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

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 $b\to c\tau {\overline{\nu }}_{\tau }$. Although the Belle measurements are in agreement with standard model (SM) predictions, the new experimental world averages still exhibit a tension. In addition, the $D^{*}$ longitudinal polarization $F_L(D^{*})$ related with the channel $B\to D^{*}\tau {\overline{\nu }}_{\tau }$ 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 $b\to c\tau {\overline{\nu }}_{\tau }$ 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 $b\to c\tau {\overline{\nu }}_{\tau }$ data and with the mono-tau signature $pp\to {\tau }_{h}X+\mathrm{MET}$ at the LHC. For comparison, we include some of the $W^{\prime }$ boson NP realizations that have already been studied in the literature.

Figure 1

The HFLAV 2018 and HFLAV 2019 averages (green and gray regions, respectively) [15, 16] in the $R(D)$ vs $R(D^{*})$ plane. The black ($1\sigma$ solid and $2\sigma$ dotted) and red (dashed) contours shows the SM predictions and the recent Belle measurements [22], respectively.

Figure 2

The 95% C.L. allowed parameter space in the $({\epsilon }_{cb}^L,{\epsilon }_{\tau {\nu }_{\tau }}^L)$ plane for (a) $M_{W^{\prime }}=0.5\mathrm{TeV}$ and (b) $M_{W^{\prime }}=1\mathrm{TeV}$. The purple region is obtained by considering only $R(D^{(*)})$ from the HFLAV 2019 average, while the green one is obtained by taking into account all of the $b\to c\tau {\overline{\nu }}_{\tau }$ observables. The black star and red hatched region represent the ACDFR model [105] and the GMR analysis [106], respectively. See the text for details.

Figure 3

The 95% C.L. allowed parameter space in the $({\epsilon }_{cb}^R,{\epsilon }_{\tau {\nu }_{\tau }}^R)$ plane for (a) $M_{W^{\prime }}=1\mathrm{TeV}$ and (b) $M_{W^{\prime }}=1.2\mathrm{TeV}$. The purple region is obtained by considering only $R(D^{(*)})$ from HFLAV 2019 averages, while the green one is obtained by taking into account all of the $b\to c\tau {\overline{\nu }}_{\tau }$ observables. The black diamond, blue squared, red hatched region, and orange circle represent the NU-LRSM model [100, 101], 3321 gauge model [109, 110], GMR analysis [106], and USM-LRSM [108], respectively. See the text for details.

Figure 4

The 95% C.L. allowed parameter space in the $({\epsilon }_{cb}^L,{\epsilon }_{\tau {\nu }_{\tau }}^R)$ and $({\epsilon }_{cb}^R,{\epsilon }_{\tau {\nu }_{\tau }}^L)$ planes for a mass value of $M_{W^{\prime }}=1\mathrm{TeV}$.