Towards Ab Initio Calculations of Double-Beta Decay Nuclear Matrix Elements Jason D. Holt R. Stroberg A. Schwenk S. Bogner H. Hergert J. Engel M. Horoi Advances in Ab Initio Nuclear Structure for Medium-Mass Exotic Nuclei Exploring the frontiers of nuclear science: Worldwide joint experimental/theoretical effort What are the properties of proton/neutron-rich matter? What are the limits of nuclear existence? 82! How do magic numbers form and evolve? Advances in many-body methods Coupled Cluster In-Medium SRG Many-Body Perturbation Theory 82! Self-Consistent Green’s Function protons 28! 20! 50! 3N forces essential for exotic nuclei 8! 28! π π π 2! 20! 2! 8! neutrons € € € Advances in Ab Initio Nuclear Structure for Medium-Mass Exotic Nuclei Exploring the frontiers of nuclear science: Worldwide joint experimental/theoretical effort What are the properties of proton/neutron-rich matter? What are the limits of nuclear existence? 82! How do magic numbers form and evolve? Advances in many-body methods Coupled Cluster In-Medium SRG Many-Body Perturbation Theory 82! Self-Consistent Green’s Function protons 28! 20! 50! 3N forces essential for exotic nuclei 8! 28! π π π 2! 20! 2! 8! neutrons € € € Improved 0νββ-Decay Calculations in Shell Model Standard SM approach: phenomenological wavefunctions + bare operator Avenue towards ab initio shell-model calculations: Consistent operators and wfs from chiral forces and currents 0⌫ 0⌫ 0⌫ MF 0⌫ M = MGT 2 + MT − gA M 0⌫ = f H(r )σ σ ⌧ +⌧ + i GT h | ab a · b a b | i Xab 1) Wavefunctions currently phenomenological; calculate ab initio IM-SRG, CC, MBPT… Part II Improved 0νββ-Decay Calculations in Shell Model Standard SM approach: phenomenological wavefunctions + bare operator Avenue towards ab initio shell-model calculations: Consistent operators and wfs from chiral forces and currents 0⌫ 0⌫ 0⌫ MF 0⌫ M = MGT 2 + MT − gA M 0⌫ = f H(r )σ σ ⌧ +⌧ + i GT h | abMeffa · b a b | i Xab 1) Wavefunctions currently phenomenological; calculate ab initio 2) Effective decay operator: correlations outside valence space MBPT… Part I Improved 0νββ-Decay Calculations in Shell Model Standard SM approach: phenomenological wavefunctions + bare operator Avenue towards ab initio shell-model calculations: Consistent operators and wfs from chiral forces and currents 0⌫ 0⌫ 0⌫ MF 0⌫ M = MGT 2 + MT − gA M 0⌫ = f H(r )σ σ ⌧ +⌧ + i GT h | ab a · b a b | i Xab 1) Wavefunctions currently phenomenological; calculate ab initio 2) Effective decay operator: correlations outside valence space 3) Operator corrections: two-body currents See talks of Menéndez, Gazit, Schwenk Calculations of Effective Operators (MBPT) Towards ab initio electroweak physics Calculation of nuclear wavefunctions ✔ Consistent calculation of effective EW operators ? M1, E2, GT, 0νββ decay… 82! References 126! • Lincoln, JDH et al., PRL 110, 012501 (2013) [LEBIT] • JDH and Engel, PRC 87, 064315 (2013) • Kwiatkowski, Brunner, JDH et al.,50! PRC 89, 045502 (2014) [TITAN] 82! protons 28! Key physics problems 20! 50! Impact on NME in 48Ca, 76Ge, 82Se 8! 28! 2! 20! 2! 8! neutrons Effective 0νββ-Decay Operator c c c ccStandardd approach:c c V phenomenologicald c c d wavefunctions + bare operator d Vlow-k d d d Vlow-klow-k d d ˆ = CalculateˆQˆ = =consistent... effective+ 0νββ+...-decay... operator using MBPT Q + Q + + + a b a b a aaDiagrammaticallybbb a a similar:bb a a replacebb one interaction vertex with M0ν operator c d c d c cc Vlow-kddd c cc ddd c d c d c d + + Qˆ ++= +++ + ... Xˆ = M + Veff V Meff low k V a b a b a aa bbb a aa bbb a b a b a low k b c d c d c c c ddd c cc ddd c d c d c d € V low k ... € + + +++ ... +++ ++... + + + a a a aa b b a aa bb b b b b € a b a b a b c c d d c d c d + + + ... + + + ... a b a b a b a b Effective 0νββ-Decay Operator c c c ccStandardd approach:c c V phenomenologicald c c d wavefunctions + bare operator d Vlow-k d d d Vlow-klow-k d d ˆ = CalculateˆQˆ = =consistent... effective+ 0νββ+...