Implications of Recent Measurements of Hadronic Charmless B Decays

TL;DR

Recent measurements of charmless B decays provide insights into form factors, effective color numbers, and CP-violating angles, challenging existing models and supporting a specific hierarchy of parameters.

Contribution

This paper analyzes recent experimental data to refine theoretical models of B decays, especially regarding form factors, effective color numbers, and CP violation angles.

Findings

Form factor F_0^{Bπ}(0) is smaller than BSW model predicts.

Effective number of colors N_c(LL) is preferred to be smaller, N_c(LR) greater than 3.

Unitarity angle γ is greater than 90°, explaining decay suppression patterns.

Abstract

Implications of recent CLEO measurements of hadronic charmless B decays are discussed. (i) Employing the Bauer-Stech-Wirbel (BSW) model for form factors as a benchmark, the $B\to\pi^+\pi^-$ data indicate that the form factor $F_0^{B\pi}(0)$ is smaller than that predicted by the BSW model, whereas the data of $B\to\omega\pi, K^*\eta$ imply that the form factors $A_0^{B\omega}(0), A_0^{BK^*}(0)$ are greater than the BSW model's values. (ii) The tree-dominated modes $B\to\pi^+\pi^-, \rho^0\pi^\pm, \omega\pi^\pm$ imply that the effective number of colors N_c(LL) for (V-A)(V-A) operators is preferred to be smaller, while the current limit on $B\to\phi K$ shows that N_c(LR)>3. The data of $B\to K\eta'$ and $K^*\eta$ clearly indicate that $N_c(LR)\gg N_c(LL)$. (iii) In order to understand the observed suppression of $\pi^+\pi^-$ and non-suppression of $K\pi$ modes, both being governed by the form factor $F_0^{B\pi}$, the unitarity angle $\gamma$ is preferred to be greater than $90^\circ$. By contrast, the new measurement of $B^\pm\to\rho^0\pi^\pm$ no longer strongly favors $\cos\gamma<0$. (iv) The observed pattern $K^-\pi^+\sim \ov K^0\pi^-\sim {2\over 3}K^-\pi^0$ is consistent with the theoretical expectation: The constructive interference between electroweak and QCD penguin diagrams in the $K^-\pi^0$ mode explains why ${\cal B}(B^-\to K^-\pi^0)>{1\over 2}{\cal B}(\ov B^0\to K^-\pi^+)$. (v) The observation $\nc(LL)<3<\nc(LR)$ and our preference for $\nc(LL)\sim 2$ and $\nc(LR)\sim 6$ are justified by a recent perturbative QCD calculation of hadronic rare B decays in the heavy quark limit.