[Paper Review] Study of charmless B decays to three-kaon final states

The Belle Collaboration, K. Abe|ArXiv.org|Aug 19, 2002

Particle physics theoretical and experimental studies1 references3 citations

TL;DR

This study measures charmless B decays to three-kaon final states using data from the Belle experiment at KEK, employing isospin symmetry and wave function decomposition to extract the fraction of CP-even states in the $K^+K^+K^-$ and $K_S K^+ K^-$ final states. The key result is $\alpha^2 = 0.86 \pm 0.15 \pm 0.05$, indicating a dominant CP-even component in the three-kaon final state, supporting its potential use in $b \to s$ penguin-induced CP violation measurements.

ABSTRACT

We report on a study of charmless B meson decays to three-kaon final states. The results are obtained with a 78.7 1/fb data sample collected on the Y(4S) resonance by the Belle detector operating at the KEKB asymmetric energy $e^+e^-$ collider. The branching fractions for B decays to three-body K+K+K-, K0K+K-, KsKsK+, and KsKsKs final states are presented. We also make a first attempt to perform an isospin analysis of the three-kaon final states.

Motivation & Objective

• To measure branching fractions for charmless B decays into three-kaon final states, including $K^+K^+K^-$, $K_S K^+ K^-$, $K_S K_S K^+$, and $K_S K_S K_S$.
• To determine the fraction of states with even orbital momentum in the $K^0\bar{K}^0$ system via isospin symmetry and wave function decomposition.
• To assess the CP-odd and CP-even components in the $K_S K^+ K^-$ final state, particularly by removing $\phi$-dominated contributions.
• To evaluate the potential of the $K_S K^+ K^-$ final state as a candidate for $b \to s$ penguin-induced CP violation measurements.

Proposed method

• Use isospin symmetry to relate branching fractions of $B^+ \to K^+K^+K^-$ and $B^0 \to K^0K^+K^-$ decays to extract $\alpha^2$, the fraction of even orbital momentum states in the $K^0\bar{K}^0$ system.
• Apply wave function decomposition: $|K^+K^0\bar{K}^0\rangle = \alpha \frac{|K^+K_S K_S\rangle + |K^+K_L K_L\rangle}{\sqrt{2}} + \beta |K^+K_S K_L\rangle$, with $\alpha^2 + \beta^2 = 1$, to model the $K^+K^0\bar{K}^0$ final state.
• Measure $\alpha^2$ using the ratio of observed event counts, corrected for detection efficiencies and lifetime ratios: $\alpha^2 = 2 \frac{N_{K^+K_S K_S}}{N_{K_S K^+ K^-}} \times \frac{\varepsilon_{K^0K^+K^-}}{\varepsilon_{K^+K_S K_S}} \times \frac{\tau_{B^0}}{\tau_{B^+}}$.
• Remove $B^0 \to \phi K_S$ events by requiring $|M(K^+K^-) - M_\phi| > 15$ MeV to isolate non-$\phi$ contributions.
• Cross-validate $\alpha^2$ using the $B^+ \to K^+K_S K_S$ and $B^+ \to K^+K^+K^-$ final states via the alternative formula: $\alpha^2 = 2 \frac{{\cal{B}}(B^+ \to K^+K_S K_S)}{{\cal{B}}(B^+ \to K^+K^+K^-)}$.
• Use the $K_S K^+ K^-$ final state to probe CP-odd and CP-even components, with $\alpha^2$ representing the CP-even fraction due to $(-1)^l$ dependence on orbital angular momentum.

Experimental results

Research questions

• RQ1 What fraction of the $K^+K^0\bar{K}^0$ final state has even orbital momentum, as characterized by $\alpha^2$?
• RQ2 How does the $K_S K^+ K^-$ final state's CP-odd and CP-even components compare, particularly after removing $\phi$-dominated contributions?
• RQ3 Can the $K_S K^+ K^-$ final state serve as a viable candidate for measuring CP violation in $b \to s$ penguin transitions?
• RQ4 How consistent are the two isospin-based methods for extracting $\alpha^2$ using $B^0$ and $B^+$ decays?
• RQ5 What is the significance of the observed $\alpha^2$ value in constraining the dynamics of charmless three-body B decays?

Key findings

• The value of $\alpha^2$ extracted from $B^0 \to K^0K^+K^-$ and $B^+ \to K^+K_S K_S$ is $0.86 \pm 0.15 \pm 0.05$, indicating a dominant contribution from even orbital momentum states in the $K^0\bar{K}^0$ system.
• After removing $\phi$-dominated events, the corrected $\alpha_{\text{non }\phi}^2 = 1.04 \pm 0.19 \pm 0.06$ is consistent with $\alpha^2 = 0.86 \pm 0.15 \pm 0.05$, supporting the dominance of CP-even states.
• Using the $B^+ \to K^+K_S K_S$ and $B^+ \to K^+K^+K^-$ final states yields $\alpha^2 = 0.82 \pm 0.12 \pm 0.06$, with $\alpha_{\text{non }\phi}^2 = 0.97 \pm 0.15 \pm 0.07$, showing good agreement between independent methods.
• The consistency between the two isospin-based methods provides strong evidence for the dominance of the CP-even component in the non-$\phi$ $K_S K^+ K^-$ final state.
• The $K_S K^+ K^-$ final state is identified as a promising candidate for future $b \to s$ penguin-induced CP violation measurements, with potential for fourfold higher statistics than the $\phi K_S$ mode.