Frontiers in Ab Initio Nuclear Structure Theory. Robert Roth

Frontiers in Ab Initio Nuclear Structure Theory Robert Roth

New Era of Nuclear Structure Theory QCD at low energies improved understanding through effective field theories & lattice simulations

New Era of Nuclear Structure Theory QCD at low energies improved understanding through effective field theories & lattice simulations quantum many-body methods advances in ab initio treatment of the nuclear many-body problem computing & algorithms increase of computational resources & improved algorithms

Ab Initio Nuclear Structure Nuclear Structure Observables Low-Energy Quantum Chromodynamics

Ab Initio Nuclear Structure Nuclear Structure Observables Lattice QCD quarks & gluon on a lattice Low-Energy Quantum Chromodynamics

Ab Initio Nuclear Structure Nuclear Structure Observables Lattice QCD quarks & gluon on a lattice Chiral EFT Hamiltonians consistent NN,3N, interactions & current operators Chiral Effective Field Theory based on relevant degrees of freedom & symmetries of QCD Low-Energy Quantum Chromodynamics

Ab Initio Nuclear Structure Nuclear Structure Observables Lattice QCD quarks & gluon on a lattice Lattice EFT nucleons & pions on a lattice Chiral EFT Hamiltonians consistent NN,3N, interactions & current operators Energy-Density Funct guided by chiral EFT Chiral Effective Field Theory based on relevant degrees of freedom & symmetries of QCD Low-Energy Quantum Chromodynamics

Ab Initio Nuclear Structure Nuclear Structure Observables Lattice QCD quarks & gluon on a lattice Lattice EFT nucleons & pions on a lattice Similarity Transformations physics-conserving unitary transformation to adapt Hamiltonian to limited model space Chiral EFT Hamiltonians consistent NN,3N, interactions & current operators Energy-Density Funct guided by chiral EFT Chiral Effective Field Theory based on relevant degrees of freedom & symmetries of QCD Low-Energy Quantum Chromodynamics

Ab Initio Nuclear Structure Nuclear Structure Observables Lattice QCD quarks & gluon on a lattice Lattice EFT nucleons & pions on a lattice Exact Solutions solve nuclear manybody problem with converged truncations Controlled Approx treat many-body problem with controlled & improvable approximations Similarity Transformations physics-conserving unitary transformation to adapt Hamiltonian to limited model space Chiral EFT Hamiltonians consistent NN,3N, interactions & current operators Energy-Density Funct guided by chiral EFT Chiral Effective Field Theory based on relevant degrees of freedom & symmetries of QCD Low-Energy Quantum Chromodynamics

Ab Initio Nuclear Structure Nuclear Structure Observables Lattice QCD quarks & gluon on a lattice Lattice EFT nucleons & pions on a lattice PREDICTION Exact Solutions solve nuclear manybody problem with converged truncations Controlled Approx treat many-body problem VALIDATION with controlled & improvable approximations Similarity Transformations physics-conserving unitary transformation to adapt Hamiltonian to limited model space Chiral EFT Hamiltonians consistent NN,3N, interactions & current operators Chiral Effective Field Theory based on relevant degrees of freedom & symmetries of QCD Energy-Density Funct guided by chiral EFT Low-Energy Quantum Chromodynamics

Ab Initio Nuclear Structure Nuclear Structure Observables Lattice QCD quarks & gluon on a lattice Lattice EFT nucleons & pions on a lattice Exact Solutions solve nuclear manybody problem with converged truncations Controlled Approx treat many-body problem with controlled & improvable approximations Similarity Transformations physics-conserving unitary transformation to adapt Hamiltonian to limited model space Chiral EFT Hamiltonians consistent NN,3N, interactions & current operators Chiral Effective Field Theory based on relevant degrees of freedom & symmetries of QCD Energy-Density Funct guided by chiral EFT Low-Energy Quantum Chromodynamics

µ µ µ ¾ ¾ µ É ¼ ¼ É É É Ç Ç Ç Ä Ç Ä Ä Æ Ä ¾ Æ Æ Nuclear Interactions from Chiral EFT Weinberg, van Kolck, Machleidt, Entem, Meißner, Epelbaum, Krebs, Bernard, low-energy effective field theory for relevant degrees of freedom (π,n) based on symmetries of QCD LO NN 3N 4N long-range pion dynamics explicitly, short-range physics absorbed in contact terms fitted to data (NN, πn,) hierarchy of consistent NN, 3N, interactions plus currents NLO standard Hamiltonian: NN at N3LO: Entem & Machleidt, 5 MeV cutoff N LO 3N at NLO: Navrátil, A=3 fit, 5 MeV cutoff many ongoing developments N 3 LO

