The Hoyle state and the fate of carbon-based life

Transcription

1 1 The Hoyle state and the fate of carbon-based life Ulf-G. Meißner, Univ. Bonn & FZ Jülich NLEFT Supported by DFG, SFB/TR-16 and by DFG, SFB/TR-110 and by EU, I3HP EPOS and by BMBF 05P12PDFTE and by HGF VIQCD VH-VI-417 Nuclear Astrophysics Virtual Institute

2 2 CONTENTS Intro I: Element generation in stars Intro II: The anthropic principle Ab initio calculation of atomic nuclei Nuclear lattice simulations: results The fate of carbon-based life as a function of fundamental parameters Summary & outlook

3 3 Element generation in stars

4 FIRST STEPS: PROTON-PROTON FUSION etc 4 Elements are generated in the Big Bang & stars through the fusion of protons & nuclei All is simple until 4 He Simply adding further protons does not work So how are the life-essential elements like 12 C and 16 O generated? BTW: nuclei make up the visible matter in the Universe

5 A SHORT HISTORY of the HOYLE STATE 5 Heavy element generation in massive stars: triple-α process 4 He + 4 He 8 Be 8 Be + 4 He 12 C 12 C + γ 12 C + 4 He 16 O + γ Bethe 1938, Öpik 1952, Salpeter 1952, Hoyle 1954,... Hoyle s contribution: calculation of relative abundances of 4 He, 12 C and 16 0 need a resonance close to the 8 Be + 4 He threshold at E R = 0.35 MeV this corresponds to a J P = 0 + excited state 7.7 MeV above the g.s. a corresponding state was experimentally confirmed at Caltech at E E(g.s.) = ± MeV Dunbar et al. 1953, Cook et al still on-going experimental activity, e.g. EM transitions at SDALINAC and how about theory? this talk side remark: NOT driven by anthropic considerations M. Chernykh et al., Phys. Rev. Lett. 98 (2007) H. Kragh, Arch. Hist. Exact Sci. 64 (2010) 721

6 THE TRIPLE-ALPHA PROCESS MOVIE 6 c ANU the 8 Be nucleus is instable, long lifetime 3 alphas must meet the Hoyle state sits just above the continuum threshold most of the excited carbon nuclei decay (about 4 out of decays produce stable carbon) carbon is further turned into oxygen but w/o a resonant condition a triple wonder!

7 AN ENIGMA for NUCLEAR THEORY 7 Ab initio calculation in the no-core shell model: 10 7 CPU hrs on JAGUAR P. Navratil et al., Phys. Rev. Lett. 99 (2007) ; R. Roth et al., Phys. Rev. Lett. 107 (2011) ; ; ; ? 12 C 13 C 0 +? 2 + ; ; ; /2-3/2 - ; 3/2 3/2 - ; 3/2 12 3/2-1/2-7/2-3/2-8 5/2-1/ /2-5/ /2-1/2-1/2 - NN+NNN Exp NN NN+NNN Exp NN excellent description, but no trace of the Hoyle state

8 8 The anthropic principle

9 THE ANTHROPIC PRINCIPLE 9 The anthropic principle: The observed values of all physical and cosmological quantities are not equally probable but they take on values restricted by the requirement that there exist sites where carbon-based life can evolve and by the requirements that the Universe be old enough for it to have already done so. Carter 1974, Barrow & Tippler 1988,... can this be tested? / have physical consequences? Ex. 1: Anthropic bound on the cosmological constant Weinberg (1987) [550 cites] Ex. 2: The anthropic string theory landscape Susskind (2003) [724 cites]

10 A PRIME EXAMPLE for the ANTHROPIC PRINCIPLE 10 Hoyle (1953): Prediction of an excited level in carbon-12 to allow for a sufficient production of heavy elements ( 12 C, 16 O,...) in stars was later heralded as a prime example for the AP: As far as we know, this is the only genuine anthropic principle prediction Carr & Rees 1989 In 1953 Hoyle made an anthropic prediction on an excited state level of life for carbon production in stars Linde 2007 A prototype example of this kind of anthropic reasoning was provided by Fred Hoyle s observation of the triple alpha process... Carter 2006

