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The radiative neutron capture on 3 He ( 3 He+n → 4 He+  ) in effective field theory

The radiative neutron capture on 3 He ( 3 He+n → 4 He+  ) in effective field theory. Young-Ho Song Seoul National University in collaboration with T.-S. Park , K. Kubodera, D.-P. Min, M. Rho. 1.Motivation and Reviews 2. Formalism 3. Numerical Results 4. Conclusion. Motivation.

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The radiative neutron capture on 3 He ( 3 He+n → 4 He+  ) in effective field theory

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  1. The radiative neutron capture on 3He (3He+n→4He+) in effective field theory Young-Ho Song Seoul National University in collaboration with T.-S. Park, K. Kubodera, D.-P. Min, M. Rho

  2. 1.Motivation and Reviews 2. Formalism 3. Numerical Results 4. Conclusion

  3. Motivation • The radiative neutron capture on 3He (3He+n→4He+) at threshold is closely related to the hep process(3He+p→4He+e+e) • They shows much similarity and both can be calculated in a same low energy effective theory scheme.

  4. 3He+p→4He+e+e No experiment Large theoretical uncertainty

  5. hep theory • Old schematic wave function (‘52-’91) • S-factor :4~630 (10-23 MeV-b) • Modern wave function (‘91-’01) • S-factor(10-23 MeV-b) • ’91 (Carlson et al.) 1.3 • ’92 (Schiavilla et al.) 1.4-3.1S0 = 2.3(“standard value”) • ’01 (Marcucci et al) 9.64 Effective field theory with hybrid method(MEEFT) TSP et al., PRC67(’03)055206, nucl-th/0107012 S(theory)=(8.6  1.3) 10-23MeV-b How can we test our prediction ? Can we test our hep prediction by applying the same method to the hen process ?

  6. 3He+n→4He+ • Experiment: (exp)= (55 ±3)b, (54 ± 6)b • Theory : • Old schematic wave function • 14-125b : (’81) Towner & Kanna • 29-65b : (’91) Wervelman • Modern wave function • (112, 140)b : (’90: VMC) Carlson et al • ( 86, 112)b : (’92: VMC) Schiavilla et al a(3He - n)= (3.50, 3.25) fm Accurate recent exp: a(3He - n)= 3.278(53) fm

  7. hen and hep • Leading One-body contribution is highly suppressed. • Pseudo-orthogonality • between initial and final wave function • →meson exchange current plays essential role. Hen matrix elements by Schiavilla et al (’92: VMC) • 2.Cancellation between one-body contribution • and meson exchange current contribution • →amplify uncertainty →We need accurate 4-body wave function and exchange current operator

  8. Formalism • Heavy baryon chiral perturbation theory • Gives a systematic way to obtain current operators up to N3LO • Gives a systematic treatment of the short range physics • However, it is yet hard to calculate 4-body system • Standard nuclear physics approach • Gives a very accurate phenomenological potential • Reliable 4-body wave function can be obtained • However, there is no systematic way of treating short range physics. There is no way of systematic error estimation

  9. EFT W.F. EFT Operator EFT W.F. Hybrid Method Short range physics <EFT| OEFT|EFT> ≈<Phen| OEFT (Λ)|Phen> SNPA W.F. C0(r) • isoscalar and isovector M1 inn + p  D +  • m-d capture rate • n-d scattering • Etc. SNPA W.F.

  10. MEEFT strategy for M=Yf | O | Yi  • hybrid method + renormalization procedure for the short ranged contributions • By using the hybrid method, 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.

  11. 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.

  12. 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.

  13. Only two constants to be fixed Up to N3LO, no three-body (and higher-body) current operators appear. 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

  14. How to fix g4s and g4v ? • They are not fixed by the symmetry. • In principle, they can be fixed by solving QCD at low-energy, but ... • Magnetic moments of 3H and 3He also depend on g4s and g4v. • For each , we fix the values of g4s and g4v by imposing the condition that the experimental values of (3H) and (3He) should be reproduced.

  15. Numerical Result

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

  17. Summary • (theory)= (49 ±7) -b , which is consistent with the exp.,(55 ±3) -b, (54 ± 6) -b. • MEEFT works well for the hen process, providing the 1st satisfactory theoretical prediction for the hen cross section. • Possible extensions (future works) • Different wavefunctions • Wave functions with Vlow-k • Going to higher order • Investigating other few-body (electro-weak) processes

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