Ab Initio Nuclear Structure Nuclear Structure Observables Lattice QCD quarks & gluon on a lattice Lattice EFT nucleons & pions on a lattice Exact Solutions solve nuclear manybody problem with converged truncations Controlled Approx treat many-body problem with controlled & improvable approximations Similarity Transformations physics-conserving unitary transformation to adapt Hamiltonian to limited model space Chiral EFT Hamiltonians consistent NN,3N, interactions & current operators Chiral Effective Field Theory based on relevant degrees of freedom & symmetries of QCD Energy-Density Funct guided by chiral EFT Low-Energy Quantum Chromodynamics

Similarity Renormalization Group Wegner, Glazek, Wilson, Perry, Bogner, Furnstahl, Hergert, Roth, Jurgenson, Navratil, continuous transformation driving Hamiltonian to band-diagonal form with respect to a uncorrelated basis unitary transformation of Hamiltonian and other observables H α =U α HU α O α =U α OU α evolution equations for H α and U α depending on generator η α d dα H d α=[η α,h α ] dα U α= U α η α dynamic generator: commutator with the operator in whose eigenbasis H α shall be diagonalized η α =(μ) [T int,h α ]

Similarity Renormalization Group Wegner, Glazek, Wilson, Perry, Bogner, Furnstahl, Hergert, Roth, Jurgenson, Navratil, continuous transformation driving Hamiltonian to band-diagonal form with respect to a uncorrelated basis simplicity and flexibility are great advantages of unitary transformation of Hamiltonian and other observables the SRG approach H α =U α HU α O α =U α OU α solve SRG evolution evolution equations for H α and U α depending equations using generator two-, η α d dα H dthree- α=[η α,h α ] dα U & four-body matrix α= U representation α η α dynamic generator: commutator with the operator in whose eigenbasis H α shall be diagonalized η α =(μ) [T int,h α ]

SRG Evolution in Three-Body Space 3B-Jacobi HO matrix elements chiral NN+3N E N3 LO + N LO, triton-fit, 5 MeV Jπ = 18 = 1, hω = 8 MeV NCSM ground state 3 H 4 E [MeV] (E, ) 1+,T 6 - -4-6 8-8 E 18 4 (E, ) 6 8 4 6 8 11141618 Nm x

SRG Evolution in Three-Body Space 3B-Jacobi HO matrix elements 4 chiral NN+3N α = fm E N3 LO + NΛ LO, triton-fit, = fm 1 5 MeV Jπ = 18 = 1, hω = 8 MeV NCSM ground state 3 H 4 E [MeV] (E, ) 1+,T 6 - -4-6 8-8 E 18 4 (E, ) 6 8 4 6 8 11141618 Nm x

SRG Evolution in Three-Body Space 3B-Jacobi HO matrix elements 4 α = 1 fm E Λ = 316 fm 1 Jπ = 18 = 1, hω = 8 MeV NCSM ground state 3 H 4 E [MeV] (E, ) 1+,T 6 - -4-6 8-8 E 18 4 (E, ) 6 8 4 6 8 11141618 Nm x

SRG Evolution in Three-Body Space 3B-Jacobi HO matrix elements 4 α = fm E Λ = 66 fm 1 Jπ = 18 = 1, hω = 8 MeV NCSM ground state 3 H 4 E [MeV] (E, ) 1+,T 6 - -4-6 8-8 E 18 4 (E, ) 6 8 4 6 8 11141618 Nm x

SRG Evolution in Three-Body Space E 3B-Jacobi HO matrix elements α=4fm 4 Λ=4fm 1 J π = 1 +,T= 1, hω=8mev (E, ) 18 4 6 E [MeV] - -4-6 NCSM ground state 3 H 8 E 18 4 6 8 (E, ) -8 4 6 8 11141618

SRG Evolution in Three-Body Space E 3B-Jacobi HO matrix elements α=8fm 4 Λ=188fm 1 J π = 1 +,T= 1, hω=8mev (E, ) 18 4 6 E [MeV] - -4-6 NCSM ground state 3 H 8 E 18 4 6 8 (E, ) -8 4 6 8 11141618

