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 q 2 , 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.

The recent LHCb measurement of RK * in two q 2 bins, when combined with the earlier measurement of RK , strongly suggests lepton flavour non-universal new physics in semi-leptonic B meson decays. Motivated by these intriguing hints of new physics, several authors have considered vector, axial vector, scalar and pseudo scalar operators as possible explanations of these measurements. However, tensor operators have widely been neglected in this context. In this paper, we consider the effect of tensor operators in RK and RK * . We find that, unlike other local operators, tensor operators can comfortably produce both of R low K * and R central K * close to their experimental central values. However, a simultaneous explanation of RK is not possible with only Tensor operators, and other vector or axial vector operators are needed. In fact, we find that combination of vector and tensor operators can provide simultaneous explanations of all the anomalies comfortably at the 1σ level, a scenario which is hard to achieve with only vector or axial vector operators. We also comment on the compatibility of the various new physics solutions with the measurements of the inclusive decay B d → Xs + − .

In this note, we discuss the impact of the recent Belle result on the various theoretical explanations of the RD and RD * anomalies. The pure tensor explanation, which was strongly disfavoured by the measurements of F D * L and high-pT p p → τ ν searches before Moriond, is now completely allowed because of reduction of the experimental world-average. Moreover, the pure right-chiral vector solution (involving right-chiral neutrinos) has now moved into the 2σ allowed range of the LHC p p → τ ν searches. We also critically re-examine the bound on B(B − c → τ −ν τ ) from LEP data and show that the bound is considerably weaker than the number 10% often used in the recent literature.The Belle collaboration has recently published results for R D and R D * with a semileptonic tag [1,2], and their result is consistent with the Standard Model (SM) expectation within 1.2σ. Consequently, the experimental world average has moved towards the SM. However, the tension between the experimental world average and the SM expectation is still more than 3σ, and thus, it is interesting to re-examine the status of the various New Physics (NP) explanations in view of the new worldaverage. In Table. I below, we collect all the experimental results related to this anomaly. SM prediction Measurement04 [6] −0.38 +0.55 −0.53 [9, 10] F D * L 0.46 ± 0.04 0.60 ± 0.087 [11] R J/ψ 0.290 0.71 ± 0.25 [12] TABLE I. Observables, their SM predictions and the experimentally measured values. The pre-Moriond experimental averages for RD and RD * are based on [9, 10, 13-19].The most general effective Lagrangian for the decay b → c τ −ν τ involving mass dimension-6 operators and only left-chiral neutrinos can be written asc. If one uses power-counting rules arising from linearlyrealised SU(2) × U(1) gauge invariance, it turns out that the Wilson Coefficient (WC) C RL V , with the possibility of lepton non-universality, is only generated at the mass dimension-8 level [20]. Thus, it is expected to be suppressed compared to the other WCs as long as the scale * bardhan@post.bgu.ac.il † diptimoy.ghosh@iiserpune.ac.in of NP is not too close to the Higgs vacuum expectation value, thus we will ignore it in this analysis. If one also assumes the existence of light right-chiral neutrino(s), as was first done in [21] to solve the R D anomaly, five additional operators can be constructed by the replacement P L → P R in the leptonic currents of Eq. 1. In particular, a pure-right chiral vector current namely,was considered by several authors [22][23][24] , and we will include it in our analysis. As the experimental situation for R D and R D * is far from clear, we do not try to perform a fit to the WCs; for an early global fit, see [25]. Instead, we show how R D and R D * vary with respect to the WCs, and overlay the current 1σ experimental world-average and the corresponding currently allowed values of the WCs.In Fig. 1, we show this for two WCs C LL V and C RR V assuming them to be real. It can be seen from the left 0.20 0.25 0.30 0.35 0.40 0.45 R D 0.90 0.95 1.00 1.05...

In recent times, one of the strongest hints of Physics Beyond the Standard Model (BSM) has been the anomaly in the ratios R D and R D * measured in the charged current decays of B-mesons. In this work, we perform a comprehensive analysis of these decay modes, first in a model independent way and subsequently, in the context of composite Higgs models. We discuss in depth as to how linearly realised SU(2) L × U(1) Y symmetry imposes severe constraint on the various scenarios because of correlations with other ∆F = 1 processes and Z τ τ and Z ν ν couplings. In the composite Higgs paradigm with partial compositeness, we show that, irrespective of the flavour structure of the composite sector, constraints from ∆F = 2 processes bring the compositeness scale down to ∼ 650 GeV which is in tension with electroweak precision observables. In the presence of composite leptoquarks, the situation improves only marginally (a factor of √ 2 in the compositeness scale), thus making the new states soon discoverable by direct searches at the LHC. We also comment on the possible explanation of the R K,K * anomalies within the composite Higgs framework.

If the LHC should fail to observe direct signals for new physics, it may become necessary to look for new physics effects in rare events such as flavour-changing decays of the top quark, which, in the Standard Model, are predicted to be too small to be observed. We set up the theoretical framework in which experimentally accessible results can be expected in models of new physics, and go on to discuss two models of supersymmetry -one with conserved R-parity, and one without R-parity -to illustrate how the flavour-changing signals are predicted in these models. In the latter case, there is a distinct possibility of detecting the rare decay t → c + Z 0 at the LHC. We also present a detailed set of very general formulae which can be used to make similar calculations in diverse models of new physics.