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Power counting and perturbative one pion exchange in heavy meson molecules

M. Pavón Valderrama*

  • Instituto de Física Corpuscular (IFIC), Centro Mixto CSIC—Universidad de Valencia, Institutos de Investigación de Paterna, Apartado 22085, E-46071 Valencia, Spain

  • *m.pavon.valderrama@ific.uv.es
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Phys. Rev. D 85, 114037 – Published 21 June, 2012

DOI: https://doi.org/10.1103/PhysRevD.85.114037

Abstract

We discuss the possible power counting schemes that can be applied in the effective field theory description of heavy meson molecules, such as the X(3872) or the recently discovered Zb(10 610) and Zb(10 650) states. We argue that the effect of coupled channels is suppressed by at least two orders in the effective field theory expansion, meaning that they can be safely ignored at lowest order. The role of the one pion exchange potential between the heavy mesons, and, in particular, the tensor force, is also analyzed. By using techniques developed in atomic physics for handling power-law singular potentials, which have been also successfully employed in nuclear physics, we determine the range of center-of-mass momenta for which the tensor piece of the one pion exchange potential is perturbative. In this momentum range, the one pion exchange potential can be considered a subleading order correction, leaving at lowest order a very simple effective field theory consisting only of contact-range interactions.

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Phys. Rev. D 85, 114037– Published 21 June, 2012
  • Received 11 April 2012

© 2012 American Physical Society

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