Novel Model-Independent Approach to Explore New Physics in Five-body Semileptonic Decays

Abstract

Substantial contribution of the tensor current in semileptonic decays is regarded as a clear signal for new physics. In this work, we propose a model-independent approach to unambiguously test contribution of the tensor current in semileptonic five-body decays $\bar{D}_{(s)}/\bar{B}_{(s)}\to V\ell\barν_{\ell}\,(\ell=e,μ,τ)$ with $V\to π^0π^+π^-$, where $V$ denotes vector particles. We derive three parameters associated with the angular asymmetry, which are always equal to one in the Standard Model regardless the data of form factor but will deviate if contribution of the tensor current doesn't vanish. The outcomes have potential applications in precisely testing the Standard Model and searching for new physics. Relevant measurements can be performed using data collected by BESIII, Belle~II, and LHCb.

Figures (4)

• Figure 1: Diagrammatic representation of how our approach probes new physics in contrast to tests of LFU in semileptonic decays of heavy mesons.
• Figure 2: Kinematics for $\bar{D} \to V\ell\bar{\nu}_{\ell}$ with $V\to \pi^0\pi^+\pi^-$Yu:2024isl. The angle between the three-momentum of $\ell$ ($\pi^0$) and $\bar{D}$ in the $\ell\bar{\nu}_{\ell}$ ($V$) rest frame is denoted as $\theta_1$ ($\theta_2$), that of $\pi^-$ and $V$ in the $\pi^+\pi^-$ rest frame as $\theta_3$, and the angle between the $\ell\bar{\nu}_{\ell}$ ($\pi^+\pi^-$) system and the $V$$(\pi^0)$ is denoted as $\phi_1$ ($\phi_3$).
• Figure 3: Integration ranges and directions of angles. The solid lines indicate positive sign and dashed lines negative sign.
• Figure 4: Distributions of $\Theta_1$, $\Theta_2$, and $\Theta_3$ as a function of $Y^2$ for (a) $D^- \to \omega \mu \bar{\nu}_\mu$, (b) $B^- \to \omega \mu \bar{\nu}_\mu$, and (c) $B^- \to \omega \tau \bar{\nu}_\tau$ with $\omega \to \pi^0 \pi^+ \pi^-$. The Dark Blue, Teal, and Dark Red lines represent $\Theta_1$, $\Theta_2$, and $\Theta_3$, respectively. The numerical values of the form factors related to the SM are taken from Refs. Ivanov:2019nqd and Ball:2004rg. To simplify the discussion of new physics contributions, we fix $\delta_1/f_1 = \delta_2/f_2 = \delta_3/f_3 = 0.01$.