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Tae-Sun Park Korea Institute for Advanced Study (KIAS)

Introduction to Effective field theory for astrophysical nuclear reactions. Tae-Sun Park Korea Institute for Advanced Study (KIAS). 2007 APCTP Workshop on Frontiers in Nuclear and Neutrino Physics , Feb. 26-28, 2007, APCTP, POSTECH, Pohang, Korea. TexPoint fonts used in EMF.

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Tae-Sun Park Korea Institute for Advanced Study (KIAS)

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  1. Introduction to Effective field theory for astrophysical nuclear reactions Tae-Sun Park Korea Institute for Advanced Study (KIAS) 2007 APCTP Workshop on Frontiers in Nuclear and Neutrino Physics, Feb. 26-28, 2007, APCTP, POSTECH, Pohang, Korea TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AA

  2. EFT and Astrophysics • One of the ultimate goal of QCD is to make precise, model independent predictions for certain processes that figure importantly in astrophysics and cosmology. • At low-energy domain, EFT is the only presently available technique.

  3. pp-chain pp hep

  4. J. Bahcall’s challenge: “... do not see any way at present to determine from experiment or first principle theoretical calculations a relevant, robust upper limit to the hep production cross section.” (hep-ex/0002018) hep: 3He + p !4He + e+ + e Virtues of EFT: systematic, consistent, model-independent, robust, easy error estimation, … . Q: Can EFT be a breakthrough ?

  5. hep history (S-factor in 10-23 MeV-b unit): Schemetic wave functions ’52 (Salpeter) 630 Single particle model ’67 (Werntz) 3.7 Symmetry group consideration ’73 (Werntz) 8.1 Better wave functions (P-wave) ’83 (Tegner) 425 D-state & MEC ’89 (Wolfs) 15.34.7 analogy to 3He+n ’91 (Wervelman) 57 3He+n with shell-model Modern wave functions ’91 (Carlson et al.) 1.3 VMC with Av14 ’92 (Schiavilla et al.) 1.4-3.1 VMC with Av28 (N+)  S0 = 2.3 (“standard value”) ’01 (MSVKRB) 9.64 CHH with Av18 (N+) + p-wave PRL84(’00)5959, PRC63(’00)015801

  6. What’s wrong with the hep ? • 1. Pseudo-orthogonality : • |4He' |  = |S4:most symmetric • |3He + p' |  = | S31:next-to-most symmetric • S4 | gA ii i | S31=0. : (Gamow-Teller) • h1B-LOi is difficult to evaluate : • We need realistic (not schematic) wave functions. • h1B-LOi is small : h1B-LOi»hMEC (N3LO)i • Meson-exchange current (MEC) plays an essential role. • 2. MEC consists of not only long-ranged contributions but also short-range contributions, and the latter is highly model-dependent.

  7. Heavy-baryon Chiral Perturbation Theory 1. Pertinent degrees of freedom: pions and nucleons. All other massive degrees of freedom (, , , ) are integrated out. Their effects appear as higher order operators of p’s and N’s. 2. Expansion parameter = Q/LcQ : typical momentum scaleand/orm,Lc : mNand/or4p fp, ' 1 GeV . 3. Weinberg’s power counting rule for irreducible diagrams.

  8. Power counting • Building blocks: • Loop ~ Q4 • Pion prop. (q2-m2)-1 ~ Q-2 • Nucleon prop. 1/v.p ~ Q-1 • Vertex with a mb ~ Qd=a+b • Feynman diagram ~ Q with = 4 L – 2 I – IN + i di = 2 – EN/2 – EE + 2 L + ii, i=di + ni/2 +ei – 2

  9. Lagrangian • L=L0 + L1 + L2 + …, whereL0, L1, L2, …: most general Lagr. with i=0,1,2,…, preserving demanded symmetries.

  10. Heavy Fermion Formalism

  11. Gamow-Teller opeator (pp and hep) p OPE 4F There is no soft-OPE (which is N2LO) contributions

  12. The values of c’s are determined from the p-N data

  13. (the coefficient of the 4F contact term) • appears in • pp • hep • 3H 3He + e- + e (tritium-b decay, TBD), • n-d scattering, … . • m-d capture, • … . • Not fixed by symmetry alone. • We fix so as to reproduce the experimental value of the TBD, then we can make predictions for all other processes. • NB: Loops and 3-body contributions are N4LO or higher order.