11 The RELEVANT QUESTION 11 Date: Sat, 25 Dec :03: From: Steven Weinberg To: Ulf-G. Meissner Subject: Re: Hoyle state in 12C E (MeV) J P = J P = J z = 0, J P = J z = 2, J P = Dear Professor Meissner, -100 Thanks for the colorful graph. It makes a nice Christmas -110 card. But I have a detailed question. Suppose you calculate not only the energy LO NLO EM+IB NNLO Exper. of the Hoyle state in C12, but also of the ground states of He4 and Be8. How sensitive is the result that the energy of the Hoyle state is near the sum of the rest energies of He4 and Be8 to the parameters of the theory? I ask because I suspect that for a pretty broad range of parameters, the Hoyle state can be well represented as a nearly bound state of Be8 and He4. All best, Steve Weinberg How does the Hoyle state move relative to the 4He+8Be threshold, if we change the fundamental parameters of QCD+QED? not possible in nature, but on a high-performance computer!

12 The NON-ANTHROPIC SCENARIO 12 Weinberg s assumption: The Hoyle state stays close to the 4He+8Be threshold energy difference Hoyle 4He+8Be g g g g+ g fundamental parameter

13 The ANTHROPIC SCENARIO 13 The AP strikes back: The Hoyle state moves away from the 4He+8Be threshold energy difference Hoyle 4He+8Be g g g g+ g fundamental parameter

14 EARLIER STUDIES of the AP 14 rate of the 3α-process: r 3α ( Nα k B T ) 3 Γ γ exp ( E k B T ) E = E 12 3E α = (18) kev too few 16 O too few 12 C how much can E be changed so that there is still enough 12 C and 16 O? E 100 kev Oberhummer et al., Science 289 (2000) 88 Csoto et al., Nucl. Phys. A 688 (2001) 560 Schlattl et al., Astrophys. Space Sci. 291 (2004) 27 [Livio et al., Nature 340 (1989) 281]

15 15 Ab initio calculations of atomic nuclei

16 EMERGENCE of STRUCTURE in QCD 16 The strong interactions are described by QuantumChromoDynamics: L QCD = 1 4g 2 G µνg µν + f =u,d,s,c,b,t up and down quarks are very light, a few MeV Quarks and gluons are confined within hadrons Protons and neutrons form atomic nuclei This requires the inclusion of electromagnetism described by QED with α EM 1/137 q f (iγ µ D µ m f ) q f Atomic nuclei make up the visible matter in the Universe So how are these strongly interacting composites generated? 0.5 α s (Q) Data Theory Deep Inelastic Scattering e + e - Annihilation Hadron Collisions Heavy Quarkonia NLO NNLO Λ(5) MS α s(μ Z) 245 MeV QCD O(α MeV s) { 181 MeV Q [GeV] Lattice

17 Ingredients 17 Nuclear binding is shallow: E/A 8 MeV m N = 940 MeV Nuclei can be calculated from the A-body Schrödinger equation: HΨ A = EΨ A Forces are of (dominant) two- and (subdominant) three-body nature: V = V NN + V NNN can be calculated systematically and to high-precision Weinberg, van Kolck, Epelbaum, UGM, Entem, Machleidt,... fit all parameters in V NN + V NNN from 2- and 3-body data exact calc s of systems with A 4 using Faddeev-Yakubowsky machinery see slides see fig. But how about ab initio calculations for systems with A 5?

