| Summary: | <p>A novel template-based technique is used to measure the q2-integrated, rate normalised angular coefficients of the B0 → D∗−τ+ντ decay with the full Run 1 + 2LHCb dataset. These coefficients capture the full angular information of the decay and have never before been measured in a comprehensive way. The technique involves creating multidimensional templates from simulated LHCb data, suitably weighted and corrected for the simulation’s imperfection. The selection of the signal decay is optimised to achieve a (28.3 ± 1.3 ± 0.9)% signal fraction in a partiallyreconstructed decay, where the first error is statistical and the second is systematic. Several data-driven control studies are performed to improve the simulation, especially for the large, double-charm backgrounds. To measure the angular coefficients, a simultaneous multi-dimensional fit is performed, utilising the 3D decay-angle distribution plus a simultaneous fit to two background-suppressing variables. The measured values of the q2-integrated, rate normalised angular coefficients are,</p></br>
<p>hI1ci = 0.612 ± 0.108 (stat.) ± 0.060 (syst.)</p>
<p>hI1si = 0.611 ± 0.066 (stat.) ± 0.032 (syst.)</p>
<p>hI2ci = 0.123 ± 0.251 (stat.) ± 0.153 (syst.)</p>
<p>hI2si = 0.689 ± 0.159 (stat.) ± 0.087 (syst.)</p>
<p>hI3i = −0.149 ± 0.141 (stat.) ± 0.077 (syst.)</p>
<p>hI4i = 0.040 ± 0.141 (stat.) ± 0.079 (syst.)</p>
<p>hI5i = −0.086 ± 0.072 (stat.) ± 0.039 (syst.)</p>
<p>hI6ci = −0.158 ± 0.191 (stat.) ± 0.117 (syst.)</p>
<p>hI6si = −0.200 ± 0.090 (stat.) ± 0.050 (syst.)</p>
<p>hI7i = 0.045 ± 0.077 (stat.) ± 0.039 (syst.)</p>
<p>hI8i = 0.130 ± 0.163 (stat.) ± 0.094 (syst.)</p>
<p>hI9i = 0.112 ± 0.137 (stat.) ± 0.075 (syst.)</p></br>
<p>From these measurements, the longitudinal polarisation fraction of the vector charm meson, fD∗L, and the forward-backward asymmetry, AF B, are calculated to be,</p></br>
<p>fD∗L = 0.428 ± 0.036 (stat.) ± 0.016 (syst.)</p>
<p>AFB = −0.209 ± 0.081 (stat.) ± 0.050 (syst.)</p></br>
<p>where the 9.2% relative precision on fD∗L is an improvement compared with the 15% relative uncertainty achieved by previous experiments while the AF B result is a world-first measurement. These measurements, in their final published form, will test the Standard Model by providing comprehensive sensitivity to new-physics effects in b → cτν transitions.</p>
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