Glauber gluons in annihilation amplitudes for heavy meson decays

TL;DR

This paper explores Glauber divergences in heavy meson decay amplitudes, showing they can be absorbed into phase-modifying factors, with significant effects observed in D meson decay data, advancing the theoretical understanding of decay processes.

Contribution

It introduces a method to incorporate Glauber effects into decay amplitude calculations, emphasizing the pion's unique role and providing a theoretical basis for decay analysis models.

Findings

Glauber divergences can be absorbed into phase factors in decay amplitudes.

Glauber effects are significant in D→ππ and πK decay modes.

The work supports a factorization approach with Glauber effects for D meson decays.

Abstract

We investigate the Glauber divergences in nonfactorizable annihilation amplitudes for two-body hadronic heavy meson decays in the $k_T$ factorization theorem at one-loop level. These divergences can be absorbed into the Glauber factors in the dominant kinematic regions of small parton momenta, which modify the interference between a nonfactorizable annihilation amplitude and other amplitudes by rotating it with a phase. We postulate that only the Glauber effect associated with a pion is significant, due to its special role as a $q\bar q$ bound state and as a pseudo Nambu-Goldstone boson simultaneously. It is elaborated that the data of the $D\to\pi\pi$ and $\pi K$ branching ratios have revealed prominent Glauber effects. This work provides a solid theoretical ground for the factorization-assisted topological-amplitude parametrization of two-body hadronic $D$ meson decays.