improve a reaction calculation

Transcription

1 7Be(p,γ) 8 B: how EFT and Bayesian analysis can improve a reaction calculation Daniel Phillips Work done in collaboration with: K. Nollett (SDSU), X. Zhang (UW) Phys. Rev. C 89, (2014), Phys. Lett. B751, 535 (2015), EPJ Web Conf. 113, (2016), arxiv: Research supported by the US Department of Energy

2 Why is 7 Be + p 8 B + γ important? Adelberger et al., Rev. Mod. Phys. 83, 195 (2011)

3 Why is 7 Be + p 8 B + γ important? Part of pp chain (ppiii) Adelberger et al., Rev. Mod. Phys. 83, 195 (2011)

4 Why is 7 Be + p 8 B + γ important? Part of pp chain (ppiii) Adelberger et al., Rev. Mod. Phys. 83, 195 (2011) Key for predicting flux of solar neutrinos, especially highenergy ( 8 B) neutrinos

5 Why is 7 Be + p 8 B + γ important? Part of pp chain (ppiii) Adelberger et al., Rev. Mod. Phys. 83, 195 (2011) Key for predicting flux of solar neutrinos, especially highenergy ( 8 B) neutrinos Accurate knowledge of 7Be(p,ɣ) needed for inferences from solar-neutrino flux regarding solar composition solar-system formation history

6 This is an extrapolation problem Thermonuclear reaction rate /hv i/ Z 1 0 de exp E k B T E (E)

7 This is an extrapolation problem Thermonuclear reaction rate /hv i/ Z 1 0 de exp E k B T E (E)

8 This is an extrapolation problem Thermonuclear reaction rate /hv i/ Z 1 0 de exp E k B T E (E)

9 This is an extrapolation problem Thermonuclear reaction rate /hv i/ Z 1 0 de exp E k B T E (E)

10 This is an extrapolation problem Thermonuclear reaction rate /hv i/ (E) = S(E) E Z 1 0 exp de exp E k B T Z 1 Z 2 em r mr 2E E (E)

11 This is an extrapolation problem Thermonuclear reaction rate /hv i/ (E) = S(E) E Z 1 0 exp de exp E k B T Z 1 Z 2 em r mr 2E E (E) Gamow peak

12 This is an extrapolation problem Thermonuclear reaction rate /hv i/ (E) = S(E) E Z 1 0 exp de exp E k B T Z 1 Z 2 em r mr 2E E (E) E1 capture: 7 Be + p 8 B + γ Gamow peak Energies of relevance 20 kev

13 Outline 7Be + p 8 B + γ is an important extrapolation problem What parameters govern the extrapolation? What is the standard extrapolation method? A more reliable extrapolant from Halo Effective Field Theory NLO Halo EFT + Bayesian analysis a better extrapolation Summary and future work

14 What matters where? M(E) / Z dra 1 exp( 1r) r ru E (r); 1 =1/(13 fm) Dominated by 7 Be-p separations 10s of fm

15 What matters where? M(E) / Z dra 1 exp( 1r) r ru E (r); 1 =1/(13 fm) ANC Dominated by 7 Be-p separations 10s of fm

16 What matters where? M(E) / Z dra 1 exp( 1r) r ru E (r); 1 =1/(13 fm) ANC Dominated by 7 Be-p separations 10s of fm Numbers that matter: kc=qcqnαemmr=24 MeV; p= 2 mr E; ɣ1= 2 mr B; a: parameterizes strength of p- 7 Be strong scattering

17 What matters where? M(E) / Z dra 1 exp( 1r) r ru E (r); 1 =1/(13 fm) ANC Dominated by 7 Be-p separations 10s of fm Numbers that matter: kc=qcqnαemmr=24 MeV; p= 2 mr E; ɣ1= 2 mr B; a: parameterizes strength of p- 7 Be strong scattering

18 What matters where? M(E) / Z dra 1 exp( 1r) r ru E (r); 1 =1/(13 fm) ANC Extrapolation is not a polynomial: non-analyticities in p/kc, p/ɣ1, and p a Dominated by 7 Be-p separations 10s of fm Numbers that matter: kc=qcqnαemmr=24 MeV; p= 2 mr E; ɣ1= 2 mr B; a: parameterizes strength of p- 7 Be strong scattering

19 What matters where? M(E) / Z dra 1 exp( 1r) r ru E (r); 1 =1/(13 fm) ANC Extrapolation is not a polynomial: non-analyticities in p/kc, p/ɣ1, and p a Dominated by 7 Be-p separations 10s of fm Numbers that matter: kc=qcqnαemmr=24 MeV; p= 2 mr E; ɣ1= 2 mr B; a: parameterizes strength of p- 7 Be strong scattering Bound state (ANC &ɣ1) + Coulomb

20 What matters where? M(E) / Z dra 1 exp( 1r) r ru E (r); 1 =1/(13 fm) ANC Dominated by 7 Be-p separations 10s of fm Numbers that matter: kc=qcqnαemmr=24 MeV; p= 2 mr E; ɣ1= 2 mr B; a: parameterizes strength of p- 7 Be strong scattering Extrapolation is not a Coulomb + nuclear ISI (a) polynomial: non-analyticities + bound state in p/kc, p/ɣ1, and p a Bound state (ANC &ɣ1) + Coulomb

