Helicity amplitudes in $$B \rightarrow D^{*} \bar{\nu } l$$B→D∗ν¯l decay

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 $$\gamma ^\mu -\alpha \gamma ^\mu \gamma _5$$γμ-αγμγ5, that can accommodate different models beyond the Standard Model and study in detail the $$B \rightarrow D^{*} \bar{\nu } l$$B→D∗ν¯l reaction for the different helicities of the $$D^*$$D∗. The results are shown for each amplitude in terms of the $$\alpha $$α parameter that is different for each model. We show that $$\frac{d \varGamma }{d M_\mathrm{inv}^{(\nu l)}}$$dΓdMinv(νl) is very different for the different components $$M=\pm \,1, 0$$M=±1,0 and in particular the magnitude $$\frac{d \varGamma }{d M_\mathrm{inv}^{(\nu l)}}|_{M=-1} -\frac{d \varGamma }{d M_\mathrm{inv}^{(\nu l)}}|_{M=+1} $$dΓdMinv(νl)|M=-1-dΓdMinv(νl)|M=+1 is very sensitive to the $$\alpha $$α parameter, which suggest to use this magnitude to test different models beyond the standard model. We show that our formalism implies the heavy quark limit and compare our results with calculations that include higher order corrections in heavy quark effective theory. We find very similar results for both approaches in normalized distributions, which are practically identical at the end point of $$ M_\mathrm{inv}^{(\nu l)}= m_B- m_{D^*}$$Minv(νl)=mB-mD∗.