Weak reactions with light nuclei
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1 Weak reactions with light nuclei Nir Barnea, Sergey Vaintraub The Hebrew University Doron Gazit INT, University of Washington Eilat, November 9-14, 2008 Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
2 Motivation PP The energy production in the sun is dominated by the pp-chain pp d + e + + ν e. k P f k q = k k q = ( ω, q) P 0 Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
3 Motivation PP The energy production in the sun is dominated by the pp-chain pp d + e + + ν e. Hep The Hep process produce the highest energy solar neutrinos through the reaction, 3 He + p 4 He + e + + ν e. k P f k q = k k q = ( ω, q) P 0 Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
4 Motivation k P f PP The energy production in the sun is dominated by the pp-chain pp d + e + + ν e. Hep The Hep process produce the highest energy solar neutrinos through the reaction, 3 He + p 4 He + e + + ν e. SNII SN type II - Energy transfer to the matter behind the accrection shock through inelastic reactions (Haxston 1988). k q = k k q = ( ω, q) P 0 Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
5 Motivation PP The energy production in the sun is dominated by the pp-chain pp d + e + + ν e. Hep The Hep process produce the highest energy solar neutrinos through the reaction, 3 He + p 4 He + e + + ν e. k k q = k k q = ( ω, q) P f P 0 SNII SN type II - Energy transfer to the matter behind the accrection shock through inelastic reactions (Haxston 1988). NS The 7 Li, 11 B nucleosynthesis reaction chains are dominated by the neutrino flux (Woosely et al. 1990). 4 He(ν, ν p) 3 H(α, γ) 7 Li(α, γ) 11 B 4 He(ν, ν n) 3 He(α, γ) 7 Be(e, ν e) 7 Li 12 C(ν, ν p) 11 B Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
6 Motivation PP The energy production in the sun is dominated by the pp-chain pp d + e + + ν e. Hep The Hep process produce the highest energy solar neutrinos through the reaction, 3 He + p 4 He + e + + ν e. k k q = k k q = ( ω, q) P f P 0 SNII SN type II - Energy transfer to the matter behind the accrection shock through inelastic reactions (Haxston 1988). NS The 7 Li, 11 B nucleosynthesis reaction chains are dominated by the neutrino flux (Woosely et al. 1990). 4 He(ν, ν p) 3 H(α, γ) 7 Li(α, γ) 11 B 4 He(ν, ν n) 3 He(α, γ) 7 Be(e, ν e) 7 Li 12 C(ν, ν p) 11 B J A The nuclear weak current. Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
7 Weak interaction with Nuclei The weak Hamiltonian H W = G 2 Z dxj (x)j (x) k P f k q = k k q = ( ω, q) P 0 Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
8 Weak interaction with Nuclei The weak Hamiltonian H W = G 2 Z dxj (x)j (x) k P f The leptonic current P 0 f j (x) i = l e iq x q = ( ω, q) k q = k k Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
9 Weak interaction with Nuclei The weak Hamiltonian H W = G 2 Z dxj (x)j (x) k P f The leptonic current f j (x) i = l e iq x k q = k k q = ( ω, q) P 0 The nuclear current J 0 = (1 2 sin 2 θ W ) τ0 2 J V + τ0 2 J A 2 sin 2 1 θ W 2 J V J ± = τ± 2 J V + τ± 2 J A Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
10 The Nuclear Current The currents are derived from EFT NLO Chiral Lagrangian and are accurate to N 3 LO. Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
11 The Nuclear Current The currents are derived from EFT NLO Chiral Lagrangian and are accurate to N 3 LO. The resulting currents contain the standard 1 body currents and the EFT derived 2 body current, J V,A = J V,A (1body) + J V,A (2body) Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
12 The Nuclear Current The currents are derived from EFT NLO Chiral Lagrangian and are accurate to N 3 LO. The resulting currents contain the standard 1 body currents and the EFT derived 2 body current, J V,A = J V,A (1body) + J V,A (2body) Charge conservation. The vector current must fulfill J V (x) = i[h, J V 0 (x)] Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
13 The Nuclear Current The currents are derived from EFT NLO Chiral Lagrangian and are accurate to N 3 LO. The resulting currents contain the standard 1 body currents and the EFT derived 2 body current, J V,A = J V,A (1body) + J V,A (2body) Charge conservation. The vector current must fulfill J V (x) = i[h, J V 0 (x)] The nuclear vector current contains convection and spin terms J(q) = J c(q) + J s(q). At low q J s(q) is suppressed. Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
14 The Nuclear Current The currents are derived from EFT NLO Chiral Lagrangian and are accurate to N 3 LO. The resulting currents contain the standard 1 body currents and the EFT derived 2 body current, J V,A = J V,A (1body) + J V,A (2body) Charge conservation. The vector current must fulfill J V (x) = i[h, J V 0 (x)] The nuclear vector current contains convection and spin terms J(q) = J c(q) + J s(q). At low q J s(q) is suppressed. At low energy, the vector current MEC are implicitly included via the Siegert theorem. Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
