Reexamining the photon polarization in B→Kππγ
AbstractWe reexamine, update and extend a suggestion we made fifteen years ago for measuring the photon polarization in b→sγ by observing in B→Kππγ an asymmetry of the photon with respect to the Kππ plane. Asymmetries are calculated for different charged final states due to intermediate K1(1400) and K1(1270) resonant states. Three distinct interference mechanisms are identified contributing to asymmetries at different levels for these two kaon resonances. For K1(1400) decays including a final state π0 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 K1(1270) to final states including a π0 a negative asymmetry is favored up to -10% if one assumes S wave dominance in decays to K*π and Kρ, 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 K1→K*π,Kρ by performing dedicated amplitude analyses of B→J/ψ(ψ′)Kππ. In order to increase statistics in studies of B→Kππγ we suggest using isospin symmetry to combine in the same analysis samples of charged and neutral B decays.