18 CHIRAL EFT for FEW-NUCLEON SYSTEMS 18 Gasser, Leutwyler, Weinberg, van Kolck, Epelbaum, Bernard, Kaiser, UGM,... Scales in nuclear physics: Natural: λ = 1/M 1.5 fm (Yukawa 1935) Vc (r) [MeV] 100 repulsive core 0 Unnatural: a np ( 1 S 0 ) = 23.8 fm, a np ( 3 S 1 ) = 5.4 fm 1/M -100 CD Bonn Reid93 AV this can be analyzed in a suitable EFT based on L QCD L EFF = L + L N + L NN +... pion and pion-nucleon sectors are perturbative in Q/Λ χ chiral perturbation th y L NN collects short-distance contact terms, to be fitted NN interaction requires non-perturbative resummation chirally expand V NN(N), use in regularized Schrödinger equation

19 CHIRAL POTENTIAL and NUCLEAR FORCES 19 2 LECs 7 LECs 15 LECs 2 LECs O((Q/Λ χ ) 0 ) O((Q/Λ χ ) 2 ) O((Q/Λ χ ) 3 ) O((Q/Λ χ ) 4 ) explains naturally the observed hierarchy of nuclear forces MANY successfull tests in few-nucleon systems (continuum calc s)

20 Examples 20 np scattering 0.8 nd scattering dσ/dω [mb/sr] (N) K X X (N) EGM N3LO EM N3LO CD Bonn 2000 Gross, Stadler Nijmegen PWA K Y Y θ [deg] A y 0,3 0, , pol. transfer in pd scattering θ [deg] 100 dσ/dω [mb/sr] 10 T ,1 0,07 T 21 0,02 10 MeV T 20 T MeV dσ/dω [mb/sr] ,2 0-0,2-0,4 0-0,1 (N) K Z X ,03-0, θ [deg] θ [deg] -0, CM [deg] Epelbaum, Hammer, UGM, Rev. Mod. Phys. 81 (2009) 1773

21 NUCLEAR LATTICE SIMULATIONS 21 Frank, Brockmann (1992), Koonin, Müller, Seki, van Kolck (2000), Lee, Borasoy, Schäfer, Phys.Rev. C70 (2004) ,... Borasoy, Krebs, Lee, UGM, Nucl. Phys. A768 (2006) 179; Borasoy, Epelbaum, Krebs, Lee, UGM, Eur. Phys. J. A31 (2007) 105 new method to tackle the nuclear many-body problem discretize space-time V = L s L s L s L t : nucleons are point-like fields on the sites p n discretized chiral potential w/ pion exchanges and contact interactions typical lattice parameters n p a Λ = a 300 MeV [UV cutoff] ~ 2 fm strong suppression of sign oscillations due to approximate Wigner SU(4) symmetry hybrid Monte Carlo & transfer matrix (similar to LQCD) J. W. Chen, D. Lee and T. Schäfer, Phys. Rev. Lett. 93 (2004)

22 CONFIGURATIONS 22 all possible configurations are sampled clustering emerges naturally perform ab initio calculations using only V NN and V NNN as input grand challenge: the spectrum of 12 C

23 COMPUTATIONAL EQUIPMENT 23 Past = JUGENE (BlueGene/P) Present = JUQUEEN (BlueGene/Q) 6 Pflops flops

24 SPECTRUM OF 12 C & the HOYLE STATE 24 Epelbaum, Krebs, Lee, UGM, Phys. Rev. Lett. 106 (2011) Epelbaum, Krebs, La hde, Lee, UGM, Phys. Rev. Lett. 109 (2012) Viewpoint: Hjorth-Jensen, Physics 4 (2011) 38 Ulf-G. Meißner, The Hoyle state and the fate of carbon-based life NC State, August 2013 C < O > B

25 RESULTS 25 fix parameters from 2N scattering and two 3N observables [NNLO: 9+2] some groundstate energies and differences E [MeV] NLEFT Exp. 3 He - 3 H 0.78(5) He 28.3(6) Be 55(2) C 92(3) O 141(1) preliminary E3 He E triton (MeV) lattice physical (infinite volume) promising results [3NFs very important] L (fm) excited states more difficult new projection MC method [large class of initial wfs]

