Semileptonic $$B \rightarrow D^*$$ decays from light to $$\tau $$ leptons: the extraction of the form factor $$F_2$$ from data

Abstract We extend the Standard Model (SM) analysis of Martinelli et al. (Phys Rev D Ser 111:013005, 2025. https://doi.org/10.1103/PhysRevD.111.013005 ), which was limited to light leptons in the final state, to the semileptonic $$B \rightarrow D^* \tau \nu _\tau $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>B</mml:mi> <mml:mo>→</mml:mo> <mml:msup> <mml:mi>D</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> <mml:mi>τ</mml:mi> <mml:msub> <mml:mi>ν</mml:mi> <mml:mi>τ</mml:mi> </mml:msub> </mml:mrow> </mml:math> decay. By using quantities that can be analised without the knowledge of $$\vert V_{cb}\vert $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mo>|</mml:mo> </mml:mrow> <mml:msub> <mml:mi>V</mml:mi> <mml:mrow> <mml:mi>cb</mml:mi> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo>|</mml:mo> </mml:mrow> </mml:mrow> </mml:math> , we derive important information about the helicity amplitudes and the hadronic form factors that can be compared with the predictions of lattice QCD calculations. In particular, there is a difficulty in reproducing simultaneously the experimental values of $$R(D^*)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>R</mml:mi> <mml:mo>(</mml:mo> <mml:msup> <mml:mi>D</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> and of other quantities relevant for the semitauonic decays within the SM. As a byproduct of our analysis, we also present a determination of $$\vert V_{cb}\vert $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mo>|</mml:mo> </mml:mrow> <mml:msub> <mml:mi>V</mml:mi> <mml:mrow> <mml:mi>cb</mml:mi> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo>|</mml:mo> </mml:mrow> </mml:mrow> </mml:math> from the total decay rate.