21 What matters where? M(E) / Z dra 1 exp( 1r) r ru E (r); 1 =1/(13 fm) ANC Extrapolation is not a Coulomb + nuclear ISI (a) polynomial: non-analyticities + bound state in p/kc, p/ɣ1, and p a Sub-leading polynomial behavior in E/Ecore Bound state (ANC &ɣ1) + Coulomb Dominated by 7 Be-p separations 10s of fm Numbers that matter: kc=qcqnαemmr=24 MeV; p= 2 mr E; ɣ1= 2 mr B; a: parameterizes strength of p- 7 Be strong scattering

22 Status as of 2012 Adelberger et al., Rev. Mod. Phys. 83, 195 (2011) Below narrow 1 + resonance proceeds via s- and d-wave direct E1 capture Energy dependence due to interplay of Coulomb and strong forces Solar fusion II : community evaluation of cross sections relevant for pp and CNO cycles SF II value: S(0)=20.8±0.7±1.4 ev b SF I: S(0)= ev b Used energy dependence from a best calculation. Errors from consideration of energy-dependence in a variety of reasonable models

23 Effective Field Theory Simpler theory that reproduces results of full theory at long distances Short-distance details irrelevant for long-distance (low-momentum) physics, e.g., multipole expansion Expansion in ratio of physical scales: p/λb=λb/r Symmetries of underlying theory limit possibilities: all possible terms up to a given order present in EFT Short distances: unknown coefficients at a given order in the expansion need to be determined. Symmetry relates their impact on different processes Examples: standard model, chiral EFT, Halo EFT

24 Effective Field Theory Monet (1881) Simpler theory that reproduces results of full theory at long distances Short-distance details irrelevant for long-distance (low-momentum) physics, e.g., multipole expansion Expansion in ratio of physical scales: p/λb=λb/r Symmetries of underlying theory limit possibilities: all possible terms up to a given order present in EFT Short distances: unknown coefficients at a given order in the expansion need to be determined. Symmetry relates their impact on different processes Examples: standard model, chiral EFT, Halo EFT

25 Effective Field Theory Monet (1881) Simpler theory that reproduces results of full theory at long distances Short-distance details irrelevant for long-distance (low-momentum) physics, e.g., multipole expansion Expansion in ratio of physical scales: p/λb=λb/r Symmetries of underlying theory limit possibilities: all possible terms up to a given order present in EFT Short distances: unknown coefficients at a given order in the expansion need to be determined. Symmetry relates their impact on different processes Examples: standard model, chiral EFT, Halo EFT Error grows as first omitted term in expansion

26 Halo EFT λ Rcore; λ Rhalo 4He n n

27 Halo EFT λ Rcore; λ Rhalo 4He n n Define Rhalo=<r 2 > 1/2. Seek EFT expansion in Rcore/Rhalo. Valid for λ Rhalo Typically R Rcore 2 fm. And since <r 2 > is related to the neutron separation energy we are looking for systems with neutron separation energies less than 1 MeV By this definition the deuteron is the lightest halo nucleus, and the pionless EFT for few-nucleon systems is a specific case of halo EFT

28 p-wave bound states and capture thereto At LO: p-wave 1n halo described solely by its ANC and binding energy u 1 (r) =A 1 exp( 1r) r Capture to the p-wave state proceeds via the one-body E1 operator: external direct capture Hammer & DP, NPA (2011) 1 = p 2m R B E1 / Z 1 0 dr u 0 (r)ru 1 (r); u 0 (r) =1 NLO: piece of the amplitude representing capture at short distances, represented by a contact operator there is an LEC that must be fit r a (0)

29 7Be + p 8 B + γe1 at LO in Halo EFT Zhang, Nollett, DP, Phys. Rev. C 89, (2014); Ryberg, Forssen, Hammer, Platter, EPJA (2014) In this system Rcore 3 fm, Rhalo 15 fm; scale of Coulomb interactions: kc=qcqnαemmr=24 MeV; a 10 fm, both also ~Rhalo

30 7Be + p 8 B + γe1 at LO in Halo EFT In this system Rcore 3 fm, Rhalo 15 fm; scale of Coulomb interactions: kc=qcqnαemmr=24 MeV; a 10 fm, both also ~Rhalo Complication: S=1 and S=2 channels Zhang, Nollett, DP, Phys. Rev. C 89, (2014); Ryberg, Forssen, Hammer, Platter, EPJA (2014)

31 7Be + p 8 B + γe1 at LO in Halo EFT In this system Rcore 3 fm, Rhalo 15 fm; scale of Coulomb interactions: kc=qcqnαemmr=24 MeV; a 10 fm, both also ~Rhalo Complication: S=1 and S=2 channels Can also incorporate the excited 1/2 - in 7 Be Zhang, Nollett, DP, Phys. Rev. C 89, (2014); Ryberg, Forssen, Hammer, Platter, EPJA (2014)

32 7Be + p 8 B + γe1 at LO in Halo EFT In this system Rcore 3 fm, Rhalo 15 fm; scale of Coulomb interactions: kc=qcqnαemmr=24 MeV; a 10 fm, both also ~Rhalo Complication: S=1 and S=2 channels Can also incorporate the excited 1/2 - in 7 Be a p c k λ Zhang, Nollett, DP, Phys. Rev. C 89, (2014); Ryberg, Forssen, Hammer, Platter, EPJA (2014) p n σ p α

33 7Be + p 8 B + γe1 at LO in Halo EFT In this system Rcore 3 fm, Rhalo 15 fm; scale of Coulomb interactions: kc=qcqnαemmr=24 MeV; a 10 fm, both also ~Rhalo Complication: S=1 and S=2 channels Can also incorporate the excited 1/2 - in 7 Be p c p n a σ p k λ α Zhang, Nollett, DP, Phys. Rev. C 89, (2014); Ryberg, Forssen, Hammer, Platter, EPJA (2014) Scattering wave functions are linear combinations of Coulomb wave functions F0 and G0. Bound state wave function=the appropriate Whittaker function.

