Bayesian Analysis for 4 7 Be + p 5 8 B + γ Based on Effective Field Theory
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1 Bayesan Analyss for 4 7 Be + p 5 8 B + γ Based on Effectve Feld Theory Xln Zhang Unversty of Washngton In collaboraton wth K. Nollett (San Dego State U.) and D. Phllps (Oho U.) INT Program INT-16-a, Bayesan Methods n Nuclear Physcs, June, 016
2 Outlne Motvaton Be7 capture n EFT: next-to-leadng order (NLO) Bayesan analyss Questons 6/8/016
3 Radatve Capture Reacton 4 7 Be + p 8 5 B + γ 6/8/016 3
4 Radatve Capture Reacton 4 7 Be + p 8 5 B + γ 6/8/016 3
5 Radatve Capture Reacton 4 7 Be + p 8 5 B + γ Knetc energy (E) between core (C) and nucleon(n) Photon takes away all the energy: Q value + E Partcles carry spn ( channels sets of parameters) Electromagnetc dpole radaton (charge separaton), and governed by strong nteracton 6/8/016 3
6 Radatve Capture Reacton 6/8/016 4
7 Radatve Capture Reacton 6/8/016 4
8 Radatve Capture Reacton 6/8/016 4
9 Radatve Capture Reacton Statstcal & systematcal uncertantes 6/8/016 4
10 Radatve Capture Reacton Statstcal & systematcal uncertantes Goal s to nfer the S factor and ts uncertanty at near-zero energes based on theory 6/8/016 4
11 Motvatons W.C. Haxton, R.G. Hamsh Robertson, and Aldo M. Serenell, Annu.Rev. Astron. Astrophys. 51, 1 (013) 6/8/016 5
12 Solar neutrno generaton 6/8/016 6
13 Solar neutrno generaton Radatve Capture 6/8/016 6
14 Solar neutrno generaton 6/8/016 7
15 Solar neutrno generaton However, Be7+p (7.5%), He3+He4 (5.4%) 6/8/016 7
16 Solar neutrno generaton Not expermentally accessble (0 kev CM energy). Involve theoretcal uncertanty However, Be7+p (7.5%), He3+He4 (5.4%) 6/8/016 7
17 The capture reacton cross sectons mpact solar neutrno oscllaton experments, and solar modelng. 6/8/016 8
18 Solar abundance problem 6/8/016 9
19 Solar abundance problem Based on surface propertes from 1-D convecton zone smulaton Based on surface propertes from 3-D convecton zone smulaton 6/8/016 9
20 Solar abundance problem Based on surface propertes from 1-D convecton zone smulaton Hgh metallcty Hgh core T Large neutrno flux Based on surface propertes from 3-D convecton zone smulaton Low metallcty Low core T Small neutrno flux 6/8/016 9
21 Solar abundance problem: Helosesmology 6/8/016 10
22 Solar abundance problem: Helosesmology The 6/8/016 revsed SSM does NOT agree wth Helosesmology measurements 10
23 Solar abundance problem: Neutrnos 6/8/016 11
24 Solar abundance problem: Neutrnos 6/8/016 11
25 Solar abundance problem: Neutrnos Two models could be dfferentated IF the theoretcal errors and those of solar neutrno experments on 8B neutrno flux can be reduced. 6/8/016 11
26 EFT at NLO A smple pcture due to scale separaton; systematc expanson (Lagrangan); uncertanty estmate X.Z., K. Nollett and D. Phllps, PRC 89, (014) PLB 751, 535(015); EPJ Web Conf. 113, (016). 6/8/016 1
27 Then and now Tombrello(1965), Aurdal(1970), Rev.Mod.Phys.(1998), Rev.Mod.Phys(011) 6/8/016 13
28 Then and now X.Z, K. Nollett, and D. Phllps (015) Tombrello(1965), Aurdal(1970), Rev.Mod.Phys.(1998), Rev.Mod.Phys(011) Based on the same data 6/8/016 13
29 Scale separaton: spectrum 6/8/016 14
30 Scale separaton: spectrum 6/8/016 14
31 Scale separaton: spectrum B8: a shallow bound state n terms of proton+be7 Proton-Be7 s-wave has large scatterng lengths Length scale ~ 1/(momentum scale) 6/8/016 14
