Di-electron and two-photon widths in charmonium
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ELEMENTARY PARTICLES AND FIELDS Theory
Di-Electron and Two-Photon Widths in Charmonium* A. M. Badalian1)** and I. V. Danilkin2) Received September 18, 2008
Abstract—The vector and pseudoscalar decay constants are calculated in the framework of the Field Correlator Method. Di-electron widths: Γee (J/ψ) = 5.41 keV, Γee (ψ (3686)) = 2.47 keV, Γee (ψ (3770)) = 0.248 keV, in good agreement with experiment, are obtained with the same coupling, αs = 0.165, in the QCD radiative corrections. We show that the larger αs = 0.191 ± 0.004 is needed to reach agreement with experiment for Γγγ (ηc ) = 7.22 keV, Γγγ (χc (3 P0 )) = 3.3 keV, Γγγ (χc (3 P2 )) = 0.54 keV, and also for Γ(J/ψ → 3g) = 59.5 keV, Γ(J/ψ → γ2g) = 5.7 keV. Meanwhile, even larger αs = 0.238 gives rise to good description of Γ(ψ → 3g) = 52.7 keV, Γ(ψ → γ2g) = 3.5 keV, and provides correct ratio of the branching B(J/ψ → light hadrons ) = 0.24. fractions: B(ψ → light hadrons) PACS numbers: 13.66.Bc, 14.40.Gx, 12.40.Yx DOI: 10.1134/S106377880907014X
1. INTRODUCTION Low-lying states of heavy quarkonia have been an important laboratory to study both perturbative and nonperturbative phenomena in QCD. However, recent discoveries of higher resonances, in particular X(3872) [1] and Y (4260) [2], have shown that these and some other new resonances cannot be interpreted ¯ mesons. To understand the naas conventional QQ ture of new resonances, evidently, two- (or many-) channel consideration is needed. However, in strict sense it cannot be done now because nonperturbative theory of strong decays is not still well developed in QCD. Therefore for identification of new resonances with J P C = 1−− , observed in e+ e− processes via the initial-state radiation [3, 4], a special role belongs to di-electron widths and also two-photon widths for C-even resonances, which are reasonably well described by existing QCD formulas. At this point it is worthwhile to remind that the di-electron width of ¯ meson is by two orders (may be even more) a QQ larger than di-electron width of a compact four-quark system [5]. In our paper, firstly, we calculate the decay constants of vector (V ) and pseudoscalar (P ) mesons in charmonium, using the Field Correlator Method (FCM), which has been successfully applied to ∗
The text was submitted by the authors in English. Institute of Theoretical and Experimental Physics, Moscow, Russia. 2) Moscow Engineering Physics Institute, Russia. ** E-mail: [email protected] 1)
heavy–light mesons [6]. Due to relativistic corrections di-electron widths and their ratios, calculated here, agree with experiment with high accuracy. Therefore from the absolute values of dielectron widths some important factors, containing the squared wave functions at the origin, can be extracted and then used in different annihilation decays. We pay a special attention to the influence of radiative corrections on different annihilation rates. The absolute values of di-electron widths are shown to agree with experimental numbers only if the QCD radiative corrections are taken into a
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