26 The SPECTRUM of CARBON After hrs JUGENE/JUQUEEN (and some human work) E [MeV] (1) (3) (3) (2) First ab initio calculation of the Hoyle state Hoyle Structure of the Hoyle state: Exp (3) Th

27 SPECTRUM of 12 C 27 Summarizing the results for carbon-12 at NNLO: N 77 MeV 74 MeV 72 MeV 70 MeV 3N 15 MeV 15 MeV 13 MeV 13 MeV 2N+3N 92(3) MeV 89(3) MeV 85(3) MeV 83(3) MeV 82.6(1) MeV [1,2] Exp MeV MeV MeV 82.32(6) MeV [3] 81.1(3) MeV [4] 82.13(11) MeV [5] [1] Freer et al., Phys. Rev. C 80 (2009) [2] Zimmermann et al., Phys. Rev. C 84 (2011) [3] Hyldegaard et al., Phys. Rev. C 81 (2010) [4] Itoh et al., Phys. Rev. C 84 (2011) [5] Zimmermann et al., arxiv: [nucl-ex] importance of consistent 2N & 3N forces good agreement w/ experiment, can be improved

28 28 The fate of carbon-based life as a function of the quark mass

29 FINE-TUNING of FUNDAMENTAL PARAMETERS 29 Fig. courtesy Dean Lee

30 FINE-TUNING: MONTE-CARLO ANALYSIS 30 Epelbaum, Krebs, Lähde, Lee, UGM, PRL 110 (2013) consider first QCD only calculate E/ M relevant quantities (energy differences) E h E 12 E 8 E 4, E b E 8 2E 4 E c E 12 E 12 energy differences depend on parameters of QCD (LO analysis) ) E i = E i (M OPE, m N (M ), g N (M ), C 0 (M ), C I (M ) g N g A /(2F ) remember: M 2 ± (m u + m d ) Gell-Mann, Oakes, Renner (1968) quark mass dependence pion mass dependence

31 PION MASS VARIATIONS 31 consider pion mass changes as small perturbations with E i M M phys x 1 m N M = E i M OPE M phys M phys, x 2 g N M E + x i 1 m N + x 3 E i C 0 M phys m phys N C phys 0, x 3 C 0 M + x 2 E i g N + x 4 E i C I M phys g phys N C phys I, x 4 C I M M phys problem reduces to the calculation of the various derivatives using AFQMC and the determination of the x i x 1 and x 2 can be obtained from LQCD plus CHPT x 3 and x 4 can be obtained from two-body scattering and its M -dependence

32 VISUALIZATION of the PION MASS VARIATIONS 32 At LO, one-pion exchange and 4N contact terms pion nucleon coupling g(m ) pion propagator 1/(q 2 M ) 2 Ā s,t a 1 s,t M M phys four nucleon couplings C(M ) nucleon mass m N (M )

33 AFQMC RESUTS for the DERIVATIVES 33 4 He 12 C(0 + 1, 0+ 2 ) E(N t ) = E( ) + const exp( N t /τ ) fit old data E [MeV] fit de dc pp [MeV] not fitted fit old data, fitted E [MeV], Hoyle state fit E [MeV], gnd state fit de dc pp [MeV] gnd state fit de/dc ii [l.u.] not fitted fit de/dg ιn [l.u.] not fitted fit de dcoul [MeV] not fitted fit -8.1 de/dc ii [l.u.] gnd state fit de/dg ιn [l.u.] gnd state fit de dcoul [MeV] gnd state fit de/dc 11 [l.u.] not fitted fit de/dm N not fitted fit de pion IB [MeV] not fitted fit de/dc 11 [l.u.] gnd state fit de/dm N gnd state fit de pion IB [MeV] gnd state fit de/dm (OPE) not fitted fit de pion dm [MeV] not fitted fit de/dm (OPE) gnd state fit de pion dm [MeV] gnd state N t N t

