Pion-less Effective Field Theory on Low-Energy Deuteron Electro-Disintegration

In view of its relation to Big-Bang Nucleo-Synthesis and a reported discrepancy between nuclear models and data taken at S-DALINAC, electro-induced deuteron break-up 2H(e,e' p)n is studied at momentum transfer q<100MeV and close to threshold in the low-energy nuclear Effective Field Theory without dynamical pions. The result at N2LO for electric dipole currents and at NLO for magnetic ones converges order-by-order better than quantitatively predicted and contains no free parameter. It is at this order determined by simple, well-known observables. Decomposing the doubly differential cross-section into the longitudinal-plus-transverse (L+T), transverse-transverse (TT) and longitudinal-transverse interference (LT) terms, we find excellent agreement with a potential-model calculation by Arenh"ovel et al using the Bonn potential. Theory and data also agree well on \sigma_{L+T}. There is however no space on the theory-side for the discrepancy of up to 30%, 3-\sigma between theory and experiment in \sigma_{LT}. From universality, we conclude that no theoretical approach with the correct deuteron asymptotic wave-function can explain the data. Un-determined short-distance contributions that could affect \sigma_{LT} enter only at high orders, i.e. at the few-percent level. We notice some issues with the kinematics and normalisation of the data reported.Comment: 30 pages LaTeX2e, including 10 figures as 34 .eps files embedded with includegraphicx. Increased figure sizes; contents identical to version approved for publication in Phys Rev C -- spelling and grammatical difference

Universal Correlations in Pion-less EFT with the Resonating Group Model: Three and Four Nucleons

The Effective Field Theory "without pions" at next-to-leading order is used to analyze universal bound state and scattering properties of the 3- and 4-nucleon system. Results of a variety of phase shift equivalent nuclear potentials are presented for bound state properties of 3H and 4He, and for the singlet S-wave 3He-neutron scattering length a_0(3He-n). The calculations are performed with the Refined Resonating Group Method and include a full treatment of the Coulomb interaction and the leading-order 3-nucleon interaction. The results compare favorably with data and values from AV18(+UIX) model calculations. A new correlation between a_0(3He-n) and the 3H binding energy is found. Furthermore, we confirm at next-to-leading order the correlations, already found at leading-order, between the 3H binding energy and the 3H charge radius, and the Tjon line. With the 3H binding energy as input, we get predictions of the Effective Field Theory "without pions" at next-to-leading order for the root mean square charge radius of 3H of (1.6\pm 0.2) fm, for the 4He binding energy of (28\pm 2.5) MeV, and for Re(a_0(3He-n)) of (7.5\pm 0.6)fm. Including the Coulomb interaction, the splitting in binding energy between 3H and 3He is found to be (0.66\pm 0.03) MeV. The discrepancy to data of (0.10\mp 0.03) MeV is model independently attributed to higher order charge independence breaking interactions. We also demonstrate that different results for the same observable stem from higher order effects, and carefully assess that numerical uncertainties are negligible. Our results demonstrate the convergence and usefulness of the pion-less theory at next-to-leading order in the 4He channel. We conclude that no 4-nucleon interaction is needed to renormalize the theory at next-to-leading order in the 4-nucleon sector.Comment: 24 pages revtex4, including 8 figures as .eps files embedded with includegraphicx, leading-order results added, calculations include the LO three-nucleon interaction explicitly, comment on Wigner bound added, minor modification