Hen process in Effective field theory

1. Hen process in Effective field theory Preliminary Young-Ho Song(SNU) Tae-Sun Park(KIAS) Dong-Pil Min (SNU) Manque Rho (Saclay) Kuniharu Kubodera(USC) (Preparing to submit to PLB) KIAS-HanYang Joint Workshop(OCT,2004)

2. Closly related to the hen What is the Hen? • (Hen) radiative neutron capture on 3He • Related topics: (hep) scattering, capture magnetic momentsofD, T, 3He isoscalar and isovector M1inn + p  D + 

3. hen history s(exp)= (55 ±3) mb, (54 ± 6) mb 14-125 mb : (’81) Towner & Kanna 29-65 mb : (’91) Wervelman (112, 140)mb : (’90: VMC) Carlson et al ( 86, 112)mb : (’92: VMC) Schiavilla et al a(3He - n)= (3.50, 3.25) fm • Accurate recent exp: a(3He - n)= 3.278(53) fm

4. Pseudo-orthogonalitybetween |4He and |3He + n : |4He= | : most symmetric +  |3He + n = | : next-to-most symmetric +  • Why is it so difficult to calculate the hen ( hep ) ? • Leading order  1B  is highly suppressed.  1B-LO is small and difficult to evaluate  We need realistic (not schematic) wave functions.  Meson-exchange current (MEC) plays an important role.

5. Hen matrix elements by Schiavilla et al (’92: VMC) 2. There is a substantial cancellation between 1B and MEC.  Errors are amplified. 3. Getting realistic/reliable 4-body wave functions is quite non-trivial. Furthermore we need w.f.s for both scattering states as well as bound states. The hen process is one of examples that SNPA have sizable discrepancies from the experimental data for light nuclei reactions.

6. EFT W.F. EFT Operator EFT W.F. Hybrid Method Principle Problems of Nuclear Physics Obtain the matrix elements Yf | O | Yi SNPA W.F. SNPA W.F.

7. Short-range physics the short-range physics can be well described by the local operators in EFT, • For most cases, it is sufficient to consider only C0 (non-derivative contact term)

8. MEEFT strategy for M=Yf | O | Yi  • hybrid method + renormalization procedure for the short ranged contributions • By using the hybrid mehod, obtain the wave function and the matrix elements. And then, fix the value of C0 at given cutoff so as to reproduce other known experimental data. • The value of C0 is model-dependent, which cancels out the model-dependence of Yf | d(r) | Yi , so as to have model-independent Yf | Oshort | Yi, which is therenormalization condition. • Once we fix the value of C0 , we can predict other processes which depends on the C0.

9. Successful applications of the MEEFT method • isoscalar and isovector M1inn + p  D +  T.-S.Park et al, Phys.Rev.Lett. 74,4153(1995) Nucl.Phys. A596, 515(1996) Phys.Lett. B472,232 (2000) • m-d capture rate, S.Ando et al, Phys.Lett. B533, 25 (2002) • n-d scattering S.Nakamura et al, Nucl.Phys. A707, 561(2002) Nucl.Phys.A721,549 (2003) S.Ando et al, Phys. Lett. B555, 49 (2003) • hep T.-S.Park et al. Phys.Rev. C 67, 055206 (2003)

10. The hen (3He + n  4He + ) process • 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 and 4He. • Differences: Coulomb interaction, M1 and GT … • hep process have not been confirmed by experiments • Accurate experimental data are available for the hen

11. Remarks on the hen process The hen process is governed by isoscalar and isovector M1 operators. there is soft-OPE contribution to the isovector M1, which is NLO compared to 1B. The N3LO of Isovector M1 corresponds to 1-loop. At N3LO, there appear two 4F contact counter-terms, g4S and g4V, which we can fix by imposing the condition to reproduce the magnetic moments of 3H and 3He Up to N3LO, three-body and four-body current operators do not appear.

12. MEEFT Strategy for M(Hen)=Yf | O | Yi  |Y :VMC wave functions with Av14 + Urbana VIII O:Up to N3LO in heavy-baryon chiral-perturbation theory (HBChPT) Weinberg’s power counting rule for irreducible diagrams.

13. AV14 potential+U8

14. VMC wave function (Wiringa 91)

15. 3He+n Scattering W.F.

16. In our work, we have fit the Woods-Saxon potential parameters to reproduce the scattering length of 3He+n an=3.278 fm and the low-E 3He-n phase shifts

17. 3He-n phase shift [deg] wrt Ecm [MeV]solid line = Woods-Saxon potentialdots= R-matrix analysis by Fofmann & Hale, NPA613(’97)

18. M1 channel (hen process)

20. the two-body currents in momentum space are valid only up to a certain cutoff L . This implies that when we go to coordinate space, the currents should be appropriately regulated. This is the key point in our approach. • Cutoff defines the energy momentum scale of EFT that divides low energy degrees of freedom and high energy d.o.f.

21. To control the short-range physics consistently, • we apply the same (Gaussian) regulator • for all the A=2,3 and 4 systems, with • L = [500, 600, 800] MeV

24. Results(hen) Preliminary

25. Preliminary • 4F contact terms have a role of removig the L-dependence

26. Summary Preliminary • s(theory)= (51 ±2 ±1) mb , which is in good agreement with the exp.,(55 ±3) mb, (54 ± 6) mb. However, there are caveats

27. 1. Potential model • (AV14+U8 is enough?) • More exact potential model is preferred. •  AV18 + U9 potential? • 2. Scattering state W.F. • The matrix elements is not sensitive • on the scattering of the 3He+n • Different from the reported calculations • Different parameters of the W-S potential? Variational W.F. for the scattering state?