Extracting CKM Phases from Angular Distributions of $B_{d,s}$ Decays into Admixtures of CP Eigenstates

TL;DR

This paper develops a formalism to extract CKM phases from angular distributions of $B_{d,s}$ decays into CP admixtures, accounting for penguin contributions, and applies it to specific decay modes to improve measurements of CKM angles and phases.

Contribution

The paper introduces a comprehensive formalism for analyzing angular distributions in $B_{d,s}$ decays, including penguin effects, to extract CKM phases and resolve ambiguities.

Findings

Formalism enables extraction of CKM phases from angular distributions.

Application to $B_d o J/\psi ho^0$ and $B_s o J/\psi \phi$ decays.

Potential to resolve discrete ambiguities in CKM angle measurements.

Abstract

The time-dependent angular distributions of certain $B_{d,s}$ decays into final states that are admixtures of CP-even and CP-odd configurations provide valuable information about CKM phases and hadronic parameters. We present the general formalism to accomplish this task, taking also into account penguin contributions, and illustrate it by considering a few specific decay modes. We give particular emphasis to the decay $B_d\to J/\psi \rho^0$, which can be combined with $B_s\to J/\psi \phi$ to extract the $B^0_d - \bar{B^0_d}$ mixing phase and - if penguin effects in the former mode should be sizeable - also the angle $\gamma$ of the unitarity triangle. As an interesting by-product, this strategy allows us to take into account also the penguin effects in the extraction of the $B^0_s - \bar{B^0_s}$ mixing phase from $B_s\to J/\psi \phi$. Moreover, a discrete ambiguity in the extraction of the CKM angle $\beta$ can be resolved, and valuable insights into SU(3)-breaking effects can be obtained. Other interesting applications of the general formalism presented in this paper, involving $B_d\to\rho \rho$ and $B_{s,d}\to K^{\ast} \bar{K^\ast}$ decays, are also briefly noted.