Joint LHCb--Belle II Prospects to Constrain New Physics in $B\to D^{(*)}\tau\nu$
Semileptonic $b\to c\tau\bar{\nu}_{\tau}$ decays are powerful probes of non-Standard-Model effects within an effective-field-theory (EFT) framework, but fully exploiting them in current and future data demands combinations that maximise sensitivity while controlling biases from Standard-Model-based modelling and from theory inputs that are shared, and therefore correlated, across analyses in different experiments. We present a first sensitivity study of a combined extraction of Wilson coefficients in $\bar{B}\to D^{(*)}\tau\bar{\nu}_{\tau}$ decays using LHCb- and Belle~II-like analysis configurations. Detector simulations for signal and backgrounds are typically generated under Standard Model assumptions; if non-SM contributions are present, this can bias the fitted Wilson coefficients. In addition, hadronic inputs such as form-factor parameters of signal and background components are common across analyses, requiring a consistent treatment of fully correlated effects in combinations. To avoid repeating large-scale detector simulation for each EFT hypothesis, we use event-by-event reweighting to map simulated samples to arbitrary combinations of Wilson coefficients. We then compare a simultaneous fit across multiple $\bar{B}\to D^{(*)}\tau\bar{\nu}_{\tau}$ channels and datasets with a combination based on post-fit averages. Sharing Wilson coefficients and common form-factor parameters in the simultaneous fit reduces model-induced biases and improves sensitivity relative to independent fits, providing a robust and scalable strategy for precision EFT constraints in $b\to c\tau\bar{\nu}_{\tau}$ transitions using forthcoming LHCb and Belle~II datasets.