32 Scale separaton: spectrum 6/8/016 15
33 Scale separaton: spectrum 6/8/016 15
34 Scale separaton: spectrum * E Shallow bound state k, k k C 0. ~ 1 6/8/016 15
35 Scale separaton: spectrum * E Be and proton total spn can be 1 or, gvng two ndependent reacton channels two sets of parameters 6/8/016 16
36 Scale separaton: reacton LO NLO 6/8/016 17
37 Scale separaton: reacton LO NLO EFT quantfes ths pcture, 6/8/016 17
38 Scale separaton: reacton LO NLO EFT quantfes ths pcture, low by expandng S-matrx n terms of 0.. 6/8/ Q
39 EFT: NLO LO: 4 parameters ncludng C 3, C 5 P ) ( P ) (, a, a 5 ( 3 S1 ) ( S ) 6/8/016 18
40 EFT: NLO LO: 4 parameters ncludng C 3, C 5 P ) ( P ) (, a, a 5 ( 3 S1 ) ( S ) r,, L, ( 3 S ) ( S ) E 1 LE NLO: another 5 parameters ncludng, r 5 1 6/8/
41 EFT: NLO LO: 4 parameters ncludng C 3, C 5 P ) ( P ) (, a, a 5 ( 3 S1 ) ( S ) r,, L, ( 3 S ) ( S ) E 1 LE NLO: another 5 parameters ncludng, r 5 1 Core exctaton 6/8/
42 Model ndependence Potental models: B. Davds and S. Typel (003) Mcroscopc calculaton: P. Descouvemont (004) 6/8/016 19
43 Model ndependence Potental models: B. Davds and S. Typel (003) Mcroscopc calculaton: P. Descouvemont (004) 6/8/016 EFT reproduces other models 19
44 Bayesan Analyss 6/8/016 0
45 Bayesan Analyss 6/8/016 1
46 Pr Bayesan Analyss g,{ } D; T PrD g,{ }; T Prg,{ T } 6/8/016 1
47 Pr Bayesan Analyss g,{ } D; T PrD g,{ }; T Prg,{ T } Data. Here only En<0.5 MeV drect capture data are used, ncludng Junghans, Flppone, Hammache, Baby (3 n total) 6/8/016 1
48 Pr Bayesan Analyss g,{ } D; T PrD g,{ }; T Prg,{ T } Data. Here only En<0.5 MeV drect capture data are used, ncludng Junghans, Flppone, Hammache, Baby (3 n total) 6/8/016 1
49 Pr Bayesan Analyss g,{ } D; T PrD g,{ }; T Prg,{ T } 6/8/016 1
50 Pr Bayesan Analyss g,{ } D; T PrD g,{ }; T Prg,{ T } Theory, here S factor 6/8/016 1
51 Pr Bayesan Analyss g,{ } D; T PrD g,{ }; T Prg,{ T } 6/8/016 1
52 Pr Bayesan Analyss g,{ } D; T PrD g,{ }; T Prg,{ T } EFT parameters 6/8/016 1
53 Pr Bayesan Analyss g,{ } D; T PrD g,{ }; T Prg,{ T } 6/8/016 1
54 Pr Bayesan Analyss g,{ } D; T PrD g,{ }; T Prg,{ T } Systematc error varables 6/8/016 1
55 Pr Bayesan Analyss g,{ } D; T PrD g,{ }; T Prg,{ T } 6/8/016 1
56 Pr Bayesan Analyss g,{ } D; T PrD g,{ }; T Prg,{ T } Pr D g,{ }; T Exp ; # data 1 S g; E 1 D 6/8/016 1
57 Pr Bayesan Analyss g,{ } D; T PrD g,{ }; T Prg,{ T } Pr D g,{ }; T Exp ; # data 1 S g; E 1 D 6/8/016 1
58 Pr Bayesan Analyss g,{ } D; T PrD g,{ }; T Prg,{ T } Pr D g,{ }; T Exp ; # data 1 S g; E 1 D Pr # sys err # para 0 j l l g,{ } T Exp Exp or flat ds. j j l g g g l 6/8/016 1
59 Pr Bayesan Analyss g,{ } D; T PrD g,{ }; T Prg,{ T } Pr D g,{ }; T Exp ; # data 1 S g; E 1 D Pr g g l j gl d Pr g,{ } D T # sys err # para 0 j l l g,{ } T Exp Exp or flat ds. j Pr g D; T ; 6/8/016 1
60 Pr Bayesan Analyss g,{ } D; T PrD g,{ }; T Prg,{ T } Pr D g,{ }; T Exp ; # data 1 S g; E 1 D Pr g g l j gl d Pr g,{ } D T # sys err # para 0 j l l g,{ } T Exp Exp or flat ds. j Pr g D; T ; Monte-Carlo Markov-Chan ensemble of parameters accordng to the parameter dstrbutons 6/8/016 1
61 Junghans BE1 and BE3 (flled crcle), Flppone (open crcle), Baby (flled damond), Hammache (flled box) Green band s our 1- standard devaton error band: 3% error 6/8/016