15 The Nuclear Current The currents are derived from EFT NLO Chiral Lagrangian and are accurate to N 3 LO. The resulting currents contain the standard 1 body currents and the EFT derived 2 body current, J V,A = J V,A (1body) + J V,A (2body) Charge conservation. The vector current must fulfill J V (x) = i[h, J V 0 (x)] The nuclear vector current contains convection and spin terms J(q) = J c(q) + J s(q). At low q J s(q) is suppressed. At low energy, the vector current MEC are implicitly included via the Siegert theorem. Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
16 The Nuclear Current The currents are derived from EFT NLO Chiral Lagrangian and are accurate to N 3 LO. The resulting currents contain the standard 1 body currents and the EFT derived 2 body current, J V,A = J V,A (1body) + J V,A (2body) Charge conservation. The vector current must fulfill J V (x) = i[h, J V 0 (x)] The nuclear vector current contains convection and spin terms J(q) = J c(q) + J s(q). At low q J s(q) is suppressed. At low energy, the vector current MEC are implicitly included via the Siegert theorem. Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
17 The Nuclear Current For the axial current the MEC must be included explicitly. Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
18 The Nuclear Current For the axial current the MEC must be included explicitly. At leading order the axial MEC contains two terms with one free parameter. Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
19 The Nuclear Current For the axial current the MEC must be included explicitly. At leading order the axial MEC contains two terms with one free parameter. a A one-pion exchange term. Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
20 The Nuclear Current For the axial current the MEC must be included explicitly. At leading order the axial MEC contains two terms with one free parameter. a A one-pion exchange term. b Renormalization, or contact, term. Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
21 The Nuclear Current For the axial current the MEC must be included explicitly. At leading order the axial MEC contains two terms with one free parameter. a A one-pion exchange term. b Renormalization, or contact, term. The MEC are fixed by the triton half-life. Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
22 The Nuclear Current For the axial current the MEC must be included explicitly. At leading order the axial MEC contains two terms with one free parameter. a A one-pion exchange term. b Renormalization, or contact, term. The MEC are fixed by the triton half-life. The renormalization coefficient depends on the cutoff. Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
23 The Nuclear Current For the axial current the MEC must be included explicitly. At leading order the axial MEC contains two terms with one free parameter. a A one-pion exchange term. b Renormalization, or contact, term. The MEC are fixed by the triton half-life. The renormalization coefficient depends on the cutoff. Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
24 The Nuclear Current For the axial current the MEC must be included explicitly. At leading order the axial MEC contains two terms with one free parameter. a A one-pion exchange term. b Renormalization, or contact, term. The MEC are fixed by the triton half-life. The renormalization coefficient depends on the cutoff. Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
25 the long wavelength q 0 limit For low momentum transfer qr ωa 1/3 1. The multipole expansion converge very fast. Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
26 the long wavelength q 0 limit For low momentum transfer qr ωa 1/3 1. The multipole expansion converge very fast. At q = 0 the leading operators are the Fermi and Gamow-Teller F = 1 4π τ ± r 2 GT = i g A [σ Y0(ˆr)](1) M 3 τ± Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
27 the long wavelength q 0 limit For low momentum transfer qr ωa 1/3 1. The multipole expansion converge very fast. At q = 0 the leading operators are the Fermi and Gamow-Teller F = 1 4π τ ± r 2 GT = i g A [σ Y0(ˆr)](1) M 3 τ± The 2 body currents contribute mainly to the GT, E1 A multipole. Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
28 the long wavelength q 0 limit For low momentum transfer qr ωa 1/3 1. The multipole expansion converge very fast. The sub-leading operators, At q = 0 the leading operators are the Fermi and Gamow-Teller F = 1 4π τ ± r 2 GT = i g A [σ Y0(ˆr)](1) M 3 τ± The 2 body currents contribute mainly to the GT, E1 A multipole. C A 0 (q) = i 4π σ L A 0 (q) = ig qr A [σ Y 1 ( ˆr)] (0) 3 C 1M V (q) = qr Y 1M ( ˆr) 3 E V 1M (q) = 2 ω q C V 1M (q) L V 1M (q) = ω q C V 1M (q) M1M V (q) = i q l M 6π 2M N M1M A (q) = g qr A [σ Y 1 ( ˆr)] (1) 3 M s E2M A 3 (q) = i q g A [σ Y 1 ( ˆr)] (2) 5 3 M L A 2M (q) = s 2 3 E A 2M (q) Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
