Kai Hebeler Hirschegg, January 19, 2017 Neutron star mergers: from gravitational waves to nucleosynthesis TECHNISCHE UNIVERSITĂT DARM STADT opean Research Counc Established by the European Commission
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since 1980's ‘Exact’ methods: nore-core shell model, Greens function Monte Carlo factorial scaling 110 100 90 Z N
since 1980's ‘Exact’ methods: nore-core shell model, Greens function Monte Carlo factorial scaling plus frameworks for few-body systems (A=3,4) Faddeev, Faddeev-Yakubovski 110 100 90 80 70 60 Z N
since year ~2000 closed-shell nuclei: coupled cluster, in-medium SRG, self-consistent Greens function polynomial scaling 110 100 90 Z N
since year ~2010 open-shell nuclei: multi-reference IMSRG, Gorkov Greens function, Bogoliubov-coupled cluster polynomial scaling 110 100 90 80 Z N
since year ~2014 ab initio valence shell model based on nonperturbative calculation of effective interactions mixed scaling 110 100 90 80 Z N
since year ~2014 110 100 90 80 Z ab initio valence shell model based on nonperturbative calculation of effective interactions mixed scaling N Ab initio nuclear structure and reaction theory nuclear structure and reaction observables Quantum Chromodynamics
nuclear structure and reaction observables
Lattice QCD
• requires extreme amounts of computational resources • currently limited to 1- or 2-nucleon systems • current accuracy insufficient for precision nuclear structure Quantum Chromodynamics
nuclear structure and reaction observables Chiral effective field theory nuclear interactions and currents Quantum Chromodynamics
nuclear structure and reaction observables ab initio many-body frameworks Faddeev, Quantum Monte Carlo, no-core shell model, coupled cluster ... Chiral effective field theory nuclear interactions and currents Quantum Chromodynamics
nuclear structure and reaction observables ab initio many-body frameworks Faddeev, Quantum Monte Carlo, no-core shell model, coupled cluster ... Renormalization Group methods Chiral effective field theory nuclear interactions and currents Quantum Chromodynamics
• constructed to fit NN scattering data (long-wavelength information) • long-range part dominated by one pion exchange interaction • short range part strongly model dependent! • traditional NN interactions contain strongly repulsive core at small distance ➤ many-body problem hard to solve using basis expansion! Systematic decoupling of high-momentum physics: The Similarity Renormalization Group • generate unitary transformation which decouples low- and high momenta: H λ = U λ HU λ   with the resolution parameter  λ • change resolution systematically in small steps: • generatorﾜｽcan be chosen and tailored to different applications • observables are preserved due to unitarity of transformation Systematic decoupling of high-momentum physics: The Similarity Renormalization Group • generate unitary transformation which decouples low- and high momenta: H λ = U λ H U λ = with the resolution parameter  λ • change resolution systematically in small steps: d λ • generatorﾜｽcan be chosen and tailored to different applications • observables are preserved due to unitarity of transformation Resolution  λ Systematic decoupling of high-momentum physics: The Similarity Renormalization Group • generate unitary transformation which decouples low- and high momenta: H λ = U λ H U !  with the resolution parameter  λ • change resolution systematically in small steps: dH χ d λ • generatorﾜｽcan be chosen and tailored to different applications • observables are preserved due to unitarity of transformation Resolution  λ Systematic decoupling of high-momentum physics: The Similarity Renormalization Group • generate unitary transformation which decouples low- and high momenta: H λ = U λ H U !  | with the resolution parameter  λ • change resolution systematically in small steps: dH χ d λ • generatorﾜｽcan be chosen and tailored to different applications • observables are preserved due to unitarity of transformation Resolution  λ Systematic decoupling of high-momentum physics: The Similarity Renormalization Group • generate unitary transformation which decouples low- and high momenta: H λ = U λ H U !  with the resolution parameter  λ • change resolution systematically in small steps: dH χ d λ • generatorﾜｽcan be chosen and tailored to different applications • observables are preserved due to unitarity of transformation Resolution  λ