  14. pp process • 1B-LO is not suppressed, NLO=N2LO=0. LO À N3LO. • At N3LO, there appear CT ( ) and 1-exchange. • The value of is determined from exp. value of TBD rate. • Bridging different A sector, A=2 $ A=3. • Aspects of the actual calculation: • Argonne v18 . • Gaussian regularization, exp(-q2/2) • No experimerimetal data yet: Coulomb repulsion makes it difficult at low-energy. TSP, L. Marcucci,..., PRC67:055206,2003, nucl-th/0106025

  15. Results(pp) with -term, L-dependence has gone !!! the astro S-factor (at threshold) Spp= 3.94 (1  0.15 %  0.10 %) 10-25 MeV-barn cf) M. Butler, J.-W. Chen & X. Kong, PRC63(’01)035501

  16. Results(M2B/M1B) of the pp process

  17. hep process • 1B-LO is strongly suppressed, NLO=N2LO=0. LO » N3LO. • At N3LO, there appear CT ( ) and 1-exchange. • The value of is determined from exp. value of TBD rate. • Bridging different A sector, A=3 $ A=4. • Aspects of the actual calculation: • CHH method with Argonne v18 + Urbana X. • Gaussian regularization, exp(-q2/2) • No experimerimetal data yet: Coulomb repulsion makes it difficult at low-energy. • Required accuracy: order of magnitude. TSP, L. Marcucci,..., PRC67(’03)055206, nucl-th/0107012 K. Kubodera & TSP, Ann. Rev. N&P Sci. vol.54, ’04

  18. Results(hep) -term removes the major L-dependence. The small L-dependence in 2B is however amplified due to the cancellation between 1B & 2B. Sizable but still very reasonable L-dependence in net amplitude.

  19. Results(M2B/M1B) of the hep process

  20. hepS-factorin10-23 MeV-barn: • Shep(theory)=(8.6  1.3) • hepneutrino flux in 103 cm-2 s-1 : • fhep(theory) = (8.4  1.3) • fhep(experiment) < 40 • Super-Kamiokande data, hep-ex/0103033

  21. Convergence ? (Higher order contributions ?)Isoscalar M1 (M1S) inn+p!d+ • Due to pseudo-orthogonality, 1B-LO is highly suppressed, NLO=N2LO=0. • At N3LO, there appear CT (g4S ) and 1-exchange. • The value of g4S is determined from the exp. value of d. • Aspects of the actual calculation: • Argonne v18 wave functions. • Hardcore regularization, (3)(r) !(r-rC)/(4 r2), rC» 1/ . • Up to N3LO and up to N4LO. • No experimerimetal data yet: it can be in principle measured via the spin observables, but requires ultra-high polarizations. TSP, K. Kubodera, D.-P. Min & M. Rho, PLB472(’00)232

  22. Results(M2B/M1B) of M1S (n+p!d+) :N3LO N4LO

  23. Results(M2B/M1B) of M1S (n+p!d+) :N3LO N4LO • Naïve N4LO contributions are large, but they are short-ranged and can be absorbed into contact-term by shifting the value of dR. • After renormalization, the actual (net) N4LO contributions are tiny.

  24. Results(M2B/M1B) of M1S, up to N4LO

  25. Discussions • Developed an EFT method which enables us to do a systematic and consistent EFT calculation on top of accurate but phenomenological wave functions. • Confirmed the RG-invariance (or -independence) numerically to a satisfactory degree. • Also demonstrated the convergence of chiral expansion in the isoscalar M1 channel of the np! d, check for other processes are future works. • For all the cases we have studied, our method works quite well • extremely high accuracy for the pp process. • the first accurate & reliable theory prediction for the hep. • -d (S. Ando etal., PLB555(’03)49), -d (S.Nakamura etal, NPA707 (’02)561,NPA721(’03)549) • works on progress in electromagnetic processes.

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