34 DETERMINATION of the x i 34 x 1 from the quark mass expansion of the nucleon mass: x ± 0.2 x 2 from the quark mass expansion of the pion decay constant and the nucleon axial-vector constant: x x 3 and x 4 can be obtained from a two-nucleon scattering analysis & can be deduced from: a 1 M A am = 1 L S (η) η M, η m N E ( L while this can straightforwardly be computed, we prefer to use a representation that substitutes x 3 and x 4 by: a 1 s a 1 t, M M we are ready to study the pertinent energy differences M phys 2 ) 2 M phys

35 RESULTS 35 putting pieces together: E h M M phys = 0.455(35) a 1 s M M phys 0.744(24) a 1 t M M phys (10) E b M M phys = 0.117(34) a 1 s M M phys 0.189(24) a 1 t M M phys (9) E c M M phys = 0.07(3) a 1 s M M phys 0.14(2) a 1 t M M phys (9) x 1 and x 2 only affect the small constant terms also calculated the shifts of the individual energies (not shown here)

36 INTERPRETATION 36 ( E h / M )/( E b / M ) 4 E h and E b cannot be independently fine-tuned Within error bars, E h / M & E b / M appear unaffected by the choice of x 1 and x 2 indication for α-clustering For E h & E b, the dependence on M is small when a 1 s / M 1.6 a 1 t / M the triple alpha process is controlled by : E h+b E h + E b = E 12 3E 4 E h+b M M phys = 0.571(14) a 1 s M M phys 0.934(11) a 1 t M M phys (6) so what can we say about the quark mass dependence of the scattering lengths?

37 CONSTRAINTS on the SCATTERING LENGTHS 37 Quark mass dependence of hadron properties: δo H δm f K f H O H m f, f = u, d, s NN scattering lengths as a function of M : a 1 s,t A s,t, M a s,t M A s,t K q a s,t K q earlier determinations from chiral EFT at NLO Beane, Savage (2003), Epelbaum, Glöckle, UGM (2003) new determination at NNLO: Berengut et al., Phys. Rev. D 87 (2013) K q a s = , Kq a t = a 1 t = M 0.10, a 1 s = M leads also to constraints from Big Bang Nucleosynthesis!

38 CORRELATIONS 38 vary the quark mass derivatives of a 1 s,t within 1,..., +1: K E*12 K E12 K E8 K Ec K E K Eb K Eh K Eh+b K E4 clear correlations: α-particle BE and the energies/energy differences the anthropic view of the Universe depends on whether the 4 He BE moves!

39 THE END-OF-THE-WORLD PLOT 39 δ( E h+b ) < 100 kev Schlattl et al. (2004) ( ) δmq 0.571(14)Ā s (11)Ā t 0.069(6) < m q Ā s,t a 1 s,t M M phys The light quark mass is fine-tuned to 2 3 % Similarly: α EM is fine-tuned to 2.5% Berengut et al., Phys. Rev. D 87 (2013)

40 SUMMARY & OUTLOOK 40 Chiral nuclear EFT: best approach to nuclear forces and few-body systems Many successes in the description of few-nucleon dynamics (A = 2, 3, 4) Nuclear lattice simulations as a new quantum many-body approach Fix parameters in few-nucleon systems predictions (ab initio calculations) 12 C spectrum at NNLO Hoyle state and its structure Fine-tuning of m quark and α EM viability of life changes in m quark of about 2-3 % and in α EM of about 2.5% are allowed Results for 16 O, 20 Ne, 24 Mg, 28 Si and 32 S forthcoming must improve and extend these calculations, e.g. α+ 12 C 16 O+γ fig. Lee et al. the strong interactions remain a challenge

41 ALPHA-CLUSTER NUCLEI 41 Preliminary results for A = 16, 20, 24, 28 t CPU = const A 2 Experiment NNLO [O(Q 3 )] + smeared 4N correction (estimated) 4 He 8 Be 12 C 16 O 20 Ne 24 Mg PRELIMINARY 28 Si E (MeV)

