### Abstract

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 _{cJ}ππ 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 _{cJ}π0 and X(3872)→χ _{cJ}ππ 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 _{c1}ππ do not receive enhancements due to the width of the D ^{*}0. We give updated predictions for the decay X(3872)→χ _{c1}ππ at leading order in XEFT.

Original language | English (US) |
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Article number | 014016 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 85 |

Issue number | 1 |

DOIs | |

State | Published - Jan 13 2012 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

**Decay of the X(3872) into χ _{cJ} and the operator product expansion in effective field theory.** / Fleming, Sean P; Mehen, Thomas.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Decay of the X(3872) into χ cJ and the operator product expansion in effective field theory

AU - Fleming, Sean P

AU - Mehen, Thomas

PY - 2012/1/13

Y1 - 2012/1/13

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84856633819&partnerID=8YFLogxK

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U2 - 10.1103/PhysRevD.85.014016

DO - 10.1103/PhysRevD.85.014016

M3 - Article

AN - SCOPUS:84856633819

VL - 85

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 0556-2821

IS - 1

M1 - 014016

ER -