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Pion interactions in the $X (3872)$

S. Fleming^1,*, M. Kusunoki^1,†, T. Mehen^2,3,4,‡, and U. van Kolck^1,5,6,§

¹Department of Physics, University of Arizona, Tucson, Arizona 85721, USA
²Department of Physics, Duke University, Durham, North Carolina 27708, USA
³Jefferson Laboratory, 12000 Jefferson Avenue, Newport News, Virginia 23606, USA
⁴Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
⁵Kernfysisch Versneller Instituut, Rijksuniversiteit Groningen, Zernikelaan 25, 9747 AA Groningen, The Netherlands
⁶Instituto de Física Teórica, Universidade Estadual Paulista, Rua Pamplona 145, 01405-900 São Paulo, São Paulo, Brazil

^*fleming@physics.arizona.edu
^†masa@physics.arizona.edu
^‡mehen@phy.duke.edu
^§vankolck@physics.arizona.edu

Phys. Rev. D 76, 034006 – Published 10 August, 2007

DOI: https://doi.org/10.1103/PhysRevD.76.034006

Abstract

We consider pion interactions in an effective field theory of the narrow resonance $X (3872)$ , assuming it is a weakly bound molecule of the charm mesons $D^{0} {\bar{D}}^{* 0}$ and $D^{* 0} {\bar{D}}^{0}$ . Since the hyperfine splitting of the $D^{0}$ and $D^{* 0}$ is only 7 MeV greater than the neutral pion mass, pions can be produced near threshold and are nonrelativistic. We show that pion exchange can be treated in perturbation theory and calculate the next-to-leading-order correction to the partial decay width $Γ [X \to D^{0} {\bar{D}}^{0} π^{0}]$ .

Article Text

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