42 42 SPARES

43 43 Nuclear lattice simulations Formalism

44 TRANSFER MATRIX METHOD 44 Correlation function for A nucleons: Z A (t) = Ψ A exp( th) Ψ A with Ψ A a Slater determinant for A free nucleons Euclidean time Ground state energy from the time derivative of the correlator E A (t) = d dt ln Z A(t) ground state filtered out at large times: E 0 A = lim t E A(t) Expectation value of any normal ordered operator O Z O A = Ψ A exp( th/2) O exp( th/2) Ψ A lim t Z O A (t) Z A (t) = Ψ A O Ψ A

45 TRANSFER MATRIX CALCULATION 45 Expectation value of any normal ordered operator O Ψ A O Ψ A = lim t Ψ A exp( th/2) O exp( th/2) Ψ A Ψ A exp( th) Ψ A Anatomy of the transfer matrix operator insertion for expectation value Ψ free Z,N SU(4) full LO O full LO SU(4) Ψ free Z,N 2L to + L ti L to + L ti L to + L ti /2 L to 0 { inexpensive filter { inexpensive filter

46 PROJECTION MONTE CARLO TECHNIQUE 46 Insert clusters of nucleons at initial/final states (spread over some time interval) allows for all type of wave functions (shell model, clusters,...) removes directional bias Example: two basic configurations in the spectrum of 12 C

47 PROJECTION MONTE CARLO TECHNIQUE 47 General wave function: ψ j ( n), j = 1,..., A States with well-defined momentum: L 3/2 m ψ j ( n + m) exp(i P m), j = 1,..., A Insert clusters of nucleons at initial/final states (spread over some time interval) allows for all type of wave functions (shell model, clusters,...) removes directional bias shell-model type cluster type ψ j ( n) = exp[ c n 2 ] ψ j ( n) = exp[ c( n m) 2 ] ψ j ( n) = n x exp[ c n 2 ] ψ j ( n) = exp[ c( n m ) 2 ] ψ j ( n) y exp[ c n 2 ] ψ j ( n) ) 2 ] ψ j ( n) z exp[ c n 2 ] ψ j ( n) ) 2 ] shell-model w.f.s do not have enough 4N correlations (N N) 2

48 MONTE CARLO with AUXILIARY FILEDS 48 Contact interactions represented by auxiliary fields s, s I exp(ρ 2 /2) + ds exp( s 2 /2 sρ), ρ N N Correlation function = path-integral over pions & auxiliary fields p p

49 49 Nuclear lattice simulations Results nuclei neutron matter

50 FIXING PARAMETERS & FIRST PREDICTIONS 50 work at NNLO including strong and em isospin breaking 1 S0 3 S1 9 NN LECs from np scattering and Q d 2 LECs for isospin-breaking (np, pp, nn) 2 LECs D, E related to the leading 3NF make predictions δ( 1 S 0 ) (degrees) LO 3 NLO 3 PWA93 (np) p CM (MeV) δ( 3 S 1 ) (degrees) 180 LO 3 NLO PWA93 (np) p CM (MeV) 1 S0 pp vs np scattering nd spin-3/2 quartet channel... δ( 1 S 0 ) (degrees) LO NLO + IB + EM PWA93 (pp) p cot δ (fm -1 ) p-d (exp.) n-d (exp.) LO NLO NNLO p CM (MeV) p 2 (fm -2 )

51 51 Ground states Epelbaum, Krebs, Lähde, Lee, UGM, arxiv:

52 PREDICTIONS: TRITON & HELIUM-3 52 Epelbaum, Krebs, Lee, UGM, Phys. Rev. Lett. 104 (2010) ; Eur. Phys. J. A 45 (2010) 335 binding energies of 3N systems: E(L) = B.E. a L exp( bl) predict the energy difference E( 3 He) E( 3 H) see also Hammer, Kreuzer (2011) lattice physical (infinite volume) E3 He E triton (MeV) (5) MeV 0.76 MeV [exp.] L (fm)

