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

More-effective EFT: Electroweak response functions of A=2,3,4. Tae-Sun Park Korea Institute for Advanced Study (KIAS) in collaboration with Y.-H. Song , K. Kubodera, D.-P. Min, M. Rho L.E. Marcucci, R. Schiavilla, M. Viviani, A. Kievsky, S. Rosati.

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

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  1. More-effective EFT: Electroweak response functions of A=2,3,4 Tae-Sun Park Korea Institute for Advanced Study (KIAS) in collaboration with Y.-H. Song, K. Kubodera, D.-P. Min, M. Rho L.E. Marcucci, R. Schiavilla, M. Viviani, A. Kievsky, S. Rosati TSP et al., PRC67(’03)055206,nucl-th/0208055 Y.-H. Song and TSP, nucl-th/0311055 K. Kubodera and TSP, Ann. Rev. Nucl. Part. Sci. vol.54 (2004) KIAS-Hanyang 2004@KIAS

  2. 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 Q: Can EFT be a breakthrough ?

  3. 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

  4. 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 is highly model-dependent, hsoft 1-exchangei =0(Ã a generic feature of GT operator).

  5. MEC in EFT (Heavy-baryon ChPT) • MEC= N2LO+N3LO +  (N2LO=0 for GT), • N3LO= (hard 1-exchange) + (r) ()ij • Long-range part (hard 1-exchange) is well-known. • The value of  is not fixed by symmetry, and should be determined either by QCD or by other experiments. • Once the value of  is fixed, no other uncertainty left.

  6. Nuclear matrix element in EFT M=hfEFT| OEFT |iEFTi • |EFTi is yet to come ! • Schematic wave functions are not good. • A few accurate phenomenological wave functions available. • How we can go further ?

  7. We are thus forced to look at the possibility to study M=hfphen| OEFT | ipheni • Can it work ?

  8. How we do with  ? • Model-dependence  cut-off dependence: M()=hf | O() | ii = Mnon-CT () + () hf | (r) | ii . • Model-dependence resides in short-range, which we explore in terms of . • Consider another known process which depends on  : M0exp =M0non-CT () + () h0f | (r) | 0ii . This step determines the value of  for a given  and a. •  have strong dependence on , but independent of the details (quantum numbers, A, Z, ...) of the process.

  9. RG-invariance •  M()= hf | O() | ii = 0 ? • O(’) = O() + c0(r) + c2r2(r) +  , thus equivalent (up to N3LO) to replace ()!(’) = () + c0, which has no effect in matrix elements. We will check the RG-inv. numerically.

  10. Model-invariance ? • M(a)= hf(a) | O | i(a)i : a-independent ? • (a: model-index) • Vlow-k: if we limit our model space to k < , then all the accurate phenomenological potentials are equivalent. Hlow-k = U(a)y H(a) U(a) is a-independent, |(a)i = U(a) |low-ki M(a)= hlow-k | Uy(a)O U(a)| low-ki = hlow-k | O(a) | low-ki We also expect O(a) = Olow-k() + d0(r) + d2r2(r) + , since the finite range-part is dictated by the chiral symmetry.

  11. Contents • Brief review on heavy-baryon chiral perturbation theory • CT contributions to the currents at N3LO • Results: • isoscalar M1 (M1S) in n+p! d+ • pp (p+p ! d + e+ + e) • hep (3He + p !4He + e+ + e) • hen (3He + n !4He + ) • Discussions

  12. Heavy-baryon Chiral Perturbation Theory 1. Pertinent degrees of freedom: pions and nucleons. Others 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 fp3. Weinberg’s power counting rule for irreducible diagrams.

  13. CT contributions to the currents at N3LO • g4S : isoscalar M1 • d, spin observables(np! d+), (3He)+(3H), hen,... • g4V : isovector M1 • (np! d+), (3He)-(3H), hen,... • pp, hep, tritium-b decay (TBD), m-d capture, n-d scattering, … .

  14. 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

  15. Results(M2B/M1B) of M1S, up to N3LO cf) J.-W. Chen, G. Rupak & M. Savage, PLB464(’99)1

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

  17. pp process • 1B-LO is not suppressed, NLO=N2LO=0. LO À N3LO. • Most solar neutrinos are due to pp process. • 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: • CHH method with Argonne v18 + Urbana X. • 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

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

  19. hep process • 1B-LO is strongly suppressed, NLO=N2LO=0. LO » N3LO. • Highest-E solar neutrinos are due to hep process. • 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

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

  21. 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

  22. The hen (3He + n  4He + ) process • Accurate experimental data are available for the hen • The hen process has much in common with hep : • The leading order 1B contribution is strongly suppressed due to pseudo-orthogonality. • A cancellation mechanism between 1B and 2B occurs. • Trivial point: both are 4-body processes that involve 3He + N !4He. Q: Can we test our hep prediction by applying the same method to the hen process ? Y.-H. Song & TSP, nucl-th/0311055

  23. Results(M2B/M1B) of the hen process

  24. hen history s(exp)= (55 ±3) mb, (54 ± 6) mb 2-14 mb : (1981) Towner & Kanna 50 mb : (1991) Wervelman (112, 140)mb : (1990) Carlson et al ( 86, 112)mb : (1992) Schiavilla et al s(our work)= ??(See Young-Ho Song’s talk)

  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 numerically to a very satisfactory degree. • Also demonstrated the convergence of chiral expansion in the isoscalar M1 channel of the np! d, check for other proceeses are future works. • For all the cases we have studied, our method works quite well • extremely high accuracy in 2-body processes, • the first accurate & reliable theory prediction for the hep and hen, • -d (S. Ando etal., PLB555(’03)49), -d (S.Nakamura etal, NPA707 (’02)561,NPA721(’03)549)

  26. Compared to Hybrid model approaches: (Chemtob-Rho type of current-algebra based phenomenological current operators + phen. wave functions) • systematic & consistent expansion scheme • full control on the short-range physics • ,,, • Compared to Pure EFT approaches: • more flexible and more powerful • ... ! so, we are calling our method as More-effective effective field theory (MEEFT)

  27. Invitation for dinner Those who have not taken dinner last night with Prof. Rho are invited for dinner tonight !

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