SRG Evolution in Three-Body Space E 3B-Jacobi HO matrix elements α=16fm 4 Λ=158fm 1 J π = 1 +,T= 1, hω=8mev (E, ) 18 4 6 E [MeV] - -4-6 NCSM ground state 3 H 8 E 18 4 6 8 (E, ) -8 4 6 8 11141618

SRG Evolution in Three-Body Space E 3B-Jacobi HO matrix elements α=3fm 4 Λ=133fm 1 J π = 1 +,T= 1, hω=8mev (E, ) 18 4 6 E [MeV] - -4-6 NCSM ground state 3 H 8 E 18 4 6 8 (E, ) -8 4 6 8 11141618

SRG Evolution in Three-Body Space E 3B-Jacobi HO matrix elements α=3fm 4 Λ=133fm 1 J π = 1 +,T= 1, hω=8mev (E, ) 18 4 6 E [MeV] - -4 NCSM ground state 3 H significant improvement of convergence behavior 8 suppression of off-diagonal coupling ˆ= pre-diagonalization E 18 4 6 8 (E, ) -6-8 4 6 8 11141618

Hamiltonian in A-Body Space evolution induces n-body contributions H [n] α H α =H [1] α +H[] α +H[3] α +H[4] α +H[5] α + to Hamiltonian truncation of cluster series formally destroys unitarity and invariance of energy eigenvalues (independence of α) flow-parameter α provides diagnostic tool to assess neglected higher-order contributions

Hamiltonian in A-Body Space evolution induces n-body contributions H [n] α to Hamiltonian H α =H [1] α +H[] α +H[3] α +H[4] α +H[5] α + truncation of cluster series formally destroys unitarity and invariance of energy eigenvalues (independence of α) flow-parameter α provides diagnostic tool to assess neglected higher-order contributions SRG-Evolved Hamiltonians NN only NN+3N ind NN+3N full use initial NN, keep evolved NN use initial NN, keep evolved NN+3N use initial NN+3N, keep evolved NN+3N NN+3N full +4N ind use initial NN+3N, keep evolved NN+3N+4N

Ab Initio Nuclear Structure Nuclear Structure Observables Lattice QCD quarks & gluon on a lattice Lattice EFT nucleons & pions on a lattice Exact Solutions solve nuclear manybody problem with converged truncations Controlled Approx treat many-body problem with controlled & improvable approximations Similarity Transformations physics-conserving unitary transformation to adapt Hamiltonian to limited model space Chiral EFT Hamiltonians consistent NN,3N, interactions & current operators Chiral Effective Field Theory based on relevant degrees of freedom & symmetries of QCD Energy-Density Funct guided by chiral EFT Low-Energy Quantum Chromodynamics

No-Core Shell Model Barrett, Vary, Navratil, Maris, Nogga, Roth, NCSM is one of the most powerful and universal exact ab-initio methods construct matrix representation of Hamiltonian using a basis of HO Slater determinants truncated wrt HO excitation energy hω solve large-scale eigenvalue problem for a few extremal eigenvalues all relevant observables can be computed from the eigenstates range of applicabilitylimited by factorial growth of basis with & A adaptive importance truncation extends the range of NCSM by reducing the model space to physically relevant states

Importance Truncated NCSM Roth, PRC 79, 6434 (9); PRL 99, 951 (7) converged NCSM calculations essentially restricted to lower/mid p-shell full =1 calculation for 16 O very difficult (basis dimension>1 1 ) Importance Truncation reduce model space to the relevant basis states using an a priori importance measure derived from MBPT E [MeV] E [MeV] -11-1 -13-14 -15-11 -1-13 -14-15 16 O NN only α=4fm 4 hω=mev 4 6 8 11141618 IT-NCSM + full NCSM 4 6 8 11141618

4 He: Ground-State Energies Roth, et al; PRL 17, 751 (11) NN only NN+3N ind NN+3N full -3-4 hω=mev E [MeV] -5-6 -7-8 -9 4 6 8 1 1 14 16 Exp 4 6 8 1 1 14 4 6 8 1 1 14 α=4fm 4 α=5fm 4 α=65fm 4 α=8fm 4 α=16fm 4 Λ=4fm 1 Λ=11fm 1 Λ=fm 1 Λ=188fm 1 Λ=158fm 1

