Joint LHCb–Belle II prospects to constrain new physics in $$B\rightarrow D^{(*)}\tau u $$

Abstract Semileptonic $$b\rightarrow c\tau \bar{\nu }_{\tau }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>b</mml:mi> <mml:mo>→</mml:mo> <mml:mi>c</mml:mi> <mml:mi>τ</mml:mi> <mml:msub> <mml:mover> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> <mml:mi>τ</mml:mi> </mml:msub> </mml:mrow> </mml:math> 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 $$\bar{B}\rightarrow D^{(*)}\tau \bar{\nu }_{\tau }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mover> <mml:mrow> <mml:mi>B</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> <mml:mo>→</mml:mo> <mml:mmultiscripts> <mml:mi>D</mml:mi> <mml:mrow/> <mml:mrow> <mml:mo>(</mml:mo> <mml:mrow/> <mml:mo>∗</mml:mo> <mml:mo>)</mml:mo> </mml:mrow> </mml:mmultiscripts> <mml:mi>τ</mml:mi> <mml:msub> <mml:mover> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> <mml:mi>τ</mml:mi> </mml:msub> </mml:mrow> </mml:math> 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 $$\bar{B}\rightarrow D^{(*)}\tau \bar{\nu }_{\tau }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mover> <mml:mrow> <mml:mi>B</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> <mml:mo>→</mml:mo> <mml:mmultiscripts> <mml:mi>D</mml:mi> <mml:mrow/> <mml:mrow> <mml:mo>(</mml:mo> <mml:mrow/> <mml:mo>∗</mml:mo> <mml:mo>)</mml:mo> </mml:mrow> </mml:mmultiscripts> <mml:mi>τ</mml:mi> <mml:msub> <mml:mover> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> <mml:mi>τ</mml:mi> </mml:msub> </mml:mrow> </mml:math> 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 $$b\rightarrow c\tau \bar{\nu }_{\tau }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>b</mml:mi> <mml:mo>→</mml:mo> <mml:mi>c</mml:mi> <mml:mi>τ</mml:mi> <mml:msub> <mml:mover> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> <mml:mi>τ</mml:mi> </mml:msub> </mml:mrow> </mml:math> transitions using forthcoming LHCb and Belle II datasets.