A closer look at the R_D and R_D* anomalies

The measurement of R_D (R_D*), the ratio of the branching fraction of B¯ → Dτν¯ _τ(B¯ → D^∗τν¯ _τ) to that of B¯ → Dlν¯ _l(B¯ → D^∗lν¯ _l) , shows 1.9σ (3.3σ) deviation from its Standard Model (SM) prediction. The combined deviation is at the level of 4σ according to the Heavy Flavour Averaging Group (HFAG). In this paper, we perform an effective field theory analysis (at the dimension 6 level) of these potential New Physics (NP) signals assuming SU(3)_C × SU(2)_L × 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 τ polarisation in B¯ → D^∗τν¯ _τ decay, P_τ(D^*) by the Belle collaboration, we study the impact of a more precise measurement of P_τ(D^*) (and a measurement of P_τ(D)) on the various possible NP explanations. Furthermore, we show that the measurement of R_D* in bins of q², the square of the invariant mass of the lepton-neutrino system, along with the information on τ polarisation and the forward-backward asymmetry of the τ lepton, can completely distinguish the various operator structures. We also provide the full expressions of the double differential decay widths for the individual τ helicities in the presence of all the 10 dimension-6 operators that can contribute to these decays.