Charged current $b \to c \tau \bar{\nu}_\tau$ anomalies in a general $W^\prime$ boson scenario

Abstract

Very recent experimental information obtained from the Belle experiment, along with that accumulated by the BABAR and LHCb experiments, has shown the existence of anomalies in the ratios $R(D)$ and $R(D^{*})$ associated with the charged-current transition $b \to c \tau \bar{\nu}_\tau$. Although the Belle measurements are in agreement with the standard model (SM) predictions, the new experimental world averages still exhibit a tension. In addition, the $D^\ast$ longitudinal polarization $F_L(D^\ast)$ related with the channel $B \to D^\ast \tau \bar{\nu}_\tau$ observed by the Belle Collaboration and the ratio $R(J/\psi)$ measured by the LHCb Collaboration also show discrepancies with their corresponding SM estimations. We present a model-independent study based on the most general effective Lagrangian that yields a tree-level effective contribution to the transition $b \to c \tau \bar{\nu}_\tau$ induced by a general $W^\prime$ boson. Instead of considering any specific new physics (NP) realization, we perform an analysis by considering all of the different chiral charges to the charm-bottom and $\tau$-$\nu_{\tau}$ interaction terms with a charged $W^\prime$ boson that explain the anomalies. We present a phenomenological study of parameter space allowed by the new experimental $b \to c \tau \bar{\nu}_\tau$ data and with the mono-tau signature $pp \to \tau_h X + \rm{MET}$ at the LHC. For comparison, we include some of the $W^\prime$ boson NP realizations that have already been studied in the literature.