[Paper Review] Probing CP Violation in $τ^- o ν(Kπ/K2π/ 3K/ K3π)^- $ Decays

I. I. Bigi|arXiv (Cornell University)|Apr 26, 2012

Particle physics theoretical and experimental studies8 references3 citations

TL;DR

This paper investigates CP violation in $τ^{-}→\nu(K\pi/K2\pi/3K/K3\pi)^{-}$ decays to probe New Dynamics (ND) beyond the Standard Model (SM), emphasizing that separate measurements of CP asymmetries in multi-body final states—especially $K\pi$, $K2\pi$, $3K$, and $K3\pi$—are essential to detect and characterize ND, as global asymmetries are suppressed. The key result is that future SuperB and Super-Belle experiments can probe these asymmetries with high sensitivity, using Dalitz plot distributions and T-odd moments to disentangle ND effects from SM contributions.

ABSTRACT

It had been suggested to probe CP violation in τ ightarrow νKπ decays with K0 -K ^{-}0 oscillation to produce ACP(τ- ightarrow νKSπ-) = (0.36\pm0.01)%. BaBar has found ACP(τ- ightarrow νKSπ-[\geq π0]) = (-0.36 \pm 0.23 \pm 0.11)% - i.e., 2.8 sigma difference with SM prediction. It is discussed, why one needs to probe ACP(τ ightarrow νKπ), ACP(τ ightarrow νK2π) and ACP(τ ightarrow νK3π) separately to establish the existence of New Dynamics and its features. It should be possible at SuperB & Super-Belle experiments.

Motivation & Objective

• To establish that CP asymmetries in $τ^{-}→\nu(K\pi/K2\pi/3K/K3\pi)^{-}$ decays are sensitive probes of New Dynamics (ND) beyond the Standard Model (SM).
• To demonstrate that global CP asymmetries are significantly suppressed and thus insufficient to detect ND, necessitating detailed analysis of individual final states.
• To identify the importance of probing resonant structures and interference effects in Dalitz plots to isolate ND contributions.
• To advocate for the use of T-odd moments and binned/unbinned multivariate analyses to enhance sensitivity to CP violation in multi-hadronic $τ$ decays.
• To enable the identification of ND features through comparisons of $τ^{-}$ vs. $τ^{+}$ decay rates and asymmetries in $K\pi$, $K2\pi$, $3K$, and $K3\pi$ final states.

Proposed method

• Comparing $τ^{-}→\nu[K\pi]^{-}$, $τ^{-}→\nu[K2\pi]^{-}$, $τ^{-}→\nu[3K]^{-}$, and $τ^{-}→\nu[K3\pi]^{-}$ decay rates and CP asymmetries with their $τ^{+}$ counterparts to detect CPT-odd effects from ND.
• Using Dalitz plot distributions to probe local CP asymmetries and resonance interferences, particularly involving $K^{*}(892)$, $K_{1}(1270)$, $K_{1}(1400)$, and $K^{*}(1410)$.
• Measuring T-odd observables such as $\langle\vec{p}_{K}\cdot(\vec{p}_{\pi_{1}}\times\vec{p}_{\pi_{2}})\rangle$ in $K2\pi$ and $K3\pi$ final states to detect direct CP violation from ND.
• Applying the 'Miranda Procedure' to partition Dalitz plots and reduce systematic uncertainties via crosschecks on detection efficiencies for positive and negative particles.
• Analyzing hadronic mass distributions ($M_{K\pi}$, $M_{K2\pi}$, $M_{3K}$, $M_{K3\pi}$) to extract kinematic correlations sensitive to ND phases and couplings.
• Utilizing unbinned multivariate and binned analysis techniques to enhance sensitivity to CP asymmetries and disentangle contributions from different resonant and non-resonant amplitudes.

Experimental results

Research questions

• RQ1 Can CP asymmetries in $τ^{-}→\nu[K\pi]^{-}$, $τ^{-}→\nu[K2\pi]^{-}$, $τ^{-}→\nu[3K]^{-}$, and $τ^{-}→\nu[K3\pi]^{-}$ decays reveal New Dynamics beyond the Standard Model?
• RQ2 Why are global CP asymmetries in $τ^{-}→\nu[K_{S}\pi^{-}]$ significantly smaller than individual asymmetries in multi-body final states?
• RQ3 How do T-odd moments and resonance interferences in Dalitz plots enhance sensitivity to CP violation from New Dynamics?
• RQ4 What role do vector and axial-vector exchanges (e.g., $W_{R}$, charged Higgs) play in generating measurable CP asymmetries in $τ$ decays?
• RQ5 Can the 'Miranda Procedure' and multivariate analysis reduce systematic uncertainties in CP asymmetry measurements across different hadronic final states?

Key findings

• The BaBar experiment observed $A_{\rm CP}(\tau^{-}\to\nu K_{S}\pi^{-}[\geq\pi^{0}])=(-0.36\pm 0.23\pm 0.11)%$, a 2.8 sigma deviation from the SM prediction of $(0.36\pm 0.01)%$.
• CP asymmetries in $τ^{-}\to\nu[K\pi]^{-}$ are dominated by $K^{*}(892)$ and $K_{0}^{*}(1430)$ resonances, with contributions from vector and scalar form factors.
• For $τ^{-}\to\nu[K2\pi]^{-}$ and $τ^{-}\to\nu[3K]^{-}$, T-odd moments involving $\vec{p}_{K}\cdot(\vec{p}_{\pi_{1}}\times\vec{p}_{\pi_{2}})$ provide sensitive probes of direct CP violation from New Dynamics.
• The $K^{*}(892)\pi$, $K_{1}(1270)$, $K_{1}(1400)$, and $K^{*}(1410)$ resonances are key to probing interference effects and ND features in multi-body decays.
• SuperB and Super-Belle experiments are expected to achieve sufficient luminosity and resolution to measure CP asymmetries in $K\pi$, $K2\pi$, $3K$, and $K3\pi$ final states with high precision.
• The use of binned and unbinned multivariate analyses is critical to control systematic uncertainties and extract local CP asymmetries from Dalitz plot distributions.