16 O: Ground-State Energies Roth, et al; PRL 17, 751 (11) -8 NN only NN+3N ind NN+3N full hω=mev -1 E [MeV] -1-14 Exp -16-18 4 6 8 1 1 14 4 6 8 1 1 4 6 8 1 1 α=4fm 4 α=5fm 4 α=65fm 4 α=8fm 4 α=16fm 4 Λ=4fm 1 Λ=11fm 1 Λ=fm 1 Λ=188fm 1 Λ=158fm 1

16 O: Ground-State Energies Roth, et al; PRL 17, 751 (11) -8 NN only NN+3N ind NN+3N full hω=mev -1 E [MeV] -1-14 Exp -16-18 4 6 8 1 1 14 in progress: explicit inclusion of induced 4N 4 6 8 1 1 clear signature of induced 4N originating from initial 3N 4 6 8 1 1 α=4fm 4 α=5fm 4 α=65fm 4 α=8fm 4 α=16fm 4 Λ=4fm 1 Λ=11fm 1 Λ=fm 1 Λ=188fm 1 Λ=158fm 1

16 O: Lowering the Initial 3N Cutoff standard reduced 3N cutoff (c E refit to 4 He binding energy) 5 MeV 45 MeV 4 MeV 35 MeV -11-115 c D = c E = 5 c D = c E = 16 c D = c E =98 c D = c E =5-1 -15 E [MeV] -13-135 -14-145 NN+3N full hω=mev -15 4 6 8 11141618 4 6 8 11141618 4 6 8 11141618 4 6 8 11141618 α=4fm 4 α=5fm 4 α=65fm 4 α=8fm 4 Λ=4fm 1 Λ=11fm 1 Λ=fm 1 Λ=188fm 1

16 O: Lowering the Initial 3N Cutoff standard reduced 3N cutoff (c E refit to 4 He binding energy) 5 MeV 45 MeV 4 MeV 35 MeV -11-115 c D = c E = 5 c D = c E = 16 c D = c E =98 c D = c E =5-1 -15 E [MeV] -13-135 -14-145 -15 4 6 8 11141618 4 6 8 11141618 4 6 8 11141618 α=4fm 4 α=5fm 4 α=65fm 4 α=8fm 4 Λ=4fm 1 Λ=11fm 1 Λ=fm 1 Λ=188fm 1 NN+3N full hω=mev lowering the initial 3N cutoff N suppresses induced m x 4 6 8 11141618 4N terms

Ground States of Oxygen Isotopes oxygen isotopic chain has received significant attention and documents the rapid progress over the past years Otsuka, Suzuki, Holt, Schwenk, Akaishi, PRL 15, 351 (1) 1: shell-model calculations with 3N effects highlighting the role of 3N interaction for drip line physics Hagen, Hjorth-Jensen, Jansen, Machleidt, Papenbrock, PRL 18, 451 (1) 1: coupled-cluster calculations with phenomenological two-body correction simulating chiral 3N forces Hergert, Binder, Calci, Langhammer, Roth, PRL 11, 451 (13) 13: ab initio IT-NCSM with explicit chiral 3N interactions

Ground States of Oxygen Isotopes Hergert et al, PRL 11, 451 (13) -4 NN+3N ind (chiral NN) 1 O NN+3N full (chiral NN+3N) 1 O -6 E [MeV] -8-1 -1-14 -16 4 6 8 1 1 14 16 18 14 O 16 O 18 O O O 4 O 6 O 4 6 8 1 1 14 16 18 14 O 16 O 18 O O O 6 O 4 O Λ 3N =4 MeV, α=8fm 4, E 3m x =14, optimal hω

Ground States of Oxygen Isotopes Hergert et al, PRL 11, 451 (13) E [MeV] -4-6 -8-1 -1-14 -16 NN+3N ind (chiral NN) A O NN+3N full (chiral NN+3N) experiment IT-NCSM -18 1 14 16 18 4 6 A 1 14 16 18 4 6 A Λ 3N =4 MeV, α=8fm 4, E 3m x =14, optimal hω

Ground States of Oxygen Isotopes Hergert et al, PRL 11, 451 (13) E [MeV] -4-6 -8-1 -1-14 NN+3N ind (chiral NN) A O NN+3N full (chiral NN+3N) experiment IT-NCSM -16 parameter-free ab initio calculations with -18 1 full14 3N interactions 16 18 4 6 1 14 16 18 4 6 A highlights predictive powera of chiral NN+3N Hamiltonians Λ 3N =4 MeV, α=8fm 4, E 3m x =14, optimal hω

