Extracting the CKM phase angle \gamma(\equiv \phi_3) from isospin analysis in B\to K \pi decays

TL;DR

This paper introduces a new method to determine the CKM phase angle gamma from B to K pi decays using isospin analysis, avoiding flavor SU(3) symmetry and Dalitz-plot complexities, thus reducing theoretical uncertainties.

Contribution

The method uniquely extracts gamma from isospin relations without relying on flavor SU(3) symmetry or Dalitz-plot analysis, minimizing hadronic uncertainties.

Findings

Estimated gamma as approximately 70° to 106°–180° with uncertainties.

Method is robust against new physics effects unless isospin relations are violated.

Provides a more precise determination of gamma with reduced theoretical assumptions.

Abstract

We propose a new method to extract the CKM phase angle \gamma (\equiv \phi_3) from the isospin analysis in B \to K \pi decays. Unlike previously proposed methods, we do not employ flavor SU(3) symmetry, so that this method is free from the hadronic uncertainty coming from the SU(3) breaking effect. Neither we adopt any Dalitz-plot analysis, which may involve multiple strong phases and large final state interactions. After including small CP violating terms in B^+ \to K^0 \pi^+ and color-suppressed electroweak penguin contribution in B^0 \to K^+ \pi^-, whose values are estimated from the QCD factorization, we obtain \gamma = ({70}^{+5 +1 +2}_{-14 -1 -3})^\circ \textrm{or} {106^\circ}< \gamma < {180^\circ}. The first error is due to the experimental errors mainly caused by mixing-induced CP asymmetry S_{{K_s} \pi^0}. The second and third errors come from the theoretical uncertainty for two above-mentioned small contributions, respectively. Since we utilize only the isospin relations in B \to K \pi decays, this method will work well, regardless of possible new physics effects unless the isospin relations do not hold.