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Light nuclei and electroweak probes Tae-Sun Park Sungkyunkwan University (SKKU)

Light nuclei and electroweak probes Tae-Sun Park Sungkyunkwan University (SKKU) in collaboration with Young-Ho Song & Rimantas Lazauskas. FB19@Bonn, Germany, Aug.31~Sep.05, 2009 . Contents. Motivations (with brief intro. to HBChPT )

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Light nuclei and electroweak probes Tae-Sun Park Sungkyunkwan University (SKKU)

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  1. Light nuclei and electroweak probes Tae-Sun Park Sungkyunkwan University (SKKU) in collaboration with Young-Ho Song&RimantasLazauskas FB19@Bonn, Germany, Aug.31~Sep.05, 2009

  2. Contents • Motivations (with brief intro. to HBChPT) • Part I: Magnetic dipole (M1) currents up to N3LO and n+d →3He+γ • Part II: Gamow-Teller(GT) currents up to N3LO and applications • Part III: M1 currents and n+3He → 4He+γ

  3. Motivation: M1 & GT are … • important in astro-nuclear physics • M1: n+p→d+γ, n+d →3He+γ, n+3He → 4He+γ (hen), … • GT: p+p→d+e++ν (pp),p+3He→4He+e++ν (hep),… • providing dynamical information not embodied in Hamiltonian • Electric channel (E1, E2) : Siegert’s theorem: (∂∙J= 0) ⇔ Hamiltonian • For M1 : ∂∙J= 0 by construction, gauge-inv says little here • For GT : ∂∙J≠ 0. • a good playing ground of EFTs (ideal to explore short-range physics )

  4. Heavy-baryon Chiral Perturbation Theory • 1. Degrees of freedom: pions& nucleons up to L • (, , , ) + high energy part => appears as local operators of p’s and N’s. • 2. Expansion parameter = Q/Lc Q : typical momentum scale and/or m,Lc : mN~4p fp~1 GeV . • L = L0 + L1 + L2 +  with L~(Q/) • 3. Weinberg’s power counting rule for irreducible diagrams.

  5. Current operators in HBChPT • J~ (Q/)with  = 2 (nB-1) + 2 L + ii, i = di + ni/2 + ei - 1 • ※Additional suppression: ~(1, Q), 5~(Q, 1) • ※ GT up to N3LO : 1B + 2B(1π-E )+ 2B(CTs) • ※ M1 up to N3LO: 1B + 2B(1π-E )+ 2B(CTs) +2B(2π-E)

  6. Comments on matrix elements <f |J |i> • Wave functions • Available potentials: phenomenological, EFT-based • Short-range behavior : highly model-dependent ! • Electro-weak current operators J • At N3LO, there appear NN contact-terms (CTs) in GT/M1 • CTs represent the contributions of short-ranged and high-energy that are integrated-out • How to fix the coefficients of them (LECs) ? • Solve QCD => Oh no ! • Determine from other experiments => usual practice of EFTs, i.e., renormalization procedure

  7. <f |JCT|i>= C0() <f |()ij(rij) |i> • For a given w.f. and , determine C0() so as to reproduce the experimental values of a selected set of observables that are sensitive on C0 • Model-dependence in short-range region: • In EFTs, differences in short-range physics is into the coefficients (LECs) of the local operators. • We expect that … • C0() : -dependent (to compensate the difference in short-range) • Net amplitude <f |(J1B +J1π+… +JCT |i>: -independent • will be proven numerically by checking -dependence • Model-dependence in long-range region: • Long-range part of ME: governed by the effective-range parameters (ERPs) such as binding energy, scattering length, effective range etc • In two-nucleon sector, practically no problem∵ most potentials are very good in 2N sector • In A ≥3, things are not quite trivial (we will see soon…)

  8. Part I: M1 properties of A=2 and A=3 systems (n+d →3He+γ)

  9. M1 currents up to N3LO J= J1B + J1 + (J1C + J2 + JCT) = LO + NLO + N3LO

  10. g4Sand g4V appear in • (2H), (3H), (3He), … • Cross sections/spin observables of npd, ndt, … • We can fix g4S and g4V by • A=2 sector: (2H) and (npd) • A=3 sector: (3H) and (3He) • …

  11. Details of (n+d →3He+γ)calculation • nd and Rc (photon polarization of nd capture) calculated • g4s and g4v : fixed by (3H) and (3He) • Various potential models are considered • Av18 (+ U9) • EFT (N3LO) NN potentials of Idaho group • EFT (N3LO) NN potentials of Bonn-Bochum group with diff.  • {, ’}= {450,500}, {450, 700}, {600, 700} MeV = (E1, E4, E5) • INOY (can describe BE’s of 3H and 3He w/o TNIs ) • Wave functions: Faddeev equation

