Study on direct pion emission in decay $D^{*+} \to D^+ \pi$

TL;DR

This paper evaluates the contribution of QCD multipole expansion to direct pion emission in the decay $D^{*+} o D^+ \pi$, finding it to be significantly suppressed compared to dominant processes, thus clarifying its limited role.

Contribution

The study provides a quantitative estimate of the smallness of QCDME contributions in $D^*$ decays, clarifying its limited applicability in this context.

Findings

QCDME contribution is much smaller than OZI allowed processes.

Direct pion emission is suppressed due to isospin violation.

Quantitative estimates support the limited role of QCDME in this decay.

Abstract

The QCD multipole expansion (QCDME) is based on the quantum field theory, so should be more reliable. However, on another aspect, it refers to the non-perturbative QCD , so that has a certain application range. Even though it successfully explains the data of transition among members of the $\Upsilon$ ($\psi$) family, as Eichten indicates, beyond the production threshold of mediate states it fails to meet data by several orders. In this work, by studying a simple decay mode $D^*\to D+\pi^0$, where a pion may be emitted before $D^*$ transiting into $D$, we analyze the contribution of QCD multipole expansion. Whereas as the $D\pi$ 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 $^3P_0$ model. Since the direct pion emission is a process which is OZI suppressed and violates the isospin conservation, its contribution must be much smaller than the dominant one. By a careful calculation, we may quantitatively estimate how small the QCDME contribution should be and offer a quantitative interpretation for Eichten's statement.