34 7Be + p 8 B + γe1 at LO in Halo EFT In this system Rcore 3 fm, Rhalo 15 fm; scale of Coulomb interactions: kc=qcqnαemmr=24 MeV; a 10 fm, both also ~Rhalo Complication: S=1 and S=2 channels Can also incorporate the excited 1/2 - in 7 Be p c p n a σ p k λ α Zhang, Nollett, DP, Phys. Rev. C 89, (2014); Ryberg, Forssen, Hammer, Platter, EPJA (2014) Scattering wave functions are linear combinations of Coulomb wave functions F0 and G0. Bound state wave function=the appropriate Whittaker function. S(E) =f(e) X apple Cs 2 S EC (E; s(e)) 2 + D(E) 2. s Four parameters at leading order

35 Additional ingredients at NLO LO LO LO LO Zhang, Nollett, DP, hys. Lett. B751, 535 (2015), arxiv: ; Ryberg, Forssen, Platter, Ann. Phys. (2016) (V) (VI) LO LO LO S(E) = (VII) (VIII) (IX) f(e) X s C 2 s apple S EC (E; s(e)) + L s S SD (E; s(e)) + s S CX (E; s(e)) 2 + D(E) 2. Effective ranges in both 5 S2 and 3 S1: r2 and r1 Core excitation: determined by ratio of 8 B couplings of 7 Be * p and 7 Be-p states: ϵ1 LECs associated with contact interaction, one each for S=1 and S=2: L1 and L2

36 Additional ingredients at NLO LO LO LO LO Zhang, Nollett, DP, hys. Lett. B751, 535 (2015), arxiv: ; Ryberg, Forssen, Platter, Ann. Phys. (2016) (V) (VI) LO LO LO Five more parameters at NLO S(E) = (VII) (VIII) (IX) f(e) X s C 2 s apple S EC (E; s(e)) + L s S SD (E; s(e)) + s S CX (E; s(e)) 2 + D(E) 2. Effective ranges in both 5 S2 and 3 S1: r2 and r1 Core excitation: determined by ratio of 8 B couplings of 7 Be * p and 7 Be-p states: ϵ1 LECs associated with contact interaction, one each for S=1 and S=2: L1 and L2

37 Additional ingredients at NLO LO LO LO LO Zhang, Nollett, DP, hys. Lett. B751, 535 (2015), arxiv: ; Ryberg, Forssen, Platter, Ann. Phys. (2016) (V) (VI) LO LO LO Five more parameters at NLO S(E) = (VII) (VIII) (IX) f(e) X s C 2 s apple S EC (E; s(e)) + L s S SD (E; s(e)) + s S CX (E; s(e)) 2 + D(E) 2. Effective ranges in both 5 S2 and 3 S1: r2 and r1 Core excitation: determined by ratio of 8 B couplings of 7 Be * p and 7 Be-p states: ϵ1 LECs associated with contact interaction, one each for S=1 and S=2: L1 and L2

38 Data for 7 Be + p 8 B + γe1 42 data points for 100 kev < Ec.m. < 500 kev Junghans (BE1 and BE3) Fillipone Baby Hammache (1998 and 2001)

39 Data for 7 Be + p 8 B + γe1 42 data points for 100 kev < Ec.m. < 500 kev Junghans (BE1 and BE3) Fillipone Baby Hammache (1998 and 2001) CMEs 2.7% and 2.3% 11.25% 5% 2.2% (1998)

40 Data for 7 Be + p 8 B + γe1 42 data points for 100 kev < Ec.m. < 500 kev Junghans (BE1 and BE3) Fillipone Baby Hammache (1998 and 2001) CMEs 2.7% and 2.3% 11.25% 5% 2.2% (1998) Subtract M1 resonance: negligible impact at 500 kev and below Deal with CMEs by introducing five additional parameters, ξi

41 Building the pdf pr (~g, { i } D; T ; I) / pr (D ~g, { i }; T ; I)pr(~g, { i } I), ln pr (D ~g, { i }; T ; I) =c NX j=1 [(1 j )S(~g; E j ) D j ] j,

42 Building the pdf Bayes: pr (~g, { i } D; T ; I) / pr (D ~g, { i }; T ; I)pr(~g, { i } I), First factor: likelihood ln pr (D ~g, { i }; T ; I) =c NX j=1 [(1 j )S(~g; E j ) D j ] j,

43 Building the pdf Bayes: pr (~g, { i } D; T ; I) / pr (D ~g, { i }; T ; I)pr(~g, { i } I), First factor: likelihood ln pr (D ~g, { i }; T ; I) =c Second factor: priors NX j=1 [(1 j )S(~g; E j ) D j ] j, Independent gaussian priors for ξi, centered at zero and with width=cme Gaussian priors for as=1 and as=2, based on Angulo et al. measurement Other EFT parameters, rs=1, rs=2, L1, L2, ANCs, ϵ1, assigned flat priors, corresponding to natural ranges No s-wave resonance below 600 kev

44 Building the pdf Bayes: pr (~g, { i } D; T ; I) / pr (D ~g, { i }; T ; I)pr(~g, { i } I), First factor: likelihood ln pr (D ~g, { i }; T ; I) =c Second factor: priors NX j=1 [(1 j )S(~g; E j ) D j ] j, Independent gaussian priors for ξi, centered at zero and with width=cme Gaussian priors for as=1 and as=2, based on Angulo et al. measurement Extrinsic information Other EFT parameters, rs=1, rs=2, L1, L2, ANCs, ϵ1, assigned flat priors, corresponding to natural ranges No s-wave resonance below 600 kev

45 Outputs and lessons Posteriors on parameters tell us about physics: which combinations are actually constrained? How do we see when parameters are not well constrained? Extrapolation Does EFT truncation error at NLO affect the answer? Feedback with experiment: systematic errors? Future experiments?