The Similarity Renormalization Group • generate unitary transformation which decouples low- and high momenta: H λ = U λ H U !  with the resolution parameter  λ • change resolution systematically in small steps: dH χ d λ • generatorﾜｽcan be chosen and tailored to different applications • observables are preserved due to unitarity of transformation Resolution  λ Systematic decoupling of high-momentum physics: The Similarity Renormalization Group • generate unitary transformation which decouples low- and high momenta: H λ = U λ H U λ = with the resolution parameter  λ • change resolution systematically in small steps: dH χ d λ • generatorﾜｽcan be chosen and tailored to different applications • observables are preserved due to unitarity of transformation Resolution  λ Systematic decoupling of high-momentum physics: The Similarity Renormalization Group • generate unitary transformation which decouples low- and high momenta: H λ = U λ H U λ = with the resolution parameter  λ • change resolution systematically in small steps: dH χ d λ • generatorﾜｽcan be chosen and tailored to different applications • observables are preserved due to unitarity of transformation Resolution  λ Systematic decoupling of high-momentum physics: The Similarity Renormalization Group • generate unitary transformation which decouples low- and high momenta: H λ = U λ H U λ = with the resolution parameter  λ • change resolution systematically in small steps: dH χ d λ • generatorﾜｽcan be chosen and tailored to different applications • observables are preserved due to unitarity of transformation Resolution  λ Systematic decoupling of high-momentum physics: The Similarity Renormalization Group • generate unitary transformation which decouples low- and high momenta: H λ = U λ H U λ = with the resolution parameter  λ • change resolution systematically in small steps: dH χ d λ • generatorﾜｽcan be chosen and tailored to different applications • observables are preserved due to unitarity of transformation Resolution  λ Systematic decoupling of high-momentum physics: The Similarity Renormalization Group • generate unitary transformation which decouples low- and high momenta: H λ = U λ H U λ with the resolution parameter  λ • change resolution systematically in small steps: dH χ d λ • generatorﾜｽcan be chosen and tailored to different applications • observables are preserved due to unitarity of transformation Resolution  λ Systematic decoupling of high-momentum physics: The Similarity Renormalization Group • generate unitary transformation which decouples low- and high momenta: H λ = U λ H U λ = with the resolution parameter  λ • change resolution systematically in small steps: dH χ d λ • generatorﾜｽcan be chosen and tailored to different applications • observables are preserved due to unitarity of transformation Resolution  λ Systematic decoupling of high-momentum physics: The Similarity Renormalization Group • generate unitary transformation which decouples low- and high momenta: H λ = U λ H U λ = with the resolution parameter  λ • change resolution systematically in small steps: dH χ d λ • generatorﾜｽcan be chosen and tailored to different applications • observables are preserved due to unitarity of transformation Resolution  λ Systematic decoupling of high-momentum physics: The Similarity Renormalization Group • generate unitary transformation which decouples low- and high momenta: H λ = U λ H U λ = with the resolution parameter  λ • change resolution systematically in small steps: dH χ d λ • generatorﾜｽcan be chosen and tailored to different applications • observables are preserved due to unitarity of transformation Resolution  λ Systematic decoupling of high-momentum physics: The Similarity Renormalization Group • generate unitary transformation which decouples low- and high momenta: H λ = U λ H U λ = with the resolution parameter  λ • change resolution systematically in small steps: dH χ d λ • generatorﾜｽcan be chosen and tailored to different applications • observables are preserved due to unitarity of transformation Resolution  λ
dr'r'²V χ (r, r') V χ (r) =  |
• if a nucleus is probed at high energies, nucleon substructure is resolved • at low energies, details are not resolved
• if a nucleus is probed at high energies, nucleon substructure is resolved • at low energies, details are not resolved • replace fine structure by something simpler (compare multipole expansion) effective field theory Resolution
• choose relevant degrees of freedom: here nucleons and pions • operators constrained by symmetries of QCD • short-range physics captured in short-range couplings ● separation of scales: Q << Λ b, breakdown scale Λь～500 MeV • power-counting: expand in Q/Ab • systematic, obtain error estimates • many-body forces appear naturally
Consider-classical analog: tidal effects in earth-sun-moon system • force between earth and mpon depends on the position of sun • tidal deformations repre ● describe system using po nposite particle f resolution change excitations, licitly nucleon forces natural n: how important are their contributions?