53 53 Ground state of 4 He L = 11.8 fm E(t) (MeV) (A) 6 LO t (MeV -1 ) (B) NLO-IS IB + EM NNLO t (MeV -1 ) LO (O(Q 0 )) NLO (O(Q 2 )) NNLO (O(Q 3 )) Exp. 28.0(3) MeV 24.9(5) MeV 28.3(6) MeV 28.3 MeV

54 54 Ground state of 8 Be L = 11.8 fm E(t) (MeV) (A) LO (B) NLO-IS IB + EM NNLO t (MeV -1 ) t (MeV -1 ) LO (O(Q 0 )) NLO (O(Q 2 )) NNLO (O(Q 3 )) Exp. 57(2) MeV 47(2) MeV 55(2) MeV 56.5 MeV

55 55 Ground state of 12 C L = 11.8 fm E(t) (MeV) (A) LO (1) LO (2) (B) NLO-IS (1) NLO-IS (2) IB + EM (1) IB + EM (2) NNLO (1) NNLO (2) t (MeV -1 ) t (MeV -1 ) LO (O(Q 0 )) NLO (O(Q 2 )) NNLO (O(Q 3 )) Exp. 96(2) MeV 77(3) MeV 92(3) MeV 92.2 MeV

56 56 Ground state of 16 O L = 11.8 fm E(t) (MeV) (A) LO (1) LO (2) (B) NLO-IS (1) NLO-IS (2) IB + EM (1) IB + EM (2) NNLO (1) NNLO (2) to be published t (MeV -1 ) t (MeV -1 ) LO (O(Q 0 )) NLO (O(Q 2 )) NNLO (O(Q 3 )) Exp. 144(4) MeV 116(6) MeV 135(6) MeV MeV

57 EXCITED STATES of 12 C 57 Lowest excited state is (as in nature) E(2 + 1 ) = 89(3) MeV [ 87.7 MeV] (A) (B) 1 0 LO NLO-IS IB + EM NNLO log [Z(t)/Z (t)] E(t) (MeV) t (MeV -1 ) t (MeV -1 )

58 THE HOYLE STATE (0 + 2 ) 58 energy: E(0 + 2 ) = 85(3) MeV close to E( 4 He) + E( 8 Be) = 83.3(2.0) MeV structure: bent alpha-chain like (not BEC ) (A) LO (1) LO (2) (B) NLO-IS (1) IB + EM (1) NNLO (1) E(t) (MeV) t (MeV -1 ) t (MeV -1 )

59 A HOYLE STATE EXCITATION (2 + 2 ) 59 a 2 + state 2 MeV above the Hoyle state interpretation: a rotational band of the Hoyle state generated from excitations of the alpha-chain what s in the data? log [Z(t)/Z (t)] (A) LO t (MeV -1 ) E(t) (MeV) (B) NLO-IS IB + EM NNLO a 2 + state 3.51 MeV above the Hoyle state seen in 11 B(d, n) 12 C not included in the level scheme! Ajzenberg-Selove, Nucl. Phys. A506 (1990) 1 t (MeV -1 ) a 2 + state 3.8(4) MeV above the Hoyle state seen in 12 C(α, α) 12 C and much more, see next slide and: talk by Henry Weller Bency John et al., Phys. Rev. C 68 (2003) ab initio prediction requires experimental confirmation

60 EARLIER STUDIES of the AP 60 By hand modification of the energy diff. & network calcs in massive stars a ±60 kev change consistent with carbon-oxygen based life a ±277 kev change leaves essentially no carbon (just oxygen) weak conclusion: the strong AP might be in trouble Livio et al., Nature 340 (1989) 281 Changing NN and em interactions in a microscopic model & network calcs Oberhummer et al., Science 289 (2000) 88 modified NN strength & fine structure constant in [0.996, 1.004] no influence on the width but on the relative position of the Hoyle state use up-to-date stellar evolution model more than 0.5[4]% in the strong coupling [α QED ] would destroy all carbon (oxygen) in stars a ±100 kev change of ε = E Hoyle 3E α = 380 kev can be tolerated should be of interest to AP considerations

61