Probing new physics with polarization components of the tau lepton in quasielastic $e^{-}p\to {\mathrm{\Lambda }}_c{\tau }^{-}$ scattering process

Kinematics restricts the ability of rare charm decays to explore the charged lepton-flavor-violation processes mediated by the quark-level $c\to u\ell \tau$ transition. To fill the gap, we propose exploring new physics (NP) through the quasielastic scattering process $e^{-}p\to {\tau }^{-}{\mathrm{\Lambda }}_c$ and the polarization of the $\tau$ lepton. As analyzing modes for the $\tau$ polarization, we consider the decays ${\tau }^{-}\to {\pi }^{-}{\nu }_{\tau }$, ${\tau }^{-}\to {\rho }^{-}{\nu }_{\tau }$, and ${\tau }^{-}\to {\ell }^{-}{\overline{\nu }}_{\ell }{\nu }_{\tau }$, and show that the $\tau$ polarization components can be extracted from analyzing the kinematics of the $\tau$ visible decay products. In the framework of a general low-energy effective Lagrangian, we then perform a detailed analysis of the polarization components in various aspects and scrutinize possible NP signals. With one upcoming experimental setup, we finally demonstrate promising event rate can be expected for the cascade process and, even in the worst-case scenario—no signals are observed at all—it can still provide a competitive potential for constraining the NP, compared with those from the high-$p_T$ dilepton invariant mass tails at high-energy colliders.

Figure 1

Criteria for selecting the electron beam energy $E$, where the red (green) curve denotes the $E\text{−}{Q}_{\max (\min )}^2$ relation given by Eq. (23), and the blue line represents the condition $Q^2\le 16{\mathrm{GeV}}^2$ required by our theoretical framework. The yellow range indicates the eligible $E$.

Figure 2

Variations of the polarization $P_L$ and $P_T$ with respect to $Q^2$ in different NP scenarios, where we have set the electron beam energy at $E=12\mathrm{GeV}$.

Figure 3

The polarization $P_{L,T}$ in various NP scenarios with three different electron beam energies. Note that the NP scenarios with right-handed lepton current are not presented and neither is the NP $g_S^{LR}$. Also only the $P_{L,T}$ within the kinematic range $Q^2\in [Q_{\min }^2,16{\mathrm{GeV}}^2]$ are presented for $E=15\mathrm{GeV}$.

Figure 4

The polarization $P_{L,T}$ as a function of $Q^2$, predicted with the form factors calculated in LQCD (red), NRQM (blue), and RCQM (green), respectively. Note that the $1\sigma$-level statistical uncertainties of the form factors in LQCD have been propagated to all the observables, as denoted by the outer red regions. In addition, the $P_{L,T}$ denoted by the three colors overlap perfectly for the NP $g_S^{LL}$, while for the NP $g_T^{LL}$ only the LQCD results are presented.