Effective Field Theory with Dibaryon Fields: Nucleon-Nucleon amplitudes at NNLO

Understand

We calculate the nucleon-nucleon scattering amplitudes in the 1S0 and 3S1-3D1 channels at next-to-next to leading order starting from a recently proposed non-relativistic chiral effective theory, which includes dibaryon fields as fundamental degrees of freedom.

• We restrict ourselves to center of mass energies (E) smaller than the pion mass (m_pi), and further divide the calculation into two relative momentum (p) regions, a high energy one p ~ m_pi >> delta m_i, \delta m_i being the dibaryon residual masses, and low energy one p ~ delta m_i.
• We first match to a lower energy effective theory in which we calculate the amplitudes in the high energy region.
• We further match this effective theory to the so called pionless effective theory in the low energy region, and carry out the calculations in the latter.