Poincaré invariance in NRQCD and potential NRQCD revisited
Matthias Berwein (Nishina Center, RIKEN, Wako, Saitama 351-0198, Japan, Physik-Department, Technische Universität München, James-Franck-Str. 1, 85748 Garching, Germany); Nora Brambilla (Institute for Advanced Study, Technische Universität München, Lichtenbergstraße 2a, 85748 Garching, Germany, Physik-Department, Technische Universität München, James-Franck-Str. 1, 85748 Garching, Germany); Sungmin Hwang (Max-Planck-Institut für Physik, Föhringer Ring 6, 80805 München, Germany, Physik-Department, Technische Universität München, James-Franck-Str. 1, 85748 Garching, Germany); Antonio Vairo (Physik-Department, Technische Universität München, James-Franck-Str. 1, 85748 Garching, Germany)
We investigate how fields transform under the Poincaré group in nonrelativistic effective field theories of QCD. In constructing these transformations, we rely only on symmetries and field redefinitions to limit the number of allowed terms. By requiring invariance of the action under these transformations, nontrivial relations between Wilson coefficients for both nonrelativistic QCD and potential nonrelativistic QCD are derived. We show explicitly how the Poincaré algebra is satisfied, and how this gives complementary information on the Wilson coefficients. We also briefly discuss the implications of our results, as well as the possibility of applying this method to other types of effective field theories.
