Abstract
We study the direct CP violation in the $\tau^\pm\rightarrow K^\pm \rho^0 (\omega)\nu_\tau \rightarrow K^\pm \pi^+\pi^-\nu_\tau$ decay process in the Standard Model. An interesting mechanism involving the charge symmetry violating mixing between $\rho^0$ and $\omega$ is applied to enlarge the CP asymmetry. With this mechanism, the maximum differential and localized integrated CP asymmetries can reach $-(5.6^{+2.9}_{-1.7})\times10^{-12}$ and $6.3^{+2.4}_{-3.3}\times 10^{-11}$, respectively, which still leave plenty room for CP-violating New Physics to be discovered through this process.
Highlights
C experiment ceased data collection in March 2008, the BESIII experiment began to collect data, and the luminosity reached 1032 cm−2 s−1 in 2013 [7]
In the framework of the standard model (SM), CP violation in the τ lepton decay process arises from a nontrivial phase in the Cabibbo– Kobayashi–Maskawa (CKM) matrix and is predicted to be zero in the leading order in G F
Delepine pointed out that the CP-odd phase can arise from the second-order weak process in the τ ± → K ±π 0ντ decay mode [22]
Summary
C experiment ceased data collection in March 2008, the BESIII experiment began to collect data, and the luminosity reached 1032 cm−2 s−1 in 2013 [7]. In the framework of the SM, the direct CP asymmetries come about due to a relative weak (CP-odd) and a relative strong (CP-even) phase This mechanism is forbidden in τ decays in the leading order of the Fermi coupling constant G F [21]. One can expect that there could be a bigger CP-violating asymmetry in the τ ± → K ±ρ0(ω)ντ → K ±π +π −ντ process It will be shown from our explicit calculations that ρ–ω mixing leads to an additional strong phase and enlarges the differential CP-violating asymmetry by a maximum of four orders of magnitude and the localized integrated CP asymmetry by a maximum of three orders of magnitude. It will be shown below that the CP-odd phase difference arises from the second-order weak processes and the CP-even phase difference is determined by the decay widths of intermediate resonances and ρ–ω mixing in the τ − → K ±ρ0(ω)ντ → K ±π +π −ντ decay mode
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