2013/11/13 by Koji Harada, Hirofumi Kubo, Harada, Koji +5
Chemistry · Physics and Astronomy · #Advanced NMR Techniques and Applications #Pulsars and Gravitational Waves Research #Quantum Chromodynamics and Particle Interactions #hep-ph #nucl-th
paper · pdf · doi:10.48550/arxiv.1311.3063
10 pages, 2 figures
arxiv created 2013/11/13 · arxiv updated 2013/11/14
We consider the nuclear effective field theory including pions in the two-nucleon sector in the S waves up to including the next-to-next-to-leading order (NNLO) terms according to the power counting suggested by the Wilsonian renormalization group analysis done in a previous paper. We treat only the leading contact interaction nonperturbatively, and the rest, including the long-distance part of pion exchange, are treated as perturbations. To define the long-distance part, it is important to introduce a separation scale, or a cutoff. We employ a hybrid regularization, in which the loops with only contact interactions are regularized with Power Divergence Subtraction (PDS), while the loops with (long-distance part of) pion exchange are regularized with a Gaussian damping factor (GDF), to simplify the (nonperturbative) leading-order amplitudes. The scale introduced by PDS is identified with the cutoff of GDF up to a numerical factor. We emphasize that the introduction of the GDF requires a careful definition of the coupling constant for the pion exchange. We obtain the analytic expressions for the phase shifts for the 1S0 and 3S1-3D1 channels. By fitting them to the Nijmegen partial wave analysis data, it is shown that the effective theory expansion with perturbative long-distance part of pion exchange is converging.