Helicity amplitudes in $B \to D^{*} \bar{\nu} l$ decay

TL;DR

This paper develops a formalism to analyze helicity amplitudes in the decay $B o D^{*} ar{ u} l$, allowing for model comparisons beyond the standard model by examining helicity-dependent decay distributions.

Contribution

It extends the weak reaction formalism to include a general operator form, enabling analysis of different beyond-standard-model scenarios in $B$ decay helicity amplitudes.

Findings

Decay distributions vary significantly with helicity components.

The difference in decay rates for $M=-1$ and $M=+1$ is highly sensitive to the model parameter $eta$.

Results are consistent with the Standard Model at the endpoint of the invariant mass.

Abstract

We use a recent formalism of the weak hadronic reactions that maps the transition matrix elements at the quark level into hadronic matrix elements, evaluated with an elaborate angular momentum algebra that allows finally to write the weak matrix elements in terms of easy analytical formulas. In particular they appear explicitly for the different spin third components of the vector mesons involved. We extend the formalism to a general case, with the operator $\gamma^\mu -\alpha\gamma^\mu \gamma_5$, that can accommodate different models beyond the standard model and study in detail the $B \to D^{*} \bar{\nu} l$ reaction for the different helicities of the $D^*$. The results are shown for each amplitude in terms of the $\alpha$ parameter that is different for each model. We show that $\frac{d \Gamma}{d M_{\rm inv}^{(\nu l)}}$ is very different for the different components $M=\pm 1, 0$ and in particular the magnitude $\frac{d \Gamma}{d M_{\rm inv}^{(\nu l)}}|_{M=-1} -\frac{d \Gamma}{d M_{\rm inv}^{(\nu l)}}|_{M=+1} $ is very sensitive to the $\alpha$ parameter, which suggest to use this magnitude to test different models beyond the standard model. We also compare our results with the standard model and find very similar results, and practically identical at the end point of $M_{\rm inv}^{(\nu l)}= m_B- m_{D^*}$.