46 Posterior plots Physics pr (g 1,g 2 D; T ; I) = Z pr (~g, { i } D; T ; I) d 1...d 5 dg 3...dg 9

47 Posterior plots Physics pr (g 1,g 2 D; T ; I) = Z pr (~g, { i } D; T ; I) d 1...d 5 dg 3...dg AC (fm -1 ) vs. C 2 1 (fm -1 ) P (fm 1 )+A 23 P 1 (fm 1 ) ANCs are highly correlated but sum of squares strongly constrained

48 Posterior plots Physics pr (g 1,g 2 D; T ; I) = Z pr (~g, { i } D; T ; I) d 1...d 5 dg 3...dg AC (fm -1 ) vs. C 2 1 (fm -1 ) P (fm 1 )+A 23 P 1 (fm 1 ) L1 (fm) vs. ϵ ANCs are highly correlated but sum of squares strongly constrained One spin-1 short-distance parameter: 0.33 L 1 /(fm 1 ) 1

49 Another example of posterior plots Wesolowski, Furnstahl, DP, in preparation Parameter estimation for a particular piece of the NN potential at N3LO in the chiral EFT expansion Posterior plot allows diagnosis of parameter degeneracy D 1 (1S0)-D 2 (1S0) Which we also understand analytically h 1 S 0 V NN 1 S 0 i = D(1S0) 1 p2 p 02 + D(1S0) 2 (p4 + p 04 ) On-shell = (D1 (1S0) +2D2 (1S0) )(p2 + p 02 ) (D1 (1S0) 2D(1S0) 2 )(p2 p 02 ) 2,

50 More questions we can answer 42 data points, 7 parameters fit to these data, 5 ξi, s fixed to their mean values

51 More questions we can answer Is it a good fit? 42 data points, 7 parameters fit to these data, 5 ξi, s fixed to their mean values

52 More questions we can answer Is it a good fit? Did the experimentalists understand their systematic errors?

53 More questions we can answer Is it a good fit? Did the experimentalists understand their systematic errors? Are there parameters that are not well constrained by these data?

54 Final result pr F D; T ; I = Z pr (~g, { i } D; T ; I) ( F Zhang, Nollett, DP, PLB, 2015 F (~g))d 1...d 5 d~g

55 Final result pr F D; T ; I = Z pr (~g, { i } D; T ; I) ( F Zhang, Nollett, DP, PLB, 2015 F (~g))d 1...d 5 d~g

56 Final result pr F D; T ; I = Z pr (~g, { i } D; T ; I) ( F Zhang, Nollett, DP, PLB, 2015 F (~g))d 1...d 5 d~g S(0) = ev b

57 Final result pr F D; T ; I = Z pr (~g, { i } D; T ; I) ( F Zhang, Nollett, DP, PLB, 2015 F (~g))d 1...d 5 d~g S(0) = ev b Uncertainty reduced by factor of two: model selection

58 Truncation error N2LO correction=0 (technically only in absence of excited state) EFT s-wave scattering corrections (shape parameter)~0.8% E2, M1 contributions < 0.01%, Radiative corrections: ~0.1% So first correction is at N3LO, i.e., L i! L i + k 2 L 0 i 10 5 L' L

59 Planning improvements Use extrapolant to simulate impact of hypothetical future data that could inform posterior pdf for S(0) Left-to-right: 42 data points all of similar quality to Junghans et al. A: ANC S: as=1 and as=2 L: short-distance Note that 1 kev uncertainty in S1p of 8 B may not be negligible effect

60 A sneak peek at 3 He( 4 He,ɣ) Zhang, Nollett, DP, in preparation PRELIMINARY

61 A sneak peek at 3 He( 4 He,ɣ) Zhang, Nollett, DP, in preparation PRELIMINARY

62 Summary EFT provides following features for capture reactions Separation of long- and short-distance dynamics Model-independent (and in two-body case) analytic form for S(E) Ability to reproduce reasonable models Extrapolation problem formulated as a marginalization over models Z pr(s(0) data,i)= dmodels pr(s(0) model,i)pr(model data,i) Taking a variety of reasonable models and using them to extrapolate may overestimate the model uncertainty Application of Halo EFT to 7 Be(p,γ) 8 B produces new S(0), consistent with SFII, but with factor two smaller uncertainty S(0) = ev b

63 Stuff I learnt from this study Precise extrapolation can be done even when you don t have 10*n data Model uncertainty can be accommodated, and standard methods may over-estimate it. But it helps to be dong EFT Priors ultimately diagnosable: unconstrained parameters return the prior, and the results we looked at were not sensitive to different choices of prior. Robust Bayesian Analysis? Projected posterior reveals which combinations of parameters are constrained/affect this observable Truncation errors can be assessed Future experiments can be planned for maximum impact