Spectroscopy of Carbon Isotopes Forssen et al, JPG 4, 5515 (13);Roth et al, in prep E [MeV] 8 6 4 1 C 1 1 16 14 1 1 8 6 4 1 C 1 1 1 4 1 1 8 6 4 14 C 1 1 4 1 1 1 1 1 4 6 8 Exp 1 4 6 8 Exp 4 6 8 Exp 1 E [MeV] 4 3 3? 4 4 3 3 3 4 3 NN+3N full Λ 3N =4MeV α=8fm 4 hω=16mev 4 1 16 C 1 18 C 1 C 4 6 Exp 4 6 Exp 3 4 6 Exp 4

Spectroscopy of Carbon Isotopes B(E, + + ) [e fm 4 ] B(E, + + ) [e fm 4 ] 8 7 6 5 4 3 1 3 5 15 1 5 1 C 4 6 8 16 C 4 6 8 7 6 5 4 3 1 3 1 C 4 6 8 IN PROGRESS 5 15 1 5 B(E, + 1 + gs ) B(E, + + gs ) 18 C 4 6 8 7 6 5 4 3 1 5 4 3 1 14 C 4 6 8 C NN+3N full Λ 3N =4MeV α=8fm 4 hω=16mev 4 6

Spectroscopy of Carbon Isotopes 8 7 6 5 4 IN PROGRESS 3 1 B(E, + + ) [e fm 4 ] 3 5 15 1 5 1 C 4 6 8 16 C 8 7 6 5 4 3 1 3 5 15 1 5 1 C B(E, + 1 + gs ) B(E, + + gs ) 4 6 8 18 C 8 7 6 5 4 3 1 5 4 3 1 14 C 4 6 8 C NN+3N full NEW EXPERIMENT NSCL, Petri et al NEW EXPERIMENT ANL, McCutchan et al NEW EXPERIMENT NSCL, Voss et al NEW EXPERIMENT NSCL, Petri et al Λ 3N =4MeV α=8fm 4 hω=16mev B(E, + + ) [e fm 4 ] 4 6 4 6 4 6 Nm x Nm x Nm x

Ab Initio Nuclear Structure Nuclear Structure Observables Lattice QCD quarks & gluon on a lattice Lattice EFT nucleons & pions on a lattice Exact Solutions solve nuclear manybody problem with converged truncations Controlled Approx treat many-body problem with controlled & improvable approximations Similarity Transformations physics-conserving unitary transformation to adapt Hamiltonian to limited model space Chiral EFT Hamiltonians consistent NN,3N, interactions & current operators Chiral Effective Field Theory based on relevant degrees of freedom & symmetries of QCD Energy-Density Funct guided by chiral EFT Low-Energy Quantum Chromodynamics

Frontier: Medium-Mass Nuclei advent of novel ab initio many-body approaches applicable in the medium-mass regime Hagen, Papenbrock, Dean, Piecuch, Binder, coupled-cluster theory: ground-state parametrized by exponential wave operator applied to single-determinant reference state truncation at doubles level (CCSD) plus triples corrections (Λ-CCSD(T)) equations of motion for excited states and near-closed-shell nuclei Bogner, Tsukiyama, Schwenk, Hergert, in-medium SRG: complete decoupling of particle-hole excitations from many-body reference state through SRG evolution normal-ordered evolving A-body Hamiltonian truncated at two-body level both closed- and open-shell ground states; excitations via EOM or SM self-consistent Green s function approaches and others Barbieri, Soma, Duguet,

Frontier: Medium-Mass Nuclei advent of novel ab initio many-body approaches applicable in the medium-mass regime Hagen, Papenbrock, Dean, Piecuch, Binder, coupled-cluster theory: ground-state parametrized by exponential wave operator applied to single-determinant reference state truncation at doubles level (CCSD) plus triples corrections (Λ-CCSD(T)) equations of motion for excited states and near-closed-shell nuclei Bogner, Tsukiyama, Schwenk, Hergert, in-medium SRG: complete decoupling of particle-hole excitations from many-body reference state through SRG evolution controllingandquantifyingthe uncertaintiesduetovarioustruncationsis majorchallenge normal-ordered evolving A-body Hamiltonian truncated at two-body level both closed- and open-shell ground states; excitations via EOM or SM self-consistent Green s function approaches and others Barbieri, Soma, Duguet,