-decay... operator using MBPT Q + Q + + + a b a b a aaDiagrammaticallybbb a a similar:bb a a replacebb one interaction vertex with M0ν operator c d c d c cc Vlow-kddd c cc ddd c d c d c d + + Qˆ ++= +++ + ... Xˆ = M + Veff V Meff low k V a b a b a aa bbb a aa bbb a b a b a low k b c d c d c c c ddd c cc ddd c d c d c d € V low k ... € + + +++ ... +++ ++... + + + a a a aa b b a aa bb b b b b € a b a b a b c d c d Previous: G-matrix calculation to c d c d + + + ... 1st-order MBPT non-convergent + + + ... Engela band Hagena, PRC (2009)b a b a b Low-momentum interactions: Improve convergence behavior? Effective 0νββ-Decay Operator Calculate in MBPT: 1st order (× 2) 2nd order (×3) 48 76 82 Calculations of M0ν in Ca, Ge, and Se Phenomenological wavefunctions from A. Poves, M. Horoi 48Ca Bare 0.77 76Ge Bare 3.12 82Se Bare 2.73 Effective 1.30 Effective 3.77 Effective 3.62 Lincoln, JDH et al., PRL (2013) Converged in 13 major oscillator shells JDH and Engel, PRC (2013) No order-by-order convergence in MBPT Kwiatkowski, et al., PRC (2014) Overall ~25-30% increase for 76Ge, 82Se; 75% for 48Ca 48 76 82 Calculations of M0ν in Ca, Ge, and Se Phenomenological wavefunctions from A. Poves, M. Horoi 48Ca Bare 0.77 76Ge Bare 3.12 82Se Bare 2.73 Effective 1.30 Effective 3.77 Effective 3.62 Lincoln, JDH et al., PRL (2013) Converged in 13 major oscillator shells JDH and Engel, PRC (2013) No order-by-order convergence in MBPT Kwiatkowski, et al., PRC (2014) Overall ~25-30% increase for 76Ge, 82Se; 75% for 48Ca Promising first steps – up next… - Consistent wavefunctions and operators in MBPT from chiral NN+3N - Operator corrections: two-body currents from chiral EFT - Nonperturbative methods (IM-SRG) - Effects of induced 3-body operators 48 76 82 Calculations of M0ν in Ca, Ge, and Se Phenomenological wavefunctions from A. Poves, M. Horoi 48Ca Bare 0.77 76Ge Bare 3.12 82Se Bare 2.73 Effective 1.30 Effective 3.77 Effective 3.62 Lincoln, JDH et al., PRL (2013) Converged in 13 major oscillator shells JDH and Engel, PRC (2013) No order-by-order convergence in MBPT Kwiatkowski, et al., PRC (2014) Overall ~25-30% increase for 76Ge, 82Se; 75% for 48Ca Promising first steps – up next… - Consistent wavefunctions and operators in MBPT from chiral NN+3N - Operator corrections: two-body currents from chiral EFT - Nonperturbative methods (IM-SRG) - Effects of induced 3-body operators IM-SRG for Valence-Space Hamiltonians Tsukiyama, Bogner, Schwenk, PRC (2012) In-Medium SRG continuous unitary trans. to decouple off-diagonal physics d od d H(s)=U(s)HU†(s) H (s)+H (s) H ( ) ⌘ ! 1 50 2v 1q1v 2q 3p1h 4p2h 2v 1q1v 2q 3p1h 4p2h 0g 9/2 H 0f5/2 eff 1p1/2 q 1p p 28 3/2 0f7/2 20 0d3/2 1s1/2 v 0d5/2 8 Inert h 0p3/2 core 0p1/2 H(s = 0) H( ) ! 1 Separate p states into valence states (v) and those above valence space (q) Define Hod to decouple valence space from excitations outside v First nonperturbative construction of valence-space Hamitonians: Heff Benchmark in Oxygen with MBPT/CCEI Compare with Coupled-Cluster effective interactions from NN+3N forces 7 9 22 6 23 + 24 O O 1 O + + 1 8 4 + + 6 1 + 5 + 3/2 2 + + + 3/2 + 2 + 7 2 + (4 ) 2 1 4 + + (2 ) + 4 + (3/2 ) 5 + + 2 2 6 + 2 4 3 + + + 4 + 0 (0 ) 3/2 5 0 + + + 3 + + 0 + 3 5/2 5/2 (5/2 ) + 3 + 4 3 5/2 + 3 2 + Energy (MeV) 2 + + 3 2 2 2 2 2 1 1 1 + + + + + + + + + + + + 0 0 0 0 0 0 1/2 1/2 1/2 1/2 0 0 0 0 0 MBPT CCEI IM-SRG Expt. MBPT CCEI IM-SRG Expt. MBPT CCEI IMSRG Expt. Bogner, Hergert, JDH, Schwenk et al., PRL (2014) Hebeler, JDH, Menéndez, Schwenk, ARNPS (2015) Many-Body Perturbation Theory in extended valence space (sdf7/2 p3/2) IM-SRG/CCEI (sd shell) spectra agree within ~300 keV; improved quality Fully Open Shell: Neutron-Rich Fluorine Spectra Fluorine spectroscopy: MBPT and IM-SRG (sd shell) from NN+3N forces + + + 24 3/2+ 4 1 4 25 7/2 4 26 + + 3 + F + + 5 F 1/2+ F 2 (2 ) + 7/2 + 2 1+ + + + + 5/2 3.5 5 2 + + 2 (4 ,2 ) + 9/2 + 5/2 1+ 9/2 + + 4 + (5/2 ) 3 5/2+ 3 + 4 1/2 + + + 3 3 + + 3/2 (3/2 ) 3/2 + 3 3/2 + + + (3 ) + 9/2 + 4 0 + (3/2 ) + + + 0 3+ 4 + + 3 1 2.5 1 4 + + (4 ) (9/2 ) 2 3 + + + 1 3 2 + 2 2 1 + + 1 + 1 + 4 + 3/2 + + 3 1 2 1/2 Energy (MeV) 1.5 + (1/2 ) + + 2 1/2 1 1 + + 2+ 1 2+ + + + 4 + 5/2 4 2 + 2 2 0.5 2 + + 2 4 + + + + + + + + + + + + 0 1 1 1 1 0 3 3 3 3 0 1/2 5/2 (5/2 ) 5/2 CC IM-SRG Expt. USDB MBPT IM-SRG Expt.