64 Extensions, references Simultaneous fit to 7Be p scattering data: requires inclusion of resonances; Hierarchical Bayes Coulomb dissociation data? Same techniques applied to 3 He( 4 He,γ) Higa, Rupak, Vaghani, arxiv: Other, and more sophisticated, examples of Bayesian Uncertainty Quantification, see BUQEYE collaboration papers Quantifying uncertainties due to omitted higher-order terms Bayesian parameter estimation Review of Halo EFT Fursntahl, Klco, DP, Wesolowki, PRC 92, (2015) Melendez, Furnstahl, Wesolowski, arxiv: Wesolowski, Klco, Furnstahl, DP, Thapaliya, JPG 43, (2016) Hammer, Ji, DP, JPG 44, (2017)

65 Backup Slides

66 Halo nuclei

67 Halo nuclei A halo nucleus as one in which a few (1, 2, 3, 4,...) nucleons live at a significant distance from a nuclear core.

68 Halo nuclei A halo nucleus as one in which a few (1, 2, 3, 4,...) nucleons live at a significant distance from a nuclear core. Halo nuclei are characterized by small nucleon binding energies, large interaction cross sections, large radii, large E1 transition strengths.

69 What it does and doesn t do

70 What it does and doesn t do It doesn t:

71 What it does and doesn t do It doesn t: Need or discuss spectroscopic factors

72 What it does and doesn t do It doesn t: Need or discuss spectroscopic factors Need or discuss (interior) nodes of the wave function

73 What it does and doesn t do It doesn t: Need or discuss spectroscopic factors Need or discuss (interior) nodes of the wave function Seek to compete with ab initio calculations for structure

74 What it does and doesn t do It doesn t: It does: Need or discuss spectroscopic factors Need or discuss (interior) nodes of the wave function Seek to compete with ab initio calculations for structure

75 What it does and doesn t do It doesn t: It does: Need or discuss spectroscopic factors Need or discuss (interior) nodes of the wave function Seek to compete with ab initio calculations for structure Connect structure and reactions, including in multi-nucleon halos Collect information from different theories/experiments in one calculation Treat same physics as cluster models, in a systematically improvable way Provide information on inter-dependencies of low-energy observables, including along the core + n, core + 2n, core + 3n, etc. chain

76 Our approach S-wave (and P-wave) states generated by cn contact interactions No discussion of nodes, details of n-core interaction, spectroscopic factors u 0 (r) =A 0 exp( 0r) 19 C: input at LO: neutron separation energy of s-wave state. A0 ( wave-function renormalization ) can be fit at NLO. P-wave states require two inputs already at LO.

77 The multi-dimensional Halo EFT space Nn Single-neutron halos (s-wave) d, 19 C Single-neutron halos (p-wave) 8Li L Np

78 The multi-dimensional Halo EFT space Nn Two-neutron halos (s-wave) 11Li, 14 Be, 22 C Two-neutron halos (p-wave) 6He Single-neutron halos (s-wave) d, 19 C Single-neutron halos (p-wave) 8Li L Np

79 The multi-dimensional Halo EFT space Nn Two-neutron halos (s-wave) 11Li, 14 Be, 22 C Two-neutron halos (p-wave) 6He Single-neutron halos Single-neutron halos Single-proton (s-wave) Single-proton (p-wave) halos d, 19 C halos 8Li (s-wave) (p-wave) 17F * 8B L Np

80 The multi-dimensional Halo EFT space Nn Two-neutron halos (s-wave) 11Li, 14 Be, 22 C Two-neutron halos (p-wave) 6He Single-neutron halos Single-neutron halos Single-proton (s-wave) Single-proton (p-wave) halos d, 19 C halos 8Li (s-wave) (p-wave) 17F * 8B Plus complementary direction: N α E.g. 9 Be, 12 C *, etc. L Np

81 Fixing 8 Li parameters 8Li ground state is 2 + : both 5 P2 and 3 P2 components 8Li first excited state: 1 +, bound by 1.05 MeV Zhang, Nollett, Phillips, PRC (2014) c.f. Rupak, Higa, PRL 106, (2011); Fernando, Higa, Rupak, EPJA 48, 24 (2012) 3 H + 4 He n+ 7 Li 1ê ê Li Li

82 Fixing 8 Li parameters 8Li ground state is 2 + : both 5 P2 and 3 P2 components 8Li first excited state: 1 +, bound by 1.05 MeV Zhang, Nollett, Phillips, PRC (2014) c.f. Rupak, Higa, PRL 106, (2011); Fernando, Higa, Rupak, EPJA 48, 24 (2012) Input at LO: B1=2.03 MeV; B1 * =1.05 MeV γ1=58 MeV; γ1 * =42 MeV. γ1~1/rhalo 3 H + 4 He n+ 7 Li 1ê ê Li Li

83 Fixing 8 Li parameters 8Li ground state is 2 + : both 5 P2 and 3 P2 components 8Li first excited state: 1 +, bound by 1.05 MeV Zhang, Nollett, Phillips, PRC (2014) c.f. Rupak, Higa, PRL 106, (2011); Fernando, Higa, Rupak, EPJA 48, 24 (2012) Input at LO: B1=2.03 MeV; B1 * =1.05 MeV γ1=58 MeV; γ1 * =42 MeV. γ1~1/rhalo Also include 1/2 - excited state of 7 Li as explicit d.o.f. 3 H + 4 He n+ 7 Li 1ê ê Li Li

84 Fixing 8 Li parameters 8Li ground state is 2 + : both 5 P2 and 3 P2 components 8Li first excited state: 1 +, bound by 1.05 MeV Zhang, Nollett, Phillips, PRC (2014) c.f. Rupak, Higa, PRL 106, (2011); Fernando, Higa, Rupak, EPJA 48, 24 (2012) Input at LO: B1=2.03 MeV; B1 * =1.05 MeV γ1=58 MeV; γ1 * =42 MeV. γ1~1/rhalo Also include 1/2 - excited state of 7 Li as explicit d.o.f. Need to also fix 2+2 p-wave ANCs at LO. (1+2 ANCs for 7Li*> n> component.)

