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A Closer Look at $R_D$ and $R_{D^*}$

D. Bardhan

in 9th International Workshop on the CKM Unitarity Triangle

Contribution: pdf


The measurement of $R_D$ ($R_{D^*}$), the ratio of the branching fraction of $\overline{B} \to D \tau \bar{\nu}_\tau (\overline{B} \to D^* \tau \bar{\nu}_\tau)$ to that of
$\overline{B} \to D l \bar{\nu}_l (\overline{B} \to D^* l \bar{\nu}_l)$, shows $1.9 \sigma$ $(3.3 \sigma)$ deviation from
its Standard Model (SM) prediction. The
combined deviation is at the level of $4 \sigma$ according to the Heavy Flavour Averaging Group (HFAG).
In the paper \cite{Bardhan:2016uhr} , we perform an effective field theory analysis (at the dimension 6 level) of these potential New Physics
(NP) signals assuming $ SU(3)_{C} \times SU(2)_{L} \times U(1)_{Y}$ gauge invariance. We first show that, in general,
$R_D$ and $R_{D^*}$ are theoretically independent observables and hence, their theoretical predictions
are not correlated. We identify the operators that can explain the experimental measurements of $R_D$ and
$R_{D^*}$ individually and also together. Motivated by the recent measurement of the
$\tau$ polarisation in $\overline{B} \to D^* \tau \bar{\nu}_\tau$ decay, $P_\tau^{D^*}$ by the BELLE collaboration, we study the
impact of a more precise measurement of $P_\tau^{D^*}$ (and a measurement of $P_\tau^D$) on the various possible NP
explanations. Furthermore, we show that the measurement of $R_{D^*}$ in bins of $q^2$, the square of the invariant mass of
the lepton neutrino system, along with the information on $\tau$ polarisation, can completely distinguish the various
operator structures.