[Paper Review] Direct CP Violation in B Decays

Michael Gronau|ArXiv.org|Jun 14, 2007

Particle physics theoretical and experimental studies3 references4 citations

TL;DR

This paper demonstrates that direct CP asymmetries in B decays—despite significant hadronic uncertainties—provide precise tests for the CKM framework and sensitive probes for New Physics. By analyzing asymmetries in $B \to D^{(*)}K^{(*)}$, $\pi^+\pi^-$, $\rho^+\rho^-$, and $B^+ \to J/\psi K^+$, it shows how measured asymmetries constrain the CKM phase $\gamma$, detect New Physics via null tests, and reveal the isospin structure of potential New Physics operators in $b \to s\bar{q}q$ transitions.

ABSTRACT

We discuss several aspects of direct CP asymmetries in B decays, which are very useful in spite of hadronic uncertainties in asymmetry calculations. 1) Asymmetries in decays to $D^{(*)}K^{(*)}$, $π^+π^-, ρ^+ρ^-$, providing precision tests for the CKM phase $γ$. 2) Null tests in $B^+ o J/ψK^+, π^+π^0$, where a nonzero asymmetry provides evidence for New Physics. 3) Isospin and broken flavor SU(3) relations among CP asymmetries in $B o Kπ, ππ$ predicting $A_{CP}(B^0 o K^0π^0)$ and $A_{CP}(B^0 o π^0π^0)$. 4) The significance of $A_{CP}(B^0 o K^+π^-) e A_{CP}(B^+ o K^+π^0)$. 5) A potentially stringent constraint on $γ$ from $A_{CP}(B^+ o K^+π^0)$ and $R_c\equiv 2Γ(B^+ o K^+π^0)/Γ(B^+ o K^0π^+)$. 6) The role of direct CP asymmetries in $b o s\bar qq$ decays for studying the origin of potential New Physics.

Motivation & Objective

• To demonstrate that direct CP asymmetries in B decays, though affected by hadronic uncertainties, offer precise constraints on the CKM phase $\gamma$.
• To identify null tests in $B^+ \to J/\psi K^+$ and $B^+ \to \pi^+\pi^0$ that can unambiguously signal New Physics if nonzero asymmetries are observed.
• To use isospin and flavor SU(3) symmetries to relate CP asymmetries across $B \to K\pi$ and $B \to \pi\pi$ modes, enabling predictions and tests of SU(3) breaking.
• To explore how direct CP asymmetries in $b \to s\bar{q}q$ decays can reveal the isospin structure of New Physics operators.
• To establish a method for distinguishing New Physics contributions from Standard Model hadronic uncertainties using combined measurements of $C$, $\Delta S$, and isospin asymmetries.

Proposed method

• Utilizes isospin symmetry to relate $B^0 \to K^0\pi^0$, $B^0 \to \pi^0\pi^0$, and $B^+ \to K^+\pi^0$ decays, deriving a sum rule predicting $A_{CP}(K^0\pi^0) = -0.140 \pm 0.043$.
• Applies flavor SU(3) symmetry to relate $A_{CP}(B^0 \to K^+\pi^-)$ and $A_{CP}(B^0 \to \pi^+\pi^-)$, predicting the ratio $A_{CP}(K^+\pi^-)/A_{CP}(\pi^+\pi^-) = -\mathcal{B}(\pi^+\pi^-)/\mathcal{B}(K^+\pi^-)$.
• Employs the $B^+ \to K^+\pi^0$ decay asymmetry and the ratio $R_c = 2\Gamma(B^+ \to K^+\pi^0)/\Gamma(B^+ \to K^0\pi^+)$ to constrain $\gamma$ with high sensitivity.
• Analyzes the $C$ and $\Delta S$ asymmetries in $B^0 \to X K^0$ decays, using their circle relation $\left(\Delta S / \cos 2\beta\right)^2 + C^2 = (2\xi \sin \gamma)^2$ to test for New Physics beyond Standard Model uncertainties.
• Introduces isospin-conserving asymmetry $A_I = [\Gamma(XK^+) - \Gamma(XK^0)] / [\Gamma(XK^+) + \Gamma(XK^0)]$ to probe the isospin structure ($\Delta I = 0$ or $1$) of New Physics operators in $b \to s\bar{q}q$ transitions.
• Uses the interplay of direct asymmetries, mixing-induced asymmetries, and isospin relations to distinguish New Physics effects from hadronic uncertainties in $B \to \pi\pi$, $B \to K\pi$, and $B \to \rho\rho$ modes.

Experimental results

Research questions

• RQ1 Can direct CP asymmetries in $B \to D^{(*)}K^{(*)}$ decays provide a precise determination of the CKM phase $\gamma$ despite hadronic uncertainties?
• RQ2 To what extent do nonzero direct CP asymmetries in $B^+ \to J/\psi K^+$ or $B^+ \to \pi^+\pi^0$ serve as unambiguous signatures for New Physics?
• RQ3 How can isospin and flavor SU(3) symmetries be used to predict and test CP asymmetries in $B \to K\pi$ and $B \to \pi\pi$ decays?
• RQ4 Can the measured asymmetries in $B^+ \to K^+\pi^0$ and $B^0 \to K^+\pi^-$ be explained within the Standard Model, or do they indicate new physics?
• RQ5 What is the isospin structure ($\Delta I = 0$ or $1$) of potential New Physics operators contributing to $b \to s\bar{q}q$ decays, as revealed by combined $C$, $\Delta S$, and $A_I$ measurements?

Key findings

• The isospin sum rule predicts $A_{CP}(B^0 \to K^0\pi^0) = -0.140 \pm 0.043$, providing a stringent test for SU(3) symmetry and hadronic dynamics.
• The ratio of direct asymmetries $A_{CP}(K^+\pi^-)/A_{CP}(\pi^+\pi^-)$ matches the inverse ratio of branching fractions, confirming the validity of flavor SU(3) symmetry with $\sim$10% accuracy.
• Small values of $A_{CP}(B^+ \to K^+\pi^0)$ and $R_c - 1$ imply a strong constraint on $\gamma$, with $\gamma = (72 \pm 6)^\circ$ being the most precise current determination.
• A nonzero direct CP asymmetry in $B^+ \to J/\psi K^+$ or $B^+ \to \pi^+\pi^0}$ at the percent level would be a clean, model-independent signature for New Physics.
• The $C$ and $\Delta S$ asymmetries in $B^0 \to X K^0$ decays lie on a circle defined by $\left(\Delta S / \cos 2\beta\right)^2 + C^2 = (2\xi \sin \gamma)^2$, allowing detection of New Physics if deviations occur beyond hadronic uncertainties.
• The isospin asymmetry $A_I$ and combined $C$, $\Delta S$, and $A_I$ measurements suggest that New Physics contributions to $b \to s\bar{q}q$ decays must be small, with further experimental precision needed to identify their isospin structure.