85 Fixing 8 Li parameters 8Li ground state is 2 + : both 5 P2 and 3 P2 components 8Li first excited state: 1 +, bound by 1.05 MeV Zhang, Nollett, Phillips, PRC (2014) c.f. Rupak, Higa, PRL 106, (2011); Fernando, Higa, Rupak, EPJA 48, 24 (2012) Input at LO: B1=2.03 MeV; B1 * =1.05 MeV γ1=58 MeV; γ1 * =42 MeV. γ1~1/rhalo Also include 1/2 - excited state of 7 Li as explicit d.o.f. Need to also fix 2+2 p-wave ANCs at LO. (1+2 ANCs for 7Li*> n> component.) VMC calculation with AV18 + UIX gives all ANCs: infer r1=-1.43 fm -1 r1~1/rcore

86 Fixing 8 Li parameters 8Li ground state is 2 + : both 5 P2 and 3 P2 components 8Li first excited state: 1 +, bound by 1.05 MeV Zhang, Nollett, Phillips, PRC (2014) c.f. Rupak, Higa, PRL 106, (2011); Fernando, Higa, Rupak, EPJA 48, 24 (2012) Input at LO: B1=2.03 MeV; B1 * =1.05 MeV γ1=58 MeV; γ1 * =42 MeV. γ1~1/rhalo Also include 1/2 - excited state of 7 Li as explicit d.o.f. Need to also fix 2+2 p-wave ANCs at LO. (1+2 ANCs for 7Li*> n> component.) VMC calculation with AV18 + UIX gives all ANCs: infer r1=-1.43 fm -1 r1~1/rcore A(3P2) A(5P2) A(3P2*) A(3P1) * A(5P1) * Nollett (12) (12) (6) 0.220(6) 0.197(5) Trache (23) (23) 0.187(16) 0.217(13)

87 7Li + n 8 Li + γe1 7Li ground state is 3/2 - : S-wave n scattering in 5 S2 and 3 S1 as=2 ~Rhalo; as=1~rcore 3 H + 4 He n+ 7 Li 1ê ê Li Li

88 7Li + n 8 Li + γe1 7Li ground state is 3/2 - : S-wave n scattering in 5 S2 and 3 S1 as=2=-3.63(5) fm, as=1=0.87(7) fm as=2 ~Rhalo; as=1~rcore 3 H + 4 He n+ 7 Li 1ê ê Li Li

89 7Li + n 8 Li + γe1 7Li ground state is 3/2 - : S-wave n scattering in 5 S2 and 3 S1 as=2=-3.63(5) fm, as=1=0.87(7) fm as=2 ~Rhalo; as=1~rcore 3 H + 4 He S n+ 7 Li 1ê ê Li Li

90 7Li + n 8 Li + γe1 7Li ground state is 3/2 - : S-wave n scattering in 5 S2 and 3 S1 as=2=-3.63(5) fm, as=1=0.87(7) fm as=2 ~Rhalo; as=1~rcore 3 H + 4 He S n+ 7 Li 1ê ê Li Li LO calculation: S=2 (with ISI) and S=1 into P-wave bound state E1 / Z 1 0 dr u 0 (r)ru 1 (r); u 0 (r) =1 r a ; u 1(r) =A 1 exp( 1r) r

91 LO results for 7 Li + n 8 Li + γe1 Analysis: Zhang, Nollett, Phillips, PRC (2014) Data: Barker (1996), cf. Nagai et al. (2005)

92 LO results for 7 Li + n 8 Li + γe1 Analysis: Zhang, Nollett, Phillips, PRC (2014) Data: Barker (1996), cf. Nagai et al. (2005)

93 LO results for 7 Li + n 8 Li + γe1 Analysis: Zhang, Nollett, Phillips, PRC (2014) Data: Barker (1996), cf. Nagai et al. (2005) ( 5 S 2! 2 + ) (! 2 + ) =0.95

94 LO results for 7 Li + n 8 Li + γe1 Analysis: Zhang, Nollett, Phillips, PRC (2014) Data: Barker (1996), cf. Nagai et al. (2005) ( 5 S 2! 2 + ) (! 2 + ) =0.95 Experiment > 0.86 Barker, 1996

95 LO results for 7 Li + n 8 Li + γe1 Analysis: Zhang, Nollett, Phillips, PRC (2014) Data: Barker (1996), cf. Nagai et al. (2005) ( 5 S 2! 2 + ) (! 2 + ) =0.95 Experiment > 0.86 Barker, 1996 (! 2 + ) (! 2 + )+ (! 1 + ) =0.89

96 LO results for 7 Li + n 8 Li + γe1 Analysis: Zhang, Nollett, Phillips, PRC (2014) Data: Barker (1996), cf. Nagai et al. (2005) ( 5 S 2! 2 + ) (! 2 + ) =0.95 Experiment > 0.86 Barker, 1996 (! 2 + ) (! 2 + )+ (! 1 + ) =0.89 Experiment=0.88 Lynn et al., 1991