Ground States of Oxygen Isotopes Hergert et al, PRL 11, 451 (13) E [MeV] -4-6 -8-1 -1-14 -16 NN+3N ind (chiral NN) A O NN+3N full (chiral NN+3N) experiment IT-NCSM MR-IM-SRG -18 1 14 16 18 4 6 A 1 14 16 18 4 6 A Λ 3N =4 MeV, α=8fm 4, E 3m x =14, optimal hω

Ground States of Oxygen Isotopes Hergert et al, PRL 11, 451 (13) E [MeV] -4-6 -8-1 -1-14 -16 NN+3N ind (chiral NN) A O NN+3N full (chiral NN+3N) experiment IT-NCSM MR-IM-SRG CCSD Λ-CCSD(T) -18 1 14 16 18 4 6 A 1 14 16 18 4 6 A Λ 3N =4 MeV, α=8fm 4, E 3m x =14, optimal hω

Ground States of Oxygen Isotopes Hergert et al, PRL 11, 451 (13) E [MeV] -4-6 -8-1 -1-14 NN+3N ind (chiral NN) A O NN+3N full (chiral NN+3N) experiment IT-NCSM MR-IM-SRG CCSD Λ-CCSD(T) -16 different many-body approaches using same -18 NN+3N Hamiltonian give 1 14 16 18 4 6 1 14 16 18 4 6 consistent results minor differences are consistent with uncertaintya A analysis Λ 3N =4 MeV, α=8fm 4, E 3m x =14, optimal hω

Towards Heavy Nuclei - Ab Initio? Roth, et al, PRL 19, 551 (1); Binder et al, PRC 87, 133(R)(13); PRC 88, 54319 (13); arxiv:1315685 (13) calculations for medium-mass and heavy nuclei are computationally feasible with CC or IM-SRG however, many of the technical truncations that are good in light nuclei fail for heavier systems we analysed and improved all of these truncations % residual uncertainty of the many-body approach for A 13

Towards Heavy Nuclei - Ab Initio! Binder et al, arxiv:1315685 (13) -6-7 CR-CC(,3) NN+3N ind (chiral NN) NN+3N full (chiral NN+3N) E/A [MeV] -8-9 -1 δe T /A 5-5 16 O 36 Ca 48 Ca 54 Ca 56 Ni 6 Ni 68 Ni 88 Sr 1 Sn 18 Sn 116 Sn 1 Sn 4 O 4 Ca 5 Ca 48 Ni 6 Ni 66 Ni 78 Ni 9 Zr 16 Sn 114 Sn 118 Sn 13 Sn Λ 3N =4 MeV, α=8 4fm 4, E 3m x =18, optimal hω

Ab Initio Nuclear Structure Nuclear Structure Observables Lattice QCD quarks & gluon on a lattice Lattice EFT nucleons & pions on a lattice Exact Solutions solve nuclear manybody problem with converged truncations Controlled Approx treat many-body problem with controlled & improvable approximations Similarity Transformations physics-conserving unitary transformation to adapt Hamiltonian to limited model space Chiral EFT Hamiltonians consistent NN,3N, interactions & current operators Chiral Effective Field Theory based on relevant degrees of freedom & symmetries of QCD Energy-Density Funct guided by chiral EFT Low-Energy Quantum Chromodynamics

Ab Initio Hyper-Nuclear Structure Hyper-Nuclear Structure Observables Lattice QCD quarks & gluon on a lattice Lattice EFT nucleons & pions on a lattice Exact Solutions solve nuclear manybody problem with converged truncations Controlled Approx treat many-body problem with controlled & improvable approximations Similarity Transformations physics-conserving unitary transformation to adapt Hamiltonian to limited model space Chiral EFT Hamiltonians consistent NN,3N,YN,YY, interactions & current operators Chiral Effective Field Theory based on relevant degrees of freedom & symmetries of QCD Energy-Density Funct guided by chiral EFT Low-Energy Quantum Chromodynamics

Ab Initio Hyper-Nuclear Structure precise data on ground states & spectroscopy of hyper-nuclei ab initio few-body (A 4) and phenomenological shell model or cluster calculations chiral YN & YY interactions at (N)LO are available constrain YN & YY interaction by ab initio hyper-nuclear structure calculations