62 S(0 kev) [S(0 kev)] E. G. Adelberger, et.al., Rev. Mod. Phys. 83, 195 (011) recommend: S( 0) ( ) 1.4 ( expt theor) ev b 6/8/016 3
63 S(0 kev) [S(0 kev)] E. G. Adelberger, et.al., Rev. Mod. Phys. 83, 195 (011) recommend: S( 0) ( ) 1.4 ( expt theor) ev b We reduce the error by more than 50%! 6/8/016 3
64 PDF for and C 3 C C 3, 5 ( P ) ( P ) C 5. ( P ) ( P ) Tabacaru et.al., measurements by transfer reacton (large eclpse) Nollett et.al., ab nto calculaton (small eclpse) 6/8/016 4
65 PDF for and C 3 C C 3, 5 ( P ) ( P ) C 5. ( P ) ( P ) C 3 C ( P ) ( P ) (3) Drect capture reacton constrans total squared ANCs! Tabacaru et.al., measurements by transfer reacton (large eclpse) Nollett et.al., ab nto calculaton (small eclpse) 6/8/016 4
66 PDF for and.33 0 L 3 ( P ) L, ( 3 P ) 6/8/016 5
67 PDF for and.33 0 L 3 ( P ) L, ( 3 P ) Core exctaton and short range term 6/8/016 not dstngushed by low energy data 5
68 PDFs Red for S=1, Blue for S=. 6/8/016 6
69 PDFs Red for S=1, Blue for S=. 6/8/016 6
70 PDFs Red for S=1, Blue for S=. L 1/ 3 fm 6/8/016 6
71 PDFs Red for S=1, Blue for S=. L 1/ 3 fm 6/8/016 6 From left to rght: Junghans (BE1and BE3 ) Baby, Hammache, Flpponne
72 Choce of data sets 6/8/016 7
73 Choce of data sets 6/8/016 7 Include data: Flppone(1983), Baby (003), Hammache (001)
74 Choce of data sets Include data: Flppone(1983), Baby (003), Hammache (001) Add Junghans BE3 (010) 6/8/016 7
75 Choce of data sets Add Junghans BE3 and BE1 (010) Include data: Flppone(1983), Baby (003), Hammache (001) Add Junghans BE3 (010) 6/8/016 7
76 EFT NLO correctons 6/8/016 8
77 EFT NLO correctons E, M1 contrbutons (S factor): < 0.01% 6/8/016 8
78 EFT NLO correctons E, M1 contrbutons (S factor): < 0.01% Radatve correctons: ~0.1% 6/8/016 8
79 EFT NLO correctons E, M1 contrbutons (S factor): < 0.01% Radatve correctons: ~0.1% EFT s-wave scatterng: ~0.8% 6/8/016 8
80 EFT NLO correctons E, M1 contrbutons (S factor): < 0.01% Radatve correctons: ~0.1% EFT s-wave scatterng: ~0.8% EFT NLO currents: ~0.8% 6/8/016 8
81 EFT NLO correctons E, M1 contrbutons (S factor): < 0.01% Radatve correctons: ~0.1% EFT s-wave scatterng: ~0.8% EFT NLO currents: ~0.8% Notce B8 BE=136.4(1.0) kev: ~ 0.8% 6/8/016 8
82 EFT NLO correctons E, M1 contrbutons (S factor): < 0.01% Radatve correctons: ~0.1% EFT s-wave scatterng: ~0.8% EFT NLO currents: ~0.8% Notce B8 BE=136.4(1.0) kev: ~ 0.8% Recall EFT ftted to varous potental model and RGM calculaton results: devaton <~1% up to 1MeV (cm E). 6/8/016 8
83 NLO mpact on Bayesan analyss N3LO NLO NLO: L L + L k Λ N3LO: L L + L k Λ NLO 6/8/016 9
84 NLO mpact on Bayesan analyss N3LO NLO NLO: L L + L k Λ N3LO: L L + L k Λ NLO Addng NLO shfts S(0) by << 1%. 6/8/016 9
85 NLO: L L + L k Λ N3LO: L L + L k Λ Data couldn t gve more nformaton 6/8/016 30
86 A few questons 6/8/016 31
87 Questons data D E g S Exp T D g # 1 1 ; ; };,{ Pr ds. or flat para l g l l err sys j j l j g g Exp Exp T g # 0 # },{ Pr 6/8/016 3
88 Pr Pr D g,{ }; T Questons Exp ; g; E 1 How to deal wth normalzaton floatng parameter? [P.S.Baranov, A.L.L vov et.al.,physcs of Partcles and Nucleus, 3, 376 (001)] # data # sys err # para 0 j l l g,{ } T Exp Exp or flat ds. j j 1 S l g g g l D 6/8/016 3
