Direct pion emission in D^*+→D⁺π decays

Abstract：

The QCD multipole expansion (QCDME) is based on quantum field theory and has been extensively applied to study transitions among Υ and ψ family members. As it refers to non-perturbative QCD, however, it has only a certain application range. Even though it successfully explains the transition data among members of the Υ (ψ) family, as Eichten indicates, beyond the production threshold of mediate states it fails to match data by several orders of magnitude. In this work, by studying a simple decay mode D^*→D+π⁰, where a pion may be emitted before D^* transitions into D, we analyze the contribution of QCD multipole expansion. As the Dπ portal is open, the dominant contribution is an OZI-allowed process where a light quark-pair is excited out from vacuum, and its contribution can be evaluated by the ³P₀ model. Since direct pion emission is OZI-suppressed and violates isospin conservation, its contribution must be much smaller than the dominant one. By a careful calculation, we estimate that the QCDME contribution should be 3-4 orders smaller than the dominant contribution and this result can offer a quantitative interpretation for Eichten's statement.