Application: Λ7 Li - -5 6 Li 7 Λ Li NN @ N3LO Λ NN =5 MeV Entem&Machleidt E[MeV] -3 3 1 3N @ NLO Λ 3N =5 MeV Navratil A=3 fit -35 7 5 Jülich 4 3 1 Haidenbauer et al scatt & hypertriton E [MeV] -4 3 1-1 4 6 8 1 1 Exp 3 1 4 6 8 1 1 Exp 7 5 3 1 α NN =8fm 4 α YN =fm 4 hω= MeV

Application: Λ7 Li - -5 6 Li 7 Λ Li NN @ N3LO Λ NN =5 MeV Entem&Machleidt E[MeV] -3 3 1 3N @ NLO Λ 3N =5 MeV Navratil A=3 fit E [MeV] -35-4 3 1-1 4 6 8 1 1 Exp 3 1 4 6 8 1 1 Exp 7 5 3 1 7 5 3 1 YN @ LO Λ YN =6 MeV Haidenbauer et al scatt & hypertriton α NN =8fm 4 α YN =fm 4 hω= MeV

Application: Λ7 Li - -5 6 Li 7 Λ Li NN @ N3LO Λ NN =5 MeV Entem&Machleidt E[MeV] -3 3 1 3N @ NLO Λ 3N =5 MeV Navratil A=3 fit E [MeV] -35-4 3 1-1 4 6 8 1 1 Exp 3 1 4 6 8 1 1 Exp 7 5 3 1 7 5 3 1 YN @ LO Λ YN =7 MeV Haidenbauer et al scatt & hypertriton α NN =8fm 4 α YN =fm 4 hω= MeV

Application: Λ9 Be -4-45 8 Be 9 Λ Be NN @ N3LO Λ NN =5 MeV Entem&Machleidt E[MeV] E [MeV] -5-55 -6-654 3 1 3 5 1 3 5 3N @ NLO Λ 3N =5 MeV Navratil A=3 fit YN @ LO Λ YN =6 MeV Haidenbauer et al scatt & hypertriton α NN =8fm 4 α YN =fm 4 hω= MeV 4 6 8 1 Exp 4 6 8 1 Exp 1

Application: Λ 13 C -75-8 -85 1 C 13 Λ C NN @ N3LO Λ NN =5 MeV Entem&Machleidt E[MeV] -9-95 -1 3 3N @ NLO Λ 3N =5 MeV Navratil A=3 fit -15 1 YN @ LO Λ YN =6 MeV -11 6 E [MeV] 4 3 Haidenbauer et al scatt & hypertriton α NN =8fm 4 α YN =fm 4 hω= MeV 4 6 8 1 Exp 4 6 8 1 Exp 1

Application: Λ 13 C -75 E[MeV] -8-85 -9-95 -1-15 -11 6 E [MeV] 4 1 C 13 Λ C 4 6 8 1 Exp hyper-nuclear structure sets tight constraints on YN interaction ready to explore physics of p-shell hyper-nuclei 4 6 8 1 Exp 3 1 3 1 NN @ N3LO Λ NN =5 MeV Entem&Machleidt 3N @ NLO Λ 3N =5 MeV Navratil A=3 fit YN @ LO Λ YN =6 MeV Haidenbauer et al scatt & hypertriton α NN =8fm 4 α YN =fm 4 hω= MeV

Frontiers ab initio theory is entering new territory QCD frontier nuclear structure connected systematically to QCD via chiral EFT precision frontier precision spectroscopy of light nuclei, including current contribution mass frontier ab initio calculations up to heavy nuclei with quantified uncertainties open-shell frontier extend to medium-mass open-shell nuclei and their excitation spectrum continuum frontier include continuum effects and scattering observables consistently strangeness frontier ab initio predictions for hyper-nuclear structure & spectroscopy providing a coherent theoretical framework for nuclear structure & reaction calculations

Epilogue thanks to my group & my collaborators S Binder, J Braun, A Calci, S Fischer, E Gebrerufael, H Spiess, J Langhammer, S Schulz, C Stumpf, A Tichai, R Trippel, R Wirth, K Vobig Institut für Kernphysik, TU Darmstadt P Navrátil TRIUMF Vancouver, Canada J Vary, P Maris Iowa State University, USA S Quaglioni, G Hupin LLNL Livermore, USA P Piecuch Michigan State University, USA H Hergert Ohio State University, USA P Papakonstantinou IBS/RISP, Korea C Forssén Chalmers University, Sweden H Feldmeier,T Neff GSI Helmholtzzentrum JUROPA LOEWE-CSC HOPPER COMPUTING TIME