neutron and nuclear matter Tews, Krüger, KH, Schwenk, PRL  I I 0, 032504 (2013) Krüger, Tews, KH, Schwenk, PRC 88, 025802 (2013) all terms predicted (no new low-energy couplings)
Krüger, Tews, KH, Schwenk, PRC 88, 025802 (2013) first calculation of matrix elements for ab initio studies of matter and nuclei KH, Krebs, Epelbaum, Golak, Skibinski, PRC 91,044001(2015)
(ce) 3NF couplings fitted to few-body systems at different resolution scales: Езн = −8.482 MeV     r4He = 1.464 fm C1, C3, C4 terms CD term CE term
C1, C3, C4 terms CD term CE term Drischler, KH, Schwenk, PRC93, 054314 (2016)
• remarkable agreement between different many-body frameworks • very good agreement between theory and experiment for masses of oxygen and calcium isotopes based on specific chiral interactions • contributions from 3N force play important role for drip line
coupled cluster (CC) framework
• spectacular increase in range of applicability of ab initio many body frameworks • significant discrepancies to experimental data for heavy nuclei for (most of) presently used nuclear interactions • need to quantify theoretical uncertainties
Hagen. et al.. Nature Phys. 12, 186 (2015)
Hagen. et al.. Nature Phys. 12, 186 (2015)
Garcia Ruiz. et al., Nature Phys. 12, 594 (2016)
Piekarewicz, Garcia Ruiz. et al., Nature Phys. 12, 594 (2016) direct connections to astrophysics!
• microscopic framework to calculate equation of state for general proton fractions • uncertainty bands determined by set of 7 Hamiltonians • many-body framework allows treatment of general 3N interaction Drischler, KH, Schwenk, PRC 054314 (2016)
• microscopic framework to calculate equation of state for general proton fractions • uncertainty bands determined by set of 7 Hamiltonians
Problem:
Calculation of neutron star properties require EOS up to high densities. Reliable calculations only possible up to ～ 1-2 N sat Strategy: Use observations to constrain the high-density part of the nuclear EOS. [/A [MeV]
incorporation of beta-equilibrium: neutron matter —→  neutron star matter parametrize our ignorance via piecewise high-density extensions of EOS: • use polytropic ansatz  p ～ ρ¹  (results insensitive to particular form) • range of parameters   Г 1 , KH, Lattimer, Pethick, Schwenk, Ap| 773, | |  (2013) KH, Lattimer, Pethick, Schwenk, PRL 105, 161102 (2010)
use the constraints: recent NS observations Mmax > 1.97 Mo causality vs(ρ) = √dP/dε < c KH, Lattimer, Pethick, Schwenk, ApJ 773, l l  (2013) constraints lead to significant reduction of EOS uncertainty band
KH, Lattimer, Pethick, Schwenk, PRL 105, 161102 (2010) • Iow-density part of EOS sets scale for allowed high-density extensions see talk by Svenja Greif
I. local EFT interactions, suitable for Quantum Monte Carlo calculations status: NN plus 3N up to N2LO, calculations of few-body systems and neutron matter PRC 90,054323 (2014) Shift [de
I. local EFT interactions, suitable for Quantum Monte Carlo calculations status: NN plus 3N up to N2LO, calculations of few-body systems and neutron matter antum Monte Carlo of neutron based on chiral EFT interactions perfect agreement for soft interactions, first direct validation "lf calculations within many-body perturbation theory
I. local EFT interactions, suitable for Quantum Monte Carlo calculations status: NN plus 3N up to N2LO, calculations of few-body systems and neutron matter PRL III,032501 (2013) PRC 90,054323 (2014) PRL 116,062501 (2016) � AFDMC LO N forces to tyo- and few-body observables 2. simultaneous fit of NN and status: NN plus 3N ữp currently in development Carlsson et al., PRX 6,011019 (2016)
3. fits of NN plus 3N forces to two-, few- and many-body observables status: NN plus 3N up to N2LO, NN phase shifts only fitted up to T ab~35 MeV
3. fits of NN plus 3N forces to two-, few- and many-body observables status: NN plus 3N up to N2LO, NN phase shifts only fitted up to T ab~35 MeV 4. semilocal NN forces, development of improved method to estimate uncertainties status: NN up to N4LO, 3N interactions in development (almost finished :-)) Epelbaum, Krebs, Meißner, PRL 115, 122301 (2015) PRC 93,044002 (2016)
3. fits of NN plus 3N forces to two-, few- and many-body observables status: NN plus 3N up to N2LO, NN phase shifts only fitted up to T ab~35 MeV 4. semilocal NN forces, development of improved method to estimate uncertainties status: NN up to N4LO, 3N interactions in development (almost finished :-)) Epelbaum, Krebs, Meißner, PRL 115, 122301 (2015) Binder et al., PRC 93,044002 (2016) nonlocal semilocal KH et al., PRC 91,044001 (2015)
significant increase in scope of ab initio many-body frameworks remarkable agreement between different ab intio many-body methods discrepancies to experiment dominated by deficiencies of present nuclear interactions Current developments and open questions presently active efforts to develop improved nucleon interactions (fits of LECs, power counting, regularization...) Key goals unified study of atomic nuclei, nuclear matter and reactions based on novel interactions systematic estimates of theoretical uncertainties