89 Pr Pr D g,{ }; T Questons Exp ; g; E 1 How to deal wth normalzaton floatng parameter? [P.S.Baranov, A.L.L vov et.al.,physcs of Partcles and Nucleus, 3, 376 (001)] Assgn flat prors for parameters? (red for Gaussan a0, blue and green wth flat a0 pror) # data # sys err # para 0 j l l g,{ } T Exp Exp or flat ds. j j 1 S l g g g l D 6/8/016 3
90 Pr Pr D g,{ }; T Questons Exp ; g; E 1 How to deal wth normalzaton floatng parameter? [P.S.Baranov, A.L.L vov et.al.,physcs of Partcles and Nucleus, 3, 376 (001)] Assgn flat prors for parameters? (red for Gaussan a0, blue and green wth flat a0 pror) # data # sys err # para 0 j l l g,{ } T Exp Exp or flat ds. j j 1 S l g g g l D 6/8/016 3
91 Pr Pr D g,{ }; T Questons Exp ; g; E 1 How to deal wth normalzaton floatng parameter? [P.S.Baranov, A.L.L vov et.al.,physcs of Partcles and Nucleus, 3, 376 (001)] Assgn flat prors for parameters? (red for Gaussan a0, blue and green wth flat a0 pror) Over fttng? Is there a best ft? # data # sys err # para 0 j l l g,{ } T Exp Exp or flat ds. j j 1 S l g g g l D 6/8/016 3
92 Pr Pr D g,{ }; T Questons Exp ; g; E 1 How to deal wth normalzaton floatng parameter? [P.S.Baranov, A.L.L vov et.al.,physcs of Partcles and Nucleus, 3, 376 (001)] Assgn flat prors for parameters? (red for Gaussan a0, blue and green wth flat a0 pror) Over fttng? Is there a best ft? # data # sys err # para 0 j l l g,{ } T Exp Exp or flat ds. j j 1 S l g g g l D 6/8/016 3
93 About MCMC 6/8/016 33
94 About MCMC Acceptance s 15%, good? 6/8/016 33
95 About MCMC Acceptance s 15%, good? How about auto-correlaton length? 6/8/016 33
96 About MCMC Acceptance s 15%, good? How about auto-correlaton length? Is 7000-samples enough? 6/8/016 33
97 About MCMC Acceptance s 15%, good? How about auto-correlaton length? Is 7000-samples enough? How to estmate the error of error? 6/8/016 33
98 About MCMC Acceptance s 15%, good? How about auto-correlaton length? Is 7000-samples enough? How to estmate the error of error? Comment on VEGAS algorthm due to Lepage? 6/8/016 33
99 Summary EFT works for ths reacton Bayesan analyss s used to quantfy uncertantes Choce of data sets, theoretcal error, and choce of prors have been tested Questons 6/8/016 34
100 Back up 6/8/016 35
101 Solar abundance problem: Neutrnos 6/8/016 36
102 Solar abundance problem: Neutrnos Extract C+N abundance W. C. Haxton et.al. (013) 6/8/016 36
103 Solar abundance problem: Neutrnos A-few-percent measurements Extract C+N abundance W. C. Haxton et.al. (013) 6/8/016 36
104 Solar abundance problem: Neutrnos To be measured A-few-percent measurements Extract C+N abundance W. C. Haxton et.al. (013) 6/8/016 36
105 Solar abundance problem: Neutrnos To be measured A-few-percent measurements Extract C+N abundance Knowng C+N can also be used to dfferentate solar models. However nuclear cross secton error agan needs to be reduced. W. C. Haxton et.al. (013) 6/8/016 36
106 Solar abundance problem: Neutrnos To be measured A-few-percent measurements Extract C+N abundance Knowng C+N can also be used to dfferentate solar models. However nuclear cross secton error agan needs to be reduced. W. C. Haxton et.al. (013) 6/8/016 36
107 Solar abundance problem: Debate! 6/8/016 37
108 Solar abundance problem: Debate! arxv: , /8/016 37
109 Solar abundance problem: Debate! arxv: , Capture reacton study wll make an mpact! 6/8/016 37
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