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Reexamining the photon polarization in $B \to K π π γ$

Michael Gronau

Dan Pirjol

Physics Department, Technion, Haifa 32000, Israel

National Institute of Physics and Nuclear Engineering, Particle Physics Department, Magurele 077125, Romania

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Phys. Rev. D 96, 013002 – Published 12 July, 2017

DOI: https://doi.org/10.1103/PhysRevD.96.013002

Abstract

We reexamine, update and extend a suggestion we made fifteen years ago for measuring the photon polarization in $b \to s γ$ by observing in $B \to K π π γ$ an asymmetry of the photon with respect to the $K π π$ plane. Asymmetries are calculated for different charged final states due to intermediate $K_{1} (1400)$ and $K_{1} (1270)$ resonant states. Three distinct interference mechanisms are identified contributing to asymmetries at different levels for these two kaon resonances. For $K_{1} (1400)$ decays including a final state $π^{0}$ an asymmetry around $+ 30 %$ is calculated, dominated by interference of two intermediate $K^{*} π$ states, while an asymmetry around $+ 10 %$ in decays including final $π^{+} π^{-}$ is dominated by interference of $S$ and $D$ wave $K^{*} π$ amplitudes. In decays via $K_{1} (1270)$ to final states including a $π^{0}$ a negative asymmetry is favored up to $- 10 %$ if one assumes $S$ wave dominance in decays to $K^{*} π$ and $K ρ$ , while in decays involving $π^{+} π^{-}$ the asymmetry can vary anywhere in the range $- 13 %$ to $+ 24 %$ depending on unknown phases. For more precise asymmetry predictions in the latter decays we propose studying phases in $K_{1} \to K^{*} π, K ρ$ by performing dedicated amplitude analyses of $B \to J / ψ (ψ^{'}) K π π$ . In order to increase statistics in studies of $B \to K π π γ$ we suggest using isospin symmetry to combine in the same analysis samples of charged and neutral $B$ decays.

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References (32)

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Reexamining the photon polarization in $B \to K π π γ$

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Reexamining the photon polarization in B→Kππγ

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Physics Subject Headings (PhySH)

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References (32)

Reexamining the photon polarization in $B \to K π π γ$