  12. nd and Rc

  13. -depdendence (model: INOY)inputs: (3H) and (3He) ※Pionless EFT: nd= 0.503(3) mb, -Rc= 0.412(3) Sadeghi, Bayegan, Griesshammer, nucl-th/0610029 Sadeghi, PRC75(‘07) 044002

  14. Model-dependence

  15. M1(J=1/2) ≈2(B3), M1(J=3/2) ≈4(B3)

  16. A trial for improvement • Replace B3 by B3exp mn=n(B3) + mn => mn’=n(B3exp) + mn = n(B3exp) + mn- n(B3) • mn’ • m2’ = -21.89±0.24, m4’ = 12.24±0.05 • nd’=0.491±0.008 mb, Rc’=0.463±0.003 • Cf) data: 0.508±0.015 mb & 0.420±0.030

  17. Another way to correct the long-range part • Adjust parameters of 3N potential to have correct scattering lengths and B.E.s • Range parameter (a cutoff parameter) and the coefficients of U9 potential is adjusted • C = 2.1 fm-2 3.1 fm-2 • A2 = -29.3 KeV -36.955 KeV • BE(3H) and 2and are OK, but BE(3He) is over-bound by 40 KeV. • Introduce charge-dependent term in U9, and all the B.E.s and scattering lengths can be reproduced • A2 -36.575 KeV for 3He

  18. Model-dependence (improved) • -independence is found to be very small, short-range physics is under control. • Model-dependence is tricky • Naively large model-dependence • But strongly correlated to the triton binding energy • Model-independent results could be obtained • either by making use of the correlation curve • or by adjusting the parameters of 3N potential to have correct ERPs

  19. Part II: Gamow-Teller channel (pp and hep) p OPE 4F There is no soft-OPE (which is NLO) contributions

  20. Thanks to Pauli principle and the fact that the contact terms are effective only for L=0 states, only one combination is relevant: The same combination enters into pp, hep, tritium-b decay (TBD), m-d capture, n-d scattering, … . We use the experimental value of TBD to fix , then all the others can be predicted !

  21. 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

  22. Results(pp)

  23. Results(hep)Reduced matrix element with respect to L (MeV)

  24. Part III: The hen process (n+3He → 4He+γ) σ(exp)= (55 ±3) μb, (54 ± 6) μb 2-14 μb : (1981) Towner & Kanna 50 μb : (1991) Wervelman (112, 140)μb : (1990) Carlson et al ( 86, 112)μb : (1992) Schiavilla et al (49.4±8.5, 44.4±6.7) μb : this work

  25. hen(M1) & hep(GT) are hard to evaluate • Leading 1B contribution (IA) is highly suppressed due to pseudo-orthogonality, : • The major part of |f> and |i> belong to different symmetry group, cannot be connected by r- independent operators, < f |J1B|i> ≈0 . • |f=4He> : most symmetric (S4) state, all N’s are in 1S state • |i> : next-to-most symmetric state (S31) ; 1-nucleon should be in higher state due to Pauli principle • < f |J|i> is sensitive to MECs and minor components of the wfs. • Requires realistic A=4 wfs for both bound and scattering states !! • Accurate evaluation of MECs needed • Short-range contributions plays crucial role !! • Coincidental cancellation between 1B and MEC occurs.

  26. Details of (n+3He → 4He+γ) calculation • Various potential models are considered • Av18 • I-N3LO: NN potentials of Idaho group • INOY (can describe BE’s of 3H and 3He w/o TNIs ) • Av18 + UIX • I-N3LO+UIX* (UIX parameter is adjusted to have B(3H) exactly) • Wave functions: Faddeev-Yakubovski equations in coordinate space • M1 currents up to N3LO • g4s and g4v : fixed by (3H) and (3He)

  27. hen cross section: model-dependent (but correlated with ERPs)

  28. How hen cross section is correlated to ERPs ?sn3He∝ζ≡ [q (anHe3/rHe4)2]-2.75 or sn3He∝q-5 PD2/3 sn3He(mb)

  29. Cutoff-dependence: (Re Mhen) vsΛ[MeV]

  30. Convergence ?

  31. Effective ME • Observation: If we omit something (say, <J2>), values of g4s and g4v should also be changed to have the correct (3H) and (3He) without <J2>. • “effective <J2>” ≡ changes in the net ME if we omit <J2>

  32. Discussions • For all the cases, short-range physics is under control. • Long-range part is tricky : To have correct results, one needs • either the potential that produces all the relevant effective range parameters (ERPs) correctly • or the correlation of the results w.r.t. ERPs • Once the correct ERPs have been used, all the results are in good agreement with the data • So far up-to N3LO. N4LO calculations will be interesting to check the convergence of the calculations.

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