Scattering of an ultrasoft pion and the Xð3872Þ

Eric Braaten, H.-W. Hammer, and Thomas Mehen Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA Helmholtz-Institut für Strahlenund Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn, 53115 Bonn, Germany Physics Department, Duke University, Durham, North Carolina 27708, USA (Received 12 May 2010; published 16 August 2010) The identification of the Xð3872Þ as a loosely-bound charm-meson molecule allows it to be described by an effective field theory, called XEFT, for the D D, D D , and D D sector of QCD at energies small compared to the pion mass. We point out that this effective field theory can be extended to the sector that includes an additional pion and used to calculate cross sections for the scattering of a pion and the Xð3872Þ. If the collision energy is much smaller than the pion mass, the cross sections are completely calculable at leading order in terms of the masses and widths of the charm mesons, pion masses, and the binding energy of the Xð3872Þ. We carry out an explicit calculation of the cross section for the breakup of the Xð3872Þ into D þ D 0 by the scattering of a very low energy þ.