø Complete calculation at N 3 LO using many-body perturbation theory (MBPT) IT, Krüger, Hebeler, Schwenk, PRL (2013) Calculation is simpler in neutron matter: Ø Only certain parts of the many- body forces contribute Ø Chiral many-body forces completely predicted from NN sector Oct. 20, 2016 Ingo Tews, NPCSM workshop 13

Neutron Ne on matter Bands: 20 Ø Include several sources of EM 500 MeV EGM 450/500 MeV uncertainty: EGM 450/700 MeV Ø Chiral Hamiltonians (cutoff, 3N LECs) 15 Ø Many-body method E/N [MeV] 10 NN interactions: Ø E/N at saturation density: 12-15 MeV 5 NN+3N interactions: Ø Have large impact on energy 0 0 0.05 0.1 0.15 and uncertainty: n [fm -3 ] 14-21 MeV IT, Krüger, Hebeler, Schwenk, PRL (2013) Oct. 20, 2016 Ingo Tews, NPCSM workshop 14

Neutron Ne on matter Good agreement with other calculations 20 EM 500 MeV EGM 450/500 MeV Ø but in those EGM 450/700 MeV no theoretical uncertainties NLO lattice (2009) QMC (2010) 15 Akmal et al. , PRC (1998) APR (1998) Gandolfi et al. , PRC (2012) GCR (2012) E/N [MeV] Chiral EFT puts constraints on 10 neutron matter EOS 5 0 0 0.05 0.1 0.15 n [fm -3 ] IT, Krüger, Hebeler, Schwenk, PRL (2013) Oct. 20, 2016 Ingo Tews, NPCSM workshop 14

Neutron Ne on matter Good agreement with other this work calculations 20 LS 180 LS 220 Ø but in those LS 375 FSU2.1 no theoretical uncertainties NL3 TM1 15 Akmal et al. , PRC (1998) DD2 Gandolfi et al. , PRC (2012) E/N [MeV] SFHo SFHx Chiral EFT puts constraints on 10 neutron matter EOS 5 0 0 0.05 0.1 0.15 n [fm -3 ] Lines from Hempel, Lattimer, G. Shen Oct. 20, 2016 Ingo Tews, NPCSM workshop 14

Sy Symmetry energy and L parameter Put constraints on symmetry energy and its density dependence L: Ø > ? = 28.9 − 34.9 MeV Ø E = 43.0 − 66.6 MeV Good agreement with experimental constraints Lattimer, Lim, ApJ (2013) Oct. 20, 2016 Ingo Tews, NPCSM workshop 15

Sy Symmetry energy and L parameter Put constraints on symmetry energy and its density dependence L: Ø > ? = 28.9 − 34.9 MeV Ø E = 43.0 − 66.6 MeV Good agreement with experimental constraints Drischler, Soma, Schwenk, PRC (2014) Oct. 20, 2016 Ingo Tews, NPCSM workshop 16

Ne Neutron on Star ars Equation of state for neutron star matter: extend results to small Y e , p Hebeler, Lattimer, Pethick, Schwenk, PRL (2010) and APJ (2013) 37 crust EOS (BPS) 3 neutron star matter 36 with c i uncertainties 2 log 10 P [dyne / cm 2 ] 35 crust 1 34 33 32 31 13.0 13.5 14.0 1 12 23 [g / cm 3 ] log 10 Agrees with standard crust EOS Extend to higher densities after inclusion of many-body forces using polytropic expansion Oct. 20, 2016 Ingo Tews, NPCSM workshop 17

Neutron Ne on Star ars Constrain resulting EOS: causality and observed 1.97 M � neutron star Hebeler, Lattimer, Pethick, Schwenk, PRL (2010) and APJ (2013) Oct. 20, 2016 Ingo Tews, NPCSM workshop 18