Non-relativistic Neutron Deuteron Scattering

Abstract

Abstract. We discuss the calculation of polarization observables, including A y , in nd scattering to next-to-next-to-next-to-leading order in pionless effective field theory.We present preliminary results of the first next-to-next-to-next-to-leading order (N 3 LO) calculation of the nd scattering amplitude in the framework of nonrelativistic pionless effective field theory (EFT / π ). In this theory, the typical momentum exchange in the scattering must be much smaller then the mass of the pion. The power counting parameter for EFT / π is the ratio Q Λ / π , where Q is the typical momentum exchange in the scattering and Λ / π is the EFT / π breakdown scale,interaction terms in the two-body sector up to N 3 LO are the two two-nucleon-to-dibaryon vertices (for the 3 S 1 and 1 S 0 channels) at LO, the effective range term at NLO, the S D-mixing interaction at N 2 LO, and the shape parameter and two-body P-wave contact interaction terms at N 3 LO. Three-body interaction terms enter first at LO and a new energy dependent term appears at N 2 LO. The two-body interaction coefficients are matched onto NN scattering data. At LO the three-body interaction coefficient is matched onto the doublet S -wave nd scattering length and the N 2 LO energy dependent three-body force to the triton binding energy. The calculation of the amplitude for nd scattering requires summing an infinite set of diagrams. This sum does not factorize as it does in the two-body case; instead an integral equation must be solved numerically [1]. The n th order correction to the nd scattering amplitude is given by the integral equation shown in Fig. 1 [2-4]. An important part of this calculation is the two-body P-wave contact interaction diagram for nd scattering shown in Fig. 2. To solve the equation shown in Fig. 1 to a given order we project it onto different partial waves and then solve the projected equations numerically [5,6]. After obtaining the numerical solution for the amplitude we are able to calculate any parity conserving observable of interest. One of the most important observables is A y , which measures the asymmetry between the cross sections induced by nucleons of opposite transverse spin polarization on an unpolarized deuteron target [7]:Varying the N 3 LO coefficients within the EFT / π uncertainty gives the results in Fig 3, which shows good agreement with the differential cross section and reasonable agreement with A y for a variety of energies. We can also pursue the calculation to higher orders to attempt to improve the agreement.

Three-body systems in pionless effective field theory

“…45 Finally, Margaryan et al calculated polarization observables in nd scattering to N 3 LO in EFT π by considering contributions from two-body P -wave contact interactions. 46 Below the formalism for nd scattering is introduced starting with the quartet channel, and then proceeded by the doublet channel. In addition the partial resummation technique is briefly reviewed but the focus is on the newer strictly perturbative techniques.…”