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Nuclear Effective Field Theory

Nuclear Effective Field Theory. Paulo Bedaque Lawrence-Berkeley Laboratory. Extracting low energy information from QCD in a model independent way:. No nucleons a chiral perturbation theory One nucleon a heavy baryon chiral perturbation theory

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Nuclear Effective Field Theory

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  1. Nuclear Effective Field Theory Paulo Bedaque Lawrence-Berkeley Laboratory

  2. Extracting low energy information from QCD in a model independent way: No nucleons a chiral perturbation theory One nucleon a heavy baryon chiral perturbation theory Two or more nucleons a Nuclear effective theory

  3. Hierarchy of scales: NN scale (spin singlet), momentum in the deuteron (spin triplet) Fermi momentum in nuclei QCD scale

  4. Two consequences: Bound states within the EFT range of validity Nuclear EFT is non-perturbative Two possible EFT’s “pionfull”Q~ mp<< mr “pionless”Q ~ 1/a << mp

  5. Pionless theory: two-nucleons That’s why nuclear physics exists ! fine tuned cancellation

  6. another way of looking at the fine tuning: trivial fixed point non-trivial fixed point

  7. Assuming this is the only fine tuning: • Expansion in powers of Q/mp, keep Qa to all orders C2 is NLO, not NNLO • Naïve dimensional analysis fails • C0is the only non-perturbative operator

  8. A good example: neutrino-deuteron collisions (Butler, Chen) Haxton et al. : no exchange currents Kubodera et al. : a model of meson exchange currents 5% difference Both calculations are reproduced by EFT with two different values of The same constant appears on pp fusion, m capture on deuterium, triton beta decay

  9. For the three-body (“pionless”) : How large is ? naïve dimensional analysis would appear only at NNNLO

  10. ultraviolet finite D0 would not not run and would not needed at leading order k p

  11. L=0, S=1/2: triton, helium 3, bosons All others: Pauli principle, centrifugal barrier Two kinds of channels: All others: Three-body force no needed until very high orders, a lot of predictive power 1) 2) ~ 1/Q2 ~ 1/L2

  12. Neutron-deuteron elastic phase shifts L=0, S=3/2 L=2, S=1/2 += AV18 + UX (Kievski et al.) m=Schmelzbach et al. = LO, = NLO, = NNLO L=0, S=3/2 scattering length: a(EFT)=5.09 + 0.89 + 0.35 + …=6.33m0.05 fm a(Exp)=6.35m0.02 fm

  13. 2) ~1/Q2 or ~1/QL (zero mode) ~1/QL change in on-shell amplitude 3H, 3He (and bosons): 1) harder in the UV

  14. Adjust H(L) so: three-body force: limit cycle: Lge p/s0L At higher orders: SUW(4) invariant three-body force terms are enhanced

  15. Neutron-deuteron elastic phase shifts: L=0, S=1/2 x = AV18 + UX (Kievski et al.) i= Schmelzbach et al. = LO, = NLO, = NNLO blue band describes the variation between L=200 g 600 MeV

  16. Phillips line: one 3-body free parameter one line

  17. “Pionfull” EFT (expansion on Q/Land mp/L) Restrictions from c symmetry Potential: Amplitude: L dependence ?

  18. Perturbatively this is inconsistent, but we now know better perturbative: destroys chiral expansion destroys the momentum expansion still inconsistent lattice extrapolations, isospin breaking, cosmology momentum expansion is consistent non-perturbative:

  19. Some NN phase shifts (Epelbaum et al.): 500<L<600 e1 3S1 =LO =NLO =NNLO* =Nijmegen PWA pN couplings fit

  20. Neutral pion photoproduction (Beane, Lee, van Kolck)

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