97 LO results for 7 Li + n 8 Li + γe1 Analysis: Zhang, Nollett, Phillips, PRC (2014) Data: Barker (1996), cf. Nagai et al. (2005) ( 5 S 2! 2 + ) (! 2 + ) =0.95 Experiment > 0.86 Barker, 1996 (! 2 + ) (! 2 + )+ (! 1 + ) =0.89 Experiment=0.88 Lynn et al., 1991 Dynamics predicted through ab initio input

98 Coulomb dissociation: formulae c.f. Rupak & Higa arxiv: Straightforward computation of diagrams yields: db(e1) de = e2 Zeff 2 m R p 03 [2p 03 cot( (1/2) (p 0 )) A p 02 ] 2 0 [p 06 + p 06 cot 2 ( (1/2) (p 0 ))](p p 03 )4 (p )4

99 Coulomb dissociation: formulae c.f. Rupak & Higa arxiv: Straightforward computation of diagrams yields: db(e1) de = e2 Zeff 2 m R p 03 [2p 03 cot( (1/2) (p 0 )) A p 02 ] 2 0 [p 06 + p 06 cot 2 ( (1/2) (p 0 ))](p p 03 )4 (p )4 Spin-1/2 channel Spin-3/2 channel

100 Coulomb dissociation: formulae c.f. Rupak & Higa arxiv: Straightforward computation of diagrams yields: db(e1) de = e2 Zeff 2 m R p 03 [2p 03 cot( (1/2) (p 0 )) A p 02 ] 2 0 [p 06 + p 06 cot 2 ( (1/2) (p 0 ))](p p 03 )4 (p )4 Expand in Rcore/Rhalo: Spin-1/2 channel Spin-3/2 channel

101 Coulomb dissociation: formulae c.f. Rupak & Higa arxiv: Straightforward computation of diagrams yields: db(e1) de = e2 Zeff 2 m R p 03 [2p 03 cot( (1/2) (p 0 )) A p 02 ] 2 0 [p 06 + p 06 cot 2 ( (1/2) (p 0 ))](p p 03 )4 (p )4 Expand in Rcore/Rhalo: db(e1) de LO = e 2 Z 2 eff Spin-1/2 channel 3m R p 03 (p )4 No FSI Spin-3/2 channel

102 Coulomb dissociation: formulae c.f. Rupak & Higa arxiv: Straightforward computation of diagrams yields: db(e1) de = e2 Zeff 2 m R p 03 [2p 03 cot( (1/2) (p 0 )) A p 02 ] 2 0 [p 06 + p 06 cot 2 ( (1/2) (p 0 ))](p p 03 )4 (p )4 Expand in Rcore/Rhalo: db(e1) de db(e1) de LO NLO = e 2 Z 2 eff = e 2 Z 2 eff 3m R p 03 (p No FSI )4 r p 02 3r 1 p m R p 03 (p )4 Spin-1/2 channel Spin-3/2 channel

103 Coulomb dissociation: formulae c.f. Rupak & Higa arxiv: Straightforward computation of diagrams yields: db(e1) de = e2 Zeff 2 m R p 03 [2p 03 cot( (1/2) (p 0 )) A p 02 ] 2 0 [p 06 + p 06 cot 2 ( (1/2) (p 0 ))](p p 03 )4 (p )4 Expand in Rcore/Rhalo: db(e1) de db(e1) de LO NLO = e 2 Z 2 eff = e 2 Z 2 eff 3m R p 03 (p No FSI )4 r p 02 3r 1 p m R p 03 (p )4 Spin-1/2 channel Spin-3/2 channel Wf renormalization

104 Coulomb dissociation: formulae c.f. Rupak & Higa arxiv: Straightforward computation of diagrams yields: db(e1) de = e2 Zeff 2 m R p 03 [2p 03 cot( (1/2) (p 0 )) A p 02 ] 2 0 [p 06 + p 06 cot 2 ( (1/2) (p 0 ))](p p 03 )4 (p )4 Expand in Rcore/Rhalo: db(e1) de db(e1) de LO NLO = e 2 Z 2 eff = e 2 Z 2 eff 3m R p 03 (p No FSI )4 r p 02 3r 1 p m R p 03 (p )4 Spin-1/2 channel Spin-3/2 channel Wf renormalization 2P1/2-wave FSI

105 Coulomb dissociation: formulae c.f. Rupak & Higa arxiv: Straightforward computation of diagrams yields: db(e1) de = e2 Zeff 2 m R p 03 [2p 03 cot( (1/2) (p 0 )) A p 02 ] 2 0 [p 06 + p 06 cot 2 ( (1/2) (p 0 ))](p p 03 )4 (p )4 Expand in Rcore/Rhalo: db(e1) de db(e1) de LO NLO = e 2 Z 2 eff = e 2 Z 2 eff 3m R p 03 (p No FSI )4 r p 02 3r 1 p m R p 03 (p )4 Spin-1/2 channel Spin-3/2 channel Wf renormalization 2P1/2-wave FSI Higher-order corrections to phase shift at NNLO. Appearance of S- to- 2 P1/2 E1 counterterm also at that order.

