Two-photon decays of pseudotensor mesons π2(1670), π2(2250), and π2(2510)

In terms of relativistic and gauge-invariant spectral-integral technique, we calculate amplitude for the π 2 → γγ decay as a three-step transition π 2 → q (2 −+ ) → γ + q (1 −− ) → γγ . Using wave functions of the q components of photon (hep-ph/0406320) and those of pseudotensor mesons π 2 (1670), π 2 (2000), π 2 (2250), and π 2 (2510) (hep-ph/0511109), we obtain the following values for partial widths: Γ π 2(1670)→ γγ = 0.072 ± 0.007 keV, Γ π 2(2000)→ γγ = 0.037 ± 0.004 keV, Γ π 2(2250)→ γγ = 0.027 ± 0.003 keV, and Γ π 2(2510)→ γγ = 0.022 ± 0.002 keV. In the calculations, we use the momentum operator expansion, and, in this connection, discuss the problem of nilpotent operators inherent in the considered amplitude. It should be emphasized that measurement of two-photon decays of the π 2 states can give valuable information about the long-range quark-antiquark forces which, as one may guess, are related to the quark confinement.