29 The JISP16 NN Potential The JISP16 reproduce the NN phase shifts in the range 0 300MeV. Binding Energies AV18+UBIX JISP16 Nature D H He He He Li AV18+UBIX - Argonne V18 + Urbana IX JISP16 - J-matrix Inverse Scattering Potential, Shirokov et al. Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
30 The JISP16 NN Potential The JISP16 reproduce the NN phase shifts in the range 0 300MeV He 6 Li Binding Energies AV18+UBIX JISP16 Nature D H He He He Li E [MeV] K max AV18+UBIX - Argonne V18 + Urbana IX JISP16 - J-matrix Inverse Scattering Potential, Shirokov et al. Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
31 Beta decay The β-decay half-life X t 1/2 = 1 GT Ψ τlog2 f σ jτ + j Ψ i f F 2 + (F A/F V ) 2 GT 2 j F Ψ f X τ + j Ψ i j Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
32 Beta decay The β-decay half-life X t 1/2 = 1 GT Ψ τlog2 f σ jτ + j Ψ i f F 2 + (F A/F V ) 2 GT 2 j F Ψ f X τ + j Ψ i j 3 H - 3 He Potential GT AV18+3NF (1) Bonn+3NF (1) JISP16 [This work] (4) Expt (3) Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
33 Beta decay The β-decay half-life X t 1/2 = 1 GT Ψ τlog2 f σ jτ + j Ψ i f F 2 + (F A/F V ) 2 GT 2 j F Ψ f X τ + j Ψ i j 3 H - 3 He Potential GT AV18+3NF (1) Bonn+3NF (1) JISP16 [This work] (4) Expt (3) 6 He - 6 Li Potential GT AV18/UIX - VMC 2.250(7) AV18/IL2 - VMC 2.22(2) AV18/IL2 - GFMC 2.182(25) AV8/TM - NCSM 2.283(2) JISP16 - [This work] 2.229(3) Expt (3) Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
34 Beta decay The β-decay half-life X t 1/2 = 1 GT Ψ τlog2 f σ jτ + j Ψ i f F 2 + (F A/F V ) 2 GT 2 j F Ψ f X τ + j Ψ i j 3 H - 3 He Potential GT AV18+3NF (1) Bonn+3NF (1) JISP16 [This work] (4) Expt (3) 6 He - 6 Li Potential GT AV18/UIX - VMC 2.250(7) AV18/IL2 - VMC 2.22(2) AV18/IL2 - GFMC 2.182(25) AV8/TM - NCSM 2.283(2) JISP16 - [This work] 2.229(3) Expt (3) 1-body currents underpredict the 3-body GT, and overpredict the 6-body GT. Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
35 Beta decay - 2-body current The Gamow-Teller 6 He - 6 Li matrix element Potential 1-body 2-body AV18/UIX - VMC 2.250(7) 2.281(7) JISP16 [This work] 2.229(3) 2.193(2) Expt (3) Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
36 Beta decay - 2-body current The Gamow-Teller 6 He - 6 Li matrix element Potential 1-body 2-body AV18/UIX - VMC 2.250(7) 2.281(7) JISP16 [This work] 2.229(3) 2.193(2) Expt (3) The VMC calculation with MEC made things even worse for 6 He! Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
37 Beta decay - 2-body current The Gamow-Teller 6 He - 6 Li matrix element Potential 1-body 2-body AV18/UIX - VMC 2.250(7) 2.281(7) JISP16 [This work] 2.229(3) 2.193(2) Expt (3) The VMC calculation with MEC made things even worse for 6 He! HH calculations with EFT 2-body currents reconcile theory and experiment! Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
38 Beta decay - 2-body current The Gamow-Teller 6 He - 6 Li matrix element Potential 1-body 2-body AV18/UIX - VMC 2.250(7) 2.281(7) JISP16 [This work] 2.229(3) 2.193(2) Expt (3) 3 The VMC calculation with MEC made things even worse for 6 He! HH calculations with EFT 2-body currents reconcile theory and experiment! The matrix-element is almost independent of the cutoff! Renorm Coef. GT Cutoff [MeV] Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
39 Conclusions 1 The 1-body current underpredict the 3 H β-decay GT. Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
40 Conclusions 1 The 1-body current underpredict the 3 H β-decay GT. 2 It overpredict the 6 He β-decay GT. Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
41 Conclusions 1 The 1-body current underpredict the 3 H β-decay GT. 2 It overpredict the 6 He β-decay GT. 3 2-body currents derived from meson exchange model go in the wrong direction for 6 He! Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
42 Conclusions 1 The 1-body current underpredict the 3 H β-decay GT. 2 It overpredict the 6 He β-decay GT. 3 2-body currents derived from meson exchange model go in the wrong direction for 6 He! 4 In contrast, EFT 2-body currents lead to reconciliation between thoery and experiment. Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
43 Conclusions 1 The 1-body current underpredict the 3 H β-decay GT. 2 It overpredict the 6 He β-decay GT. 3 2-body currents derived from meson exchange model go in the wrong direction for 6 He! 4 In contrast, EFT 2-body currents lead to reconciliation between thoery and experiment. 5 The predicted 6 He β-decay half life is independent of the cutoff. Nir Barnea (HUJI) Weak reactions with light nuclei PANIC / 11
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