$B\to D^{*}\tau {\overline{\nu }}_{\tau }$ sensitivity to new physics

$B$ physics has played a prominent role in investigations of new physics effects at low-energies. Presently, the largest discrepancy between a standard model prediction and experimental measurements appears in the branching ratio of the charged current mediated $B\to \tau {\overline{\nu }}_{\tau }$ decay, where the large $\tau$ mass lifts the helicity suppression arising in leptonic $B$ decays. Less significant systematic deviations are also observed in the semileptonic $B\to D^{(*)}\tau {\overline{\nu }}_{\tau }$ rates. Because of the rich spin structure of the final state, the decay mode $B\to D^{*}\tau {\overline{\nu }}_{\tau }$ offers a number of tests of such possible standard model deviations. We investigate the most general set of lowest dimensional effective operators leading to helicity suppressed modifications of $b\to c$ (semi)leptonic transitions. We explore such contributions to the $B\to D^{*}\tau {\overline{\nu }}_{\tau }$ decay amplitudes by determining the differential decay rate, longitudinal $D^{*}$ polarization fraction, $D^{*}-\tau$ opening angle asymmetry and the $\tau$ helicity asymmetry. We identify the size of possible new physics contributions to these observables constrained by the present $B\to D^{(*)}\tau {\overline{\nu }}_{\tau }$ rate measurements and find significant modifications are still possible in all of them. In particular, the opening angle asymmetry can be shifted by almost 30%, relative to the standard model prediction, while the $\tau$ helicity asymmetry can still deviate by as much as 80%.

Figure 1

The 68% (in darker green shade) and 95% (in lighter yellow shade) C.L. allowed regions in the complex plane of NP parameters appearing in the effective $b\to c$ charged current in Eq. (2). Shown are fixed combinations (the orthogonal combinations are set to zero): $g_{SR}+g_{SL}$ (left-hand plot) bounded by $B\to D\tau {\overline{\nu }}_{\tau }$, $g_{SR}-g_{SL}$ (center plot) constrained only by $B\to D^{*}\tau {\overline{\nu }}_{\tau }$, and $g_{SL}$ (right-hand plot) contributing to both modes. The best fit NP benchmark point in the later case is marked with the symbol $*$. All the shown constraints have been obtained from the ratios $R^{(*)}$.

Figure 2

The differential ratios $R^{*}(q^2)$ (left-hand plot) and $R_L^{*}(q^2)$ (right-hand plot) as functions of $q^2$. The black dashed curves are the SM predictions, while the (bright yellow) dotted lines denote predictions for the NP benchmark point (see text for details). The 95% C.L. allowed regions (due to existing constraints from the $B\to D^{(*)}\tau {\overline{\nu }}_{\tau }$ branching ratio measurements) for fixed NP parameter combinations (the orthogonal combinations being set to zero) $g_{SR}-g_{SL}$ and $g_{SL}$ are shown in lighter (green) and darker (red) shades, respectively. The $g_{SR}$ case is almost degenerate with $g_{SL}$ and is therefore not shown.

Figure 3

The differential asymmetries $A_{\theta }(q^2)$ (left-hand plot) and $A_{\lambda }(q^2)$ (right-hand plot) as functions of $q^2$. The black dashed curves are the SM predictions, while the (bright yellow) dotted lines denote predictions for the NP benchmark point (see text for details). The 95% C.L. allowed regions (due to existing constraints from the $B\to D^{(*)}\tau {\overline{\nu }}_{\tau }$ branching ratio measurements) for fixed NP parameter combinations (the orthogonal combinations being set to zero) $g_{SR}-g_{SL}$ and $g_{SL}$ are shown in lighter (green) and darker (red) shades, respectively. The $g_{SR}$ case is almost degenerate with $g_{SL}$ and is therefore not shown.

Figure 4

Regions allowed by potential future 10% relative precision measurement of $R_L^{*}$ (shaded in gray and bounded by dot-dashed lines), 10% precision determination of $A_{\lambda }$ (shaded in green and bounded by dashed lines), and 5% precision measurement of $A_{\theta }$ (shaded in red and bounded by dotted lines) in the complex plane of NP parameter $g_{SL}$ appearing in the effective $b\to c$ charged current in Eq. (2) ($g_{SR}$ is set to zero identically). All observables are assumed to be SM-like. The present $B\to D^{(*)}\tau {\overline{\nu }}_{\tau }$ decay rates’ best fit NP benchmark point is marked with the symbol $*$.