Beyond Form Factors: Precise Angular Tests in Hadronic $τ$ Decays

TL;DR

This work tackles the challenge of nonperturbative hadronization in semileptonic $\tau$ decays by constructing angular observables that are largely independent of hadronic form factors within the SM when long-distance electromagnetic corrections are neglected. Employing the Weak EFT (WEFT), the authors parameterize possible new-physics influences through five couplings ($\epsilon_L^D$, $\epsilon_R^D$, $\epsilon_S^D$, $\epsilon_P^D$, $\hat{\epsilon}_T^D$) and relate hadronic matrix elements to vector, scalar, and tensor form factors, with a dispersive-inspired relation between tensor and vector form factors. They derive the doubly differential width to first order in NP couplings and define even angular moments $I_{2n}$, focusing on $I_2$ which carries a tensor-induced interference term proportional to $\operatorname{Re}(\hat{\epsilon}_T^D)$; integrated observables $J_2$ and $J_0$ provide experimentally accessible benchmarks. Using Belle data for $\tau^- \to \pi^-\pi^0$ and $\tau^- \to \pi^-K_S$, they present SM predictions for $I_2$ and quantify NP sensitivity through parameters $a$ and $b$, illustrating a clean path to detect deviations from the SM or to benchmark long-distance electromagnetic effects. The approach offers a robust framework for testing the SM at low energies and for constraining or revealing NP, with future extensions to more channels and polarized analyses.

Abstract

Semileptonic $τ$ decays mainly proceed via interactions between charged lepton and quark currents. The hadronization of the quark current is intrinsically nonperturbative and generally cannot be addressed analytically. In these proceedings, we propose using symmetry arguments alone to construct clean angular observables, which, within the Standard Model and in the absence of long-distance electromagnetic corrections, remain form-factor independent. These predictions can be experimentally tested, and any observed deviation could signal either effects of physics beyond the Standard Model or provide a clean benchmark for long-distance electromagnetic corrections. We also perform a first estimate of the expected impact of new physics in an EFT framework.

Figures (1)

• Figure 1: SM prediction for the second moment spectra in the $\tau^-\rightarrow\pi^-\pi^0$ (\ref{['fig_i2a']}) and $\tau^-\rightarrow\pi^-K_S$ (\ref{['fig_i2b']}) channels using data from Refs. Belle_pipiBelle_kpi.