Probing sensitivity to charged scalars through partial differential widths: $\tau \to K\pi \pi {\nu }_{\tau }$ decays

We define and test $CP$-even and $CP$-odd partial differential widths for the process $\tau \to K\pi \pi {\nu }_{\tau }$ assuming that an intermediate heavy charged scalar contributes to the decay amplitude. Adopting a model-independent approach, we use a Monte Carlo simulation in order to study the number of events needed to recover information on the new physics from these observables. Our analysis of the $CP$-odd observables indicates that the magnitude of $f_H{\eta }_P$, which is related to the new-physics contribution, can be recovered with an uncertainty smaller than 3% for $3\times 10^6$ events. This number of events would also allow one to retrieve certain parameters appearing in the Standard Model amplitude at the percent level. In addition, we discuss the possibility of using the proposed observables to study specific models involving two Higgs doublets, such as the aligned two-Higgs-doublet model. This analysis is undertaken within the context of the upcoming super B-factories, which are expected to provide a considerably larger number of events than that which was supplied by the B-factories. Moreover, a similar set of observables could be employed to study other decay modes such as $\tau \to \pi \pi \pi {\nu }_{\tau }$, $\tau \to KK\pi {\nu }_{\tau }$ and $\tau \to KKK{\nu }_{\tau }$.

Figure 1

Plots of the differential widths $d\mathrm{\Gamma }/dM$, including the different contributions from the decay chains along with the simulated data points obtained by using our MC generator. The $|f_H{\eta }_P|$ curve displays the NP contribution.

Figure 2

Plots of the distributions obtained from the observable $6(-)$ for $|f_H{\eta }_P|=17.9$ (blue solid line) and $|f_H{\eta }_P|=0.92{\mathrm{GeV}}^{-1}(Q^2/m_s)$ (red dashed line). In the panels (a), (b), and (c), the projections onto $Q^2,s_1$, and $s_2$ are displayed, respectively. The distributions are normalized to the total width of the $\tau$.

Figure 3

Projection onto $s_2$ of the observable $6(-)$ extracted from a set of $10^6$ events along with the corresponding allowed region within the A2HDM. The data in the simulation correspond to the NP parameter choice $f_H{\eta }_P=1.79e^{i\pi /4}$. Note that the plot of the allowed region assumes that the parameters associated with the form factors ($A$, $B$, etc.) have zero uncertainty.

Figure 4

Projection onto $s_1$ of the observable $6(-)$, obtained by using a set of $3\times 10^6$ simulated events. The zero-crossing point can be clearly extracted from the plot with an uncertainty given by the size of the bins ($s_1=0.56\pm 0.03{\mathrm{GeV}}^2$).