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Generalized structure functions in semileptonic tau decays

Daniel A. López Aguilar, Antonio Rodríguez Sánchez, Pablo Roig, Hanchen Yu

TL;DR

The paper extends the Kühn–Mirkes structure-function framework to include interference between antisymmetric tensor currents and SM currents in three-meson tau decays, necessitating a generalized set of spectral functions. It develops a self-dual, moment-based formalism that yields 12 generalized SFs and allows isolation of these functions via Euler-angle moments, applying it to decays like $\tau^-\to\eta^{(\prime)}\pi^-\pi^0\nu_\tau$. A CP-violating observable $A_{CP}(Q^2,s_1,s_2)$ is defined, with a numerator proportional to $\Im m \epsilon_T\, \Im m(\widehat{F}_T F_3^V)$, and preliminary Dalitz-plot studies indicate potentially large asymmetries. The work emphasizes that generalized SFs enable model-independent CP/T violation searches and should guide measurements at Belle-II and future facilities.

Abstract

In case there are tensor interactions beyond the SM in the low-energy effective Lagrangian, their interference with the SM V-A currents yields a contribution for tau decays into three or more mesons that cannot be included in the famous structure functions introduced by Kühn and Mirkes in their seminal 1992 paper. We present this generalization here, highlighting again the importance of measuring the (generalized) spectral functions, as being model-independent and exploiting maximally the data. This can be particularly relevant for CP and T violation studies with at least three mesons in the final state of the tau decay.

Generalized structure functions in semileptonic tau decays

TL;DR

The paper extends the Kühn–Mirkes structure-function framework to include interference between antisymmetric tensor currents and SM currents in three-meson tau decays, necessitating a generalized set of spectral functions. It develops a self-dual, moment-based formalism that yields 12 generalized SFs and allows isolation of these functions via Euler-angle moments, applying it to decays like . A CP-violating observable is defined, with a numerator proportional to , and preliminary Dalitz-plot studies indicate potentially large asymmetries. The work emphasizes that generalized SFs enable model-independent CP/T violation searches and should guide measurements at Belle-II and future facilities.

Abstract

In case there are tensor interactions beyond the SM in the low-energy effective Lagrangian, their interference with the SM V-A currents yields a contribution for tau decays into three or more mesons that cannot be included in the famous structure functions introduced by Kühn and Mirkes in their seminal 1992 paper. We present this generalization here, highlighting again the importance of measuring the (generalized) spectral functions, as being model-independent and exploiting maximally the data. This can be particularly relevant for CP and T violation studies with at least three mesons in the final state of the tau decay.
Paper Structure (3 sections, 8 equations, 1 figure)

This paper contains 3 sections, 8 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Main results
  3. Conclusions

Figures (1)

  • Figure 1: Dalitz plot for the CP asymmetry distribution, eq. (\ref{['eq_ACP']}), with $\Re e\{\epsilon_T\} = 5\cdot 10^{-3}\,$ and $\Im m\{\epsilon_T \} = 8\cdot\,10^{-5}$Cirigliano:2021yto and a fixed $Q^2= (1000)^2$ MeV$^2$, for the $\tau \rightarrow \eta\pi\pi\nu_{\tau}$ channel (left). Same for the $\eta^\prime$ channel, with $Q^2=(1400)^2$ MeV$^2$ (right).