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Decay of the X(3872) into χ cJ and the operator product expansion in effective field theory

Publication ,  Journal Article
Fleming, S; Mehen, T
Published in: Physical Review D - Particles, Fields, Gravitation and Cosmology
January 13, 2012

We consider a low-energy effective theory for the X(3872) (XEFT) that can be used to systematically analyze the decay and production of the X(3872) meson, assuming that it is a weakly bound state of charmed mesons. In a previous paper, we calculated the decays of X(3872) into χ cJ plus pions using a two-step procedure in which Heavy Hadron Chiral Perturbation Theory (HHχPT) amplitudes are matched onto XEFT operators and then X(3872) decay rates are calculated using these operators. The procedure leads to IR divergences in the three-body decay X(3872)→χ cJππ when virtual D mesons can go on shell in tree level HHχPT diagrams. In previous work, we regulated these IR divergences with the D *0 width. In this work, we carefully analyze X(3872)→χ cJπ0 and X(3872)→χ cJππ using the operator product expansion in XEFT. Forward scattering amplitudes in HHχPT are matched onto local operators in XEFT, the imaginary parts of which are responsible for the decay of the X(3872). Here we show that the IR divergences are regulated by the binding momentum of the X(3872) rather than the width of the D *0 meson. In the operator product expansion, these IR divergences cancel in the calculation of the matching coefficients so the correct predictions for the X(3872)→χ c1ππ do not receive enhancements due to the width of the D *0. We give updated predictions for the decay X(3872)→χ c1ππ at leading order in XEFT. © 2012 American Physical Society.

Duke Scholars

Published In

Physical Review D - Particles, Fields, Gravitation and Cosmology

DOI

EISSN

1550-2368

ISSN

1550-7998

Publication Date

January 13, 2012

Volume

85

Issue

1

Related Subject Headings

  • Nuclear & Particles Physics
  • 5107 Particle and high energy physics
  • 5101 Astronomical sciences
  • 4902 Mathematical physics
  • 0206 Quantum Physics
  • 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics
  • 0201 Astronomical and Space Sciences
 

Citation

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Fleming, S., & Mehen, T. (2012). Decay of the X(3872) into χ cJ and the operator product expansion in effective field theory. Physical Review D - Particles, Fields, Gravitation and Cosmology, 85(1). https://doi.org/10.1103/PhysRevD.85.014016
Fleming, S., and T. Mehen. “Decay of the X(3872) into χ cJ and the operator product expansion in effective field theory.” Physical Review D - Particles, Fields, Gravitation and Cosmology 85, no. 1 (January 13, 2012). https://doi.org/10.1103/PhysRevD.85.014016.
Fleming S, Mehen T. Decay of the X(3872) into χ cJ and the operator product expansion in effective field theory. Physical Review D - Particles, Fields, Gravitation and Cosmology. 2012 Jan 13;85(1).
Fleming, S., and T. Mehen. “Decay of the X(3872) into χ cJ and the operator product expansion in effective field theory.” Physical Review D - Particles, Fields, Gravitation and Cosmology, vol. 85, no. 1, Jan. 2012. Scopus, doi:10.1103/PhysRevD.85.014016.
Fleming S, Mehen T. Decay of the X(3872) into χ cJ and the operator product expansion in effective field theory. Physical Review D - Particles, Fields, Gravitation and Cosmology. 2012 Jan 13;85(1).

Published In

Physical Review D - Particles, Fields, Gravitation and Cosmology

DOI

EISSN

1550-2368

ISSN

1550-7998

Publication Date

January 13, 2012

Volume

85

Issue

1

Related Subject Headings

  • Nuclear & Particles Physics
  • 5107 Particle and high energy physics
  • 5101 Astronomical sciences
  • 4902 Mathematical physics
  • 0206 Quantum Physics
  • 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics
  • 0201 Astronomical and Space Sciences