Large off-shell effects in the $\bar{D}^*$ contribution to $B \to \bar{D} \pi \pi$ and $B \to \bar{D} \pi \bar{\ell} \nu_{\ell}$ decays.}}

TL;DR

This paper investigates the significant off-shell effects of the narrow $D^*$ resonance in certain B meson decays, highlighting the importance of considering the resonance tail and off-shell contributions in theoretical and experimental analyses.

Contribution

It demonstrates that off-shell effects are surprisingly large in $D^*$ contributions to B decays, even with a narrow width, and provides methods to estimate and account for these effects.

Findings

Off-shell effects can reach several percent in B decay processes.

The zero width approximation can be extracted despite large off-shell contributions.

Virtual $D^*_V$ contributions are consistent with theoretical expectations but sensitive to cuts.

Abstract

We stress that, although the $D^*$ is very narrow (one hundred of keV), the difference between the full $D^*$ contribution to $B \to \bar{D} \pi \pi$ and its zero width limit, which stems from the resonance tail, is surprisingly large~: several percents. This phenomenon is a general effect which appears when considering the production of particles that are coupled to an intermediate virtual state, stable or not, and it persists whether the width is large or not. The effects of various cuts and of the inclusion of damping factors at the strong and weak vertices are discussed. It is shown how the zero width limit, needed to compare with theoretical expectations, can be extracted. One also evaluates the virtual $D^*_V$ contribution, which comes out roughly as expected from theory, but which is however much more dependent on cuts and uncontrollable "off-shell" effects. We suggest a way to estimate the impact of the damping factors.