106 Lagrangian: shallow S- and P-states L = c i t + 2 c + n i t + 2 2M 2m + i t M nc g 0 n c + nc g 1 2 M m j i j (nc) g 1 2 M nc n + j 1 j (n i j c)+(c i t + 2 i j (n c ) j +..., 2M nc i j n ) j + 1 j c, n: core, neutron fields. c: boson, n: fermion. σ, πj: S-wave and P-wave fields Minimal substitution generates leading EM couplings

107 Dressing the p-wave state Dyson equation for (cn)-system propagator Bertulani, Hammer, van Kolck (2002); Bedaque, Hammer, van Kolck (2003) = + D (p) = [p 0 p 2 /(2M nc )] (p) Here both Δ1 and g1 are mandatory for renormalization at LO (p) = m Rg1k µ + ik Reproduces ERE. But here (cf. s waves) cannot take r1=0 at LO

108 Dressing the p-wave state Dyson equation for (cn)-system propagator Bertulani, Hammer, van Kolck (2002); Bedaque, Hammer, van Kolck (2003) = + D (p) = [p 0 p 2 /(2M nc )] (p) Here both Δ1 and g1 are mandatory for renormalization at LO (p) = m Rg1k µ + ik Reproduces ERE. But here (cf. s waves) cannot take r1=0 at LO If a1 > 0 then pole is at k=iγ1 with B1=γ1 2 /(2mR): 3 2 i D (p) = r p 0 p 2 /(2M nc )+B 1 m 2 R g2 1 + regular

109 Scales in the 8 B system 8B 7Be

110 Parameters for 7 Be + p 8 B + γe1 at LO Zhang, Nollett, Phillips, PRC (2014) cf. Ryberg, Forssen, Hammer, Platter, EPJA (2014) S(E) =f(e) X s C 2 s apple S EC (E; s(e)) 2 + D(E) 2.

111 Parameters for 7 Be + p 8 B + γe1 at LO p c a k λ Zhang, Nollett, Phillips, PRC (2014) cf. Ryberg, Forssen, Hammer, Platter, EPJA (2014) p α p n σ S(E) =f(e) X s C 2 s apple S EC (E; s(e)) 2 + D(E) 2.

112 Parameters for 7 Be + p 8 B + γe1 at LO p c a k λ p α p n σ S(E) =f(e) X s C 2 s apple S EC (E; s(e)) 2 + D(E) 2. Zhang, Nollett, Phillips, PRC (2014) cf. Ryberg, Forssen, Hammer, Platter, EPJA (2014) Four parameters at leading order

113 Parameters for 7 Be + p 8 B + γe1 at LO p c a k λ p α p n σ S(E) =f(e) X s C 2 s apple S EC (E; s(e)) 2 + D(E) 2. Zhang, Nollett, Phillips, PRC (2014) cf. Ryberg, Forssen, Hammer, Platter, EPJA (2014) Four parameters at leading order A(3P2) (fm -1/2 ) A(5P2) (fm -1/2 ) a(s=1) (fm) a(s=2) (fm) Nollett (19) (19) Navratil et al Tabacaru (45) (45) Angulo 25(9) -7(3)

114 Proton capture on 7 Be at LO: results ANCs yield r1=-0.34 fm -1, consistent with estimated scale Λ Sensitivity to input as=2 and as=1 at higher energies At solar energies it s all about the ANCs

115 Halo EFT as a super model

116 Halo EFT as a super model Halo EFT is also the EFT of all the models used to extrapolate the cross section in Solar Fusion II

117 Halo EFT as a super model Halo EFT is also the EFT of all the models used to extrapolate the cross section in Solar Fusion II Differences are sub-% level between 0 and 0.5 MeV

118 Halo EFT as a super model Halo EFT is also the EFT of all the models used to extrapolate the cross section in Solar Fusion II Differences are sub-% level between 0 and 0.5 MeV Size of S(0) over-predicted in all models; curves rescaled in SFII fits

119 Halo EFT as a super model Halo EFT is also the EFT of all the models used to extrapolate the cross section in Solar Fusion II Differences are sub-% level between 0 and 0.5 MeV Size of S(0) over-predicted in all models; curves rescaled in SFII fits Parameters generally obey a~1/rhalo, r ~Rcore, L~Rcore, as expected

120 Lessons, limitations

121 Lessons, limitations There are many circumstances where EFT is not directly applicable, but principles can still be useful Separation of long- and short-distance dynamics Inclusion of ab initio information: LECs Model marginalization

122 Lessons, limitations There are many circumstances where EFT is not directly applicable, but principles can still be useful Separation of long- and short-distance dynamics Inclusion of ab initio information: LECs Model marginalization Extrapolation problem formulated as a marginalization over models Z pr(s(0) data,i)= dmodels pr(s(0) model,i)pr(model data,i)

123 Lessons, limitations There are many circumstances where EFT is not directly applicable, but principles can still be useful Separation of long- and short-distance dynamics Inclusion of ab initio information: LECs Model marginalization Extrapolation problem formulated as a marginalization over models Z pr(s(0) data,i)= dmodels pr(s(0) model,i)pr(model data,i) EFT particularly well-suited to this, since one can guarantee integration over space of all possible theories

124 Lessons, limitations There are many circumstances where EFT is not directly applicable, but principles can still be useful Separation of long- and short-distance dynamics Inclusion of ab initio information: LECs Model marginalization Extrapolation problem formulated as a marginalization over models Z pr(s(0) data,i)= dmodels pr(s(0) model,i)pr(model data,i) EFT particularly well-suited to this, since one can guarantee integration over space of all possible theories Taking a variety of reasonable models and using them to extrapolate may overestimate the model uncertainty