cc¯ interaction above threshold and the radiative decay X(3872)J/ψγ

A. M. Badalian, Yu. A. Simonov, and B. L. G. Bakker
Phys. Rev. D 91, 056001 – Published 2 March 2015

Abstract

Radiative decays of X(3872) are studied in single-channel approximation (SCA) and in the coupled-channel (CC) approach, where the decay channels DD¯* are described with the string-breaking mechanism. In SCA the transition rate Γ˜2=Γ(2P31ψγ)=71.8keV and large Γ˜1=Γ(2P31J/ψγ)=85.4keV are obtained, giving for their ratio the value Rψγ˜=Γ˜2Γ˜1=0.84. In the CC approach, three factors are shown to be equally important: First, the admixture of the 1P31 component in the normalized wave function of X(3872) due to the CC effects. Its weight cX(ER)=0.200±0.015 is calculated. Second, the use of the multipole function g(r) instead of r in the overlap integrals, determining the partial widths. Third, the choice of the gluon-exchange interaction for X(3872), as well as for other states above threshold. If for X(3872) the gluon-exchange potential is taken to be the same as for low-lying charmonium states, then in the CC approach Γ1=Γ(X(3872)J/ψγ)3keV is very small, giving the large ratio Rψγ=B(X(3872)ψ(2S)γ)B(X(3872)J/ψγ)1.0. Arguments are presented why the gluon-exchange interaction may be suppressed for X(3872) and in this case Γ1=42.7keV, Γ2=70.5keV, and Rψγ=1.65 are predicted for the minimal value cX(min)=0.185, while for the maximal value cX=0.215 we obtain Γ1=30.8keV, Γ2=73.2keV, and Rψγ=2.38, which agrees with the LHCb data.

  • Received 6 January 2015

DOI:https://doi.org/10.1103/PhysRevD.91.056001

© 2015 American Physical Society

Authors & Affiliations

A. M. Badalian* and Yu. A. Simonov

  • Institute of Theoretical and Experimental Physics, B. Cheremushkinskaya 25, 117218 Moscow, Russia

B. L. G. Bakker

  • Department of Physics and Astronomy, Vrije Universiteit, De Boelelaan 1081, 1081HV Amsterdam, The Netherlands

  • *badalian@itep.ru
  • simonov@itep.ru
  • b.l.g.bakker@vu.nl

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Issue

Vol. 91, Iss. 5 — 1 March 2015

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